 About the authors
 Abstract
 1. Introduction
 2. NetCDF Files and Components
 3. Description of the Data
 4. Coordinate Types
 5. Coordinate Systems and Domain
 5.1. Independent Latitude, Longitude, Vertical, and Time Axes
 5.2. TwoDimensional Latitude, Longitude, Coordinate Variables
 5.3. Reduced Horizontal Grid
 5.4. Timeseries of Station Data
 5.5. Trajectories
 5.6. Horizontal Coordinate Reference Systems, Grid Mappings, and Projections
 5.7. Scalar Coordinate Variables
 5.8. Domain Variables
 5.9. Mesh Topology Variables
 6. Labels and Alternative Coordinates
 7. Data Representative of Cells
 8. Reduction of Dataset Size
 8.1. Packed Data
 8.2. Lossless Compression by Gathering
 8.3. Lossy Compression by Coordinate Subsampling
 8.3.1. Tie Points and Interpolation Subareas
 8.3.2. Coordinate Interpolation Attribute
 8.3.3. Interpolation Variable
 8.3.4. Subsampled, Interpolated and NonInterpolated Dimensions
 8.3.5. Tie Point Mapping Attribute
 8.3.6. Tie Point Dimension Mapping
 8.3.7. Tie Point Index Mapping
 8.3.8. Interpolation Parameters
 8.3.9. Interpolation of Cell Boundaries
 8.3.10. Interpolation Method Implementation
 9. Discrete Sampling Geometries
 Appendix A: Attributes
 Appendix B: Standard Name Table Format
 Appendix C: Standard Name Modifiers
 Appendix D: Parametric Vertical Coordinates
 Atmosphere natural log pressure coordinate
 Atmosphere sigma coordinate
 Atmosphere hybrid sigma pressure coordinate
 Atmosphere hybrid height coordinate
 Atmosphere smooth level vertical (SLEVE) coordinate
 Ocean sigma coordinate
 Ocean scoordinate
 Ocean scoordinate, generic form 1
 Ocean scoordinate, generic form 2
 Ocean sigma over z coordinate
 Ocean double sigma coordinate
 Appendix E: Cell Methods
 Appendix F: Grid Mappings
 Appendix G: Revision History
 Appendix H: Annotated Examples of Discrete Geometries
 H.1. Point Data
 H.2. Time Series Data
 H.2.1. Orthogonal multidimensional array representation of time series
 H.2.2. Incomplete multidimensional array representation of time series
 H.2.3. Single time series, including deviations from a nominal fixed spatial location
 H.2.4. Contiguous ragged array representation of time series
 H.2.5. Indexed ragged array representation of time series
 H.3. Profile Data
 H.4. Trajectory Data
 H.5. Time Series of Profiles
 H.6. Trajectory of Profiles
 Appendix I: The CF data model
 Introduction
 Design criteria of the CF data model
 Elements of CFnetCDF
 The CF data model
 Field construct
 Domain construct
 Domain axis construct and the data array
 Coordinates: dimension coordinate and auxiliary constructs
 Coordinate reference construct
 Domain ancillary construct
 Cell measure construct
 Domain topology construct
 Cell connectivity construct
 Field ancillary constructs
 Cell method construct
 Appendix J: Coordinate Interpolation Methods
 Appendix K: Mesh Topologies
 Revision History
 Working version (most recent first)
 Version 1.11 (05 December 2023)
 Version 1.10 (31 August 2022)
 Version 1.9 (10 September 2021)
 Version 1.8 (11 February 2020)
 Version 1.7 (7 August 2017)
 Version 1.6 (5 December 2011)
 Version 1.5 (25 October 2010)
 Version 1.4 (27 February 2009)
 Version 1.3 (4 May 2008)
 Version 1.2 (4 May 2008)
 Version 1.1 (17 January 2008)
 Version 1.0 (28 October 2003)
 Bibliography
List of Tables
3.1. Prefixes for decimal multiples and submultiples of units
3.2. Flag Variable Bits (from Example)
3.3. Flag Variable Bit 2 and Bit 3 (from Example)
A.1. Attributes
C.1. Standard Name Modifiers
D.1. Consistent sets of values for the standard_names of formula terms and the computed_standard_name needed in defining the ocean sigma coordinate, the ocean scoordinate, the ocean_sigma over z coordinate, and the ocean double sigma coordinate.
E.1. Cell Methods
F.1. Grid Mapping Attributes
I.1. The elements of the CFnetCDF conventions. The relationships to netCDF elements are shown in [figurecfconcepts].
I.2. The constructs of the CF data model. The relationships between the constructs and CFnetCDF elements are shown in in [figurefield], [figuredimaux] and [figurecoordinatereference].
K.2. Mesh topology attributes
List of Figures
7.1. figure 1
7.2. figure 2
8.1. Figure 8.1
8.2. Figure 8.2
8.3. Figure 8.3
8.4. Figure 8.4
I.1. Figure I.1
I.2. Figure I.2
I.3. Figure I.3
I.4. Figure I.4
I.5. Figure I.5
J.1. Figure J.1
J.2. Figure J.2
J.3. Figure J.3
J.4. Figure J.4
J.5. Figure J.5
List of Examples
2.1. String Variable Representations
3.1. Use of units_metadata
to distinguish temperature quantities
3.2. Use of standard_name
3.3. Ancillary instrument data
3.4. Ancillary quality flag data
3.5. A flag variable, using flag_values
3.6. A flag variable, using flag_masks
3.7. A region variable, using flag_values
3.8. A flag variable, using flag_masks
and flag_values
4.1. Latitude axis
4.2. Longitude axis
4.3. Atmosphere sigma coordinate
4.4. Time axis
4.5. Perpetual time axis
4.6. Paleoclimate time axis
5.1. Independent coordinate variables
5.2. Twodimensional coordinate variables
5.3. Reduced horizontal grid
5.6. Rotated pole grid
5.7. "Lambert conformal projection"
5.8. Latitude and longitude on a spherical Earth
5.9. Latitude and longitude on the WGS 1984 datum
5.10. British National Grid
5.11. Latitude and longitude on the WGS 1984 datum + CRS WKT
5.12. British National Grid + Newlyn Datum in CRS WKT format
5.13. British National Grid + Newlyn Datum + referenced WGS84 Geodetic in CRS WKT format
5.14. "Multiple forecasts from a single analysis"
5.15. A domain with independent coordinate variables.
5.16. A domain with a rotated pole grid and a scalar coordinate variable.
5.17. A domain containing cell areas for a spherical geodesic grid.
5.18. A domain with no explicit dimensions.
5.19. A domain containing a timeseries geometry.
5.20. A domain containing a timeseries of station data in the indexed ragged array representation.
5.21. A twodimensional UGRID mesh topology variable
6.1. Northward heat transport in Atlantic Ocean
6.1.2. Taxon names and identifiers
6.2. Model level numbers
7.1. Specifying formula_terms
when a parametric coordinate variable has bounds.
7.2. Cells on a latitude axis
7.3. Cells in a nonrectangular grid
7.4. Cell areas for a spherical geodesic grid
7.5. Methods applied to a timeseries
7.6. Surface air temperature variance
7.7. Mean surface temperature over land and sensible heat flux averaged separately over land and sea.
7.8. Thickness of seaice and snow on seaice averaged over sea area.
7.9. Climatological seasons
7.10. Decadal averages for January
7.11. Temperature for each hour of the average day
7.12. Extreme statistics and spelllengths
7.13. Temperature for each hour of the typical climatological day
7.14. Monthlymaximum daily precipitation totals
7.15. Timeseries with geometry.
7.16. Polygons with holes
8.1. Horizontal compression of a threedimensional array
8.2. Compression of a threedimensional field
8.3. Twodimensional tie point interpolation
8.4. Onedimensional tie point interpolation of twodimensional domain.
8.5. Multiple interpolation variables with interpolation parameter attributes.
8.6. Combining a grid mapping and coordinate interpolation, with time as a noninterpolated dimension.
8.7. Interpolation of 2D Cell Boundaries corresponding to Figure 8.4
B.1. A name table containing three entries
H.1. "Point data"
H.2. Timeseries with common element times in a time coordinate variable using the orthogonal multidimensional array representation.
H.3. Timeseries of station data in the incomplete multidimensional array representation.
H.4. A single timeseries.
H.5. A single timeseries with timevarying deviations from a nominal point spatial location
H.6. Timeseries of station data in the contiguous ragged array representation.
H.7. Timeseries of station data in the indexed ragged array representation.
H.8. "Atmospheric sounding profiles for a common set of vertical coordinates stored in the orthogonal multidimensional array representation."
H.9. Data from a single atmospheric sounding profile.
H.10. Atmospheric sounding profiles for a common set of vertical coordinates stored in the contiguous ragged array representation.
H.11. Atmospheric sounding profiles for a common set of vertical coordinates stored in the indexed ragged array representation.
H.12. Trajectories recording atmospheric composition in the incomplete multidimensional array representation.
H.13. A single trajectory recording atmospheric composition.
H.14. Trajectories recording atmospheric composition in the contiguous ragged array representation.
H.15. Trajectories recording atmospheric composition in the indexed ragged array representation.
H.16. Time series of atmospheric sounding profiles from a set of locations stored in a multidimensional array representation.
H.17. Time series of atmospheric sounding profiles from a set of locations stored in an orthogonal multidimensional array representation.
H.18. Time series of atmospheric sounding profiles from a single location stored in a multidimensional array representation.
H.19. Time series of atmospheric sounding profiles from a set of locations stored in a ragged array representation.
H.20. Time series of atmospheric sounding profiles along a set of trajectories stored in a multidimensional array representation.
H.21. Time series of atmospheric sounding profiles along a trajectory stored in a multidimensional array representation.
H.22. Time series of atmospheric sounding profiles along a set of trajectories stored in a ragged array representation.
I.1. A single CFnetCDF variable corresponding to two data model constructs.
About the authors

Brian Eaton, NCAR

Jonathan Gregory, University of Reading and UK Met Office Hadley Centre

Bob Drach, PCMDI, LLNL

Karl Taylor, PCMDI, LLNL

Steve Hankin, PMEL, NOAA

Jon Blower, University of Reading

John Caron, UCAR

Rich Signell, USGS

Phil Bentley, UK Met Office Hadley Centre

Greg Rappa, MIT

Heinke Höck, DKRZ

Alison Pamment, BADC

Martin Juckes, BADC

Martin Raspaud, SMHI

Randy Horne, Excalibur Laboratories, Inc., Melbourne Beach Florida USA

Timothy Whiteaker, University of Texas

David Blodgett, USGS

Charlie Zender, University of California, Irvine

Daniel Lee, EUMETSAT

David Hassell, NCAS and University of Reading

Alan D. Snow, Corteva Agriscience

Tobias Kölling, MPIM

Dave Allured, CIRES/University of Colorado/NOAA/PSL

Aleksandar Jelenak, HDF Group

Anders Meier Soerensen, EUMETSAT

Lucile Gaultier, OceanDataLab

Sylvain Herlédan, OceanDataLab

Fernando Manzano, Puertos del Estado

Lars Bärring, SMHI

Christopher Barker, NOAA

Sadie Bartholomew, NCAS and University of Reading
Many others have contributed to the development of CF through their participation in discussions about proposed changes.
Abstract
This document describes the CF conventions for climate and forecast metadata designed to promote the processing and sharing of files created with the netCDF Application Programmer Interface [NetCDF]. The conventions define metadata that provide a definitive description of what the data in each variable represents, and of the spatial and temporal properties of the data. This enables users of data from different sources to decide which quantities are comparable, and facilitates building applications with powerful extraction, regridding, and display capabilities.
The CF conventions generalize and extend the COARDS conventions [COARDS]. The extensions include metadata that provides a precise definition of each variable via specification of a standard name, describes the vertical locations corresponding to dimensionless vertical coordinate values, and provides the spatial coordinates of nonrectilinear gridded data. Since climate and forecast data are often not simply representative of points in space/time, other extensions provide for the description of coordinate intervals, multidimensional cells and climatological time coordinates, and indicate how a data value is representative of an interval or cell. This standard also relaxes the COARDS constraints on dimension order and specifies methods for reducing the size of datasets.
1. Introduction
1.1. Goals
The NetCDF library [NetCDF] is designed to read and write data that has been structured according to welldefined rules and is easily ported across various computer platforms. The netCDF interface enables but does not require the creation of selfdescribing datasets. The purpose of the CF conventions is to require conforming datasets to contain sufficient metadata that they are selfdescribing in the sense that each variable in the file has an associated description of what it represents, including physical units if appropriate, and that each value can be located in space (relative to earthbased coordinates) and time.
An important benefit of a convention is that it enables software tools to display data and perform operations on specified subsets of the data with minimal user intervention. It is possible to provide the metadata describing how a field is located in time and space in many different ways that a human would immediately recognize as equivalent. The purpose in restricting how the metadata is represented is to make it practical to write software that allows a machine to parse that metadata and to automatically associate each data value with its location in time and space. It is equally important that the metadata be easy for human users to write and to understand.
This standard is intended for use with climate and forecast data, for atmosphere, surface and ocean, and was designed with modelgenerated data particularly in mind. We recognise that there are limits to what a standard can practically cover; we restrict ourselves to issues that we believe to be of common and frequent concern in the design of climate and forecast metadata. Our main purpose therefore, is to propose a clear, adequate and flexible definition of the metadata needed for climate and forecast data. Although this is specifically a netCDF standard, we feel that most of the ideas are of wider application. The metadata objects could be contained in file formats other than netCDF. Conversion of the metadata between files of different formats will be facilitated if conventions for all formats are based on similar ideas.
This convention is designed to be backward compatible with the COARDS conventions [COARDS], by which we mean that a conforming COARDS dataset also conforms to the CF standard. Thus new applications that implement the CF conventions will be able to process COARDS datasets.
We have also striven to maximize conformance to the COARDS standard, that is, wherever the COARDS metadata conventions provide an adequate description we require their use. Extensions to COARDS are implemented in a manner such that the content that doesn’t depend on the extensions is still accessible to applications that adhere to the COARDS standard.
1.2. Principles for design
The following principles are followed in the design of these conventions:

CFnetCDF metadata is designed to make datasets selfdescribing as far as practically possible. A selfdescribing dataset is one which can be interpreted without need for reference to resources outside itself, and the CF principle is to minimise that need. Therefore CFnetCDF does not use codes, but instead relies on controlled vocabularies containing terms that are chosen to be selfexplanatory (but more detailed definitions of them are provided in CF documents).

The conventions are changed only as actually required by common usecases, and not for needs which cannot be anticipated with certainty.

In order to keep them logical, consistent in approach and as simple as possible, the netCDF conventions are devised with and within the conceptual framework of the CF data model, and new standard names are constructed as far as possible to follow the syntax and vocabulary of existing standard names.

The conventions should be practicable for both producers and users of data.

The metadata should be both easily readable by humans and easily parsable by programs.

To avoid potential inconsistency within the metadata, the conventions should minimise redundancy.

The conventions should minimise the possibility for mistakes by datawriters and datareaders.

Conventions are provided to allow dataproducers to describe the data they wish to produce, rather than attempting to prescribe what data they should produce; consequently most CF conventions are optional.

Because many datasets remain in use for a long time after production, it is desirable that metadata written according to previous versions of the convention should also be compliant with and have the same interpretation under later versions.

Because all previous versions must generally continue to be supported in software for the sake of archived datasets, and in order to limit the complexity of the conventions, there is a strong preference against introducing any new capability to the conventions when there is already some method that can adequately serve the same purpose (even if a different method would arguably be better than the existing one).
1.3. Terminology
The terms in this document that refer to components of a netCDF file are defined in the NetCDF User’s Guide (NUG) [NUG] NUG. Some of those definitions are repeated below for convenience.
 ancestor group

A group from which the referring group is descended via direct parentchild relationships
 auxiliary coordinate variable

Any netCDF variable that contains coordinate data, but is not a coordinate variable (in the sense of that term defined by the NUG and used by this standard  see below). Unlike coordinate variables, there is no relationship between the name of an auxiliary coordinate variable and the name(s) of its dimension(s).
 boundary variable

A boundary variable is associated with a variable that contains coordinate data. When a data value provides information about conditions in a cell occupying a region of space/time or some other dimension, the boundary variable provides a description of cell extent.
 CDL syntax

The ascii format used to describe the contents of a netCDF file is called CDL (network Common Data form Language). This format represents arrays using the indexing conventions of the C programming language, i.e., index values start at 0, and in multidimensional arrays, when indexing over the elements of the array, it is the last declared dimension that is the fastest varying in terms of file storage order. The netCDF utilities ncdump and ncgen use this format (see NUG section on CDL syntax). All examples in this document use CDL syntax.
 cell

A region in one or more dimensions whose boundary can be described by a set of vertices. The term interval is sometimes used for onedimensional cells.
 coordinate variable

We use this term precisely as it is defined in the NUG section on coordinate variables. It is a onedimensional variable with the same name as its dimension [e.g.,
time(time)
], and it is defined as a numeric data type with values in strict monotonic order (all values are different, and they are arranged in either consistently increasing or consistently decreasing order). Missing values are not allowed in coordinate variables.  grid mapping variable

A variable used as a container for attributes that define a specific grid mapping. The type of the variable is arbitrary since it contains no data.
 interpolation variable

A variable used as a container for attributes that define a specific interpolation method for uncompressing tie point variables. The type of the variable is arbitrary since it contains no data.
 latitude dimension

A dimension of a netCDF variable that has an associated latitude coordinate variable.
 local apex group

The nearest (to a referring group) ancestor group in which a dimension of an outofgroup coordinate is defined. The word "apex" refers to position of this group at the vertex of the tree of groups formed by it, the referring group, and the group where a coordinate is located.
 longitude dimension

A dimension of a netCDF variable that has an associated longitude coordinate variable.
 multidimensional coordinate variable

An auxiliary coordinate variable that is multidimensional.
 nearest item

The item (variable or group) that can be reached via the shortest traversal of the file from the referring group following the rules set forth in the Section 2.7, "Groups".
 outofgroup reference

A reference to a variable or dimension that is not contained in the referring group.
 path

Paths must follow the UNIX style path convention and may begin with either a '/', '..', or a word.
 recommendation

Recommendations in this convention are meant to provide advice that may be helpful for reducing common mistakes. In some cases we have recommended rather than required particular attributes in order to maintain backwards compatibility with COARDS. An application must not depend on a dataset’s adherence to recommendations.
 referring group

The group in which a reference to a variable or dimension occurs.
 scalar coordinate variable

A scalar variable (i.e. one with no dimensions) that contains coordinate data. Depending on context, it may be functionally equivalent either to a sizeone coordinate variable (Section 5.7, "Scalar Coordinate Variables") or to a sizeone auxiliary coordinate variable (Section 6.1, "Labels" and Section 9.2, "Collections, instances, and elements").
 sibling group

Any group with the same parent group as the referring group
 spatiotemporal dimension

A dimension of a netCDF variable that is used to identify a location in time and/or space.
 tie point variable

A netCDF variable that contains coordinates that have been compressed by sampling. There is no relationship between the name of a tie point variable and the name(s) of its dimension(s).
 time dimension

A dimension of a netCDF variable that has an associated time coordinate variable.
 vertical dimension

A dimension of a netCDF variable that has an associated vertical coordinate variable.
1.4. Overview
No variable or dimension names are standardized by this convention. Instead we follow the lead of the NUG and standardize only the names of attributes and some of the values taken by those attributes. Variable or dimension names can either be a single variable name or a path to a variable. The overview provided in this section will be followed with more complete descriptions in following sections. Appendix A, Attributes contains a summary of all the attributes used in this convention.
Files using this version of the CF Conventions must set the NUG defined attribute Conventions
to contain the string value "CF1.12draft
" to identify datasets that conform to these conventions.
The general description of a file’s contents should be contained in the following attributes: title
, history
, institution
, source
, comment
and references
(Section 2.6.2, "Description of file contents").
For backwards compatibility with COARDS none of these attributes is required, but their use is recommended to provide human readable documentation of the file contents.
Each variable in a netCDF file has an associated description which is provided by the attributes units
, long_name
, and standard_name
.
The units
, and long_name
attributes are defined in the NUG and the standard_name
attribute is defined in this document.
The units
attribute is required for all variables that represent dimensional quantities (except for boundary variables defined in Section 7.1, "Cell Boundaries").
The values of the units
attributes are character strings that are recognized by UNIDATA’s UDUNITS package [UDUNITS] (with exceptions allowed as discussed in Section 3.1, "Units").
The long_name
and standard_name
attributes are used to describe the content of each variable.
For backwards compatibility with COARDS neither is required, but use of at least one of them is strongly recommended.
The use of standard names will facilitate the exchange of climate and forecast data by providing unambiguous identification of variables most commonly analyzed.
Four types of coordinates receive special treatment by these conventions: latitude, longitude, vertical, and time. Every variable must have associated metadata that allows identification of each such coordinate that is relevant. Two independent parts of the convention allow this to be done. There are conventions that identify the variables that contain the coordinate data, and there are conventions that identify the type of coordinate represented by that data.
There are two methods used to identify variables that contain coordinate data.
The first is to use the NUGdefined "coordinate variables."
The use of coordinate variables is required for all dimensions that correspond to one dimensional space or time coordinates.
In cases where coordinate variables are not applicable, the variables containing coordinate data are identified by the coordinates
attribute.
Once the variables containing coordinate data are identified, further conventions are required to determine the type of coordinate represented by each of these variables.
Latitude, longitude, and time coordinates are identified solely by the value of their units
attribute.
Vertical coordinates with units of pressure may also be identified by the units
attribute.
Other vertical coordinates must use the attribute positive
which determines whether the direction of increasing coordinate value is up or down.
Because identification of a coordinate type by its units involves the use of an external package [UDUNITS], we provide the optional attribute axis
for a direct identification of coordinates that correspond to latitude, longitude, vertical, or time axes.
Latitude, longitude, and time are defined by internationally recognized standards, and hence, identifying the coordinates of these types is sufficient to locate data values uniquely with respect to time and a point on the earth’s surface.
On the other hand identifying the vertical coordinate is not necessarily sufficient to locate a data value vertically with respect to the earth’s surface.
In particular a model may output data on the parametric (usually dimensionless) vertical coordinate used in its mathematical formulation.
To achieve the goal of being able to spatially locate all data values, this convention provides a mapping, via the standard_name
and formula_terms
attributes of a parametric vertical coordinate variable, between its values and dimensional vertical coordinate values that can be uniquely located with respect to a point on the earth’s surface (Section 4.3.3, "Parametric Vertical Coordinate"; Appendix D, Parametric Vertical Coordinates).
It is often the case that data values are not representative of single points in time and/or space, but rather of intervals or multidimensional cells.
This convention defines a bounds
attribute to specify the extent of intervals or cells.
When data that is representative of cells can be described by simple statistical methods, those methods can be indicated using the cell_methods
attribute.
An important application of this attribute is to describe climatological and diurnal statistics.
Methods for reducing the total volume of data include both packing and compression.
Packing reduces the data volume by reducing the precision of the stored numbers.
It is implemented using the attributes add_offset
and scale_factor
which are defined in the NUG.
Compression on the other hand loses no precision, but reduces the volume by not storing missing data.
The attribute compress
is defined for this purpose.
1.5. Relationship to the COARDS Conventions
These conventions generalize and extend the COARDS conventions [COARDS]. A major design goal has been to maintain backward compatibility with COARDS. Hence applications written to process datasets that conform to these conventions will also be able to process COARDS conforming datasets. We have also striven to maximize conformance to the COARDS standard so that datasets that only require the metadata that was available under COARDS will still be able to be processed by COARDS conforming applications. But because of the extensions that provide new metadata content, and the relaxation of some COARDS requirements, datasets that conform to these conventions will not necessarily be recognized by applications that adhere to the COARDS conventions. The features of these conventions that allow writing netCDF files that are not COARDS conforming are summarized below.
COARDS standardizes the description of grids composed of independent latitude, longitude, vertical, and time axes. In addition to standardizing the metadata required to identify each of these axis types COARDS restricts the axis (equivalently dimension) ordering to be longitude, latitude, vertical, and time (with longitude being the most rapidly varying dimension). Because of I/O performance considerations it may not be possible for models to output their data in conformance with the COARDS requirement. The CF convention places no rigid restrictions on the order of dimensions, however we encourage data producers to make the extra effort to stay within the COARDS standard order. The use of nonCOARDS axis ordering will render files inaccessible to some applications and limit interoperability. Often a buffering operation can be used to miminize performance penalties when axis ordering in model code does not match the axis ordering of a COARDS file.
COARDS addresses the issue of identifying dimensionless vertical coordinates, but does not provide any mechanism for mapping the dimensionless values to dimensional ones that can be located with respect to the earth’s surface.
For backwards compatibility we continue to allow (but do not require) the units
attribute of dimensionless vertical coordinates to take the values "level", "layer", or "sigma_level."
But we recommend that the standard_name
and formula_terms
attributes be used to identify the appropriate definition of the dimensionless vertical coordinate (see Section 4.3.3, "Parametric Vertical Coordinate").
The CF conventions define attributes which enable the description of data properties that are outside the scope of the COARDS conventions. These new attributes do not violate the COARDS conventions, but applications that only recognize COARDS conforming datasets will not have the capabilities that the new attributes are meant to enable. Briefly the new attributes allow:

Identification of quantities using standard names.

Description of dimensionless vertical coordinates.

Associating dimensions with auxiliary coordinate variables.

Linking data variables to scalar coordinate variables.

Associating dimensions with labels.

Description of intervals and cells.

Description of properties of data defined on intervals and cells.

Description of climatological statistics.

Data compression for variables with missing values.
1.6. UGRID Conventions
These conventions implicitly incorporate parts of the UGRID conventions for storing unstructured (or flexible mesh) data in netCDF files using mesh topologies [UGRID]. Only version 1.0 of the UGRID conventions is allowed. The UGRID conventions description is referenced from, rather than rewritten into, this document and the canonical description of how to store mesh topologies is only to be found at [UGRID]. A summary indicating how UGRID relates to other parts of the CF conventions, and which features of UGRID are excluded from CF, can be found in Section 5.9, "Mesh Topology Variables". To reduce the chance of ambiguities arising from their accidental reuse, all of the UGRID standardized attributes are specified in Appendix K, Mesh Topology Attributes and Appendix A, Attributes.
The UGRID conventions have their own conformance document, which should be used in conjunction with the CF conformance document when checking the validity of datasets.
2. NetCDF Files and Components
The components of a netCDF file are described in section 2 of the NUG [NUG]. In this section we describe conventions associated with filenames and the basic components of a netCDF file. We also introduce new attributes for describing the contents of a file.
2.2. Data Types
Data variables must be one of the following data types: string
, char
, byte
, unsigned byte
, short
, unsigned short
, int
, unsigned int
, int64
, unsigned int64
, float
or real
, and double
(which are all the netCDF external data types supported by netCDF4).
The string
type is only available in files using the netCDF version 4 (netCDF4) format.
The char
and string
types are not intended for numeric data.
One byte numeric data should be stored using the byte
or unsigned byte
data types.
It is possible to treat the byte
and short
types as unsigned by using the NUG convention of indicating the unsigned range using the valid_min
, valid_max
, or valid_range
attributes.
In many situations, any integer type may be used.
When the phrase "integer type" is used in this document, it should be understood to mean byte
, unsigned byte
, short
, unsigned short
, int
, unsigned int
, int64
, or unsigned int64
.
Strings in variables may be represented one of two ways  as atomic strings or as character arrays.
An ndimensional array of strings may be implemented as a variable of type string
with n dimensions, or as a variable of type char
with n+1 dimensions where the last (most rapidly varying) dimension is large enough to contain the longest string in the variable.
For example, a character array variable of strings containing the names of the months would be dimensioned (12,9) in order to accommodate "September", the month with the longest name.
The other strings, such as "May", should be padded with trailing NULL or space characters so that every array element is filled.
If the atomic string option is chosen, each element of the variable can be assigned a string with a different length.
The CDL example below shows one variable of each type.
dimensions: strings = 30 ; strlen = 10 ; variables: char char_variable(strings,strlen) ; char_variable:long_name = "strings of type char" ; string str_variable(strings) ; str_variable:long_name = "strings of type string" ;
The examples in this document that use stringvalued variables alternate between these two forms.
2.3. Naming Conventions
It is recommended that variable, dimension, attribute and group names begin with a letter and be composed of letters, digits, and underscores.
By the word letters we mean the standard ASCII letters uppercase A
to Z
and lowercase a
to z
.
By the word digits we mean the standard ASCII digits 0
to 9
, and similarly underscores means the standard ASCII underscore _
.
Note that this is in conformance with the COARDS conventions, but is more restrictive than the netCDF interface which allows almost all Unicode characters encoded as multibyte UTF8 characters (NUG Appendix B).
The netCDF interface also allows leading underscores in names, but the NUG states that this is reserved for system use.
ASCII period (.) and ASCII hyphen () are also allowed in attribute names only.
Case is significant in netCDF names, but it is recommended that names should not be distinguished purely by case, i.e., if case is disregarded, no two names should be the same. It is also recommended that names should be obviously meaningful, if possible, as this renders the file more effectively selfdescribing.
This convention does not standardize any variable or dimension names.
Attribute names and their contents, where standardized, are given in English in this document and should appear in English in conforming netCDF files for the sake of portability.
Languages other than English are permitted for variables, dimensions, and nonstandardized attributes.
The content of some standardized attributes are string values that are not standardized, and thus are not required to be in English.
For example, a description of what a variable represents may be given in a nonEnglish language using the long_name
attribute (see Section 3.2, "Long Name") whose contents are not standardized, but a description given by the standard_name
attribute (see Section 3.3, "Standard Name") must be taken from the standard name table which is in English.
2.4. Dimensions
A variable may have any number of dimensions, including zero, and the dimensions must all have different names. COARDS strongly recommends limiting the number of dimensions to four, but we wish to allow greater flexibility. The dimensions of the variable define the axes of the quantity it contains. Dimensions other than those of space and time may be included. Several examples can be found in this document. Under certain circumstances, one may need more than one dimension in a particular quantity. For instance, a variable containing a twodimensional probability density function might correlate the temperature at two different vertical levels, and hence would have temperature on both axes.
If any or all of the dimensions of a variable have the interpretations of "date or time" (T
), "height or depth" (Z
), "latitude" (Y
), or "longitude" (X
) then we recommend, but do not require (see Section 1.5, "Relationship to the COARDS Conventions"), those dimensions to appear in the relative order T
, then Z
, then Y
, then X
in the CDL definition corresponding to the file.
All other dimensions should, whenever possible, be placed to the left of the spatiotemporal dimensions.
Dimensions may be of any size, including unity. When a single value of some coordinate applies to all the values in a variable, the recommended means of attaching this information to the variable is by use of a dimension of size unity with a oneelement coordinate variable. It is also acceptable to use a scalar coordinate variable which eliminates the need for an associated size one dimension in the data variable. The advantage of using either a coordinate variable or an auxiliary coordinate variable is that all its attributes can be used to describe the singlevalued quantity, including boundaries. For example, a variable containing data for temperature at 1.5 m above the ground has a singlevalued coordinate supplying a height of 1.5 m, and a timemean quantity has a singlevalued time coordinate with an associated boundary variable to record the start and end of the averaging period.
2.5. Variables
This convention does not standardize variable names.
NetCDF variables that contain coordinate data are referred to as coordinate variables, auxiliary coordinate variables, scalar coordinate variables, or multidimensional coordinate variables.
2.5.1. Missing data, valid and actual range of data
The NUG conventions
(NUG Appendix A, Attribute Conventions)
provide the _FillValue
, missing_value
, valid_min
, valid_max
, and valid_range
attributes to indicate missing data.
Missing data is allowed in data variables and auxiliary coordinate variables.
Generic applications should treat the data as missing where any auxiliary coordinate variables have missing values; specialpurpose applications might be able to make use of the data.
Missing data is not allowed in coordinate variables.
The NUG conventions for missing data changed significantly between version 2.3 and version 2.4.
Since version 2.4 the NUG defines missing data as all values outside of the valid_range
, and specifies how the valid_range
should be defined from the _FillValue
(which has library specified default values) if it hasn’t been explicitly specified.
If only one missing value is needed for a variable then we recommend that this value be specified using the _FillValue
attribute.
Doing this guarantees that the missing value will be recognized by generic applications that follow either the before or after version 2.4 conventions.
The scalar attribute with the name _FillValue
and of the same type as its variable is recognized by the netCDF library as the value used to prefill disk space allocated to the variable.
This value is considered to be a special value that indicates undefined or missing data, and is returned when reading values that were not written.
The _FillValue
should be outside the range specified by valid_range
(if used) for a variable.
The netCDF library defines a default fill value for each data type (See the "Note on fill values" in NUG Appendix B, File Format Specifications).
The missing values of a variable with scale_factor
and/or add_offset
attributes (see Section 8.1, "Packed Data") are interpreted relative to the variable’s external values (a.k.a. the packed values, the raw values, the values stored in the netCDF file), not the values that result after the scale and offset are applied.
Applications that process variables that have attributes to indicate both a transformation (via a scale and/or offset) and missing values should first check that a data value is valid, and then apply the transformation.
Note that values that are identified as missing should not be transformed.
Since the missing value is outside the valid range it is possible that applying a transformation to it could result in an invalid operation.
For example, the default _FillValue
is very close to the maximum representable value of IEEE single precision floats, and multiplying it by 100 produces an "Infinity" (using single precision arithmetic).
This convention defines a twoelement vector attribute actual_range
for variables containing numeric data.
If the variable is packed using the scale_factor
and add_offset
attributes (see Section 8.1, "Packed Data"), the elements of the actual_range
should have the type intended for the unpacked data.
The elements of actual_range
must be exactly equal to the minimum and the maximum data values which occur in the variable (when unpacked if packing is used), and both must be within the valid_range
if specified.
If the data is all missing or invalid, the actual_range
attribute cannot be used.
2.6. Attributes
This standard describes many attributes (some mandatory, others optional), but a file may also contain nonstandard attributes. Such attributes do not represent a violation of this standard. Application programs should ignore attributes that they do not recognise or which are irrelevant for their purposes. Conventional attribute names should be used wherever applicable. Nonstandard names should be as meaningful as possible. Before introducing an attribute, consideration should be given to whether the information would be better represented as a variable. In general, if a proposed attribute requires ancillary data to describe it, is multidimensional, requires any of the defined netCDF dimensions to index its values, or requires a significant amount of storage, a variable should be used instead. When this standard defines string attributes that may take various prescribed values, the possible values are generally given in lower case. However, applications programs should not be sensitive to case in these attributes. Several string attributes are defined by this standard to contain "blankseparated lists". Consecutive words in such a list are separated by one or more adjacent spaces. The list may begin and end with any number of spaces. See Appendix A, Attributes for a list of attributes described by this standard.
2.6.1. Identification of Conventions
Files that follow this version of the CF Conventions must indicate this by setting the NUG defined global attribute Conventions
to a string value that contains "CF1.12draft
".
The Conventions version number contained in that string can be used to find the web based versions of this document are from the netCDF Conventions web page.
Subsequent versions of the CF Conventions will not make invalid a compliant usage of this or earlier versions of the CF terms and forms.
It is possible for a netCDF file to adhere to more than one set of conventions, even when there is no inheritance relationship among the conventions. In this case, the value of the Conventions attribute may be a single text string containing a list of the convention names separated by blank space (recommended) or commas (if a convention name contains blanks). This is the Unidata recommended syntax from NetCDF Users Guide, Appendix A. If the string contains any commas, it is assumed to be a commaseparated list.
When CF is listed with other conventions, this asserts the same full compliance with CF requirements and interpretations as if CF was the sole convention. It is the responsibility of the datawriter to ensure that all common metadata is used with consistent meaning between conventions.
The UGRID conventions, which are fully incorporated into the CF conventions, do not need to be included in the Conventions
attribute.
2.6.2. Description of file contents
The following attributes are intended to provide information about where the data came from and what has been done to it. This information is mainly for the benefit of human readers. The attribute values are all character strings. For readability in ncdump outputs it is recommended to embed newline characters into long strings to break them into lines. For backwards compatibility with COARDS none of these global attributes is required.
The NUG defines title
and history
to be global attributes.
We wish to allow the newly defined attributes, i.e., institution
, source
, references
, and comment
, to be either global or assigned to individual variables.
When an attribute appears both globally and as a variable attribute, the variable’s version has precedence.
title

A succinct description of what is in the dataset.
institution

Specifies where the original data was produced.
source

The method of production of the original data. If it was modelgenerated,
source
should name the model and its version, as specifically as could be useful. If it is observational,source
should characterize it (e.g., "surface observation
" or "radiosonde
"). history

Provides an audit trail for modifications to the original data. Wellbehaved generic netCDF filters will automatically append their name and the parameters with which they were invoked to the global history attribute of an input netCDF file. We recommend that each line begin with a timestamp indicating the date and time of day that the program was executed.
references

Published or webbased references that describe the data or methods used to produce it.
comment

Miscellaneous information about the data or methods used to produce it.
2.6.3. External Variables
The global external_variables
attribute is a blankseparated list of the names of variables which are named by attributes in the file but which are not present in the file.
These variables are to be found in other files (called "external files") but CF does not provide conventions for identifying the files concerned.
The only attribute for which CF standardises the use of external variables is cell_measures
.
2.7. Groups
Groups provide a powerful mechanism to structure data hierarchically. This convention does not standardize group names. It may be of benefit to name groups in such a way that human readers can interpret them. However, files that conform to this standard shall not require software to interpret or decode information from group names. References to outofgroup variable and dimensions shall be found by applying the scoping rules outlined below.
2.7.1. Scope
The scoping mechanism is in keeping with the following principal:
"Dimensions are scoped such that they are visible to all child groups. For example, you can define a dimension in the root group, and use its dimension id when defining a variable in a subgroup."
Any variable or dimension can be referred to, as long as it can be found with one of the following search strategies:

Search by absolute path

Search by relative path

Search by proximity
These strategies are explained in detail in the following sections.
If any dimension of an outofgroup variable has the same name as a dimension of the referring variable, the two must be the same dimension (i.e. they must have the same netCDF dimension ID).
Search by absolute path
A variable or dimension specified with an absolute path (i.e., with a leading slash "/") is at the indicated location relative to the root group, as in a UNIXstyle file convention.
For example, a coordinates
attribute of /g1/lat
refers to the lat
variable in group /g1
.
Search by relative path
As in a UNIXstyle file convention, a variable or dimension specified with a relative path (i.e., containing a slash but not with a leading slash, e.g. child/lat
) is at the location obtained by affixing the relative path to the absolute path of the referring attribute.
For example, a coordinates
attribute of g1/lat
refers to the lat
variable in subgroup g1
of the current (referring) group.
Upward path traversals from the current group are indicated with the UNIX convention.
For example, ../g1/lat
refers to the lat
variable in the sibling group g1
of the current (referring) group.
Search by proximity
A variable or dimension specified with no path (for example, lat
) refers to the variable or dimension of that name, if there is one, in the referring group.
If not, the ancestors of the referring group are searched for it, starting from the direct ancestor and proceeding toward the root group, until it is found.
A special case exists for coordinate variables. Because coordinate variables must share dimensions with the variables that reference them, the ancestor search is executed only until the local apex group is reached. For coordinate variables that are not found in the referring group or its ancestors, a further strategy is provided, called lateral search. The lateral search proceeds downwards from the local apex group widthwise through each level of groups until the sought coordinate is found. The lateral search algorithm may only be used for NUG coordinate variables; it shall not be used for auxiliary coordinate variables.
Note

This use of the lateral search strategy to find them is discouraged. They are allowed mainly for backwardscompatibility with existing datasets, and may be deprecated in future versions of the standard. 
2.7.2. Application of attributes
The following attributes are optional for nonroot groups. They are allowed in order to provide additional provenance and description of the subsidiary data. They do not override attributes from parent groups.

title

history
If these attributes are present, they may be applied additively to the parent attributes of the same name. If a file containing groups is modified, the user or application need only update these attributes in the root group, rather than traversing all groups and updating all attributes that are found with the same name. In the case of conflicts, the root group attribute takes precedence over pergroup instances of these attributes.
The following attributes may only be used in the root group and shall not be duplicated or overridden in child groups:

Conventions

external_variables
Furthermore, pervariable attributes must be attached to the variables to which they refer. They may not be attached to a group, even if all variables within that group use the same attribute and value.
If attributes are present within groups without being attached to a variable, these attributes apply to the group where they are defined, and to that group’s descendants, but not to ancestor or sibling groups. If a group attribute is defined in a parent group, and one of the child group redefines the same attribute, the definition within the child group applies for the child and all of its descendants.
3. Description of the Data
The attributes described in this section are used to provide a description of the content and the units of measurement for each variable.
We continue to support the use of the units
and long_name
attributes as defined in COARDS.
We extend COARDS by adding the optional standard_name
attribute which is used to provide unique identifiers for variables.
This is important for data exchange since one cannot necessarily identify a particular variable based on the name assigned to it by the institution that provided the data.
The standard_name
attribute can be used to identify variables that contain coordinate data.
But since it is an optional attribute, applications that implement these standards must continue to be able to identify coordinate types based on the COARDS conventions.
3.1. Units
The units
attribute is required for all variables that represent dimensional quantities (except for boundary variables defined in Section 7.1, "Cell Boundaries" and climatology variables defined in Section 7.4, "Climatological Statistics").
The units
attribute is permitted but not required for dimensionless quantities (see Section 3.1.1, "Dimensionless units").
The value of the units
attribute is a string that can be recognized by the UDUNITS package [UDUNITS], with the exceptions that are given in Section 3.1.1, "Dimensionless units" and Section 3.1.3, "Scale factors and offsets".
Note that case is significant in the units
strings.
Note also that CF depends on UDUNITS only for the definition of legal units
strings.
CF does not assume or require that the UDUNITS software will be used for units
conversion.
In most units
conversions, the sole operation on the data is multiplication by a scale factor.
Special treatment is required in converting the units
of variables that involve temperature (Section 3.1.2, "Temperature units") and the units
of time coordinate variables (Section 4.4, "Time Coordinate").
The COARDS convention prohibits the unit degrees
altogether, but this unit is not forbidden by the CF convention because it may in fact be appropriate for a variable containing, say, solar zenith angle.
The unit degrees
is also allowed on coordinate variables such as the latitude and longitude coordinates of a transformed grid.
In this case the coordinate values are not true latitudes and longitudes, which must always be identified using the more specific forms of degrees
as described in Section 4.1, "Latitude Coordinate" and Section 4.2, "Longitude Coordinate".
3.1.1. Dimensionless units
A variable with no units
attribute is assumed to be dimensionless.
However, a units
attribute specifying a dimensionless unit may optionally be included.
The canonical unit (see also Section 3.3, "Standard Name") for dimensionless quantities that represent fractions, or parts of a whole, is 1
.
The UDUNITS package defines a few dimensionless units, such as percent
, ppm
(parts per million, 1e6), and ppb
(parts per billion, 1e9).
As an alternative to the canonical units
of 1
or some other unitless number, the units
for a dimensionless quantity may be given as a ratio of dimensional units, for instance mg kg1
for a mass ratio of 1e6, or microlitre litre1
for a volume ratio of 1e6. Dataproducers are invited to consider whether this alternative would be more helpful to the users of their data.
The CF convention supports dimensionless units that are UDUNITS compatible, with one exception, concerning the dimensionless units defined by UDUNITS for volume ratios, such as ppmv
and ppbv
.
These units are allowed in the units
attribute by CF only if the data variable has no standard_name
.
These units are prohibited by CF if there is a standard_name
, because the standard_name
defines whether the quantity is a volume ratio, so the units
are needed only to indicate a dimensionless number.
Information describing a dimensionless physical quantity itself (e.g.
"area fraction" or "probability") does not belong in the units
attribute, but should be given in the long_name
or standard_name
attributes (see Section 3.2, "Long Name" and Section 3.3, "Standard Name"), in the same way as for physical quantities with dimensional units.
As an exception, to maintain backwards compatibility with COARDS, the text strings level
, layer
, and sigma_level
are allowed in the units
attribute, in order to indicate dimensionless vertical coordinates.
This use of units
is not compatible with UDUNITS, and is deprecated by this standard because conventions for more precisely identifying dimensionless vertical coordinates are available (see Section 4.3.2, "Dimensionless Vertical Coordinate").
The UDUNITS syntax that allows scale factors and offsets to be applied to a unit is not supported by this standard, except for case of specifying reference time, see section Section 4.4, "Time Coordinate".
The application of any scale factors or offsets to data should be indicated by the scale_factor
and add_offset
attributes.
Use of these attributes for data packing, which is their most important application, is discussed in detail in Section 8.1, "Packed Data".
3.1.2. Temperature units
The units
of temperature imply an origin (i.e. zero point) for the associated measurement scale.
When the temperature value is the degree of warmth with respect to the origin of the measurement scale, we call it an onscale temperature.
When units
of onscale temperature are converted, the data may require the addition of an offset as well as multiplication by a scale factor, because the physical meaning of a numerical value of zero for an onscale temperature depends on the unit of measurement.
Onscale temperature is unique among quantities in the respect that the origin and the unit of measurement are both defined by the units
and therefore cannot be chosen independently.
For all other quantities, the origin and the unit of measurement are independent.
Converting the unit of measurement alone, without changing the origin, does not change the meaning of zero.
For example (using bold to indicate a numerical data value), 0 kilogram
is the same mass as 0 pound
, and 0 seconds since 197011
means the same as 0 days since 197011
, but 0 degC
is not the same temperature as 0 degF
(= 17.8 degC
), because these two temperature units
implicitly refer to measurement scales which have different origins.
On the other hand, when the temperature value is a temperature difference, which compares two onscale temperatures with the same origin, the value of that origin is irrelevant as it cancels out when taking the difference.
Therefore to convert the units
of a temperature difference requires only multiplication by a scale factor, without the addition of an offset.
The units
attribute does not distinguish between onscale temperatures and temperature differences.
This ambiguity also affects units of temperature raised to some power e.g. K^2
or multiplied by other units e.g. W m2 K1
, degF/foot
or degC m s1
.
A standard_name
(Section 3.3, "Standard Name") or standard_name
modifier (Appendix C, Standard Name Modifiers) may clarify the intention, but they are optional.
Some statistical operations described by the cell_methods
attribute (Section 7.3, "Cell Methods"; Appendix E, Cell Methods) imply that temperature must be interpreted as temperature difference, but this attribute is optional too.
In order to convert the units
correctly, it is essential to know whether a temperature is onscale or a difference.
Therefore this standard strongly recommends that any variable whose units
involve a temperature unit should also have a units_metadata
attribute to make the distinction.
This attribute must have one of the following three values: temperature: on_scale
, temperature: difference
, temperature: unknown
.
The units_metadata
attribute, standard_name
modifier (Appendix C, Standard Name Modifiers) and cell_methods
attribute (Appendix E, Cell Methods) must be consistent if present.
A variable must not have a units_metadata
attribute if it has no units
attribute or if its units
do not involve a temperature unit.
units_metadata
to distinguish temperature quantitiesvariables: float Tonscale; Tonscale:long_name="globalmean surface temperature"; Tonscale:standard_name="surface_temperature"; Tonscale:units="degC"; Tonscale:units_metadata="temperature: on_scale"; Tonscale:cell_methods="area: mean"; float Tdifference; Tdifference:long_name="change in globalmean surface temperature relative to preindustrial"; Tdifference:standard_name="surface_temperature"; Tdifference:units="degC"; Tdifference:units_metadata="temperature: difference"; Tdifference:cell_methods="area: mean";
With temperature: unknown
, correct conversion of the units
cannot be guaranteed.
This value of units_metadata
indicates that the datawriter does not know whether the temperature is onscale or a difference.
If the units_metadata
attribute is not present, the datareader should assume temperature: unknown
.
The units_metadata
attribute was introduced in CF 1.11.
In data written according to versions before 1.11, temperature: unknown
should be assumed for all units
involving temperature, if it cannot be deduced from other metadata.
We note (for guidance only regarding temperature: unknown
, not as a CF convention) that the UDUNITS software assumes temperature: on_scale
for units
strings containing only a unit of temperature, and temperature: difference
for units
strings in which a unit of temperature is raised to any power other than unity, or multiplied or divided by any other unit.
With temperature: on_scale
, correct conversion can be guaranteed only for pure temperature units
.
If the quantity is an onscale temperature multiplied by some other quantity, it is not possible to convert the data from the units
given to any other units
that involve a temperature with a different origin, given only the units
.
For instance, when temperature is onscale, a value in kg degree_C m2
can be converted to a value in kg K m2
only if we know separately the values in degree_C
and kg m2
of which it is the product.
3.1.3. Scale factors and offsets
UDUNITS recognises the SI prefixes shown in Prefixes for decimal multiples and submultiples of units for decimal multiples and submultiples of units, and allows them to be applied to nonSI units as well.
UDUNITS offers a syntax for indicating arbitrary scale factors and offsets to be applied to a unit.
(Note that this is different from the scale factors and offsets used for converting between units
, as discussed for temperature in Section 3.1.2, "Temperature units".)
This UDUNITS syntax for arbitrary transformation of units
is not supported by the CF standard, except for the case of specifying reference time (Section 4.4, "Time Coordinate").
The application of any scale factors or offsets to data should be indicated by the scale_factor
and add_offset
attributes.
Use of these attributes for data packing, which is their most important application, is discussed in detail in Section 8.1, "Packed Data".
Factor  Prefix  Abbreviation  Factor  Prefix  Abbreviation  

1e1 
deca,deka 
da 
1e1 
deci 
d 

1e2 
hecto 
h 
1e2 
centi 
c 

1e3 
kilo 
k 
1e3 
milli 
m 

1e6 
mega 
M 
1e6 
micro 
u 

1e9 
giga 
G 
1e9 
nano 
n 

1e12 
tera 
T 
1e12 
pico 
p 

1e15 
peta 
P 
1e15 
femto 
f 

1e18 
exa 
E 
1e18 
atto 
a 

1e21 
zetta 
Z 
1e21 
zepto 
z 

1e24 
yotta 
Y 
1e24 
yocto 
y 
3.2. Long Name
The long_name
attribute is defined by the NUG to contain a long descriptive name which may, for example, be used for labeling plots.
For backwards compatibility with COARDS this attribute is optional.
But it is highly recommended that either this or the standard_name
attribute defined in the next section be provided for all data variables and variables containing coordinate data, in order to make the file selfdescribing.
If a variable has no long_name
attribute then an application may use, as a default, the standard_name
if it exists, or the variable name itself.
3.3. Standard Name
A fundamental requirement for exchange of scientific data is the ability to describe precisely the physical quantities being represented.
To some extent this is the role of the long_name
attribute as defined in the NUG.
However, usage of long_name
is completely adhoc.
For many applications it is desirable to have a more definitive description of the quantity, which allows users of data from different sources (some of which might be models and others observational) to determine whether quantities are in fact comparable.
For this reason each variable may optionally be given a "standard name", whose meaning is defined by this convention.
There may be several variables in a dataset with any given standard name, and these may be distinguished by other metadata, such as coordinates (Chapter 4, Coordinate Types) and cell_methods
(Section 7.3, "Cell Methods").
A standard name is associated with a variable via the attribute standard_name
which takes a string value comprised of a standard name optionally followed by one or more blanks and a standard name modifier (a string value from Appendix C, Standard Name Modifiers).
The set of permissible standard names is contained in the standard name table. The table entry for each standard name contains the following:
 standard name

The name used to identify the physical quantity. A standard name contains no whitespace and is case sensitive.
 canonical units

Representative units of the physical quantity. Unless it is dimensionless, a variable with a
standard_name
attribute must have units which are physically equivalent (not necessarily identical) to the canonical units, possibly modified by an operation specified by the standard name modifier (see below and Appendix C, Standard Name Modifiers) or by thecell_methods
attribute (see Section 7.3, "Cell Methods" and Appendix E, Cell Methods) or both.  description

The description is meant to clarify the qualifiers of the fundamental quantities such as which surface a quantity is defined on or what the flux sign conventions are. We don’t attempt to provide precise definitions of fundumental physical quantities (e.g., temperature) which may be found in the literature. The description may define rules on the variable type, attributes and coordinates which must be complied with by any variable carrying that standard name (such as in Example 3.5).
When appropriate, the table entry also contains the corresponding GRIB parameter code(s) (from ECMWF and NCEP) and AMIP identifiers.
The standard name table is located at
https://cfconventions.org/Data/cfstandardnames/current/src/cfstandardnametable.xml,
written in compliance with the XML format, as described in Appendix B, Standard Name Table Format.
Knowledge of the XML format is only necessary for application writers who plan to directly access the table.
A formatted text version of the table is provided at
https://cfconventions.org/Data/cfstandardnames/current/build/cfstandardnametable.html,
and this table may be consulted in order to find the standard name that should be assigned to a variable.
Some standard names (e.g. region
and area_type
) are used to indicate quantities which are permitted to take only certain standard values.
This is indicated in the definition of the quantity in the standard name table, accompanied by a list or a link to a list of the permitted values.
Standard names by themselves are not always sufficient to describe a quantity.
For example, a variable may contain data to which spatial or temporal operations have been applied.
Or the data may represent an uncertainty in the measurement of a quantity.
These quantity attributes are expressed as modifiers of the standard name.
Modifications due to common statistical operations are expressed via the cell_methods
attribute (see Section 7.3, "Cell Methods" and Appendix E, Cell Methods).
Other types of quantity modifiers are expressed using the optional modifier part of the standard_name
attribute.
The permissible values of these modifiers are given in Appendix C, Standard Name Modifiers.
standard_name
float psl(lat,lon) ; psl:long_name = "mean sea level pressure" ; psl:units = "hPa" ; psl:standard_name = "air_pressure_at_sea_level" ;
The description in the standard name table entry for air_pressure_at_sea_level
clarifies that "sea level" refers to the mean sea level, which is close to the geoid in sea areas.
3.4. Ancillary Data
When one data variable provides metadata about the individual values of another data variable it may be desirable to express this association by providing a link between the variables.
For example, instrument data may have associated measures of uncertainty.
The attribute ancillary_variables
is used to express these types of relationships.
It is a string attribute whose value is a blank separated list of variable names.
The nature of the relationship between variables associated via ancillary_variables
must be determined by other attributes.
The variables listed by the ancillary_variables
attribute will often have the standard name of the variable which points to them including a modifier (Appendix C, Standard Name Modifiers) to indicate the relationship.
The dimensions of an ancillary variable must be the same as or a subset of the dimensions of the variable to which it is related, but their order is not restricted, and with one exception:
If an ancillary variable of a data variable that has been compressed by gathering (Section 8.2, "Lossless Compression by Gathering") does not span the compressed dimension, then its dimensions may be any subset of the data variable’s uncompressed dimensions, i.e. any of the dimensions of the data variable except the compressed dimension, and any of the dimensions listed by the compress
attribute of the compressed coordinate variable.
float q(time) ; q:standard_name = "specific_humidity" ; q:units = "g/g" ; q:ancillary_variables = "q_error_limit q_detection_limit" ; float q_error_limit(time) q_error_limit:standard_name = "specific_humidity standard_error" ; q_error_limit:units = "g/g" ; float q_detection_limit(time) q_detection_limit:standard_name = "specific_humidity detection_minimum" ; q_detection_limit:units = "g/g" ;
Alternatively, ancillary_variables
may be used as status flags indicating the operational status of an instrument producing the data or as quality flags indicating the results of a quality control test, or some other quantitative quality assessment, performed against the measurements contained in the source variable.
In these cases, the flag variable will include a standard name that differs from that of the source variable and indicates the specific type of flag the variable represents.
The standard names table includes many names intended to be used in this situation, both general names meant to be used to flexibly represent any type of status or quality assessment, as well as names for specific quality control tests commonly applied to geophysical phenomena timeseries data. Several examples are listed below:

status_flag
andquality_flag
: general flag categories for instrument status or quality assessment 
climatology_test_quality_flag
,flat_line_test_quality_flag
,gap_test_quality_flag
,spike_test_quality_flag
: a subset of standard name flags used to indicate the results of commonlyused geophysical timeseries data quality control tests (consult the standard names table for a full list of published flags) 
aggregate_quality_flag
: flag indicating an aggregate summary of all quality tests performed on the data variable, both automated and manual (i.e. a master quality flag for a particular variable)
The following example illustrates the use of three of these flags to represent two independent quality control tests and an aggregate flag that combines the results of the two tests.
float salinity(time, z); salinity:units = "1"; salinity:long_name = "Salinity"; salinity:standard_name = "sea_water_practical_salinity"; salinity:ancillary_variables = "salinity_qc_generic salinity_qc_flat_line_test salinity_qc_agg"; int salinity_qc_generic(time, z); salinity_qc_generic:long_name = "Salinity Generic QC Process Flag"; salinity_qc_generic:standard_name = "quality_flag"; int salinity_qc_flat_line_test(time, z); salinity_qc_flat_line_test:long_name = "Salinity Flat Line Test Flag"; salinity_qc_flat_line_test:standard_name = "flat_line_test_quality_flag"; int salinity_qc_agg(time, z); salinity_qc_agg:long_name = "Salinity Aggregate Flag"; salinity_qc_agg:standard_name = "aggregate_quality_flag";
Note that the ancillary variables in this example are simplified to exclude flag_values
, flag_masks
and flag_meanings
attributes described in Section 3.5, "Flags" that they would ordinarily require
3.5. Flags
The attributes flag_values
, flag_masks
and flag_meanings
are intended to make variables that contain flag values self describing.
Status codes and Boolean (binary) condition flags may be expressed with different combinations of flag_values
and flag_masks
attribute definitions.
The flag_values
and flag_meanings
attributes describe a status flag consisting of mutually exclusive coded values.
The flag_values
attribute is the same type as the variable to which it is attached, and contains a list of the possible flag values.
The flag_meanings
attribute is a string whose value is a blank separated list of descriptive words or phrases, one for each flag value.
Each word or phrase should consist of characters from the alphanumeric set and the following five: '_', '', '.', '+', '@'.
If multiword phrases are used to describe the flag values, then the words within a phrase should be connected with underscores.
The following example illustrates the use of flag values to express a speed quality with an enumerated status code.
flag_values
byte current_speed_qc(time, depth, lat, lon) ; current_speed_qc:long_name = "Current Speed Quality" ; current_speed_qc:standard_name = "status_flag" ; current_speed_qc:_FillValue = 128b ; current_speed_qc:valid_range = 0b, 2b ; current_speed_qc:flag_values = 0b, 1b, 2b ; current_speed_qc:flag_meanings = "quality_good sensor_nonfunctional outside_valid_range" ;
Note that the data variable containing current speed has an ancillary_variables attribute with a value containing current_speed_qc.
The flag_masks and flag_meanings attributes describe a number of independent Boolean conditions using bit field notation by setting unique bits in each flag_masks value. The flag_masks attribute is the same type as the variable to which it is attached, and contains a list of values matching unique bit fields. The flag_meanings attribute is defined as above, one for each flag_masks value. A flagged condition is identified by performing a bitwise AND of the variable value and each flag_masks value; a nonzero result indicates a true condition. Thus, any or all of the flagged conditions may be true, depending on the variable bit settings. The following example illustrates the use of flag_masks to express six sensor status conditions.
flag_masks
byte sensor_status_qc(time, depth, lat, lon) ; sensor_status_qc:long_name = "Sensor Status" ; sensor_status_qc:standard_name = "status_flag" ; sensor_status_qc:_FillValue = 0b ; sensor_status_qc:valid_range = 1b, 63b ; sensor_status_qc:flag_masks = 1b, 2b, 4b, 8b, 16b, 32b ; sensor_status_qc:flag_meanings = "low_battery processor_fault memory_fault disk_fault software_fault maintenance_required" ;
A variable with standard name of region
, area_type
or any other standard name which requires stringvalued values from a defined list may use flags together with flag_values
and flag_meanings
attributes to record the translation to the string values.
The following example illustrates this using integer flag values for a variable with standard name region
and flag_values
selected from the standardized region names (see section 6.1.1).
flag_values
int basin(lat, lon); standard_name: region; flag_values: 1, 2, 3; flag_meanings:"atlantic_arctic_ocean indo_pacific_ocean global_ocean"; data: basin: 1, 1, 1, 1, 2, ..... ;
The flag_masks
, flag_values
and flag_meanings
attributes, used together, describe a blend of independent Boolean conditions and enumerated status codes.
The flag_masks
and flag_values
attributes are both the same type as the variable to which they are attached.
A flagged condition is identified by a bitwise AND of the variable value and each flag_masks
value; a result that matches the flag_values
value indicates a true
condition.
Repeated flag_masks
define a bit field mask that identifies a number of status conditions with different flag_values
.
The flag_meanings
attribute is defined as above, one for each flag_masks
bit field and flag_values
definition.
Each flag_values
and flag_masks
value must coincide with a flag_meanings
value.
The following example illustrates the use of flag_masks
and flag_values
to express two sensor status conditions and one enumerated status code.
flag_masks
and flag_values
byte sensor_status_qc(time, depth, lat, lon) ; sensor_status_qc:long_name = "Sensor Status" ; sensor_status_qc:standard_name = "status_flag" ; sensor_status_qc:_FillValue = 0b ; sensor_status_qc:valid_range = 1b, 15b ; sensor_status_qc:flag_masks = 1b, 2b, 12b, 12b, 12b ; sensor_status_qc:flag_values = 1b, 2b, 4b, 8b, 12b ; sensor_status_qc:flag_meanings = "low_battery hardware_fault offline_mode calibration_mode maintenance_mode" ;
In this case, mutually exclusive values are blended with Boolean values to maximize use of the available bits in a flag value.
The table below represents the four binary digits (bits) expressed by the sensor_status_qc
variable in the previous example.
Bit 0 and Bit 1 are Boolean values indicating a low battery condition and a hardware fault, respectively. The next two bits (Bit 2 and Bit 3) express an enumeration indicating abnormal sensor operating modes. Thus, if Bit 0 is set, the battery is low and if Bit 1 is set, there is a hardware fault  independent of the current sensor operating mode.
Bit 3 (MSB)  Bit 2  Bit 1  Bit 0 (LSB) 

H/W Fault 
Low Batt 
The remaining bits (Bit 2 and Bit 3) are decoded as follows:
Bit 3  Bit 2  Mode 

0 
1 
offline_mode 
1 
0 
calibration_mode 
1 
1 
maintenance_mode 
The "12b" flag mask is repeated in the sensor_status_qc
flag_masks
definition to explicitly declare the recommended bit field masks to repeatedly AND with the variable value while searching for matching enumerated values.
An application determines if any of the conditions declared in the flag_meanings
list are true
by simply iterating through each of the flag_masks
and AND’ing them with the variable.
When a result is equal to the corresponding flag_values
element, that condition is true
.
The repeated flag_masks
enable a simple mechanism for clients to detect all possible conditions.
4. Coordinate Types
The commonest use of coordinate variables is to locate the data in space and time, but coordinates may be provided for any other continuous geophysical quantity (e.g. density, temperature, radiation wavelength, zenith angle of radiance, sea surface wave frequency) or discrete category (see Section 4.5, "Discrete Axis", e.g. area type, model level number, ensemble member number) on which the data variable depends.
Four types of coordinates receive special treatment by these conventions: latitude, longitude, vertical, and time.
We continue to support the special role that the units
and positive
attributes play in the COARDS convention to identify coordinate type.
As an extension to COARDS, we strongly recommend that a parametric (usually dimensionless) vertical coordinate variable should be associated, via standard_name
and formula_terms
attributes, with its explicit definition, which provides a mapping between its values and dimensional vertical coordinate values that can be uniquely located with respect to a point on the earth’s surface.
Because identification of a coordinate type by its units is complicated by requiring the use of an external package [UDUNITS], we provide two optional methods that yield a direct identification.
The attribute axis
may be attached to a coordinate variable and given one of the values X
, Y
, Z
or T
which stand for a longitude, latitude, vertical, or time axis respectively.
Alternatively the standard_name
attribute may be used for direct identification.
But note that these optional attributes are in addition to the required COARDS metadata.
To identify generic spatial coordinates we recommend that the axis
attribute be attached to these coordinates and given one of the values X
, Y
or Z
.
The values X
and Y
for the axis attribute should be used to identify horizontal coordinate variables.
If both X and Yaxis are identified, XYup
should define a righthanded coordinate system, i.e. rotation from the positive X direction to the positive Y direction is anticlockwise if viewed from above.
We strongly recommend that coordinate variables be used for all coordinate types whenever they are applicable.
The methods of identifying coordinate types described in this section apply both to coordinate variables and to auxiliary coordinate variables named by the coordinates
attribute (see Chapter 5, Coordinate Systems and Domain).
The values of a coordinate variable or auxiliary coordinate variable indicate the locations of the gridpoints. The locations of the boundaries between cells are indicated by bounds variables (see Section 7.1, "Cell Boundaries"). If bounds are not provided, an application might reasonably assume the gridpoints to be at the centers of the cells, but we do not require that in this standard.
4.1. Latitude Coordinate
Variables representing latitude must always explicitly include the units
attribute; there is no default value.
The recommended value of the units
attribute is the string degrees_north
. Also accepted are degree_north
, degree_N
, degrees_N
, degreeN
, and degreesN
.
float lat(lat) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ;
Application writers should note that the UDUNITS package does not recognize the directionality implied by the "north" part of the unit specification.
It only recognizes its size, i.e., 1 degree is defined to be pi/180 radians.
Hence, determination that a coordinate is a latitude type should be done via a string match between the given unit and one of the acceptable forms of degrees_north
.
Optionally, the latitude type may be indicated additionally by providing the standard_name
attribute with the value latitude
, and/or the axis
attribute with the value Y
.
Coordinates of latitude with respect to a rotated pole should be given units of degrees
, not degrees_north
or equivalents, because applications which use the units to identify axes would have no means of distinguishing such an axis from real latitude, and might draw incorrect coastlines, for instance.
4.2. Longitude Coordinate
Variables representing longitude must always explicitly include the units
attribute; there is no default value.
The recommended value of the units
attribute is the string degrees_east
. Also accepted are degree_east
, degree_E
, degrees_E
, degreeE
, and degreesE
.
float lon(lon) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ;
Application writers should note that the UDUNITS package has limited recognition of the directionality implied by the "east" part of the unit specification.
It defines degrees_east
to be pi/180 radians, and hence equivalent to degrees_north
.
We recommend the determination that a coordinate is a longitude type should be done via a string match between the given unit and one of the acceptable forms of degrees_east
.
Optionally, the longitude type may be indicated additionally by providing the standard_name
attribute with the value longitude
, and/or the axis
attribute with the value X
.
Coordinates of longitude with respect to a rotated pole should be given units of degrees
, not degrees_east
or equivalents, because applications which use the units to identify axes would have no means of distinguishing such an axis from real longitude, and might draw incorrect coastlines, for instance.
4.3. Vertical (Height or Depth) Coordinate
Variables representing dimensional height or depth axes must always explicitly include the units
attribute; there is no default value.
The direction of positive (i.e., the direction in which the coordinate values are increasing), whether up or down, cannot in all cases be inferred from the units.
The direction of positive is useful for applications displaying the data.
For this reason the attribute positive
as defined in the COARDS standard is required if the vertical axis units are not a valid unit of pressure (as determined by the UDUNITS package [UDUNITS]) — otherwise its inclusion is optional.
The positive
attribute may have the value up
or down
(case insensitive).
This attribute may be applied to either coordinate variables or auxiliary coordinate variables that contain vertical coordinate data.
For example, if an oceanographic netCDF file encodes the depth of the surface as 0 and the depth of 1000 meters as 1000 then the axis would use attributes as follows:
axis_name:units = "meters" ; axis_name:positive = "down" ;
If, on the other hand, the depth of 1000 meters were represented as 1000 then the value of the positive
attribute would have been up
.
If the units
attribute value is a valid pressure unit the default value of the positive
attribute is down
.
A vertical coordinate will be identifiable by:

units of pressure; or

the presence of the
positive
attribute with a value ofup
ordown
(case insensitive).
Optionally, the vertical type may be indicated additionally by providing the standard_name
attribute with an appropriate value, and/or the axis
attribute with the value Z
.
If both positive
and standard_name
are provided, it is recommended that they should be consistent.
For instance, if a depth of 1000 metres is represented by 1000 and positive
is up
, it would be inconsistent to give the standard_name
as depth
, whose definition (vertical distance below the surface) implies positive down.
If an application detects such an inconsistency, the user should be warned, and the positive
attribute should be used to determine the sign convention.
Recommendations: The positive
attribute should be consistent with the sign convention implied by the definition of the standard_name
, if both are provided.
4.3.1. Dimensional Vertical Coordinate
Variables representing dimensional vertical coordinates for or height must always explicitly include the units
attribute.
The acceptable units for a vertical (depth or height) coordinate variable must a UDUNITS [UDUNITS] representation of one of the following:

units of pressure. For vertical axes the most commonly used of these include
bar
,millibar
,decibar
,atmosphere (atm)
,pascal (Pa)
, andhPa
. 
units of length. For vertical axes the most commonly used of these include
meter (metre, m)
, andkilometer (km)
. 
other units that may under certain circumstances reference vertical position such as units of density or temperature.
Plural forms are also acceptable.
4.3.2. Dimensionless Vertical Coordinate
The units
attribute is not required for dimensionless coordinates.
For backwards compatibility with COARDS we continue to allow the units
attribute to take one of the values: level
, layer
, or sigma_level
.
These values are not recognized by the UDUNITS package, and are considered a deprecated feature in the CF standard.
4.3.3. Parametric Vertical Coordinate
In some cases dimensional vertical coordinates are a function of horizontal location as well as parameters which depend on vertical location, and therefore cannot be stored in the onedimensional vertical coordinate variable, which is in most of these cases is dimensionless.
The standard_name
of the parametric (usually dimensionless) vertical coordinate variable can be used to find the definition of the associated computed (always dimensional) vertical coordinate in Appendix D, Parametric Vertical Coordinates.
The definition provides a mapping between the parametric vertical coordinate values and computed values that can positively and uniquely indicate the location of the data.
The formula_terms
attribute can be used to associate terms in the definitions with variables in a netCDF file, and the computed_standard_name
attribute can be used to supply the standard_name
of the computed vertical coordinate values computed according to the definition.
To maintain backwards compatibility with COARDS the use of these attributes is not required, but is strongly recommended.
Some of the definitions may be supplemented with information stored in the grid_mapping
variable about the datum used as a vertical reference (e.g. geoid, other geopotential datum or reference ellipsoid; see Section 5.6, "Horizontal Coordinate Reference Systems, Grid Mappings, and Projections" and Appendix F, Grid Mappings).
float lev(lev) ; lev:long_name = "sigma at layer midpoints" ; lev:positive = "down" ; lev:standard_name = "atmosphere_sigma_coordinate" ; lev:formula_terms = "sigma: lev ps: PS ptop: PTOP" ; lev:computed_standard_name = "air_pressure" ;
In this example the standard_name
value atmosphere_sigma_coordinate
identifies the following definition from Appendix D, Parametric Vertical Coordinates which specifies how to compute pressure at gridpoint (n,k,j,i)
where j
and i
are horizontal indices, k
is a vertical index, and n
is a time index:
p(n,k,j,i) = ptop + sigma(k)*(ps(n,j,i)ptop)
The formula_terms
attribute associates the variable lev
with the term sigma
, the variable PS
with the term ps
, and the variable PTOP
with the term ptop
.
Thus the pressure at gridpoint (n,k,j,i)
would be calculated by
p(n,k,j,i) = PTOP + lev(k)*(PS(n,j,i)PTOP)
The computed_standard_name
attribute indicates that the values in variable
p
would have a standard_name
of air_pressure
.
4.4. Time Coordinate
Variables representing reference time must always explicitly include the units
attribute; there is no default value.
The units
attribute takes a string value that follows the formatting requirements of the [UDUNITS] package. These requirements can best be described by an example with explanatory comments:
The time unit specification seconds since 1992108 15:15:42.5 6:00
indicates seconds since October 8th, 1992 at 3 hours, 15 minutes and 42.5 seconds in the afternoon in the time zone which is six hours to the west of Coordinated Universal Time (i.e. Mountain Daylight Time).
The time zone specification can also be written without a colon using one or two digits (indicating hours) or three or four digits (indicating hours and minutes).
The acceptable units for time are given by the UDUNITS package.
The most commonly used of these strings (and their abbreviations) includes day
(d
), hour
(hr
, h
), minute
(min
) and second
(sec
, s
).
Plural forms are also acceptable.
UDUNITS permits a number of alternatives to the word since
in the units of time coordinates. All the alternatives have exactly the same meaning in UDUNITS. For compatibility with other software, CF strongly recommends that since
should be used.
The reference date/time string (appearing after the identifier since
) is required.
It may include date alone, or date and time, or date, time and time zone.
If the time zone is omitted the default is UTC, and if both time and time zone are omitted the default is 00:00:00 UTC.
UDUNITS defines a year
to be exactly 365.242198781 days (the interval between 2 successive passages of the sun through vernal equinox).
It is not a calendar year. UDUNITS defines a month
to be exactly year/12
, which is not a calendar month.
The CF standard follows UDUNITS in the definition of units, but we recommend that year
and month
should not be used, because of the potential for mistakes and confusion.
double time(time) ; time:long_name = "time" ; time:units = "days since 199011 0:0:0" ;
A reference time coordinate is identifiable from its units string alone.
Optionally, the time coordinate may be indicated additionally by providing the standard_name
attribute with an appropriate value, and/or the axis
attribute with the value T
.
4.4.1. Calendar
A date/time is the set of numbers which together identify an instant of time, namely its year, month, day, hour, minute and second, where the second may have a fraction but the others are all integer.
A time coordinate value represents a date/time.
In order to calculate a time coordinate value from a date/time, or the reverse, one must know the units
attribute of the time coordinate variable (containing the time unit of the coordinate values and the reference date/time) and the calendar.
The choice of calendar defines the set of dates (yearmonthday combinations) which are permitted, and therefore it specifies the number of days between the times of 0:0:0
(midnight) on any two dates.
Date/times which are not permitted in a given calendar are prohibited in both the encoded time coordinate values, and in the reference date/time string.
It is recommended that the calendar be specified by the calendar
attribute of the time coordinate variable.
When a time coordinate value is calculated from a date/time, or the reverse, it is assumed that the coordinate value increases by exactly 60 seconds from the start of any minute (identified by year, month, day, hour, minute, all being integers) to the start of the next minute, with no leap seconds, in all CF calendars. This assumption has various consequences when realworld date/times from calendars which do contain leap seconds (such as UTC) are stored in time coordinate variables:

Any date/times between the end of the 60th second of the last minute of one hour and the start of the first second of the next hour cannot be represented by time coordinates e.g.
20161231 23:59:60.5
cannot be represented. 
A time coordinate value must not be interpreted as representing a date/time in the excluded range. For instance,
60 seconds after 23:59
means00:00
on the next day. 
A date/time in the excluded range must not be used as a reference date/time e.g.
seconds since 20161231 23:59:60
is not a permitted value forunits
. 
It is important to realise that a time coordinate value does not necessarily exactly equal the actual length of the interval of time between the reference date/time and the date/time it represents.
The values currently defined for calendar
are listed below.
In all calendars except 360_day
and none
, the lengths of the months are the same as in the Gregorian calendar for leap years and nonleap years.
In the julian
and the default standard
mixed Gregorian/Julian calendar, dates in years before year 0 (i.e. before 011 0:0:0) are not allowed, and the year in the reference date/time of the units must not be negative.
In these calendars, year zero has a special use to indicate a climatology (see Section 7.4, "Climatological Statistics"), but this use of year zero is deprecated.
In other calendars, years before year 1 are allowed.
standard

Mixed Gregorian/Julian calendar as defined by UDUNITS. This is the default. A deprecated alternative name for this calendar is
gregorian
. In this calendar, date/times after (and including) 15821015 0:0:0 are in the Gregorian calendar, in which a year is a leap year if either (i) it is divisible by 4 but not by 100 or (ii) it is divisible by 400. Date/times before (and excluding) 1582105 0:0:0 are in the Julian calendar. Year 1 AD or CE in thestandard
calendar is also year 1 of thejulian
calendar. In thestandard
calendar, 15821015 0:0:0 is exactly 1 day later than 1582104 0:0:0 and the intervening dates are undefined. Therefore it is recommended that date/times in the range from (and including) 1582105 0:0:0 until (but excluding) 15821015 0:0:0 should not be used as reference inunits
, and that a time coordinate variable should not include any date/times in this range, because their interpretation is unclear. It is also recommended that a reference date/time before the discontinuity should not be used for date/times after the discontinuity, and viceversa. proleptic_gregorian

A calendar with the Gregorian rules for leapyears extended to dates before 15821015. All dates consistent with these rules are allowed, both before and after 15821015 0:0:0.
julian

Julian calendar, in which a year is a leap year if it is divisible by 4, even if it is also divisible by 100.
noleap
or365_day

A calendar with no leap years, i.e., all years are 365 days long.
all_leap
or366_day

A calendar in which every year is a leap year, i.e., all years are 366 days long.
360_day

A calendar in which all years are 360 days, and divided into 30 day months.
none

No calendar.
The calendar
attribute may be set to none
in climate experiments that simulate a fixed time of year.
The time of year is indicated by the date in the reference time of the units
attribute.
The time coordinates that might apply in a perpetual July experiment are given in the following example.
variables: double time(time) ; time:long_name = "time" ; time:units = "days since 1715 0:0:0" ; time:calendar = "none" ; data: time = 0., 1., 2., ...;
Here, all days simulate the conditions of 15th July, so it does not make sense to give them different dates. The time coordinates are interpreted as 0, 1, 2, etc. days since the start of the experiment.
If none of the calendars defined above applies (e.g., calendars appropriate to a different paleoclimate era), a nonstandard calendar can be defined.
The lengths of each month are explicitly defined with the month_lengths
attribute of the time axis:
month_lengths

A vector of size 12, specifying the number of days in the months from January to December (in a nonleap year).
If leap years are included, then two other attributes of the time axis should also be defined:
leap_year

An example of a leap year. It is assumed that all years that differ from this year by a multiple of four are also leap years. If this attribute is absent, it is assumed there are no leap years.
leap_month

A value in the range 112, specifying which month is lengthened by a day in leap years (1=January). If this attribute is not present, February (2) is assumed. This attribute is ignored if
leap_year
is not specified.
The calendar
attribute is not required when a nonstandard calendar is being used.
It is sufficient to define the calendar using the month_lengths
attribute, along with leap_year
, and leap_month
as appropriate.
However, the calendar
attribute is allowed to take nonstandard values and in that case defining the nonstandard calendar using the appropriate attributes is required.
double time(time) ; time:long_name = "time" ; time:units = "days since 111 0:0:0" ; time:calendar = "126 kyr B.P." ; time:month_lengths = 34, 31, 32, 30, 29, 27, 28, 28, 28, 32, 32, 34 ;
4.5. Discrete Axis
The spatiotemporal coordinates described in sections 4.14.4 are continuous variables, and other geophysical quantities may likewise serve as continuous coordinate variables, for instance density, temperature or radiation wavelength. By contrast, for some purposes there is a need for an axis of a data variable which indicates either an ordered list or an unordered collection, and does not correspond to any continuous coordinate variable. Consequently such an axis may be called “discrete”. A discrete axis has a dimension but might not have a coordinate variable. Instead, there might be one or more auxiliary coordinate variables with this dimension (see preamble to section 5). Following sections define various applications of discrete axes, for instance section 6.1.1 “Geographical regions”, section 7.3.3 “Statistics applying to portions of cells”, section 9.3 “Representation of collections of features in data variables”.
5. Coordinate Systems and Domain
A data variable’s dimensions are used to locate data values in time and space or as a function of other independent variables. This is accomplished by associating these dimensions with the relevant set of latitude, longitude, vertical, time and any nonspatiotemporal coordinates. This section presents two methods for making that association: the use of coordinate variables, and the use of auxiliary coordinate variables.
Any of a variable’s dimensions that is an independently varying latitude, longitude, vertical, or time dimension (see Section 1.3, "Terminology") and that has a size greater than one must have a corresponding coordinate variable, i.e., a onedimensional variable with the same name as the dimension (see examples in Chapter 4, Coordinate Types). This is the only method of associating dimensions with coordinates that is supported by [COARDS].
Any longitude, latitude, vertical or time coordinate which depends on more than one spatiotemporal dimension must be identified by the coordinates
attribute of the data variable.
The value of the coordinates
attribute is a blank separated list of the names of auxiliary coordinate variables.
There is no restriction on the order in which the auxiliary coordinate variables appear in the coordinates
attribute string.
The dimensions of an auxiliary coordinate variable must be a subset of the dimensions of the variable with which the coordinate is associated, with three exceptions.
First, stringvalued coordinates (Section 6.1, "Labels") will have a dimension for maximum string length if the coordinate variable has a type of char
rather than a type of string
.
Second, if an auxiliary coordinate variable of a data variable that has been compressed by gathering (Section 8.2, "Lossless Compression by Gathering") does not span the compressed dimension, then its dimensions may be any subset of the data variable’s uncompressed dimensions, i.e. any of the dimensions of the data variable except the compressed dimension, and any of the dimensions listed by the compress
attribute of the compressed coordinate variable.
Third, in the ragged array representations of data (Chapter 9, Discrete Sampling Geometries), special methods are needed to connect the data and coordinates.
We recommend that the name of a multidimensional coordinate variable should not match the name of any of its dimensions because that precludes supplying a coordinate variable for the dimension. This practice also avoids potential bugs in applications that determine coordinate variables by only checking for a name match between a dimension and a variable and not checking that the variable is one dimensional.
If the longitude, latitude, vertical or time coordinate is multivalued, varies in only one dimension, and varies independently of other spatiotemporal coordinates, it is not permitted to store it as an auxiliary coordinate variable.
This is both to enhance conformance to COARDS and to facilitate the use of generic applications that recognize the NUG convention for coordinate variables.
An application that is trying to find the latitude coordinate of a variable should always look first to see if any of the variable’s dimensions correspond to a latitude coordinate variable.
If the latitude coordinate is not found this way, then the auxiliary coordinate variables listed by the coordinates
attribute should be checked.
Note that it is permissible, but optional, to list coordinate variables as well as auxiliary coordinate variables in the coordinates
attribute.
If the longitude, latitude, vertical or time coordinate is singlevalued, it may be stored either as a coordinate variable with a dimension of size one, or as a scalar coordinate variable (Section 5.7, "Scalar Coordinate Variables").
If an axis
attribute is attached to an auxiliary coordinate variable, it can be used by applications in the same way the axis
attribute attached to a coordinate variable is used.
However, it is not permissible for a data variable to have both a coordinate variable and an auxiliary coordinate variable, or more than one of either type of variable, having an axis
attribute with any given value e.g. there must be no more than one axis
attribute for X
for any data variable.
Note that if the axis
attribute is not specified for an auxiliary coordinate variable, it may still be possible to determine if it is a spatiotemporal dimension from its own units or standard_name
, or from the units and standard_name
of the coordinate variable corresponding to its dimensions (see Chapter 4, Coordinate Types).
For instance, auxiliary coordinate variables which lie on the horizontal surface can be identified as such by their dimensions being horizontal.
Horizontal dimensions are those whose coordinate variables have an axis
attribute of X
or Y
, or a units
attribute indicating latitude and longitude.
To georeference data horizontally with respect to the Earth, a grid mapping variable may be provided by the data variable, using the grid_mapping
attribute.
If the coordinate variables for a horizontal grid are not longitude and latitude, then a grid_mapping variable provides the information required to derive longitude and latitude values for each grid location.
If no grid mapping variable is referenced by a data variable, then longitude and latitude coordinate values shall be supplied in addition to the required coordinates.
For example, the Cartesian coordinates of a map projection may be supplied as coordinate variables and, in addition, twodimensional latitude and longitude variables may be supplied via the coordinates
attribute on a data variable.
The use of the axis
attribute with values X
and Y
is recommended for the coordinate variables (see Chapter 4, Coordinate Types).
It is sometimes not practical to specify the latitudelongitude location of data which is representative of geographic regions with complex boundaries. For this purpose, provision is made in Section 6.1.1, "Geographic Regions" for indicating the region by a standardized name.
5.1. Independent Latitude, Longitude, Vertical, and Time Axes
When each of a variable’s spatiotemporal dimensions is a latitude, longitude, vertical, or time dimension, then each axis is identified by a coordinate variable.
dimensions: lat = 18 ; lon = 36 ; pres = 15 ; time = 4 ; variables: float xwind(time,pres,lat,lon) ; xwind:long_name = "zonal wind" ; xwind:units = "m/s" ; float lon(lon) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(lat) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float pres(pres) ; pres:long_name = "pressure" ; pres:units = "hPa" ; double time(time) ; time:long_name = "time" ; time:units = "days since 199011 0:0:0" ;
xwind(n,k,j,i)
is associated with the coordinate values lon(i)
, lat(j)
, pres(k)
, and time(n)
.
5.2. TwoDimensional Latitude, Longitude, Coordinate Variables
The latitude and longitude coordinates of a horizontal grid that was not defined as a Cartesian product of latitude and longitude axes, can sometimes be represented using twodimensional coordinate variables.
These variables are identified as coordinates by use of the coordinates
attribute.
dimensions: xc = 128 ; yc = 64 ; lev = 18 ; variables: float T(lev,yc,xc) ; T:long_name = "temperature" ; T:units = "K" ; T:coordinates = "lon lat" ; float xc(xc) ; xc:axis = "X" ; xc:long_name = "xcoordinate in Cartesian system" ; xc:units = "m" ; float yc(yc) ; yc:axis = "Y" ; yc:long_name = "ycoordinate in Cartesian system" ; yc:units = "m" ; float lev(lev) ; lev:long_name = "pressure level" ; lev:units = "hPa" ; float lon(yc,xc) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(yc,xc) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ;
T(k,j,i)
is associated with the coordinate values lon(j,i)
, lat(j,i)
, and lev(k)
.
The vertical coordinate is represented by the coordinate variable lev(lev)
and the latitude and longitude coordinates are represented by the auxiliary coordinate variables lat(yc,xc)
and lon(yc,xc)
which are identified by the coordinates
attribute.
Note that coordinate variables are also defined for the xc
and yc
dimensions.
This faciliates processing of this data by generic applications that don’t recognize the multidimensional latitude and longitude coordinates.
5.3. Reduced Horizontal Grid
A "reduced" longitudelatitude grid is one in which the points are arranged along constant latitude lines with the number of points on a latitude line decreasing toward the poles.
Storing this type of gridded data in twodimensional arrays wastes space, and results in the presence of missing values in the 2D coordinate variables.
We recommend that this type of gridded data be stored using the compression scheme described in Section 8.2, "Lossless Compression by Gathering".
Compression by gathering preserves structure by storing a set of indices that allows an application to easily scatter the compressed data back to twodimensional arrays.
The compressed latitude and longitude auxiliary coordinate variables are identified by the coordinates
attribute.
dimensions: londim = 128 ; latdim = 64 ; rgrid = 6144 ; variables: float PS(rgrid) ; PS:long_name = "surface pressure" ; PS:units = "Pa" ; PS:coordinates = "lon lat" ; float lon(rgrid) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(rgrid) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; int rgrid(rgrid); rgrid:compress = "latdim londim";
PS(n)
is associated with the coordinate values lon(n)
, lat(n)
.
Compressed grid index (n)
would be assigned to 2D index (j,i)
(C index conventions) where
j = rgrid(n) / 128 i = rgrid(n)  128*j
Notice that even if an application does not recognize the compress
attribute, the grids stored in this format can still be handled, by an application that recognizes the coordinates
attribute.
5.4. Timeseries of Station Data
This section has been superseded by the treatment of time series as a type of discrete sampling geometry in Chapter 9.
5.5. Trajectories
This section has been superseded by the treatment of time series as a type of discrete sampling geometry in Chapter 9.
5.6. Horizontal Coordinate Reference Systems, Grid Mappings, and Projections
A grid mapping variable may be referenced by a data variable in order to explicitly declare the coordinate reference system (CRS) used for the horizontal spatial coordinate values. For example, if the horizontal spatial coordinates are latitude and longitude, the grid mapping variable can be used to declare the figure of the earth (WGS84 ellipsoid, sphere, etc.) they are based on. If the horizontal spatial coordinates are easting and northing in a map projection, the grid mapping variable declares the map projection CRS used and provides the information needed to calculate latitude and longitude from easting and northing.
When the horizontal spatial coordinate variables are not longitude and latitude, it is required that further information is provided to geolocate the horizontal position. A grid mapping variable provides this information.
If no grid mapping variable is provided and the coordinate variables for a horizontal grid are not longitude and latitude, then it is required that the latitude and longitude coordinates are supplied via the coordinates
attribute.
Such coordinates may be provided in addition to the provision of a grid mapping variable, but that is not required.
A grid mapping variable provides the description of the mapping via a collection of attached attributes.
It is of arbitrary type since it contains no data.
Its purpose is to act as a container for the attributes that define the mapping.
The one attribute that all grid mapping variables must have is grid_mapping_name
, which takes a string value that contains the mapping’s name.
The other attributes that define a specific mapping depend on the value of grid_mapping_name
.
The valid values of grid_mapping_name
along with the attributes that provide specific map parameter values are described in Appendix F, Grid Mappings.
The grid mapping variables are associated with the data and coordinate variables by the grid_mapping
attribute.
This attribute is attached to data variables so that variables with different mappings may be present in a single file.
The attribute takes a string value with two possible formats.
In the first format, it is a single word, which names a grid mapping variable.
In the second format, it is a blankseparated list of words <gridMappingVariable>: <coordinatesVariable> [<coordinatesVariable> …] [<gridMappingVariable>: <coordinatesVariable>…]
, which identifies one or more grid mapping variables, and with each grid mapping associates one or more coordinatesVariables, i.e. coordinate variables or auxiliary coordinate variables.
Where an extended <gridMappingVariable>: <coordinatesVariable> [<coordinatesVariable>]
entity is defined, then the order of the <coordinatesVariable>
references within the definition provides an explicit order for these coordinate value variables, which is used if they are to be combined into individual coordinate tuples.
This order is only significant if crs_wkt
is also specified within the referenced grid mapping variable.
Explicit 'axis order' is important when the grid mapping variable contains an attribute crs_wkt
as it is mandated by the OGC CRSWKT standard that coordinate tuples with correct axis order are provided as part of the reference to a Coordinate Reference System.
Using the simple form, where the grid_mapping
attribute is only the name of a grid mapping variable, 2D latitude and longitude coordinates for a projected coordinate reference system use the same geographic coordinate reference system (ellipsoid and prime meridian) as the projection is projected from.
The grid_mapping
variable may identify datums (such as the reference ellipsoid, the geoid or the prime meridian) for horizontal or vertical coordinates.
Therefore a grid mapping variable may be needed when the coordinate variables for a horizontal grid are longitude and latitude.
The grid_mapping_name
of latitude_longitude
should be used in this case.
The expanded form of the grid_mapping
attribute is required if one wants to store coordinate information for more than one coordinate reference system.
In this case each coordinate or auxiliary coordinate is defined explicitly with respect to no more than one grid_mapping
variable.
This syntax may be used to explicitly link coordinates and grid mapping variables where only one coordinate reference system is used.
In this case, all coordinates and auxiliary coordinates of the data variable not named in the grid_mapping
attribute are unrelated to any grid mapping variable.
All coordinate names listed in the grid_mapping
attribute must be coordinate variables or auxiliary coordinates of the data variable.
In order to make use of a grid mapping to directly calculate latitude and longitude values it is necessary to associate the coordinate variables with the independent variables of the mapping.
This is done by assigning a standard_name
to the coordinate variable.
The appropriate values of the standard_name
depend on the grid mapping and are given in Appendix F, Grid Mappings.
dimensions: rlon = 128 ; rlat = 64 ; lev = 18 ; variables: float T(lev,rlat,rlon) ; T:long_name = "temperature" ; T:units = "K" ; T:coordinates = "lon lat" ; T:grid_mapping = "rotated_pole" ; char rotated_pole ; rotated_pole:grid_mapping_name = "rotated_latitude_longitude" ; rotated_pole:grid_north_pole_latitude = 32.5 ; rotated_pole:grid_north_pole_longitude = 170. ; float rlon(rlon) ; rlon:long_name = "longitude in rotated pole grid" ; rlon:units = "degrees" ; rlon:standard_name = "grid_longitude"; float rlat(rlat) ; rlat:long_name = "latitude in rotated pole grid" ; rlat:units = "degrees" ; rlat:standard_name = "grid_latitude"; float lev(lev) ; lev:long_name = "pressure level" ; lev:units = "hPa" ; float lon(rlat,rlon) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(rlat,rlon) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ;
A CF compliant application can determine that rlon and rlat are longitude and latitude values in the rotated grid by recognizing the standard names grid_longitude
and grid_latitude
.
Note that the units of the rotated longitude and latitude axes are given as degrees
.
This should prevent a COARDS compliant application from mistaking the variables rlon
and rlat
to be actual longitude and latitude coordinates.
The entries for these names in the standard name table indicate the appropriate sign conventions for the units of degrees
.
dimensions: y = 228; x = 306; time = 41; variables: int Lambert_Conformal; Lambert_Conformal:grid_mapping_name = "lambert_conformal_conic"; Lambert_Conformal:standard_parallel = 25.0; Lambert_Conformal:longitude_of_central_meridian = 265.0; Lambert_Conformal:latitude_of_projection_origin = 25.0; double y(y); y:units = "km"; y:long_name = "y coordinate of projection"; y:standard_name = "projection_y_coordinate"; double x(x); x:units = "km"; x:long_name = "x coordinate of projection"; x:standard_name = "projection_x_coordinate"; double lat(y, x); lat:units = "degrees_north"; lat:long_name = "latitude coordinate"; lat:standard_name = "latitude"; double lon(y, x); lon:units = "degrees_east"; lon:long_name = "longitude coordinate"; lon:standard_name = "longitude"; int time(time); time:long_name = "forecast time"; time:units = "hours since 20040623T22:00:00Z"; float Temperature(time, y, x); Temperature:units = "K"; Temperature:long_name = "Temperature @ surface"; Temperature:missing_value = 9999.0; Temperature:coordinates = "lat lon"; Temperature:grid_mapping = "Lambert_Conformal";
An application can determine that x
and y
are the projection coordinates by recognizing the standard names projection_x_coordinate
and projection_y_coordinate
.
The grid mapping variable Lambert_Conformal
contains the mapping parameters as attributes, and is associated with the Temperature
variable via its grid_mapping
attribute.
dimensions: lat = 18 ; lon = 36 ; variables: double lat(lat) ; double lon(lon) ; float temp(lat, lon) ; temp:long_name = "temperature" ; temp:units = "K" ; temp:grid_mapping = "crs" ; int crs ; crs:grid_mapping_name = "latitude_longitude" crs:semi_major_axis = 6371000.0 ; crs:inverse_flattening = 0 ;
dimensions: lat = 18 ; lon = 36 ; variables: double lat(lat) ; double lon(lon) ; float temp(lat, lon) ; temp:long_name = "temperature" ; temp:units = "K" ; temp:grid_mapping = "crs" ; int crs ; crs:grid_mapping_name = "latitude_longitude"; crs:longitude_of_prime_meridian = 0.0 ; crs:semi_major_axis = 6378137.0 ; crs:inverse_flattening = 298.257223563 ;
dimensions: z = 100; y = 100000 ; x = 100000 ; variables: double x(x) ; x:standard_name = "projection_x_coordinate" ; x:long_name = "Easting" ; x:units = "m" ; double y(y) ; y:standard_name = "projection_y_coordinate" ; y:long_name = "Northing" ; y:units = "m" ; double z(z) ; z:standard_name = "height_above_reference_ellipsoid" ; z:long_name = "height_above_osgb_newlyn_datum_masl" ; z:units = "m" ; double lat(y, x) ; lat:standard_name = "latitude" ; lat:units = "degrees_north" ; double lon(y, x) ; lon:standard_name = "longitude" ; lon:units = "degrees_east" ; float temp(z, y, x) ; temp:standard_name = "air_temperature" ; temp:units = "K" ; temp:coordinates = "lat lon" ; temp:grid_mapping = "crsOSGB: x y crsWGS84: lat lon" ; float pres(z, y, x) ; pres:standard_name = "air_pressure" ; pres:units = "Pa" ; pres:coordinates = "lat lon" ; pres:grid_mapping = "crsOSGB: x y crsWGS84: lat lon" ; int crsOSGB ; crsOSGB:grid_mapping_name = "transverse_mercator"; crsOSGB:semi_major_axis = 6377563.396 ; crsOSGB:inverse_flattening = 299.3249646 ; crsOSGB:longitude_of_prime_meridian = 0.0 ; crsOSGB:latitude_of_projection_origin = 49.0 ; crsOSGB:longitude_of_central_meridian = 2.0 ; crsOSGB:scale_factor_at_central_meridian = 0.9996012717 ; crsOSGB:false_easting = 400000.0 ; crsOSGB:false_northing = 100000.0 ; crsOSGB:unit = "metre" ; int crsWGS84 ; crsWGS84:grid_mapping_name = "latitude_longitude"; crsWGS84:longitude_of_prime_meridian = 0.0 ; crsWGS84:semi_major_axis = 6378137.0 ; crsWGS84:inverse_flattening = 298.257223563 ;
5.6.1. Use of the CRS Wellknown Text Format
An optional grid mapping attribute called crs_wkt
may be used to specify multiple coordinate system properties in socalled wellknown text format (usually abbreviated to CRS WKT or OGC WKT).
The CRS WKT format is widely recognised and used within the geoscience software community.
As such it represents a versatile mechanism for encoding information about a variety of coordinate reference system parameters in a highly compact notational form.
The translation of CF coordinate variables to/from OGC WellKnown Text (WKT) format is shown in Examples 5.11 and 5.12 below and described in detail in
https://github.com/cfconvention/cfconventions/wiki/MappingfromCFGridMappingAttributestoCRSWKTElements.
The crs_wkt
attribute should comprise a text string that conforms to the WKT syntax as specified in reference [OGC_WKTCRS].
If desired the text string may contain embedded newline characters to aid human readability.
However, any such characters are purely cosmetic and do not alter the meaning of the attribute value.
It is envisaged that the value of the crs_wkt
attribute typically will be a single line of text, one intended primarily for machine processing.
Other than the requirement to be a valid WKT string, the CF convention does not prescribe the content of the crs_wkt
attribute since it will necessarily be contextdependent.
Where a crs_wkt
attribute is added to a grid_mapping
, the extended syntax for the grid_mapping
attribute enables the list of variables containing coordinate values being referenced to be explicitly stated and the CRS WKT Axis order to be explicitly defined.
The explicit definition of WKT CRS Axis order is expected by the OGC standards for referencing by coordinates.
Software implementing these standards are likely to expect to receive coordinate value tuples, with the correct coordinate value order, along with the coordinate reference system definition that those coordinate values are defined with respect to.
The order of the <coordinatesVariable>
references within the grid_mapping
attribute definition defines the order of elements within a derived coordinate value tuple.
This enables an application reading the data from a file to construct an array of coordinate value tuples, where each tuple is ordered to match the specification of the coordinate reference system being used whilst the array of tuples is structured according to the netCDF definition.
It is the responsibility of the data producer to ensure that the <coordinatesVariable>
list is consistent with the CRS WKT definition of CS AXIS, with the correct number of entries in the correct order (note: this is not a conformance requirement as CF conformance is not dependent on CRS WKT parsing).
For example, a file has two coordinate variables, lon and lat, and a grid mapping variable crs
with an associated crs_wkt
attribute; the WKT definition defines the AXIS order as ["latitude", "longitude"]
.
The grid_mapping
attribute is thus given a value crs:lat lon
to define that where coordinate pairs are required, these shall be ordered (lat, lon), to be consistent with the provided crs_wkt
string (and not order inverted).
A 2D array of (lat, lon) tuples can then be explicitly derived from the combination of the lat and lon variables.
The crs_wkt
attribute is intended to act as a supplement to other singleproperty CF grid mapping attributes (as described in Appendix F); it is not intended to replace those attributes.
If data producers omit the singleproperty grid mapping attributes in favour of the crs_wkt
attribute, software which cannot interpret crs_wkt
will be unable to use the grid_mapping
information.
Therefore the CRS should be described as thoroughly as possible with the singleproperty grid mapping attributes as well as by crs_wkt
.
In cases where CRS property values can be represented by both a singleproperty grid mapping attribute and the crs_wkt
attribute, the grid mapping should be provided, and if both are provided, the onus is on data producers to ensure that their property values are consistent.
Therefore information from either one (or both) may be read in by the user without needing to check both.
However, if the two values of a given property are different, the CRS information cannot be interpreted accurately and users should inform the provider so the issue can be addressed.
For example, if the semimajor axis length of the ellipsoid defined by the grid mapping attribute semi_major_axis
disagrees with the crs_wkt
attribute (via the WKT SPHEROID[…]
element), the value of this attribute cannot be interpreted accurately.
Naturally if the two values are equal then no ambiguity arises.
Likewise, in those cases where the value of a CRS WKT element should be used consistently across the CFnetCDF community (names of projections and projection parameters, for example) then, the values shown in https://github.com/cfconvention/cfconventions/wiki/MappingfromCFGridMappingAttributestoCRSWKTElements should be preferred; these are derived from the OGP/EPSG registry of geodetic parameters, which is considered to represent the definitive authority as regards CRS property names and values.
Examples 5.11 illustrates how the coordinate system properties specified via the crs
grid mapping variable in Example 5.9 might be expressed using a crs_wkt
attribute.
Example 5.12 also illustrates the addition of the crs_wkt
attribute, but here the attribute is added to the crs
variable of a simplified variant of Example 5.10.
For brevity in Example 5.11, only the grid mapping variable and its grid_mapping_name
and crs_wkt
attributes are included; all other elements are as per the Example 5.9.
Names of projection. PARAMETERs
follow the spellings used in the EPSG geodetic parameter registry.
Example 5.12 illustrates how certain WKT elements  all of which are optional  can be used to specify CRS properties not covered by existing CF grid mapping attributes, including:

use of the
VERT_DATUM
element to specify vertical datum information 
use of additional
PARAMETER
elements (albeit not essential ones in this example) to define the location of the false origin of the projection 
use of
AUTHORITY
elements to specify object identifier codes assigned by an external authority, OGP/EPSG in this instance
... float data(latitude, longitude) ; data:grid_mapping = "crs: latitude, longitude" ; ... int crs ; crs:grid_mapping_name = "latitude_longitude"; crs:longitude_of_prime_meridian = 0.0 ; crs:semi_major_axis = 6378137.0 ; crs:inverse_flattening = 298.257223563 ; crs:crs_wkt = GEODCRS["WGS 84", DATUM["World Geodetic System 1984", ELLIPSOID["WGS 84",6378137,298.257223563, LENGTHUNIT["metre",1.0]]], PRIMEM["Greenwich",0], CS[ellipsoidal,3], AXIS["(lat)",north,ANGLEUNIT["degree",0.0174532925199433]], AXIS["(lon)",east,ANGLEUNIT["degree",0.0174532925199433]], AXIS["ellipsoidal height (h)",up,LENGTHUNIT["metre",1.0]]] ...
Note: To enhance readability of these examples, the WKT value has been split across multiple lines and embedded quotation marks (") left unescaped  in real netCDF files such characters would need to be escaped.
In CDL, within the CRS WKT definition string, newlines would need to be encoded within the string as \n
and double quotes as \"
.
Also for readability, we have dropped the quotation marks which would delimit the entire crs_wkt
string.
This pseudo CDL will not parse directly.
dimensions: lat = 648 ; lon = 648 ; y = 18 ; x = 36 ; variables: double x(x) ; x:standard_name = "projection_x_coordinate" ; x:units = "m" ; double y(y) ; y:standard_name = "projection_y_coordinate" ; y:units = "m" ; float temp(y, x) ; temp:long_name = "temperature" ; temp:units = "K" ; temp:coordinates = "lat lon" ; temp:grid_mapping = "crs: x y" ; int crs ; crs:grid_mapping_name = "transverse_mercator" ; crs:longitude_of_central_meridian = 2. ; crs:false_easting = 400000. ; crs:false_northing = 100000. ; crs:latitude_of_projection_origin = 49. ; crs:scale_factor_at_central_meridian = 0.9996012717 ; crs:longitude_of_prime_meridian = 0. ; crs:semi_major_axis = 6377563.396 ; crs:inverse_flattening = 299.324964600004 ; crs:projected_coordinate_system_name = "OSGB 1936 / British National Grid" ; crs:geographic_coordinate_system_name = "OSGB 1936" ; crs:horizontal_datum_name = "OSGB_1936" ; crs:reference_ellipsoid_name = "Airy 1830" ; crs:prime_meridian_name = "Greenwich" ; crs:towgs84 = 375., 111., 431., 0., 0., 0., 0. ; crs:crs_wkt = "COMPOUNDCRS ["OSGB 1936 / British National Grid + ODN", PROJCRS ["OSGB 1936 / British National Grid", GEODCRS ["OSGB 1936", DATUM ["OSGB 1936", ELLIPSOID ["Airy 1830", 6377563.396, 299.3249646, LENGTHUNIT[“metre”,1.0]], TOWGS84[375, 111, 431, 0, 0, 0, 0] ], PRIMEM ["Greenwich", 0], UNIT ["degree", 0.0174532925199433] ], CONVERSION["OSGB", METHOD["Transverse Mercator", PARAMETER["False easting", 400000, LENGTHUNIT[“metre”,1.0]], PARAMETER["False northing", 100000, LENGTHUNIT[“metre”,1.0]], PARAMETER["Longitude of natural origin", 2.0, ANGLEUNIT[“degree”,0.0174532925199433]], PARAMETER["Latitude of natural origin", 49.0, ANGLEUNIT[“degree”,0.0174532925199433]], PARAMETER["Longitude of false origin", 7.556, ANGLEUNIT[“degree”,0.0174532925199433]], PARAMETER["Latitude of false origin", 49.766, ANGLEUNIT[“degree”,0.0174532925199433]], PARAMETER["Scale factor at natural origin", 0.9996012717, SCALEUNIT[“Unity”,1.0]], AUTHORITY["EPSG", "27700"]] CS[Cartesian,2], AXIS["easting (X)",east], AXIS["northing (Y)",north], LENGTHUNIT[“metre”, 1.0], ], VERTCRS ["Newlyn", VDATUM ["Ordnance Datum Newlyn", 2005], AUTHORITY ["EPSG", "5701"] CS[vertical,1], AXIS["gravityrelated height (H)",up], LENGTHUNIT[“metre”,1.0] ] ]" ; ...
Note: There are unescaped double quotes and newlines and the quotation marks which would delimit the entire crs_wkt
string are missing in this example.
This is to enhance readability, but it means that this pseudo CDL will not parse directly.
The preceding two example (5.11 and 5.12) may be combined, if the data provider desires to provide explicit latitude and longitude coordinates as well as projection coordinates and to provide CRS WKT referencing for both sets of coordinates. This is demonstrated in example 5.13.
... double x(x) ; x:standard_name = "projection_x_coordinate" ; x:units = "m" ; double y(y) ; y:standard_name = "projection_y_coordinate" ; y:units = "m" ; double lat(y, x) ; lat_standard_name = "latitude" ; lat:units = "degrees_north" ; double lon(y, x) ; lon_standard_name = "longitude" ; lon:units = "degrees_east" ; float temp(y, x) ; temp:long_name = "temperature" ; temp:units = "K" ; temp:coordinates = "lat lon" ; temp:grid_mapping = "crs_osgb: x y crs_wgs84: latitude longitude" ; ... int crs_wgs84 ; crs_wgs84:grid_mapping_name = "latitude_longitude"; crs_wgs84:crs_wkt = ... int crs_osgb ; crs_osgb:grid_mapping_name = "transverse_mercator" ; crs_osgb:crs_wkt = ... ...
Note: There are unescaped double quotes and newlines and the quotation marks which would delimit the entire crs_wkt
string are missing in this example.
This is to enhance readability, but it means that this pseudo CDL will not parse directly.
5.7. Scalar Coordinate Variables
When a variable has an associated coordinate which is singlevalued, that coordinate may be represented as a scalar variable (i.e. a data variable which has no netCDF dimensions).
Since there is no associated dimension these scalar coordinate variables should be attached to a data variable via the coordinates
attribute.
The use of scalar coordinate variables is a convenience feature which avoids adding size one dimensions to variables. A numeric scalar coordinate variable has the same information content and can be used in the same contexts as a size one numeric coordinate variable. Similarly, a stringvalued scalar coordinate variable has the same meaning and purposes as a size one stringvalued auxiliary coordinate variable (Section 6.1, "Labels"). Note however that use of this feature with a latitude, longitude, vertical, or time coordinate will inhibit COARDS conforming applications from recognizing them.
Once a name is used for a scalar coordinate variable it can not be used for a 1D coordinate variable. For this reason we strongly recommend against using a name for a scalar coordinate variable that matches the name of any dimension in the file.
If a data variable has two or more scalar coordinate variables, they are regarded as though they were all independent coordinate variables with dimensions of size one. If two or more singlevalued coordinates are not independent, but have related values (this might be the case, for instance, for time and forecast period, or vertical coordinate and model level number, Section 6.2, "Alternative Coordinates"), they should be stored as coordinate or auxiliary coordinate variables of the same size one dimension, not as scalar coordinate variables.
dimensions: lat = 180 ; lon = 360 ; time = UNLIMITED ; variables: double atime atime:standard_name = "forecast_reference_time" ; atime:units = "hours since 19990101 00:00" ; double time(time); time:standard_name = "time" ; time:units = "hours since 19990101 00:00" ; double lon(lon) ; lon:long_name = "station longitude"; lon:units = "degrees_east"; double lat(lat) ; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; double p500 p500:long_name = "pressure" ; p500:units = "hPa" ; p500:positive = "down" ; float height(time,lat,lon); height:long_name = "geopotential height" ; height:standard_name = "geopotential_height" ; height:units = "m" ; height:coordinates = "atime p500" ; data: time = 6., 12., 18., 24. ; atime = 0. ; p500 = 500. ;
In this example both the analysis time and the single pressure level are represented using scalar coordinate variables.
The analysis time is identified by the standard name forecast_reference_time
while the valid time of the forecast is identified by the standard name time
.
5.8. Domain Variables
A domain describes data locations and cell properties. It defines cells that span a collection of dimensions with cell coordinates, cell measures, and coordinate reference systems.
A data variable defines its domain via its own attributes, but a domain variable provides the description of a domain in the absence of any data values. The variable should be a scalar (i.e. it has no dimensions) of arbitrary type, and the value of its single element is immaterial. It acts as a container for the attributes that define the domain. The purpose of a domain variable is to provide domain information to applications that have no need of data values at the domain’s locations, thus removing any ambiguity when retrieving a domain from a dataset. Ancillary variables and cell methods are not part of the domain, because they are only defined in relation to data values.
The domain variable supports the same attributes as are allowed on a data variable for describing a domain, with exactly the same meanings and syntaxes, as described in Appendix A, Attributes. If an attribute is needed by a particular data variable to describe its domain, then that attribute would also be needed by the equivalent domain variable.
The dimensions of the domain must be stored with the dimensions
attribute, and the presence of a dimensions
attribute will identify the variable as a domain variable.
Therefore the dimensions
attribute must not be present on any variables that are to be interpreted as data variables.
It is necessary to list these dimensions, rather than inferring them from the contents of the other attributes, as it can not be guaranteed that the referenced variables span all of the required dimensions (as could be the case for a discrete axis, for instance).
The value of the dimensions
attribute is a blank separated list of the dimension names.
There is no restriction on the order in which the dimensions appear in the dimensions
attribute string.
If a domain has no named dimensions then the value of the dimensions
attribute must be an empty string, as could be the case if the dimensions of the domain are all defined implicitly by scalar coordinate variables.
The dimensions listed by the dimensions
attribute constrain the dimensions that may be spanned by variables referenced from any of the other attributes, in the same way that the array dimensions perform that role for a data variable.
For instance, all variables named by the cell_measures
attribute (Section 7.2, "Cell Measures") of a domain variable must span a subset of zero or more of the dimensions given by the dimensions
attribute.
It is optional for coordinate variables to be listed by a domain variable’s coordinates
attribute.
Any coordinate variable that shares its name with a dimension given by the dimensions
attribute will be considered as part of the domain definition.
It is recommended that a domain variable has a long_name
attribute to describe its contents.
It is recommended that a domain variable does not have any of the attributes marked in Appendix A, Attributes as applicable to data variables except those which are also marked as applicable to domain variables.
Multiple domain variables may exist in a file with, or without, data variables. Note that the data variable attributes describing its domain can not be replaced by a reference to a domain variable.
dimensions: lat = 18 ; lon = 36 ; pres = 15 ; time = 4 ; variables: char domain ; domain:dimensions = "time pres lat lon" ; domain:long_name = "Domain with independent coordinate variables" ; float lon(lon) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(lat) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float pres(pres) ; pres:long_name = "pressure" ; pres:units = "hPa" ; double time(time) ; time:long_name = "time" ; time:units = "days since 199011 0:0:0" ;
In this example the data variable xwind
from the Independent coordinate variables example has been replaced by the domain variable domain
.
dimensions: rlon = 128 ; rlat = 64 ; lev = 18 ; variables: char domain ; domain:dimensions = "lev rlat rlon" ; domain:coordinates = "lon lat time" ; domain:grid_mapping = "rotated_pole" ; domain:long_name = "Domain with grid mapping and scalar coordinate" ; char rotated_pole ; rotated_pole:grid_mapping_name = "rotated_latitude_longitude" ; rotated_pole:grid_north_pole_latitude = 32.5 ; rotated_pole:grid_north_pole_longitude = 170. ; double time time:standard_name = "time" ; time:units = "days since 20001201 00:00" ; float rlon(rlon) ; rlon:long_name = "longitude in rotated pole grid" ; rlon:units = "degrees" ; rlon:standard_name = "grid_longitude" ; float rlat(rlat) ; rlat:long_name = "latitude in rotated pole grid" ; rlat:units = "degrees" ; rlat:standard_name = "grid_latitude" ; float lev(lev) ; lev:long_name = "pressure level" ; lev:units = "hPa" ; float lon(rlat,rlon) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(rlat,rlon) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ;
dimensions: cell = 2562 ; // number of grid cells time = 12 ; nv = 6 ; // maximum number of cell vertices variables: char domain ; domain:dimensions = "time cell" ; domain:coordinates = "lon lat" ; domain:cell_measures = "area: cell_area" ; domain:long_name = "Domain with cell measures" ; float lon(cell) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; lon:bounds = "lon_vertices" ; float lat(cell) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; lat:bounds = "lat_vertices" ; float time(time) ; time:long_name = "time" ; time:units = "days since 19790101" ; float cell_area(cell) ; cell_area:long_name = "area of grid cell" ; cell_area:standard_name = "cell_area" ; cell_area:units = "m2" float lon_vertices(cell, nv) ; float lat_vertices(cell, nv) ;
In this example the data variable PS
from the Cell areas for a spherical geodesic grid example has been replaced by the domain variable domain
.
dimensions: variables: char domain ; domain:dimensions = "" ; domain:coordinates = "t" ; domain:long_name = "Domain with no explicit dimensions" ; double t ; t:standard_name = "time" ; t:units = "days since 20210101" ;
dimensions: instance = 2 ; node = 5 ; time = 4 ; variables: char domain ; domain:dimensions = "instance time" ; domain:coordinates = "lat lon" ; domain:grid_mapping = "datum" ; domain:geometry = "geometry_container" ; domain:long_name = "Domain with a geometry variable" ; int time(time) ; double lat(instance) ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ; lat:nodes = "y" ; double lon(instance) ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ; lon:nodes = "x" ; int datum ; datum:grid_mapping_name = "latitude_longitude" ; datum:longitude_of_prime_meridian = 0.0 ; datum:semi_major_axis = 6378137.0 ; datum:inverse_flattening = 298.257223563 ; int geometry_container ; geometry_container:geometry_type = "line" ; geometry_container:node_count = "node_count" ; geometry_container:node_coordinates = "x y" ; int node_count(instance) ; double x(node) ; x:units = "degrees_east" ; x:standard_name = "longitude" ; x:axis = "X" ; double y(node) ; y:units = "degrees_north" ; y:standard_name = "latitude" ; y:axis = "Y" ;
In this example the data variable someData
from the Timeseries with geometry. example has been replaced by the domain variable domain
.
dimensions: station = 23 ; obs = UNLIMITED ; name_strlen = 23 ; variables: char domain ; domain:dimensions = "obs" ; domain:coordinates = "time lat lon alt station_name" ; domain:long_name = "Domain with a discrete sampling geometry" ; float lon(station) ; lon:standard_name = "longitude" ; lon:long_name = "station longitude" ; lon:units = "degrees_east" ; float lat(station) ; lat:standard_name = "latitude" ; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(station) ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m" ; alt:positive = "up" ; alt:axis = "Z" ; char station_name(station, name_strlen) ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id" ; int station_info(station) ; station_info:long_name = "some kind of station info" ; int stationIndex(obs) ; stationIndex:long_name = "which station this obs is for" ; stationIndex:instance_dimension = "station" ; double time(obs) ; time:standard_name = "time" ; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; attributes: :featureType = "timeSeries" ;
In this example the data variables humidity
and temp
from the Timeseries of station data in the indexed ragged array representation. example have been replaced by the domain variable domain
.
5.9. Mesh Topology Variables
A mesh topology variable defines the geospatial topology of cells arranged in two or three dimensions in real space but indexed by a single dimension. It explicitly describes the topological relationships between cells, i.e. spatial relationships which do not depend on the cell locations, via a mesh of connected nodes. A mesh topology variable may provide the topology for one or more domains, defined at the nodes, edges, or faces of the mesh. See the Domain topology construct and Cell connectivity construct descriptions in the CF data model for more details, including on how the mesh relates to the cells of the domain.
The canonical definitions of mesh topology variables and location index set variables are given externally by the UGRID conventions [UGRID], but their standardized attributes, many of which are optional, are listed in Appendix K, Mesh Topology Attributes and Appendix A, Attributes. Some features of the UGRID conventions [UGRID] are not currently recognized by the CF conventions: mesh topology volume cells (that are used to describe fully threedimensional unstructured mesh topologies); and the "boundary node connectivity" variable (that specifies an index variable identifying the nodes that define where boundary condtions have been provided).
A data or domain variable may use one of a mesh topology variable’s domains by referencing the mesh topology variable with the mesh
attribute; along with the identity of required domain provided by the location
attribute (see example A twodimensional UGRID mesh topology variable).
The variables containing the coordinate values for cells indexed by the mesh topology are defined by the mesh topology variable but are equivalent to onedimensional auxiliary coordinate variables, and so may also be provided by the data or domain variable’s coordinates
attribute.
Note that the mesh topology variable allows cell bounds to be provided without any cell coordinate values, via its node_coordinates
attribute.
A location index set variable defines a subset of locations of a mesh topology variable, e.g. only special locations like weirs and gates.
It is provided as a space saving device to prevent the need to redefine parts of an existing mesh topology variable, and as such is logically equivalent to a mesh topology variable.
A data or domain variable references a location index set variable via its location_index_set
attribute.
dimensions: node = 5 ; // Number of mesh nodes edge = 6 ; // Number of mesh edges face = 2 ; // Number of mesh faces two = 2 ; // Number of nodes per edge four = 4 ; // Maximum number of nodes per face time = 12 ; variables: // Mesh topology variable integer mesh ; mesh:cf_role = "mesh_topology" ; mesh:long_name = "Topology of a 2d unstructured mesh" ; mesh:topology_dimension = 2 ; mesh:node_coordinates = "mesh_node_x mesh_node_y" ; mesh:edge_node_connectivity = "mesh_edge_nodes" ; mesh:face_node_connectivity = "mesh_face_nodes" ; // Mesh node coordinates double mesh2_node_x(node) ; mesh_node_x:standard_name = "longitude" ; mesh_node_x:units = "degrees_east" ; double mesh2_node_y(node) ; mesh_node_y:standard_name = "latitude" ; mesh_node_y:units = "degrees_north" ; // Mesh connectivity variables integer mesh_face_nodes(face, four) ; mesh_face_nodes:long_name = "Maps each face to its 3 or 4 corner nodes" ; integer mesh_edge_nodes(edge, two) ; mesh_edge_nodes:long_name = "Maps each edge to the 2 nodes it connects" ; // Coordinate variables float time(time) ; time:standard_name = "time" ; time:units = "days since 20040601" ; // Data at mesh faces double volume_at_faces(time, face) ; volume_at_faces:standard_name = "air_density" ; volume_at_faces:units = "kg m3" ; volume_at_faces:mesh = "mesh" ; volume_at_faces:location = "face" ; // Data at mesh edges double flux_at_edges(time, edge) ; fluxe_at_edges:standard_name = "northward_wind" ; fluxe_at_edges:units = "m s1" ; fluxe_at_edges:mesh = "mesh" fluxe_at_edges:location = "edge" ; // Data at mesh nodes double height_at_nodes(time, node) ; height_at_nodes:standard_name = "sea_surface_height_above_geoid" ; height_at_nodes:units = "m" ; height_at_nodes:mesh = "mesh" ; height_at_nodes:location = "node" ;
A twodimensional UGRID mesh topology variable for the mesh depicted in Figure I.5, with data variables defined at face, edge and node elements of the mesh. All optional attributes have been omitted.
6. Labels and Alternative Coordinates
6.1. Labels
Character strings can be used to provide a name or label for each element of an axis. This is particularly useful for discrete axes (section 4.5). For instance, if a data variable contains time series of observational data from a number of observing stations, it may be convenient to provide the names of the stations as labels for the elements of the station dimension (Section H.2, "Time Series Data"). There are several other uses for labels in CF. For instance, Northward heat transport in Atlantic Ocean shows the use of labels to indicate geographic regions.
Character strings labelling the elements of an axis are regarded as stringvalued auxiliary coordinate variables.
The coordinates
attribute of the data variable names the variable that contains the string array.
An application processing the variables listed in the coordinates
attribute can recognize a stringvalued auxiliary coordinate variable because it has a type of char
or string
.
If the variable has a type of char
, the inner dimension (last dimension in CDL terms) is the maximum length of each string, and the other dimensions are axis dimensions.
If an auxiliary coordinate variable has a type of string
and has no dimensions, or has a type of char
and has only one dimension (the maximum length of the string), it is a stringvalued scalar coordinate variable (see Section 5.7, "Scalar Coordinate Variables").
As such, it has the same information content and can be used in the same contexts as a stringvalued auxiliary coordinate variable of a size one dimension.
This is a convenience feature.
6.1.1. Geographic Regions
When data is representative of geographic regions which can be identified by names but which have complex boundaries that cannot practically be specified using longitude and latitude boundary coordinates, a labeled axis should be used to identify the regions.
We recommend that the names be chosen from the list of standardized region names whenever possible.
To indicate that the label values are standardized the variable that contains the labels must be given the standard_name
attribute with the value region
.
Suppose we have data representing northward heat transport across a set of zonal slices in the Atlantic Ocean. Note that the standard names to describe this quantity do not include location information. That is provided by the latitude coordinate and the labeled axis:
dimensions: times = 20 ; lat = 5 lbl = 1 ; variables: float n_heat_transport(time,lat,lbl); n_heat_transport:units="W"; n_heat_transport:coordinates="geo_region"; n_heat_transport:standard_name="northward_ocean_heat_transport"; double time(time) ; time:long_name = "time" ; time:units = "days since 199011 0:0:0" ; float lat(lat) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; string geo_region(lbl) ; geo_region:standard_name="region" data: geo_region = "atlantic_ocean" ; lat = 10., 20., 30., 40., 50. ;
6.1.2. Taxon Names and Identifiers
A taxon is a named level within a biological classification, such as a class, genus and species. Quantities dependent on taxa have generic standard names containing the phrase "organisms_in_taxon", and the taxa are identified by auxiliary coordinate variables.
The taxon auxiliary coordinate variables are stringvalued.
The plainlanguage name of the taxon must be contained in a variable with standard_name
of biological_taxon_name
.
A Life Science Identifier (LSID) may be contained in a variable with standard_name
of biological_taxon_lsid
.
This is a URN with the syntax "urn:lsid:<Authority>:<Namespace>:<ObjectID>[:<Version>]".
This includes the reference classification in the <Authority> element and these are restricted by the LSID governance.
It is strongly recommended in CF that the authority chosen is World Register of Marine Species (WoRMS) for oceanographic data and Integrated Taxonomic Information System (ITIS) for freshwater and terrestrial data.
WoRMS LSIDs are built from the WoRMS AphiaID taxon identifier such as "urn:lsid:marinespecies.org:taxname:104464" for AphiaID 104464.
This may be converted to a URL by adding prefixes such as https://www.lsid.info/.
ITIS LSIDs are built from the ITIS Taxonomic Serial Number (TSN), such as "urn:lsid:itis.gov:itis_tsn:180543".
The biological_taxon_name
auxiliary coordinate variable included for human readability is mandatory.
The biological_taxon_lsid
auxliary coordinate variable included for software agent readability is optional, but strongly recommended.
If both are present then each biological_taxon_name
coordinate must exactly match the name resolved from the biological_taxon_lsid
coordinate.
If LSIDs are available for some taxa in a dataset then the biological_taxon_lsid
auxiliary coordinate variable should be included and missing data given for those taxa that do not have an identifier.
A skeleton example for taxonomic abundance time series.
dimension: time = 100 ; string80 = 80 ; taxon = 2 ; variables: float time(time); time:standard_name = "time" ; time:units = "days since 20190101" ; float abundance(time,taxon) ; abundance:standard_name = "number_concentration_of_biological_taxon_in_sea_water" ; abundance:coordinates = "taxon_lsid taxon_name" ; char taxon_name(taxon,string80) ; taxon_name:standard_name = "biological_taxon_name" ; char taxon_lsid(taxon,string80) ; taxon_lsid:standard_name = "biological_taxon_lsid" ; data: time = // 100 values ; abundance = // 200 values ; taxon_name = "Calanus finmarchicus", "Calanus helgolandicus" ; taxon_lsid = "urn:lsid:marinespecies.org:taxname:104464", "urn:lsid:marinespecies.org:taxname:104466" ;
6.2. Alternative Coordinates
In some situations a dimension may have alternative sets of coordinates values. Since there can only be one coordinate variable for the dimension (the variable with the same name as the dimension), any alternative sets of values have to be stored in auxiliary coordinate variables. For such alternative coordinate variables, there are no mandatory attributes, but they may have any of the attributes allowed for coordinate variables.
Levels on a vertical axis may be described by both the physical coordinate and the ordinal model level number.
float xwind(sigma,lat); xwind:coordinates="model_level"; float sigma(sigma); // physical height coordinate sigma:long_name="sigma"; sigma:positive="down"; int model_level(sigma); // model level number at each height model_level:long_name="model level number"; model_level:positive="up";
7. Data Representative of Cells
When gridded data does not represent the point values of a field but instead represents some characteristic of the field within cells of finite "volume," a complete description of the variable should include metadata that describes the domain or extent of each cell, and the characteristic of the field that the cell values represent. It is possible for a single data value to be the result of an operation whose domain is a disjoint set of cells. This is true for many types of climatological averages, for example, the mean January temperature for the years 19702000. The methods that we present below for describing cells only provides an association of a grid point with a single cell, not with a collection of cells. However, climatological statistics are of such importance that we provide special methods for describing their associated computational domains in Section 7.4, "Climatological Statistics". For cases when data pertain to geospatial features with highly variable geometry node counts such as river lines or watershed boundaries, we provide <<geometries> as an alternative to bounds.
7.1. Cell Boundaries
To represent cells we add the attribute bounds
to the appropriate coordinate variable(s).
The value of bounds
is the name of the variable that contains the vertices of the cell boundaries.
We refer to this type of variable as a "boundary variable."
A boundary variable will have one more dimension than its associated coordinate or auxiliary coordinate variable. The additional dimension should be the most rapidly varying one, and its size is the maximum number of cell vertices.
A boundary variable inherits the values of some attributes from its parent coordinate variable. If a coordinate variable has any of the attributes marked "BI" (for "inherit") in the "Use" column of Appendix A, Attributes, they are assumed to apply to its bounds variable as well. It is recommended that BI attributes not be included on a boundary variable. If a BI attribute is included, it must also be present in the parent variable, and it must exactly match the parent attribute’s data type and value. A boundary variable can only have inheritable attributes if they are also present on its parent coordinate variable. A bounds variable may have any of the attributes marked "BO" for ("own") in the "Use" column of Appendix A, Attributes. These attributes take precedence over any corresponding attributes of the parent variable. In these cases, the parent variable’s attribute does not apply to the bounds variable, regardless of whether the latter has its own attribute.
If a parametric coordinate variable with a formula_terms
attribute (section 4.3.2) also has a bounds
attribute, its boundary variable must have a formula_terms
attribute too.
In this case the same terms would appear in both (as specified in Appendix D), since the transformation from the parametric coordinate values to physical space is realized through the same formula.
For any term that depends on the vertical dimension, however, the variable names appearing in the formula terms would differ from those found in the formula_terms
attribute of the coordinate variable itself because the boundary variables for formula terms are twodimensional while the formula terms themselves are onedimensional.
Whenever a formula_terms
attribute is attached to a boundary variable, the formula terms may additionally be identified using a second method: variables appearing in the vertical coordinates' formula_terms
may be declared to be coordinate, scalar coordinate or auxiliary coordinate variables, and those coordinates may have bounds
attributes that identify their boundary variables.
In that case, the bounds
attribute of a formula terms variable must be consistent with the formula_terms
attribute of the boundary variable.
Software digesting legacy datasets (constructed prior to version 1.7 of this standard) may have to rely in some cases on the first method of identifying the formula term variables and in other cases, on the second.
Starting from version 1.7, however, the first method will be sufficient.
formula_terms
when a parametric coordinate variable has bounds.float eta(eta) ; eta:long_name = "eta at full levels" ; eta:positive = "down" ; eta:standard_name = " atmosphere_hybrid_sigma_pressure_coordinate" ; eta:formula_terms = "a: A b: B ps: PS p0: P0" ; eta:bounds="eta_bnds" ; float eta_bnds(eta, 2) ; eta_bnds:formula_terms = "a: A_bnds b: B_bnds ps: PS p0: P0" ; // This attribute is mandatory float A(eta) ; A:long_name = "'a' coefficient for vertical coordinate at full levels" ; A:units = "Pa" ; A:bounds = "A_bnds" ; // This attribute is included for the optional second method float B(eta) ; B:long_name = "'b' coefficient for vertical coordinate at full levels" ; B:units = "1" ; B:bounds = "B_bnds" ; // This attribute is included for the optional second method float A_bnds(eta, 2) ; float B_bnds(eta, 2) ; float PS(lat, lon) ; PS:units = "Pa" ; float P0 ; P0:units = "Pa" ; float temp(eta, lat, lon) ; temp:standard_name = "air_temperature" ; temp:units = "K"; temp:coordinates = "A B" ; // This attribute is included for the optional second method
Note that the boundary variable for a set of N contiguous intervals is an array of shape (N,2). Although in this case there will be a duplication of the boundary coordinates between adjacent intervals, this representation has the advantage that it is general enough to handle, without modification, noncontiguous intervals, as well as intervals on an axis using the unlimited dimension.
Applications that process cell boundary data often times need to determine whether or not adjacent cells share an edge. In order to facilitate this type of processing the following restrictions are placed on the data in boundary variables.
 Bounds for 1D coordinate variables

For a coordinate variable such as
lat(lat)
with associated boundary variablelatbnd(x,2)
, the interval endpoints must be ordered consistently with the associated coordinate, e.g., for an increasing coordinate,lat(1)
>lat(0)
implieslatbnd(i,1)
>=latbnd(i,0)
for alli
(Figure 7.1).If adjacent intervals are contiguous, the shared endpoint must be represented indentically in each instance where it occurs in the boundary variable. For example, if the intervals that contain grid points
lat(i)
andlat(i+1)
are contiguous, thenlatbnd(i+1,0)
=latbnd(i,1)
.Figure 7.1. Order oflonbnd(i,0)
andlonbnd(i,1)
as well as oflatbnd(i,0)
andlatbnd(i,1)
in the case of onedimensional horizontal coordinate axes. Tuples(lon(i),lat(j))
represent grid cell centers. The four grid cell vertices are given by(lonbnd(i,0),latbnd(j,0))
,(lonbnd(i,1),latbnd(j,0))
,(lonbnd(i,1),latbnd(j,1))
and(lonbnd(i,0),latbnd(j,1))
.  Bounds for 2D coordinate variables with 4sided cells

In the case where the horizontal grid is described by twodimensional auxiliary coordinate variables in latitude
lat(n,m)
and longitudelon(n,m)
, and the associated cells are foursided, then the boundary variables are given in the formlatbnd(n,m,4)
andlonbnd(n,m,4)
, where the trailing index runs over the four vertices of the cells. Let us call the side of cell(j,i)
facing cell(j,i1)
the "i1
" side, the side facing cell(j,i+1)
the "i+1
" side, and similarly for "j1
" and "j+1
". Then we can refer to the vertex formed by sidesi1
andj1
as(j1,i1)
. With this notation, the four vertices are indexed as follows:0=(j1,i1)
,1=(j1,i+1)
,2=(j+1,i+1)
,3=(j+1,i1)
.Figure 7.2. Order oflonbnd(j,i,0)
tolonbnd(j,i,3)
and oflatbnd(j,i,0)
andlatbnd(j,i,3)
in the case of twodimensional horizontal coordinate axes. Tuples(lon(j,i),lat(j,i))
represent grid cell centers and tuples(lonbnd(j,i,n),latbnd(j,i,n))
represent the grid cell vertices.If ijupward is a righthanded coordinate system (like lonlatupward), this ordering means the vertices will be traversed anticlockwise on the lonlat surface seen from above (Figure 7.2). If ijupward is lefthanded, they will be traversed clockwise on the lonlat surface.
The bounds can be used to decide whether cells are contiguous via the following relationships. In these equations the variable
bnd
is used generically to represent either the latitude or longitude boundary variable.
For 0 < j < n and 0 < i < m, If cells (j,i) and (j,i+1) are contiguous, then bnd(j,i,1)=bnd(j,i+1,0) bnd(j,i,2)=bnd(j,i+1,3) If cells (j,i) and (j+1,i) are contiguous, then bnd(j,i,3)=bnd(j+1,i,0) and bnd(j,i,2)=bnd(j+1,i,1)
 Bounds for multidimensional coordinate variables with psided cells

In all other cases, the bounds should be dimensioned
(…,n,p)
, where(…,n)
are the dimensions of the auxiliary coordinate variables, andp
the number of vertices of the cells. The vertices must be traversed anticlockwise in the lonlat plane as viewed from above. The starting vertex is not specified.
dimensions: lat = 64; nv = 2; // number of vertices variables: float lat(lat); lat:long_name = "latitude"; lat:units = "degrees_north"; lat:bounds = "lat_bnds"; float lat_bnds(lat,nv);
The boundary variable lat_bnds
associates a latitude gridpoint i
with the interval whose boundaries are lat_bnds(i,0)
and lat_bnds(i,1)
.
The gridpoint location, lat(i)
, should be contained within this interval.
For rectangular grids, twodimensional cells can be expressed as Cartesian products of onedimensional cells of the type in the preceding example. However for nonrectangular grids a "rectangular" cell will in general require specifying all four vertices for each cell.
dimensions: imax = 128; jmax = 64; nv = 4; variables: float lat(jmax,imax); lat:long_name = "latitude"; lat:units = "degrees_north"; lat:bounds = "lat_bnds"; float lon(jmax,imax); lon:long_name = "longitude"; lon:units = "degrees_east"; lon:bounds = "lon_bnds"; float lat_bnds(jmax,imax,nv); float lon_bnds(jmax,imax,nv);
The boundary variables lat_bnds
and lon_bnds
associate a gridpoint (j,i)
with the cell determined by the vertices (lat_bnds(j,i,n),lon_bnds(j,i,n))
, n=0,..,3
.
The gridpoint location, (lat(j,i),lon(j,i))
, should be contained within this region.
7.2. Cell Measures
For some calculations, information is needed about the size, shape or location of the cells that cannot be deduced from the coordinates and bounds without special knowledge that a generic application cannot be expected to have. For instance, in computing the mean of several cell values, it is often appropriate to "weight" the values by area. When computing an areamean each grid cell value is multiplied by the gridcell area before summing, and then the sum is divided by the sum of the gridcell areas. Area weights may also be needed to map data from one grid to another in such a way as to preserve the area mean of the field. The preservation of areamean values while regridding may be essential, for example, when calculating surface heat fluxes in an atmospheric model with a grid that differs from the ocean model grid to which it is coupled.
In many cases the areas can be calculated from the cell bounds, but there are exceptions.
Consider, for example, a spherical geodesic grid composed of contiguous, roughly hexagonal cells.
The vertices of the cells can be stored in the variable identified by the bounds
attribute, but the cell perimeter is not uniquely defined by its vertices (because the vertices could, for example, be connected by straight lines, or, on a sphere, by lines following a great circle, or, in general, in some other way).
Thus, given the cell vertices alone, it is generally impossible to calculate the area of a grid cell.
This is why it may be necessary to store the gridcell areas in addition to the cell vertices.
In other cases, the grid cellvolume might be needed and might not be easily calculated from the coordinate information. In ocean models, for example, it is not uncommon to find "partial" grid cells at the bottom of the ocean. In this case, rather than (or in addition to) indicating grid cell area, it may be necessary to indicate volume.
To indicate extra information about the spatial properties of a variable’s grid cells, a cell_measures
attribute may be defined for a variable.
This is a string attribute comprising a list of blankseparated pairs of words of the form "measure: name
".
For the moment, "area
" and "volume
" are the only defined measures, but others may be supported in future.
The "name" is the name of the variable containing the measure values, which we refer to as a "measure variable".
The dimensions of a measure variable must be the same as or a subset of the dimensions of the variable to which it is related, but their order is not restricted, and with one exception:
If a cell measure variable of a data variable that has been compressed by gathering (Section 8.2, "Lossless Compression by Gathering") does not span the compressed dimension, then its dimensions may be any subset of the data variable’s uncompressed dimensions, i.e. any of the dimensions of the data variable except the compressed dimension, and any of the dimensions listed by the compress
attribute of the compressed coordinate variable.
In the case of area, for example, the field itself might be a function of longitude, latitude, and time, but the variable containing the area values would only include longitude and latitude dimensions (and the dimension order could be reversed, although this is not recommended).
The variable must have a units
attribute and may have other attributes such as a standard_name
.
For rectangular longitudelatitude grids, the area of grid cells can be calculated from the bounds: the area of a cell is proportional to the product of the difference in the longitude bounds of the cell and the difference between the sine of each latitude bound of the cell.
In this case supplying gridcell areas via the cell_measures
attribute is unnecessary because it may be assumed that applications can perform this calculation, using their own value for the radius of the Earth.
A variable referenced by cell_measures
is not required to be present in the file containing the data variable.
If the cell_measures
variable is located in another file (an "external file"), rather than in the file where it is referenced, it must be listed in the external_variables
attribute of the referencing file (Section 2.6.3).
dimensions: cell = 2562 ; // number of grid cells time = 12 ; nv = 6 ; // maximum number of cell vertices variables: float PS(time,cell) ; PS:units = "Pa" ; PS:coordinates = "lon lat" ; PS:cell_measures = "area: cell_area" ; float lon(cell) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; lon:bounds="lon_vertices" ; float lat(cell) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; lat:bounds="lat_vertices" ; float time(time) ; time:long_name = "time" ; time:units = "days since 19790101 0:0:0" ; float cell_area(cell) ; cell_area:long_name = "area of grid cell" ; cell_area:standard_name="cell_area"; cell_area:units = "m2" float lon_vertices(cell,nv) ; float lat_vertices(cell,nv) ;
7.3. Cell Methods
To describe the characteristic of a field that is represented by cell values, we define the cell_methods
attribute of the variable.
This is a string attribute comprising a list of blankseparated words of the form "name: method".
Each "name: method" pair indicates that for an axis identified by name, the cell values representing the field have been determined or derived by the specified method.
For example, if data values have been generated by computing time means, then this could be indicated with cell_methods="t: mean"
, assuming here that the name of the time dimension variable is "t".
In the specification of this attribute, name can be a dimension of the variable, a scalar coordinate variable, a valid standard name, or the word "area
".
(See Section 7.3.4, "Cell methods when there are no coordinates" concerning the use of standard names in cell_methods.)
The values of method should be selected from the list in Appendix E, Cell Methods, which includes point
, sum
, mean
, among others.
Case is not significant in the method name.
Some methods (e.g., variance
) imply a change of units of the variable, as is indicated in Appendix E, Cell Methods.
It must be remembered that the method applies only to the axis designated in cell_methods
by name, and different methods may apply to other axes.
If, for instance, a precipitation value in a longitudelatitude cell is given the method maximum
for these axes, it means that it is the maximum within these spatial cells, and does not imply that it is also the maximum in time.
Furthermore, it should be noted that if any method other than "point
" is specified for a given axis, then bounds
should also be provided for that axis (except for the relatively rare exceptions described in Section 7.3.4, "Cell methods when there are no coordinates").
The default interpretation for variables that do not have the cell_methods
attribute specified depends on whether the quantity is extensive (which depends on the size of the cell) or intensive (which does not).
Suppose, for example, the quantities "accumulated precipitation" and "precipitation rate" each have a time axis.
A variable representing accumulated precipitation is extensive in time because it depends on the length of the time interval over which it is accumulated.
For correct interpretation, it therefore requires a time interval to be completely specified via a boundary variable (i.e., via a bounds
attribute for the time axis).
In this case the default interpretation is that the cell method is a sum over the specified time interval.
This can be (optionally) indicated explicitly by setting the cell method to sum
.
A precipitation rate on the other hand is intensive in time and could equally well represent either an instantaneous value or a mean value over the time interval specified by the cell.
In this case the default interpretation for the quantity would be "instantaneous" (which, optionally, can be indicated explicitly by setting the cell method to point
).
More often, however, cell values for intensive quantities are means, and this should be indicated explicitly by setting the cell method to mean
and specifying the cell bounds.
Because the default interpretation for an intensive quantity differs from that of an extensive quantity and because this distinction may not be understood by some users of the data, it is recommended that every data variable include for each of its dimensions and each of its scalar coordinate variables the cell_methods
information of interest (unless this information would not be meaningful).
It is especially recommended that cell_methods
be explicitly specified for each spatiotemporal dimension and each spatiotemporal scalar coordinate variable.
Consider 12hourly timeseries of pressure, temperature and precipitation from a number of stations, where pressure is measured instantaneously, maximum temperature for the preceding 12 hours is recorded, and precipitation is accumulated in a rain gauge. For a period of 48 hours from 6 a.m. on 19 April 1998, the data is structured as follows:
dimensions: time = UNLIMITED; // (5 currently) station = 10; nv = 2; variables: float pressure(time,station); pressure:long_name = "pressure"; pressure:units = "kPa"; pressure:cell_methods = "time: point"; float maxtemp(time,station); maxtemp:long_name = "temperature"; maxtemp:units = "K"; maxtemp:cell_methods = "time: maximum"; float ppn(time,station); ppn:long_name = "depth of waterequivalent precipitation"; ppn:units = "mm"; ppn:cell_methods = "time: sum"; double time(time); time:long_name = "time"; time:units = "h since 1998419 6:0:0"; time:bounds = "time_bnds"; double time_bnds(time,nv); data: time = 0., 12., 24., 36., 48.; time_bnds = 12.,0., 0.,12., 12.,24., 24.,36., 36.,48.;
Note that in this example the time axis values coincide with the end of each interval.
It is sometimes desirable, however, to use the midpoint of intervals as coordinate values for variables that are representative of an interval.
An application may simply obtain the midpoint values by making use of the boundary data in time_bnds
.
7.3.1. Statistics for more than one axis
If more than one cell method is to be indicated, they should be arranged in the order they were applied.
The leftmost operation is assumed to have been applied first.
Suppose, for example, that within each grid cell a quantity varies in both longitude and time and that these dimensions are named "lon" and "time", respectively.
Then values representing the timeaverage of the zonal maximum are labeled cell_methods="lon: maximum time: mean"
(i.e. find the largest value at each instant of time over all longitudes, then average these maxima over time); values of the zonal maximum of timeaverages are labeled cell_methods="time: mean lon: maximum"
.
If the methods could have been applied in any order without affecting the outcome, they may be put in any order in the cell_methods
attribute.
If a data value is representative of variation over a combination of axes, a single method should be prefixed by the names of all the dimensions involved (listed in any order, since in this case the order must be immaterial).
Dimensions should be grouped in this way only if there is an essential difference from treating the dimensions individually.
For instance, the standard deviation of topographic height within a longitudelatitude gridbox could have cell_methods="lat: lon: standard_deviation"
.
(Note also, that in accordance with the recommendation of the following paragraph, this could be equivalently and preferably indicated by cell_methods="area: standard_deviation"
.)
This is not the same as cell_methods="lon: standard_deviation lat: standard_deviation"
, which would mean finding the standard deviation along each parallel of latitude within the zonal extent of the gridbox, and then the standard deviation of these values over latitude.
To indicate variation over horizontal area, it is recommended that instead of specifying the combination of horizontal dimensions, the special string "area
" be used.
The common case of an areamean can thus be indicated by cell_methods="area: mean"
(rather than, for example, "lon: lat: mean
").
The horizontal coordinate variables to which "area
" refers are in this case not explicitly indicated in cell_methods
but can be identified, if necessary, from attributes attached to the coordinate variables, scalar coordinate variables, or auxiliary coordinate variables, as described in Chapter 4, Coordinate Types.
7.3.2. Recording the spacing of the original data and other information
To indicate more precisely how the cell method was applied, extra information may be included in parentheses () after the identification of the method.
This information includes standardized and nonstandardized parts.
Currently the only standardized information is to provide the typical interval between the original data values to which the method was applied, in the situation where the present data values are statistically representative of original data values which had a finer spacing.
The syntax is (interval
: value unit), where value is a numerical value and unit is a string that can be recognized by UNIDATA’s UDUNITS package [UDUNITS].
The unit will usually be dimensionally equivalent to the unit of the corresponding dimension, but this is not required (which allows, for example, the interval for a standard deviation calculated from points evenly spaced in distance along a parallel to be reported in units of length even if the zonal coordinate of the cells is given in degrees).
Recording the original interval is particularly important for standard deviations.
For example, the standard deviation of daily values could be indicated by cell_methods="time: standard_deviation (interval: 1 day)"
and of annual values by cell_methods="time: standard_deviation (interval: 1 year)"
.
If the cell method applies to a combination of axes, they may have a common original interval e.g. cell_methods="lat: lon: standard_deviation (interval: 10 km)"
.
Alternatively, they may have separate intervals, which are matched to the names of axes by position e.g. cell_methods="lat: lon: standard_deviation (interval: 0.1 degree_N interval: 0.2 degree_E)"
, in which 0.1 degree applies to latitude and 0.2 degree to longitude.
If there is both standardized and nonstandardized information, the nonstandardized follows the standardized information and the keyword comment:
.
If there is no standardized information, the keyword comment:
should be omitted.
For instance, an areaweighted mean over latitude could be indicated as lat: mean (areaweighted)
or lat: mean (interval: 1 degree_north comment: areaweighted)
.
A dimension of size one may be the result of "collapsing" an axis by some statistical operation, for instance by calculating a variance from time series data.
We strongly recommend that dimensions of size one be retained (or scalar coordinate variables be defined) to enable documentation of the method (through the cell_methods
attribute) and its domain (through the bounds
attribute).
The variance of the diurnal cycle on 1 January 1990 has been calculated from hourly instantaneous surface air temperature measurements. The time dimension of size one has been retained.
dimensions: lat=90; lon=180; time=1; nv=2; variables: float TS_var(time,lat,lon); TS_var:long_name="surface air temperature variance" TS_var:units="K2"; TS_var:cell_methods="time: variance (interval: 1 hr comment: sampled instantaneously)"; float time(time); time:units="days since 19900101 00:00:00"; time:bounds="time_bnds"; float time_bnds(time,nv); data: time=.5; time_bnds=0.,1.;
Notice that a parenthesized comment in the cell_methods
attribute provides the nature of the samples used to calculate the variance.
7.3.3. Statistics applying to portions of cells
By default, the statistical method indicated by cell_methods
is assumed to have been evaluated over the entire horizontal area of the cell.
Sometimes, however, it is useful to limit consideration to only a portion of a cell (e.g. a mean over the seaice area).
To indicate this, one of two conventions may be used.
The first convention is a method that can be used for the common case of a single areatype.
In this case, the cell_methods
attribute may include a string of the form "name: method where
type".
Here name could, for example, be area
and type may be any of the strings permitted for a variable with a standard_name
of area_type
.
As an example, if the method were mean
and the area_type
were sea_ice
, then the data would represent a mean over only the sea ice portion of the grid cell.
If the data writer expects type to be interpreted as one of the standard area_type
strings, then none of the variables in the netCDF file should be given a name identical to that of the string (because the second convention, described in the next paragraph, takes precedence).
The second convention is the more general.
In this case, the cell_methods
entry is of the form "name: method where
typevar".
Here typevar is a stringvalued auxiliary coordinate variable or stringvalued scalar coordinate variable (see Section 6.1, "Labels") with a standard_name
of area_type
.
The variable typevar contains the name(s) of the selected portion(s) of the grid cell to which the method is applied.
This convention can accommodate cases in which a method is applied to more than one area type and the result is stored in a single data variable (with a dimension which ranges across the various area types).
It provides a convenient way to store output from land surface models, for example, since they deal with many area types within each surface gridbox (e.g., vegetation
, bare_ground
, snow
, etc.).
dimensions: lat=73; lon=96; maxlen=20; ls=2; variables: float surface_temperature(lat,lon); surface_temperature:cell_methods="area: mean where land"; float surface_upward_sensible_heat_flux(ls,lat,lon); surface_upward_sensible_heat_flux:coordinates="land_sea"; surface_upward_sensible_heat_flux:cell_methods="area: mean where land_sea"; char land_sea(ls,maxlen); land_sea:standard_name="area_type"; data: land_sea="land","sea";
If the method is mean
, various ways of calculating the mean can be distinguished in the cell_methods
attribute with a string of the form "mean where type1 [over type2]".
Here, type1 can be any of the possibilities allowed for typevar or type (as specified in the two paragraphs preceding above Example).
The same options apply to type2, except it is not allowed to be the name of an auxiliary coordinate variable with a dimension greater than one (ignoring the possible dimension accommodating the maximum string length).
A cell_methods
attribute with a string of the form "mean where type1 over type2" indicates the mean is calculated by summing over the type1 portion of the cell and dividing by the area of the type2 portion.
In particular, a cell_methods
string of the form "mean where all_area_types over type2" indicates the mean is calculated by summing over all types of area within the cell and dividing by the area of the type2 portion.
(Note that all_area_types
is one of the valid strings permitted for a variable with the standard_name
area_type
.)
If "over type2" is omitted, the mean is calculated by summing over the type1 portion of the cell and dividing by the area of this portion.
variables: float sea_ice_thickness(lat,lon); sea_ice_thickness:cell_methods="area: mean where sea_ice over sea"; sea_ice_thickness:standard_name="sea_ice_thickness"; sea_ice_thickness:units="m"; float snow_thickness(lat,lon); snow_thickness:cell_methods="area: mean where sea_ice over sea"; snow_thickness:standard_name="lwe_thickness_of_surface_snow_amount"; snow_thickness:units="m";
In the case of seaice thickness, the phrase “where sea_ice” could be replaced by “where all_area_types” without changing the meaning since the integral of seaice thickness over all area types is obviously the same as the integral over the seaice area only. In the case of snow thickness, “where sea_ice” differs from “where all_area_types” because “where sea_ice” excludes snow on land from the average.
7.3.4. Cell methods when there are no coordinates
To provide an indication that a particular cell method is relevant to the data without having to provide a precise description of the corresponding cell, the "name" that appears in a "name: method" pair may be an appropriate standard_name
(which identifies the dimension) or the string, "area" (rather than the name of a scalar coordinate variable or a dimension with a coordinate variable).
This convention cannot be used, however, if the name of a dimension or scalar coordinate variable is identical to name.
There are two situations where this convention is useful.
First, it allows one to provide some indication of the method when the cell coordinate range cannot be precisely defined.
For example, a climatological mean might be based on any data that exists, and, in general, the data might not be available over the same time periods everywhere.
In this case, the time range would not be well defined (because it would vary, depending on location), and it could not be precisely specified through a time dimension’s bounds.
Nevertheless, useful information can be conveyed by a cell_methods
entry of "time: mean
" (where time
, it should be noted, is a valid standard_name
).
(As required by this convention, it is assumed here that for the data referred to by this cell_methods
attribute, "time" is not a dimension or coordinate variable.)
Second, for a few special dimensions, this convention allows one to indicate (without explicitly defining the coordinates) that the method applies to the domain covering the entire permitted range of those dimensions. This is allowed only for longitude, latitude, and area (indicating a combination of horizontal coordinates). For longitude, the domain is indicated according to this provision by the string "longitude" (rather than the name of a longitude coordinate variable), and this implies that the method applies to all possible longitudes (i.e., from 0E to 360E). For latitude, the string "latitude" is used and implies the method applies to all possible latitudes (i.e., from 90S to 90N). For area, the string "area" is used and implies the method applies to the whole world.
In the second case if, in addition, the data variable has a dimension with a corresponding labeled axis that specifies a geographic region (Section 6.1.1, "Geographic Regions"), the implied range of longitude and latitude is the valid range for each specified region, or in the case of area
the domain is the geographic region.
For example, there could be a cell_methods
entry of "longitude: mean
", where longitude
is not the name of a dimension or coordinate variable (but is one of the special cases given above).
That would indicate a mean over all longitudes.
Note, however, that if in addition the data variable had a scalar coordinate variable with a standard_name
of region
and a value of atlantic_ocean
, it would indicate a mean over longitudes that lie within the Atlantic Ocean, not all longitudes.
We recommend that whenever possible, cell bounds should be supplied by giving the variable a dimension of size one and attaching bounds to the associated coordinate variable.
7.4. Climatological Statistics
Climatological statistics may be derived from corresponding portions of the annual cycle in a set of years, e.g., the average January temperatures in the climatology of 19611990, where the values are derived by averaging the 30 Januarys from the separate years. Portions of the climatological cycle are specified by references to dates within the calendar year. However, a calendar year is not a welldefined unit of time, because it differs between leap years and other years, and among calendars. Nonetheless for practical purposes we wish to compare statistics for months or seasons from different calendars, and to make climatologies from a mixture of leap years and other years. Hence we provide special conventions for indicating dates within the climatological year. Climatological statistics may also be derived from corresponding portions of a range of days, for instance the average temperature for each hour of the average day in April 1997. In addition the two concepts may be used at once, for instance to indicate not April 1997, but the average April of the five years 19951999.
Climatological variables have a climatological time axis.
Like an ordinary time axis, a climatological time axis may have a dimension of unity (for example, a variable containing the January average temperatures for 19611990), but often it will have several elements (for example, a climatological time axis with a dimension of 12 for the climatological average temperatures in each month for 19611990, a dimension of 3 for the January mean temperatures for the three decades 19611970, 19711980, 19811990, or a dimension of 24 for the hours of an average day).
Intervals of climatological time are conceptually different from ordinary time intervals; a given interval of climatological time represents a set of subintervals which are not necessarily contiguous.
To indicate this difference, a climatological time coordinate variable does not have a bounds
attribute.
Instead, it has a climatology
attribute, which names a variable with dimensions (n,2), n being the dimension of the climatological time axis.
Using the units and calendar of the time coordinate variable, element (i,0) of the climatology variable specifies the beginning of the first subinterval and element (i,1) the end of the last subinterval used to evaluate the climatological statistics with index i in the time dimension.
The time coordinates should be values that are representative of the climatological time intervals, such that an application which does not recognise climatological time will nonetheless be able to make a reasonable interpretation.
For compatibility with the COARDS standard, a climatological time coordinate in the default standard
and julian
calendars may be indicated by setting the date/time reference string in the time coordinate’s units
attribute to midnight on 1 January in year 0 (i.e., since 011
).
This convention is deprecated because it does not provide any information about the intervals used to compute the climatology, and there may be inconsistencies among software packages in the interpretation of the time coordinates with a reference time of year 0.
Use of year 0 for this purpose is impossible in all other calendars, because year 0 is a valid year.
A climatological axis may use different statistical methods to represent variation among years, within years and within days.
For example, the average January temperature in a climatology is obtained by averaging both within years and over years.
This is different from the average Januarymaximum temperature and the maximum Januaryaverage temperature.
For the former, we first calculate the maximum temperature in each January, then average these maxima; for the latter, we first calculate the average temperature in each January, then find the largest one.
As usual, the statistical operations are recorded in the cell_methods
attribute, which may have two or three entries for the climatological time dimension.
Valid values of the cell_methods
attribute must be in one of the forms from the following list.
The intervals over which various statistical methods are applied are determined by decomposing the date and time specifications of the climatological time bounds of a cell, as recorded in the variable named by the climatology
attribute.
(The date and time specifications must be calculated from the time coordinates expressed in units of "time interval since reference date and time".)
In the descriptions that follow we use the abbreviations y, m, d, H, M, and S for year, month, day, hour, minute, and second respectively.
The suffix 0 indicates the earlier bound and 1 the latter.
 time: method1
within years
time: method2over years

method1 is applied to the time intervals (mdHMS0mdHMS1) within individual years and method2 is applied over the range of years (y0y1).
 time: method1
within days
time: method2over days

method1 is applied to the time intervals (HMS0HMS1) within individual days and method2 is applied over the days in the interval (ymd0ymd1).
 time: method1
within days
time: method2over days
time: method3over years

method1 is applied to the time intervals (HMS0HMS1) within individual days and method2 is applied over the days in the interval (md0md1), and method3 is applied over the range of years (y0y1).
The methods which can be specified are those listed in Appendix E, Cell Methods and each entry in the cell_methods
attribute may also, as usual, contain nonstandardised information in parentheses after the method.
For instance, a mean over ENSO years might be indicated by "time: mean over years (ENSO years)
".
When considering intervals within years, if the earlier climatological time bound is later in the year than the later climatological time bound, it implies that the time intervals for the individual years run from each year across January 1 into the next year e.g. DJF intervals run from December 1 0:00 to March 1 0:00. Analogous situations arise for daily intervals running across midnight from one day to the next.
When considering intervals within days, if the earlier time of day is equal to the later time of day, then the method is applied to a full 24 hour day.
We have tried to make the examples in this section easier to understand by translating all time coordinate values to date and time formats. This is not currently valid CDL syntax.
This example shows the metadata for the average seasonalminimum temperature for the four standard climatological seasons MAM JJA SON DJF, made from data for March 1960 to February 1991.
dimensions: time=4; nv=2; variables: float temperature(time,lat,lon); temperature:long_name="surface air temperature"; temperature:cell_methods="time: minimum within years time: mean over years"; temperature:units="K"; double time(time); time:climatology="climatology_bounds"; time:units="days since 196011"; double climatology_bounds(time,nv); data: // time coordinates translated to date/time format time="1960416", "1960716", "19601016", "1961116" ; climatology_bounds="196031", "199061", "196061", "199091", "196091", "1990121", "1960121", "199131" ;
Average January precipitation totals are given for each of the decades 19611970, 19711980, 19811990.
dimensions: time=3; nv=2; variables: float precipitation(time,lat,lon); precipitation:long_name="precipitation amount"; precipitation:cell_methods="time: sum within years time: mean over years"; precipitation:units="kg m2"; double time(time); time:climatology="climatology_bounds"; time:units="days since 190111"; double climatology_bounds(time,nv); data: // time coordinates translated to date/time format time="1965115", "1975115", "1985115" ; climatology_bounds="196111", "197021", "197111", "198021", "198111", "199021" ;
Hourly average temperatures are given for April 1997.
dimensions: time=24; nv=2; variables: float temperature(time,lat,lon); temperature:long_name="surface air temperature"; temperature:cell_methods="time: mean within days time: mean over days"; temperature:units="K"; double time(time); time:climatology="climatology_bounds"; time:units="hours since 199741"; double climatology_bounds(time,nv); data: // time coordinates translated to date/time format time="199741 0:30", "199741 1:30", ... "199741 23:30" ; climatology_bounds="199741 0:00", "1997430 1:00", "199741 1:00", "1997430 2:00", ... "199741 23:00", "199751 0:00" ;
Number of frost days during NH winter 20072008, and maximum length of spells of consecutive frost days.
A "frost day" is defined as one during which the minimum temperature falls below freezing point (0 degC).
This is described as a climatological statistic, in which the minimum temperature is first calculated within each day, and then the number of days or spell lengths meeting the specified condition are evaluated.
In this operation, the standard name is also changed; the original data are air_temperature
.
variables: float n1(lat,lon); n1:standard_name="number_of_days_with_air_temperature_below_threshold"; n1:coordinates="threshold time"; n1:cell_methods="time: minimum within days time: sum over days"; float n2(lat,lon); n2:standard_name="spell_length_of_days_with_air_temperature_below_threshold"; n2:coordinates="threshold time"; n2:cell_methods="time: minimum within days time: maximum over days"; float threshold; threshold:standard_name="air_temperature"; threshold:units="degC"; double time; time:climatology="climatology_bounds"; time:units="days since 200061"; double climatology_bounds(time,nv); data: // time coordinates translated to date/time format time="2008116 6:00"; climatology_bounds="2007121 6:00", "200831 6:00"; threshold=0.;
This is a modified version of the previous example, "Temperature for each hour of the average day". It now applies to April from a 19611990 climatology.
variables: float temperature(time,lat,lon); temperature:long_name="surface air temperature"; temperature:cell_methods="time: mean within days ", "time: mean over days time: mean over years"; temperature:units="K"; double time(time); time:climatology="climatology_bounds"; time:units="days since 196111"; double climatology_bounds(time,nv); data: // time coordinates translated to date/time format time="196141 0:30", "196141 1:30", ..., "196141 23:30" ; climatology_bounds="196141 0:00", "1990430 1:00", "196141 1:00", "1990430 2:00", ... "196141 23:00", "199051 0:00" ;
Maximum of daily precipitation amounts for each of the three months June, July and August 2000 are given. The first daily total applies to 6 a.m. on 1 June to 6 a.m. on 2 June, the 30th from 6 a.m. on 30 June to 6 a.m. on 1 July. The maximum of these 30 values is stored under time index 0 in the precipitation array.
dimensions: time=3; nv=2; variables: float precipitation(time,lat,lon); precipitation:long_name="Accumulated precipitation"; precipitation:cell_methods="time: sum within days time: maximum over days"; precipitation:units="kg"; double time(time); time:climatology="climatology_bounds"; time:units="days since 200061"; double climatology_bounds(time,nv); data: // time coordinates translated to date/time format time="2000616", "2000716", "2000816" ; climatology_bounds="200061 6:00:00", "200071 6:00:00", "200071 6:00:00", "200081 6:00:00", "200081 6:00:00", "200091 6:00:00" ;
7.5. Geometries
For many geospatial applications, data values are associated with a geometry, which is a spatial representation of a realworld feature, for instance a timeseries of areal average precipitation over a watershed. Polygonal cells with an arbitrary number of vertices can be described using Section 7.1, "Cell Boundaries", but in that case every cell must have the same number of vertices and must be a single polygon ring. In contrast, each geometry may have a different number of nodes, the geometries may be lines (as alternatives to points and polygons), and they may be multipart, i.e., include several disjoint parts. While line and point geometries don’t describe an interval along a dimension as the traditional cell bounds described above do, they do describe the extent of a geometry or realworld feature so are included in this section. The approach described here specifies how to encode such geometries following the pattern in 9.3.3 Contiguous ragged array representation and attach them to variables in a way that is consistent with the cell bounds approach.
All geometries are made up of one or more nodes. The geometry type specifies the set of topological assumptions to be applied to relate the nodes (see Table 7.1). For example, multipoint and line geometries are nearly the same except nodes are interpreted as being connected for lines. Lines and polygons are also nearly the same except that the first and last nodes are assumed to be connected for polygons. Note that CF does not require the first and last node to be identical but allows them to be coincident if desired. Polygons that have holes, such as waterbodies in a land unit, are encoded as a collection of polygon ring parts, each identified as exterior or interior polygons. Multipart geometries, such as multiple lines representing the same river or multiple islands representing the same jurisdiction, are encoded as collections of unconnected points, lines, or polygons that are logically grouped into a single geometry.
Any data variable can be given a geometry
attribute that indicates the geometry for the quantity held in the variable.
One of the dimensions of the data variable must be the number of geometries to which the data applies.
As shown in Example 7.15, if the data variable has a discrete sampling geometry, the number of geometries is the length of the instance dimension (Section 9.2).
dimensions: instance = 2 ; node = 5 ; time = 4 ; variables: int time(time) ; time:units = "days since 20000101" ; double lat(instance) ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ; lat:nodes = "y" ; double lon(instance) ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ; lon:nodes = "x" ; int datum ; datum:grid_mapping_name = "latitude_longitude" ; datum:longitude_of_prime_meridian = 0.0 ; datum:semi_major_axis = 6378137.0 ; datum:inverse_flattening = 298.257223563 ; int geometry_container ; geometry_container:geometry_type = "line" ; geometry_container:node_count = "node_count" ; geometry_container:node_coordinates = "x y" ; int node_count(instance) ; double x(node) ; x:units = "degrees_east" ; x:standard_name = "longitude" ; x:axis = "X" ; double y(node) ; y:units = "degrees_north" ; y:standard_name = "latitude" ; y:axis = "Y" ; double someData(instance, time) ; someData:coordinates = "time lat lon" ; someData:grid_mapping = "datum" ; someData:geometry = "geometry_container" ; // global attributes: :featureType = "timeSeries" ; data: time = 1, 2, 3, 4 ; lat = 30, 50 ; lon = 10, 60 ; someData = 1, 2, 3, 4, 1, 2, 3, 4 ; node_count = 3, 2 ; x = 30, 10, 40, 50, 50 ; y = 10, 30, 40, 60, 50 ;
The time series variable, someData, is associated with line geometries via the geometry attribute. The first line geometry is comprised of three nodes, while the second has two nodes. Client applications unaware of CF geometries can fall back to the lat and lon variables to locate feature instances in space. In this example, lat and lon coordinates are identical to the first node in each line geometry, though any representative point could be used.
A geometry container variable acts as a container for attributes that describe a set of geometries.
The geometry
attribute of the data variable contains the name of a geometry container variable.
The geometry container variable must hold geometry_type
and node_coordinates
attributes.
The grid_mapping
and coordinates
attributes can be carried by the geometry container variable provided they are also carried by the data variables associated with the container.
The geometry_type
attribute indicates the type of geometry present.
Its allowable values are: point, line, polygon.
Multipart geometries are allowed for all three geometry types.
For example, polygon geometries could include single part geometries like the State of Colorado and multipart geometries like the State of Hawaii.
The node_coordinates
attribute contains the blankseparated names of the variables that contain geometry node coordinates (one variable for each spatial dimension).
The geometry node coordinate variables must each have an axis
attribute whose allowable values are X, Y, and Z.
If a coordinates
attribute is carried by the geometry container variable or its parent data variable, then those coordinate variables that have a meaningful correspondence with node coordinates are indicated as such by a nodes
attribute that names the corresponding node coordinates, but only if the grid_mapping
associated with the geometry node variables is the same as that of the coordinate variables.
If a different grid mapping is used, then the provided coordinates must not have the nodes
attribute.
Whether linked to normal CF spacetime coordinates with a nodes
attribute or not, inclusion of such coordinates is recommended to maintain backward compatibility with software that has not implemented geometry capabilities.
The geometry node coordinate variables must all have the same single dimension, which is the total number of nodes in all the geometries. The nodes must be stored consecutively for each geometry and in the order of the geometries, and within each multipart geometry the nodes must be stored consecutively for each part and in the order of the parts. Polygon exterior rings must be stored before any interior rings they may contain. Nodes for polygon exterior rings must be ordered using the righthand rule, e.g., anticlockwise in the lonlat plane as viewed from above. Polygon interior rings must be in clockwise order. They are put in opposite orders to facilitate calculation of area and consistency with the typical implementation pattern.
When more than one geometry instance is present, the geometry container variable must have a node_count
attribute that contains the name of a variable indicating the count of nodes per geometry.
The node count is the total number of nodes in all the parts.
The exception is when all geometries are single part point geometries, in which case a node count is not needed since each geometry contains a single node.
However in that case, the dimension of the node coordinate variables must be one of the dimensions of the data variable (because it serves also as the instance dimension for geometries).
For multipart lines, multipart polygons, and polygons with holes, the geometry container variable must have a part_node_count
attribute that indicates a variable of the count of nodes per geometry part.
Note that because multipoint geometries always have a single node per part, the part_node_count
is not required for point geometry types.
The single dimension of the part node count variable must equal the total number of parts in all the geometries.
For polygon geometries with holes, the geometry container variable must have an interior_ring
attribute that contains the name of a variable that indicates if the polygon parts are interior rings (i.e., holes) or not.
This interior ring variable must contain the value 0 to indicate an exterior ring polygon and 1 to indicate an interior ring polygon.
The single dimension of the interior ring variable must be the same dimension as that of the part node count variable.
The geometry types included in this convention are listed in Table 7.1.
geometry_type  Dimensionality  Description of Geometry Instance  Additional required attributes on geometry container variable 

point 
0 
A collection of one or more points, where a point is a single location in space 
node_count (if multipart geometries are present) 
line 
1 
A collection of one or more lines, where a line is an ordered set of data points connected by linearly interpolating between points 
node_count, part_node_count (if multipart geometries are present) 
polygon 
2 
A collection of one or more polygons, where a polygon is a planar surface comprised of an exterior ring and zero or more interior rings (i.e., holes), where a ring is a closed line (i.e., the last point in the line is assumed to be connected to the first point) 
node_count, part_node_count (if holes or multipart geometries are present), interior_ring (if holes are present) 
Table 7.1. Dimensionality, description, and additional required attributes for geometry_types.
This example demonstrates all potential attributes and variables for encoding geometries.
dimensions: node = 12 ; instance = 2 ; part = 4 ; time = 4 ; variables: int time(time) ; time:units = "days since 20000101" ; double x(node) ; x:units = "degrees_east" ; x:standard_name = "longitude" ; x:axis = "X" ; double y(node) ; y:units = "degrees_north" ; y:standard_name = "latitude" ; y:axis = "Y" ; double lat(instance) ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ; lat:nodes = "y" ; double lon(instance) ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ; lon:nodes = "x" ; float geometry_container ; geometry_container:geometry_type = "polygon" ; geometry_container:node_count = "node_count" ; geometry_container:node_coordinates = "x y" ; geometry_container:grid_mapping = "datum" ; geometry_container:coordinates = "lat lon" ; geometry_container:part_node_count = "part_node_count" ; geometry_container:interior_ring = "interior_ring" ; int node_count(instance) ; int part_node_count(part) ; int interior_ring(part) ; float datum ; datum:grid_mapping_name = "latitude_longitude" ; datum:semi_major_axis = 6378137. ; datum:inverse_flattening = 298.257223563 ; datum:longitude_of_prime_meridian = 0. ; double someData(instance, time) ; someData:coordinates = "time lat lon" ; someData:grid_mapping = "datum" ; someData:geometry = "geometry_container" ; // global attributes: :featureType = "timeSeries" ; data: time = 1, 2, 3, 4 ; x = 20, 10, 0, 5, 10, 15, 20, 10, 0, 50, 40, 30 ; y = 0, 15, 0, 5, 10, 5, 20, 35, 20, 0, 15, 0 ; lat = 25, 7 ; lon = 10, 40 ; node_count = 9, 3 ; part_node_count = 3, 3, 3, 3 ; interior_ring = 0, 1, 0, 0 ; someData = 1, 2, 3, 4, 1, 2, 3, 4 ;
8. Reduction of Dataset Size
There are three methods for reducing dataset size: packing, lossless compression, and lossy compression. By packing we mean altering the data in a way that reduces its precision (but has no other effect on accuracy). By lossless compression we mean techniques that store the data more efficiently and result in no loss of precision or accuracy. By lossy compression we mean techniques that store the data more efficiently and retain its precision but result in some loss in accuracy.
Lossless compression only works in certain circumstances, e.g., when a variable contains a significant amount of missing or repeated data values.
In this case it is possible to make use of standard utilities, e.g., UNIX compress
or GNU gzip
, to compress the entire file after it has been written.
In this section we offer an alternative compression method that is applied on a variable by variable basis.
This has the advantage that only one variable need be uncompressed at a given time.
The disadvantage is that generic utilities that don’t recognize the CF conventions will not be able to operate on compressed variables.
8.1. Packed Data
At the current time the netCDF interface does not provide for packing data.
However a simple packing may be achieved through the use of the optional NUG defined attributes scale_factor
and add_offset
.
After the data values of a variable have been read, they are to be multiplied by the scale_factor
, and have add_offset
added to them.
If both attributes are present, the data are scaled before the offset is added.
When scaled data are written, the application should first subtract the offset and then divide by the scale factor.
The units of a variable should be representative of the unpacked data.
This standard is more restrictive than the NUG with respect to the use of the scale_factor
and add_offset
attributes; ambiguities and precision problems related to data type conversions are resolved by these restrictions.
When packed data is written, the scale_factor
and add_offset
attributes must be of the same type as the unpacked data, which must be either float
or double
. Data of type float
must be packed into one of these types: byte
, unsigned byte
, short
, unsigned short
. Data of type double
must be packed into one of these types: byte
, unsigned byte
, short
, unsigned short
, int
, unsigned int
.
When packed data is read, it should be unpacked to the type of the scale_factor
and add_offset
attributes, which must have the same type if both are present. For guidance only, we suggest that packed data which does not conform to the rules of this section regarding the types of the data variable and attributes should be unpacked to double
type, in order to minimise the risk of loss of precision.
When data to be packed contains missing values the attributes that indicate missing values (_FillValue
, valid_min
, valid_max
, valid_range
) must be of the same data type as the packed data.
See Section 2.5.1, "Missing data, valid and actual range of data" for a discussion of how applications should treat variables that have attributes indicating both missing values and transformations defined by a scale and/or offset.
8.2. Lossless Compression by Gathering
To save space in the netCDF file, it may be desirable to eliminate points from data arrays that are invariably missing. Such a compression can operate over one or more adjacent axes, and is accomplished with reference to a list of the points to be stored. The list is constructed by considering a mask array that only includes the axes to be compressed, and then mapping this array onto one dimension without reordering. The list is the set of indices in this onedimensional mask of the required points. In the compressed array, the axes to be compressed are all replaced by a single axis, whose dimension is the number of wanted points. The wanted points appear along this dimension in the same order they appear in the uncompressed array, with the unwanted points skipped over. Compression and uncompression are executed by looping over the list.
The list is stored as the coordinate variable for the compressed axis of the data variable.
Thus, the list variable and its dimension have the same name.
If any auxiliary coordinate variable has all the dimensions to be compressed, adjacent and in the same order as in the data variable, and if the auxiliary coordinate variable has missing data at all the points which are to be eliminated from the data variable, then the affected dimensions can optionally be replaced by the list dimension for the auxiliary coordinate variable just as for the data variable.
The list variable has a string attribute compress
, containing a blankseparated list of the dimensions which were affected by the compression in the order of the CDL declaration of the uncompressed array.
The presence of this attribute identifies the list variable as such.
The list, the original dimensions and coordinate variables (including boundary variables), and the compressed variables with all the attributes of the uncompressed variables are written to the netCDF file.
The uncompressed variables can be reconstituted exactly as they were using this information.
The list variable must not have an associated boundary variable.
We eliminate sea points at all depths in a longitudelatitudedepth array of soil temperatures.
In this case, only the longitude and latitude axes would be affected by the compression.
We construct a list landpoint(landpoint)
containing the indices of land points.
dimensions: lat=73; lon=96; landpoint=2381; depth=4; variables: int landpoint(landpoint); landpoint:compress="lat lon"; float landsoilt(depth,landpoint); landsoilt:long_name="soil temperature"; landsoilt:units="K"; float depth(depth); float lat(lat); float lon(lon); data: landpoint=363, 364, 365, ...;
Since landpoint(0)=363
, for instance, we know that landsoilt(*,0)
maps on to point 363 of the original data with dimensions (lat,lon)
.
This corresponds to indices (3,75)
, i.e., 363 = 3*96 + 75
.
We compress a longitudelatitudedepth field of ocean salinity by eliminating points below the seafloor. In this case, all three dimensions are affected by the compression, since there are successively fewer active ocean points at increasing depths.
variables: float salinity(time,oceanpoint); int oceanpoint(oceanpoint); oceanpoint:compress="depth lat lon"; float depth(depth); float lat(lat); float lon(lon); double time(time);
This information implies that the salinity field should be uncompressed to an array with dimensions (depth,lat,lon)
.
In A single timeseries with timevarying deviations from a nominal point spatial location, two auxiliary coordinate variables are compressed as described in this section, although their data variable is not.
8.3. Lossy Compression by Coordinate Subsampling
For some applications the coordinates of a data variable can require considerably more storage than the data itself. Space may be saved in the netCDF file by storing a subsample of the coordinates that describe the data. The uncompressed coordinate and auxiliary coordinate variables can be reconstituted by interpolation, from the subsampled coordinate values to the domain of the data (i.e. the target domain). This process will likely result in a loss in accuracy (as opposed to precision) in the uncompressed variables, due to rounding and approximation errors in the interpolation calculations, but it is assumed that these errors will be small enough to not be of concern to users of the uncompressed dataset. The creator of the compressed dataset can control the accuracy of the reconstituted coordinates through the degree of subsampling and the choice of interpolation method, see Appendix J, Coordinate Interpolation Methods.
The subsampled coordinates are called tie points and are stored in tie point coordinate variables.
In addition to the tie point coordinate variables themselves, metadata defining the coordinate interpolation method is stored in attributes of the data variable and of the associated interpolation variable. The partitioning of metadata between the data variable and the interpolation variable has been designed to minimise redundancy and maximise the reusability of the interpolation variable within a dataset.
The metadata that define the interpolation formula and its inputs are complete, so that the results of the coordinate reconstitution process are well defined and of a predictable accuracy.
8.3.1. Tie Points and Interpolation Subareas
Reconstitution of the uncompressed coordinate and auxiliary coordinate variables is based on interpolation. To accomplish this, the target domain is segmented into smaller interpolation subareas, for each of which the interpolation method is applied independently. For onedimensional interpolation, an interpolation subarea is defined by two tie points, one at each end of the interpolation subarea; for twodimensional interpolation, an interpolation subarea is defined by four tie points, one at each corner of a rectangular area aligned with the domain axes; etc. For the reconstitution of the uncompressed coordinate and auxiliary coordinate variables within an interpolation subarea, the interpolation method is permitted to access its defining tie points, and no others.
As an interpolation method relies on the regularity and continuity of the coordinate values within each interpolation subarea, special attention must be given to the case when uncompressed coordinates contain discontinuities. A discontinuity could be an overlap or a gap in the coordinates' coverage, or a change in cell size or cell alignment. As an example, such discontinuities are common in remote sensing data and may be caused by combinations of the instrument scan motion, the motion of the sensor platform and changes in the instrument scan mode. When discontinuities are present, the domain is first divided into multiple continuous areas, each of which is free of discontinuities. When no discontinuities are present, the whole domain is a single continuous area. Following this step, each continuous area is segmented into interpolation subareas. The processes of generating interpolation subareas for a domain without discontinuities and for a domain with discontinuities is illustrated in Figure 8.1, and described in more detail in Appendix J, Coordinate Interpolation Methods.
For each interpolated dimension, i.e. a target domain dimension for which coordinate interpolation is required, the locations of the tie point coordinates are defined by a corresponding tie point index variable, which also indicates the locations of the continuous areas (Section 8.3.7, "Tie Point Index Mapping").
The interpolation subareas within a continuous area do not overlap, ensuring that each coordinate of an interpolated dimension is computed from a unique interpolation subarea.
These interpolation subareas, however, share the tie point coordinates that define their common boundaries.
Such a shared tie point coordinate can only be located in one of a pair of adjacent interpolation subareas, which is always the first of the pair in index space.
For instance, in Figure 8.1, the interpolation subarea labelled (0,0)
contains all four of its tie point coordinates, and the interpolation subarea (0,1)
only contains two of them.
When applied for a given interpolation subarea, interpolation methods (such as those described in Appendix J, Coordinate Interpolation Methods) must ensure that reconstituted coordinate points are only generated inside the interpolation subarea being processed, even if some of the tie point coordinates lie outside of that interpolation subarea.
Adjacent interpolation subareas that are in different continuous areas never share tie point coordinates, as consequence of the grid discontinuity between them. This results in a different number of tie point coordinates in the two cases shown in Figure 8.1.
For each interpolated dimension, the number of interpolation subareas is equal to the number of tie points minus the number of continuous areas.
Tie point coordinate variables for both coordinate and auxiliary coordinate variables must be defined as numeric data types and are not allowed to have missing values.
8.3.2. Coordinate Interpolation Attribute
To indicate that coordinate interpolation is required, a coordinate_interpolation
attribute must be defined for a data variable.
This is a string attribute that both identifies the tie point coordinate variables, and maps nonoverlapping subsets of them to their corresponding interpolation variables.
It is a blankseparated list of words of the form "tie_point_coordinate_variable: [tie_point_coordinate_variable: …] interpolation_variable [tie_point_coordinate_variable: [tie_point_coordinate_variable: …] interpolation_variable …]".
For example, to specify that the tie point coordinate variables lat
and lon
are to be interpolated according to the interpolation variable bi_linear
could be indicated with lat: lon: bi_linear
.
8.3.3. Interpolation Variable
The method used to uncompress the tie point coordinate variables is described by an interpolation variable that acts as a container for the attributes that define the interpolation technique and the parameters that should be used. The variable should be a scalar (i.e. it has no dimensions) of arbitrary type, and the value of its single element is immaterial.
The interpolation method must be identified in one of two ways.
Either by the interpolation_name
attribute, which takes a string value that contains the method’s name, or else by the interpolation_description
attribute, which takes a string value that contains a nonstandardized description of the method.
These attributes must not be both set.
The valid values of interpolation_name
are given in Appendix J, Coordinate Interpolation Methods.
This appendix describes the interpolation technique for each method, and optional interpolation variable attributes for configuring the interpolation process.
If a standardized interpolation name is not given, the interpolation variable must have an interpolation_description
attribute defined instead, containing a description of the nonstandardised interpolation (in a similar manner to a long name being used instead of a standard name).
This description is free text that can take any form (including fully qualified URLs, for example).
Whilst it is recommended that a standardised interpolation is provided, the alternative is provided to promote interoperability in cases where a well defined user community needs to use sophisticated interpolation techniques that may also be under development.
The definition of the interpolation method, however it is specified, may include instructions to treat groups of physically related coordinates simultaneously, if such tie points are present. For example, there are cases where longitudes cannot be interpolated without considering the corresponding latitudes. It is up to the interpolation description to describe how such coordinates are to be identified (e.g. it may be that such tie point coordinate variables require particular units or standard names).
Note that the interpolation method is always applied on a per interpolation subarea basis, for which the construction of the uncompressed coordinates may only access those tie points that define the extent of the of the interpolation subarea.
In addition to the interpolation_name
and interpolation_description
attributes described in this section, further attributes of the interpolation variable are described in Section 8.3.5, "Tie Point Mapping Attribute" and Section 8.3.8, "Interpolation Parameters", Section 8.3.9, "Interpolation of Cell Boundaries" and Section 8.3.10, "Interpolation Method Implementation".
8.3.4. Subsampled, Interpolated and NonInterpolated Dimensions
For each interpolation variable identified in the coordinate_interpolation
attribute, all of the associated tie point coordinate variables must share the same set of one or more dimensions.
This set of dimensions must correspond to the set of dimensions of the uncompressed coordinate or auxiliary coordinate variables, such that each of these dimensions must be either the uncompressed dimension itself, or a dimension that is to be interpolated to the uncompressed dimension.
Dimensions of the tie point coordinate variable which are to be interpolated are called subsampled dimensions, and the corresponding data variable dimensions are called interpolated dimensions, while those for which no interpolation is required, being the same in the data variable and the tie point coordinate variable, are called noninterpolated dimensions. The dimensions of a tie point coordinate variable must contain at least one subsampled dimension, for each of which the corresponding interpolated dimension cannot be included.
The size of a subsampled dimension will be less than the size of the corresponding interpolated dimension.
For example, if the interpolated dimensions are xc = 30
and yc = 10
, interpolation could be applied in both of these dimensions, based on tie point variables of the dimensions tp_xc = 4
and tp_yc = 2
.
Here, tp_xc
is the subsampled dimension related to the interpolated dimension xc
, and tp_yc
is the subsampled dimension related to the interpolated dimension yc
.
The presence of noninterpolated dimensions in the tie point coordinate variable impacts the interpolation process in that there must be a separate application of the interpolation method for each combination of indices of the noninterpolated dimensions.
For example, if xc = 30
is an interpolated dimension and yc = 10
is a noninterpolated dimension, interpolation could be applied in the xc
dimension only, based on tie point variables that have the subsampled dimension tp_xc = 4
and the noninterpolated dimension yc = 10
.
The interpolation in the xc
dimension would then be repeated for each of the 10 indices of the yc
noninterpolated dimension.
8.3.5. Tie Point Mapping Attribute
The tie_point_mapping
attribute provides mapping at two levels.
It associates interpolated dimensions with the corresponding subsampled dimensions, and for each of these sets of corresponding dimensions, it associates index values of the interpolated dimension with index values of the subsampled dimension, thereby uniquely associating the tie points with their corresponding location in the target domain.
The mappings are stored in the interpolation variable’s tie_point_mapping
attribute that contains a blankseparated list of words of the form "interpolated_dimension: tie_point_index_variable subsampled_dimension [interpolation_subarea_dimension] [interpolated_dimension: …]", the details of which are described in the following two sections.
8.3.6. Tie Point Dimension Mapping
The tie_point_mapping
attribute defined above associates each interpolated dimension with its corresponding subsampled dimension and, if required, its corresponding interpolation subarea dimension that defines the number of interpolation subareas which partition the interpolated dimension.
It is only required to associate an interpolated dimension to an interpolation subarea dimension in the case that the interpolation subarea dimension is spanned by an interpolation parameter variable, as described in Section 8.3.8, "Interpolation Parameters".
If an interpolation subarea dimension is provided, then it must be the second of the two named dimensions following the tie point index variable.
Note that the size of an interpolation subarea dimension is, by definition, the size of the corresponding subsampled dimension minus the number of continuous areas.
An overview of the different dimensions for coordinate interpolation is shown in Figure 8.2.
8.3.7. Tie Point Index Mapping
The tie_point_mapping
attribute defined in Section 8.3.5, "Tie Point Mapping Attribute" identifies for each subsampled dimension a tie point index variable.
The tie point index variable defines the relationship between the indices of the subsampled dimension and the indices of its corresponding interpolated dimension.
A tie point index variable is a onedimensional integer variable that must span the subsampled dimension. Each tie point index variable value is a zerobased index of the related interpolated dimension which maps an element of that interpolated dimension to the corresponding location in the subsampled dimension.
The tie point index values must be strictly monotonically increasing. The location in index space of a continuous area boundary that relates to a grid discontinuity (Section 8.3.1, "Tie Points and Interpolation Subareas") is indicated by a pair of adjacent tie point index values differing by one. In this case, each tie point index of the pair defines a boundary of a different continuous area. As a consequence, any pair of tie point index values that defines an extent of an interpolation subarea must differ by two or more, i.e. in general, an interpolation subarea spans at least two points in each of its interpolated dimensions. Interpolation subareas that are the first in index space of a continuous area, in one or more of the subsampled dimensions are, however, special. These interpolation subareas contain tie points at both of the subarea boundaries with respect to those subsampled dimensions and so must span at least three points in the corresponding interpolated dimensions (see Figure 8.1).
For instance, in example Twodimensional tie point interpolation the tie point coordinate variables represent a subset of the target domain and the tie point index variable int x_indices(tp_xc)
contains the indices x_indices = 0, 9, 19, 29
that identify the location in the interpolated dimension xc
of size 30.
The corresponding tie_point_mapping
attribute of the interpolation variable is xc: x_indices tp_xc yc: y_indices tp_yc
.
dimensions: xc = 30; yc = 10; tp_xc = 4 ; tp_yc = 2 ; variables: // Data variable float Temperature(yc, xc) ; Temperature:standard_name = "air_temperature" ; Temperature:units = "K" ; Temperature:coordinate_interpolation = "lat: lon: bl_interpolation" ; // Interpolation variable char bl_interpolation ; bl_interpolation:interpolation_name = "bi_linear" ; bl_interpolation:tie_point_mapping = "xc: x_indices tp_xc yc: y_indices tp_yc" ; bl_interpolation:computational_precision = "64" ; // tie point coordinate variables double lat(tp_yc, tp_xc) ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ; double lon(tp_yc, tp_xc) ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ; // Tie point index variables int y_indices(tp_yc) ; int x_indices(tp_xc) ; data: x_indices = 0, 9, 19, 29 ; y_indices = 0, 9 ; ...
dimensions: xc = 30; yc = 10; tp_xc = 4 ; variables: // Data variable float Temperature(yc, xc) ; Temperature:standard_name = "air_temperature" ; Temperature:units = "K" ; Temperature:coordinate_interpolation = "lat: lon: l_interpolation" ; // Interpolation variables char l_interpolation ; l_interpolation:interpolation_name = "linear" ; l_interpolation:tie_point_mapping = "xc: x_indices tp_xc" ; l_interpolation:computational_precision = "64" ; // tie point coordinate variables double lat(yc, tp_xc) ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ; double lon(yc, tp_xc) ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ; // Tie point index variables int x_indices(tp_xc) ; data: x_indices = 0, 9, 19, 29 ; ...
8.3.8. Interpolation Parameters
The interpolation variable attribute interpolation_parameters
may be used to provide extra information to the interpolation process.
This attribute names interpolation parameter variables that provide values for coefficient terms in the interpolation equation, or for any other terms that configure the interpolation process.
The interpolation_parameters
attribute takes a string value, the string comprising blankseparated elements of the form "term: variable"
, where term
is a caseinsensitive keyword that defines one of the terms in the interpolation method’s definition given in Appendix J, Coordinate Interpolation Methods, and variable
is the name of the interpolation parameter variable that contains the values for that term.
The order of elements is not significant.
Any numerical term that is specified as optional in Appendix J, Coordinate Interpolation Methods and is omitted from the interpolation_parameters
attribute should be assumed to be zero.
The interpolation_parameters
attribute may only be provided if allowed by the definition of the interpolation method.
Interpolation parameters may always be provided to nonstandardized interpolation methods.
The interpolation parameters are not permitted to contain absolute coordinate information, such as additional tie points, but may contain relative coordinate information, for example an offset with respect to a tie point or with respect to a combination of tie points. This is to ensure that interpolation methods are equally applicable to both coordinate and bounds interpolation.
The interpolation parameter variable dimensions must include, for all of the interpolated dimensions, either the associated subsampled dimension or the associated interpolation subarea dimension. Additionally, any subset of zero or more of the noninterpolated dimensions of the tie point coordinate variable are permitted as interpolation parameter variable dimensions.
The application of an interpolation parameter variable is independent of its noninterpolated dimensions, but depends on its set of subsampled dimensions and interpolation subarea dimensions:

If the set only contains subsampled dimensions, then the variable provides values for every tie point and therefore equally applicable to the interpolation subareas that share that tie point, see example a) in Figure 8.3;

If the set only contains interpolation subarea dimensions, then the variable provides values for every interpolation subarea and therefore only applicable to that interpolation subarea, see example b) in Figure 8.3;

If the set contains both subsampled dimensions and interpolation subarea dimensions, then the variable’s values are to be shared by the interpolation subareas that are adjacent along each of the specified subsampled dimensions. This case is akin to the values being defined at the interpolation subarea boundaries, and therefore equally applicable to the interpolation subareas that share that boundary, see example c) and d) in Figure 8.3;
dimensions : // VIIRS IBand (375 m resolution imaging) track = 1536 ; scan = 6400 ; // Tie points and interpolation subareas tp_track = 96 ; // 48 VIIRS scans tp_scan = 205 ; subarea_track = 48 ; // track interpolation subarea subarea_scan= 200 ; // scan interpolation subarea // Time, stored at scanstart and scanend of each scan tp_time_scan = 2; variables: // VIIRS IBand Channel 04 float I04_radiance(track, scan) ; I04_radiance:coordinate_interpolation = "lat: lon: tp_interpolation t: time_interpolation" ; I04_radiance:standard_name = "toa_outgoing_radiance_per_unit_wavelength" ; I04_radiance:units = "W m2 sr1 m1" ; float I04_brightness_temperature(track, scan) ; I04_brightness_temperature:coordinate_interpolation = "lat: lon: tp_interpolation t: time_interpolation" ; I04_brightness_temperature:standard_name = "brightness_temperature" ; I04_brightness_temperature:units = "K" ; // Interpolation variable char tp_interpolation ; tp_interpolation:interpolation_name = "bi_quadratic_latitude_longitude" ; tp_interpolation:tie_point_mapping = "track: track_indices tp_track subarea_track scan: scan_indices tp_scan subarea_scan" ; tp_interpolation:interpolation_parameters = "ce1: ce1 ca2: ca2 ce3: ce3 interpolation_subarea_flags: interpolation_subarea_flags" ; tp_interpolation:computational_precision = "32" ; // Interpolation parameters short ce1(tp_track , subarea_scan) ; short ca2(subarea_track , tp_scan) ; short ce3(subarea_track, subarea_scan) ; byte interpolation_subarea_flags(subarea_track , subarea_scan) ; interpolation_subarea_flags:valid_range = 1b, 7b ; interpolation_subarea_flags:flag_masks = 1b, 2b, 4b ; interpolation_subarea_flags:flag_meanings = "location_use_3d_cartesian sensor_direction_use_3d_cartesian solar_direction_use_3d_cartesian" ; // Tie point index variables int track_indices(tp_track) ; // shared by tp_interpolation and time_interpolation int scan_indices(tp_scan) ; int time_scan_indices(tp_time_scan) // Tie points float lat(tp_track, tp_scan) ; lat:standard_name = "latitude" ; lat:units = "degrees_north" ; float lon(tp_track, tp_scan) ; lon:standard_name = "longitude" ; lon:units = "degrees_east" ; // Time interpolation variable char time_interpolation ; time_interpolation:interpolation_name = "bi_linear" ; time_interpolation:tie_point_mapping = "track: track_indices tp_track scan: time_scan_indices tp_time_scan" ; time_interpolation:computational_precision = "64" ; // Time tie points double t(tp_track, tp_time_scan) ; t:standard_name = "time" ; t:units = "days since 199011 0:0:0" ;
This example demonstrates the use of multiple interpolation variables, the reusability of the interpolation variable between data variables of different dimensions and the use of the interpolation parameter attribute.
dimensions: y = 228; x = 306; time = 41; // Tie point dimensions tp_y = 58; tp_x = 52; variables: // Data variable float Temperature(time, y, x) ; Temperature:standard_name = "air_temperature" ; Temperature:units = "K" ; Temperature:grid_mapping = "lambert_conformal" ; Temperature:coordinate_interpolation = "lat: lon: bi_linear x: linear_x y: linear_y" ; int lambert_conformal ; lambert_conformal:grid_mapping_name = "lambert_conformal_conic" ; lambert_conformal:standard_parallel = 25.0 ; lambert_conformal:longitude_of_central_meridian = 265.0 ; lambert_conformal:latitude_of_projection_origin = 25.0 ; // Interpolation variables char bi_linear ; bi_linear:interpolation_name = "bi_linear" ; bi_linear:tie_point_mapping = "y: y_indices tp_y x: x_indices tp_x" ; bi_linear:computational_precision = "64" ; char linear_x ; linear_x:interpolation_name = "linear" ; linear_x:tie_point_mapping = "x: x_indices tp_x" ; linear_x:computational_precision = "64" ; char linear_y ; linear_y:interpolation_name = "linear" ; linear_y:tie_point_mapping = "y: y_indices tp_y" ; linear_y:computational_precision = "64" ; // tie point coordinate variables double time(time) ; time:standard_name = "time" ; time:units = "days since 20210301" ; double y(time, tp_y) ; y:units = "km" ; y:standard_name = "projection_y_coordinate" ; double x(time, tp_x) ; x:units = "km" ; x:standard_name = "projection_x_coordinate" ; double lat(time, tp_y, tp_x) ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ; double lon(time, tp_y, tp_x) ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ; // Tie point index variables int y_indices(tp_y) ; y_indices:long_name = "Mapping of y dimension to its ", "corresponding tie point dimension" ; int x_indices(tp_x) ; x_indices:long_name = "Mapping of x dimension to its ", "corresponding tie point dimension" ;
In this the projection coordinates are twodimensional, but are only linearly interpolated in one of their dimensions  the one which is given by the tie_point_mapping
attribute.
8.3.9. Interpolation of Cell Boundaries
Coordinates may have cell bounds. For the case that the reconstituted cells are contiguous and have exactly two cell bounds along each interpolated dimension, cell bounds of interpolated dimensions can be stored as bounds tie points and reconstituted through interpolation. In this process, the coordinate tie points are a prerequisite for the bounds tie points and the same interpolation method used for the coordinate interpolation is used for the bounds interpolation.
For the reconstituted coordinates, cell bounds are stored separately for each coordinate point, as shown in the left part of Figure 8.4 for the example of 2D bounds. Since the cell bounds are contiguous, bounds points of adjacent cells will coincide and so the full set of bounds points may be represented as a grid, comparable to the coordinate points grid. In the middle part of Figure 8.4, both the reconstituted bounds points grid and the reconstituted coordinate points grid are shown for a continuous area, where each bounds point may be shared by up to four cells.
Bounds interpolation uses the same tie point index variables and therefore the same tie point cells as coordinate interpolation. One of the vertices of each coordinate tie point cell is chosen as the bounds tie point for the cell. It is selected as the vertex of the tie point cell that is the closest to the boundary of the interpolation subarea with respect to each interpolated dimension. For the example of 2D bounds, the resulting set of bounds tie points are marked in Figure 8.4, where the selected vertices are those closest to the corners of the interpolation subareas.
Note that within a continuous area, there is one more reconstituted bounds point than there are reconstituted coordinate points in each dimension. For this reason, a virtual interpolated bounds dimension is introduced for each dimension, having a size equal to the size of the interpolated dimension plus one. This dimension is used for solely descriptive purposes, and is not required in a compressed dataset.
Both the process of compressing bounds and the process of uncompressing bounds requires the steps to be carried out for a full continuous area, however, individual continuous areas can be processed independently. In the following description of these processes, indices relative to the origin of each continuous area are used for the interpolated dimension and the interpolated bounds dimension. Consequently, for both coordinate tie points and bounds tie points, the first point in index space of the continuous area has got index 0 in all the interpolated dimensions and interpolated bounds dimensions, respectively.
Note that the numbering of the bounds B0
, B1
, etc, in this section is identical to the numbering in Section 7.1, "Cell Boundaries".
A bounds tie point is located in the same interpolation subarea as its corresponding coordinate tie point. The interpolation subareas do not overlap, ensuring that each bound point is computed from a unique interpolation subarea, see also the description of interpolation subareas in Section 8.3.1, "Tie Points and Interpolation Subareas". That bounds are computed only once ensures that the reconstituted bounds are contiguous.
For the generation of bounds tie points as part of the process of compressing bounds, the indices of the corresponding coordinate tie points are available in the tie point index variables, see Section 8.3.7, "Tie Point Index Mapping".
Compressing onedimensional coordinate bounds
In the onedimensional case, a coordinate point at index i
in the interpolated dimension will be bounded by the two bounds:
B0 = (n0) = (i) B1 = (n1) = (i+1)
where n
is the bound index in the interpolated bound dimension.
For onedimensional bound interpolation, an interpolation subarea is defined by two bounds tie points.
The full set of bounds tie points is formed by appending, for each continuous area of the domain, the bound point B0
of the first coordinate tie points of the continuous area, followed by the bound points B1
of all subsequent coordinate tie point of the continuous area.
Compressing twodimensional coordinate bounds
In the twodimensional case, a coordinate point at indices (j, i)
in the interpolated dimension will be bounded by the four bounds:
B0 = (n0, m0) = (j, i) B1 = (n1, m1) = (j, i+1) B3 = (n3, m3) = (j+1, i) B2 = (n2, m2) = (j+1, i+1)
where (n, m)
are the bounds point indices in the interpolated bound dimensions.
For twodimensional bound interpolation, an interpolation subarea is defined by four bounds tie points.
The full set of bounds tie points is formed by appending, for each continuous area of the domain, the bound point B0
of the coordinate tie point at origin the of the continuous area (0, 0)
, followed by the bound points B1
of all remaining coordinate tie point of the continuous area with index j = 0
, followed by the bound points B3
of all remaining coordinate tie point of the continuous area with index i = 0
, followed by the bound points B2
of all remaining coordinate tie point of the continuous area.
Bounds Tie Point Attribute and Bounds Tie Point Variable
A bounds_tie_points
attribute must be defined for each tie point coordinate variable corresponding to reconstituted coordinates with cell boundaries.
It is a single word of the form “bounds_tie_point_variable” that identifies a bounds tie point variable, containing a bounds tie point coordinate value for each tie point stored in its tie point coordinate variable, and therefore the bounds tie point variable has the same set of dimensions as its tie point coordinate variable.
An example of the usage of the bounds_tie_points
is shown in Interpolation of 2D Cell Boundaries corresponding to Figure 8.4.
Since a bounds tie point variable is considered to be part of a tie point coordinate variable’s metadata, it is not necessary to provide it with attributes such as long_name and units, following the same rules as for the bounds of an uncompressed coordinate variable, see Section 7.1, "Cell Boundaries".
Uncompressing coordinate bounds
The reconstitution of the full set of bounds from the bounds tie point is a twostep process.
In a first step, which must be carried out for a full continuous area at a time, each bound point is reconstituted by interpolation between the bounds tie points within each interpolation subarea, using the same interpolation method as defined for the ordinary tie points.
This step results in a grid of bound points spanning the interpolated bound dimensions.
In a second step the reconstituted bounds vertices are replicated to the boundary variables of the reconstituted coordinates.
Uncompressing onedimensional coordinate bounds
For onedimensional coordinate bounds, in the second step of the process, for each index i
of the interpolated dimension, the two bounds of the boundary variable are set to the value of the interpolated bounds point grid at the indices B0
and B1
, respectively, where the indices are defined above under "Compressing onedimensional coordinate bounds".
Uncompression of twodimensional coordinate bounds
For twodimensional coordinate bounds, in the second step of the process, for each index pair (j, i)
of the interpolated dimension, the four bounds of the boundary variable is set to the value of the interpolated bounds point grid at index pairs B0
, B1
, B2
and B3
, respectively, where the index pairs are defined above under "Compressing twodimensional coordinate bounds".
dimensions: ic = 10; itp = 3; jc = 10; jtp = 3; variables: // Data variable float Temperature(jc, ic) ; Temperature:standard_name = "air_temperature" ; Temperature:units = "K" ; Temperature:coordinate_interpolation = "lat: lon: bl_interpolation" ; // Interpolation variable char bl_interpolation ; bl_interpolation:interpolation_name = "bi_linear" ; bl_interpolation:tie_point_mapping = "ic: i_indices itp jc: j_indices jtp" ; bl_interpolation:computational_precision = "64" ; // Tie point index variables int i_indices(itp) ; int j_indices(jtp) ; // Tie point coordinate variables double lat(jtp, itp) ; lat:units = "degrees_north" ; lat:standard_name = "latitude" ; lat:bounds_tie_points = "lat_bounds" ; double lon(jtp, itp) ; lon:units = "degrees_east" ; lon:standard_name = "longitude" ; lon:bounds_tie_points = "lon_bounds" ; // Bounds tie point variables double lat_bounds(jtp, itp) ; double lon_bounds(jtp, itp) ;
8.3.10. Interpolation Method Implementation
The accuracy of the reconstituted coordinates depends mainly on the degree of subsampling and the choice of interpolation method, both of which are set by the creator of the dataset. The accuracy and reproducibility will also depend, however, on how the interpolation method is implemented and on the computer platform carrying out the computations. To facilitate a good level of reproducibility of the processes of compressing and uncompressing coordinates, requirements are placed on the specification of interpolation methods and on stating the computational precision.
Interpolation Method Specification
The interpolation method specifications provided in Appendix J, Coordinate Interpolation Methods are complete in their description of steps and formulas required for compressing and uncompressing coordinate data. Formulas are structured in a way that encourages an efficient implementation of the interpolation method in a highlevel programming language.
For instance, expressions that are constant within a computational loop should be externalised from that loop.
Computational Precision Attribute
The data creator shall specify the floatingpoint arithmetic precision used during the preparation and validation of the compressed coordinates by setting the interpolation variable’s computational_precision
attribute to one of the following values:
Value 
Description 
"32" 
32bit floatingpoint arithmetic, comparable to the binary32 standard in [[IEEE_754]] 
"64" 
64bit floatingpoint arithmetic, comparable to the binary64 standard in [[IEEE_754]] 
Using the given computational precision in the interpolation computations is a necessary, but not sufficient, condition for the data user to be able to reconstitute the coordinates to an accuracy comparable to that intended by the data creator.
For instance, a computational_precision
value of "64"
would specify that, using the same implementation and hardware as the creator of the compressed dataset, sufficient accuracy could not be reached when using a floatingpoint precision lower than 64bit floatingpoint arithmetic in the interpolation computations required to reconstitute the coordinates.
9. Discrete Sampling Geometries
This chapter provides representations for discrete sampling geometries, such as time series, vertical profiles and trajectories. Discrete sampling geometry datasets are characterized by a dimensionality that is lower than that of the spacetime region that is sampled; discrete sampling geometries are typically “paths” through spacetime.
9.1. Features and feature types
Each type of discrete sampling geometry (point, time series, profile or trajectory) is defined by the relationships among its spatiotemporal coordinates. We refer to the type of discrete sampling geometry as its featureType. The term “ feature ” refers herein to a single instance of the discrete sampling geometry (such as a single time series). The representation of such features in a CF dataset was supported previous to the introduction of this chapter using a particular convention, which is still supported (that described by section 9.3.1). This chapter describes further conventions which offer advantages of efficiency and clarity for storing a collection of features in a single file. When using these new conventions, the features contained within a collection must always be of the same type; and all the collections in a CF file must be of the same feature type. (Future versions of CF may allow mixing of multiple feature types within a file.) Table 9.1 presents the feature types covered by this chapter. Details and examples of storage of each of these feature types are provided in Appendix H, as indicated in the table.
featureType  Description of a single feature with this discrete sampling geometry  Link  

Form of a data variable containing values defined on a collection of these features 
Mandatory spacetime coordinates for a collection of these features 

point 
a single data point (having no implied coordinate relationship to other points) 

data(i) 
x(i) y(i) t(i) 

timeSeries 
a series of data points at the same spatial location with time values in strict monotonically increasing order 

data(i,o) 
x(i) y(i) t(i,o) 

trajectory 
a series of data points along a path through space with time values in strict monotonically increasing order 

data(i,o) 
x(i,o) y(i,o) t(i,o) 

profile 
an ordered set of data points along a vertical line at a fixed horizontal position and fixed time 

data(i,o) 
x(i) y(i) z(i,o) t(i) 

timeSeriesProfile 
a series of profile features at the same horizontal position with time values in strict monotonically increasing order 

data(i,p,o) 
x(i) y(i) z(i,p,o) t(i,p) 

trajectoryProfile 
a series of profile features located at points ordered along a trajectory 

data(i,p,o) 
x(i,p) y(i,p) z(i,p,o) t(i,p) 
Table 9.1. Logical structure and mandatory coordinates for discrete sampling geometry featureTypes. Other spacetime coordinates may be included which are not mandatory.
In Table 9.1 the spatial coordinates x and y typically refer to longitude and latitude but other horizontal coordinates could also be used (see sections 4 and 5.6).
The spatial coordinate z refers to vertical position.
The time coordinate is indicated as t.
The spacetime coordinates that are indicated for each feature are mandatory.
However a featureType may also include other spacetime coordinates which are not mandatory (notably the z coordinate, and for instance a forecast_reference_time
coordinate in addition to a mandatory time coordinate).
The array subscripts that are shown illustrate only the logical structure of the data.
The subscripts found in actual CF files are determined by the specific type of representations (see section 9.3).
The designation of dimensions as mandatory precludes the encoding of data variables where geopositioning cannot be described as a discrete point location. Problematic examples include:

time series that refer to a geographical region (e.g. the northern hemisphere), a volume (e.g. the troposphere), or a geophysical quantity in which geolocation information is inherent (e.g. the Southern Oscillation Index (SOI) is the difference between values at two point locations);

vertical profiles that similarly represent geographically areaaveraged values; and

paths in space that indicate a geographically located feature, but lack a suitable time coordinate (e.g. a meteorological front).
Future versions of CF will generalize the concepts of geolocation to encompass these cases. As of CF version 1.6 such data can be stored using the representations that are documented here by two means: 1) by utilizing the orthogonal multidimensional array representation and omitting the featureType attribute; or 2) by assigning arbitrary coordinates to the mandatory dimensions. For example a globallyaveraged latitude position (90s to 90n) could be represented arbitrarily (and poorly) as a latitude position at the equator.
9.2. Collections, instances and elements
In Table 9.1 the dimension with subscript i identifies a particular feature within a collection of features. It is called the instance dimension. Onedimensional variables in a Discrete Geometry CF file, which have only this dimension (such as x(i), y(i) and z(i) for a timeseries), are instance variables. Instance variables provide the metadata that differentiates individual features.
The subscripts o and p distinguish the data elements that compose a single feature. For example in a collection of timeSeries features, each time series instance, i, has data values at various times, o. In a collection of profile features, the subscript, o, provides the index position along the vertical axis of each profile instance. We refer to data values in a feature as its elements, and to the dimensions of o and p as element dimensions. Each feature can have its own set of element subscripts o and p. For instance, in a collection of timeSeries features, each individual timeSeries can have its own set of times. The notation t(i,o) means there is a set of times with subscripts o for the elements of each feature i. Feature instances within a collection need not have the same numbers of elements. If the features do all have the same number of elements, and the sequence of element coordinates is identical for all features, savings in simplicity and space are achievable by storing only one copy of these coordinates. This is the essence of the orthogonal multidimensional representation (see section 9.3.1).
If there is only a single feature to be stored in a data variable, there is no need for an instance dimension and it is permitted to omit it. The data will then be onedimensional, which is a special (degenerate) case of the multidimensional array representation. The instance variables will be scalar coordinate variables; the data variable and other auxiliary coordinate variables will have only an element dimension and not have an instance dimension, e.g. data(o) and t(o) for a single timeSeries.
9.3. Representations of collections of features in data variables
The individual features within a collection need not necessarily contain the same number of elements. For instance observed in situ time series will commonly contain unique numbers of time points, reflecting different deployment dates of the instruments. Other data sources, such as the output of numerical models, may commonly generate features of identical size. CF offers multiple representations to allow the storage to be optimized for the character of the data. Four types of representation are utilized in this chapter:

two multidimensional array representations, in which each feature instance is allocated the identical amount of storage space. In these representations the instance dimension and the element dimension(s) are distinct CF coordinate axes (typical of coordinate axes discussed in chapter 4); and

two ragged array representations, in which each feature is provided with the minimum amount of space that it requires. In these representations the instances of the individual features are stacked sequentially along the same array dimension as the elements of the features; we refer to this combined dimension as the sample dimension.
In the multidimensional array representations, data variables have both an instance dimension and an element dimension. The dimensions may be given in any order. If there is a need for either the instance or an element dimension to be the netCDF unlimited dimension (so that more features or more elements can be appended), then that dimension must be the outer dimension of the data variable i.e. the leading dimension in CDL.
In the ragged array representations, the instance dimension (i
), which sequences the individual features within the collection, and the element dimension, which sequences the data elements of each feature (o
and p
), both occupy the same dimension (the sample dimension).
If the sample dimension is the netCDF unlimited dimension, new data can be appended to the file.
In all representations, the instance dimension (which is also the sample dimension in ragged representations) may be set initially to a size that is arbitrarily larger than what is required for the features which are available at the time that the file is created. Allocating unused array space in this way (prefilled with missing values — see also section 9.6, Missing data), can be useful as a means to reserve space that will be available to add features at a later time.
9.3.1. Orthogonal multidimensional array representation
The orthogonal multidimensional array representation, the simplest representation, can be used if each feature instance in the collection has identical coordinates along the element axis of the features. For example, for a collection of the timeSeries that share a common set of times, or a collection of profiles that share a common set of vertical levels, this is likely to be the natural representation to use. In both examples, there will be longitude and latitude coordinate variables, x(i), y(i), that are onedimensional and defined along the instance dimension.
Table 9.2 illustrates the storage of a data variable using the orthogonal multidimensional array representation. The data variable holds a collection of 4 features. The individual features, distinguished by color, are sequenced along the horizontal axis by the instance dimension indices, i1, i2, i3, i4. Each instance contains three elements, sequenced along the vertical with element dimension indices, o1, o2, o3. The i and o subscripts would be interchanged (i.e. Table 9.2 would be transposed) if the element dimension were the netCDF unlimited dimension.
(i1, o1) 
(i2, o1) 
(i3, o1) 
(i4, o1) 
(i1, o2) 
(i2, o2) 
(i3, o2) 
(i4, o2) 
(i1, o3) 
(i2, o3) 
(i3, o3) 
(i4, o3) 
Table 9.2 The storage of a data variable using the orthogonal multidimensional array representation (subscripts in CDL order).
The instance variables of a dataset corresponding to Table 9.2 will be onedimensional with size 4 (for example, the latitude locations of timeSeries),
lat(i1) 
lat(i2) 
lat(i3) 
lat(i4) 
and the element coordinate axis will be onedimensional with size 3 (for example, the time
time(o1) 
time(o2) 
time(o3) 
coordinates that are shared by all of the timeSeries). This representation is consistent with the multidimensional fields described in chapter 5; the characteristic that makes it atypical from chapter 5 (though not incompatible) is that the instance dimension is a discrete axis (see section 4.5).
9.3.2. Incomplete multidimensional array representation
The incomplete multidimensional array representation can used if the features within a collection do not all have the same number of elements, but sufficient storage space is available to allocate the number of elements required by the longest feature to all features. That is, features that are shorter than the longest feature must be padded with missing values to bring all instances to the same storage size. This representation sacrifices storage space to achieve simplicity for reading and writing.
Table 9.3 illustrates the storage of a data variable using the orthogonal multidimensional array representation. The data variable holds a collection of 4 features. The individual features, distinguished by color, are sequenced by the instance dimension indices, i1, i2, i3, i4. The instances contain respectively 2, 4, 3 and 6 elements, sequenced by the element dimension index with values of o1, o2, o3, … . The i and o subscripts would be interchanged (i.e. Table 9.3 would be transposed) if the element dimension were the netCDF unlimited dimension.
(i1, o1) 
(i2, o1) 
(i3, o1) 
(i4, o1) 
(i1, o2) 
(i2, o2) 
(i3, o2) 
(i4, o2) 
(i2, o3) 
(i3, o3) 
(i4, o3) 

(i2, o4) 
(i4, o4) 

(i4, o5) 

(i4, o6) 
Table 9.3. The storage of data using the incomplete multidimensional array representation (subscripts in CDL order).
9.3.3. Contiguous ragged array representation
The contiguous ragged array representation can be used only if the size of each feature is known at the time that it is created. In this representation the data for each feature will be contiguous on disk, as shown in Table 9.4.
(i1, o1) 
(i1, o2) 
(i2, o1) 
(i2, o2) 
(i2, o3) 
(i2, o4) 
(i3, o1) 
(i3, o2) 
(i3, o3) 
(i4, o1) 
(i4, o2) 
(i4, o3) 
(i4, o4) 
(i4, o5) 
(i4, o6) 
Table 9.4. The storage of data using the contiguous ragged representation (subscripts in CDL order).
In this representation, the file contains a count variable, which must be an integer type and
count(i1) 
count(i2) 
count(i3) 
count(i4) 
2 
4 
3 
6 
must have the instance dimension as its sole dimension.
The count variable contains the number of elements that each feature has.
This representation and its count variable are identifiable by the presence of an attribute, sample_dimension
, found on the count variable, which names the sample dimension being counted.
For indices that correspond to features, whose data have not yet been written, the count variable should have a value of zero or a missing value.
9.3.4. Indexed ragged array representation
The indexed ragged array representation stores the features interleaved along the sample dimension in the data variable as shown in Table 9.4. The canonical use case for this representation is the storage of realtime data streams that contain reports from many sources; the data can be written as it arrives.
(i1, o1) 

0 
(i2, o1) 
1 

(i3, o1) 
2 

(i4, o1) 
3 

(i4, o2) 
3 

(i2, o2) 
1 

(i4, o3) 
3 

(i4, o4) 
3 

(i1, o2) 
0 

(i2, o3) 
1 

(i3, o2) 
2 

(i4, o5) 
3 

(i3, o3) 
2 

(i2, o4) 
1 

(i4, o6) 
3 
Table 9.4 The storage of data using the indexed ragged representation (subscripts in CDL order). The left hand side of the table illustrates a data variable; the right hand side of the table contains the values of the index variable.
In this representation, the file contains an index variable, which must be an integer type, and must have the sample dimension as its single dimension.
The index variable contains the zerobased index of the feature to which each element belongs.
This representation is identifiable by the presence of an attribute, instance_dimension
, on the index variable, which names the dimension of the instance variables.
For those indices of the sample dimension, into which data have not yet been written, the index variable should be prefilled with missing values.
9.4. The featureType attribute
A global attribute, featureType, is required for all Discrete Geometry representations except the orthogonal multidimensional array representation, for which it is highly recommended.
The exception is allowed for backwards compatibility, as discussed in 9.3.1.
A Discrete Geometry file may include arbitrary numbers of data variables, but (as of CF v1.6) all of the data variables contained in a single file must be of the single feature type indicated by the global featureType
attribute, if it is present.1 The value assigned to the featureType
attribute is caseinsensitive; it must be one of the string values listed in the left column of Table 9.1.
9.5. Coordinates and metadata
Every feature within a Discrete Geometry CF file must be unambiguously associated with an extensible collection of instance variables that identify the feature and provide other metadata as needed to describe it.
Every element of every feature must be unambiguously associated with its space and time coordinates and with the feature that contains it.
The coordinates
attribute must be attached to every data variable to indicate the spatiotemporal coordinate variables that are needed to geolocate the data.
Where feasible, one of the coordinate or auxiliary coordinate variables of a discrete sampling geometry should have an attribute named cf_role
, whose only permitted values for this purposes are timeseries_id
, profile_id
, and trajectory_id
.
(Despite its generalsounding name, this attribute only one other function, namely in Section 5.9, "Mesh Topology Variables".)
The variable carrying the cf_role
attribute may have any data type.
When a variable is assigned this attribute, it must provide a unique identifier for each feature instance.
CF files that contain timeSeries, profile or trajectory featureTypes, should include only a single occurrence of a cf_role
attribute; CF files that contain timeSeriesProfile or trajectoryProfile may contain two occurrences, corresponding to the two levels of structure in these feature types.
It is not uncommon for observational data to have two sets of coordinates for particular coordinate axes of a feature: a nominal point location and a more precise location that varies with the elements in the feature. For example, although an idealized vertical profile is measured at a fixed horizontal position and time, a realistic representation might include the time variations and horizontal drift that occur during the duration of the sampling. Similarly, although an idealized time series exists at a fixed latlong position, a realistic representation of a moored ocean time series might include the “watch cycle” excursions of horizontal position that occur as a result of tidal currents.
CF Discrete Geometries provides a mechanism to encode both the nominal and the precise positions, while retaining the semantics of the idealized feature type.
Only the set of coordinates which are regarded as the nominal (default or preferred) positions should be indicated by the attribute axis
, which should be assigned string values to indicate the orientations of the axes (X
, Y
, Z
, or T
).
See A single timeseries with timevarying deviations from a nominal point spatial location (a single timeseries with timevarying deviations from a nominal point spatial location):
Auxiliary coordinate variables containing the nominal and the precise positions should be listed in the relevant coordinates
attributes of data variables.
In orthogonal representations the nominal positions could be coordinate variables, which do not need to be listed in the coordinates
attribute, rather than auxiliary coordinate variables.
Coordinate bounds may optionally be associated with coordinate variables and auxiliary coordinate variables using the bounds attribute, following the conventions described in section 7.1. Coordinate bounds are especially important for accurate representations of model output data using discrete geometry representations; they record the boundaries of the model grid cells.
If there is a vertical coordinate variable or auxiliary coordinate variable, it must be identified by the means specified in section 4.3.
The use of the attribute axis=Z
is recommended for clarity.
A standard_name
attribute (see section 3.3) that identifies the vertical coordinate is recommended, e.g. "altitude", "height", etc.
(See the CF Standard Name Table).
9.6. Missing Data
In data for discrete sampling geometries written according to the rules of this section, wherever there are unused elements in data storage, the data variable and all its auxiliary coordinate variables (spatial and time) must contain missing values. This situation may arise for the incomplete multidimensional array representation, and in any representation if the instance dimension is set to a larger size than the number of features currently stored. Data variables should (as usual) also contain missing values to indicate when there is no valid data available for the element, although the coordinates are valid.
Similarly, for indices where the instance variable identified by cf_role
contains a missing value indicator, all other instance variables should also contain missing values.
Appendix A: Attributes
All CF attributes are listed here except for those that are used to describe grid mappings and mesh topologies. See Appendix F, Grid Mappings for the grid mapping attributes, and Appendix K, Mesh Topology Attributes for mesh topology attributes.
The "Type" values are S for string, N for numeric, and D for the type of the data variable. Each attribute may be used in any of the ways shown in its "Use" entry. G indicates it can appear as a global attribute, and Gr as a group attribute. For variable attributes, the possible values of "Use" are: C for variables containing coordinate data, D for data variables, M for geometry container variables, Do for domain variables, BI and BO for boundary variables (see Section 7.1, "Cell Boundaries" for the distinction between BI and BO), and  for variables with some other purpose. CF does not prohibit any of these attributes from being attached to variables of different kinds from those listed as their "Use" in this table, but their meanings are not defined by CF if they are used in these other ways. "Links" indicates the location of the attribute"s original definition (first link) and sections where the attribute is discussed in this document (additional links as necessary).
Attribute  Type  Use  Links  Description 


N 
C, D, BO 
Section 2.5.1, "Missing data, valid and actual range of data" 
The smallest and the largest valid nonmissing values occurring in the variable. 

N 
C, D, BO 
NUG Appendix A, "Attribute Conventions", and Section 8.1, "Packed Data" 
If present for a variable, this number is to be added to the data after it is read by an application.
If both 

S 
D 
Identifies a variable that contains closely associated data, e.g., the measurement uncertainties of instrument data. 


S 
C, BI 
Identifies latitude, longitude, vertical, or time axes. 


S 
C 
Identifies a boundary variable. 


S 
C, BI 
Calendar used for encoding time axes. 


S 
D, Do 
Identifies variables that contain cell areas or volumes. 


S 
D 
Section 7.3, "Cell Methods", Section 7.4, "Climatological Statistics" 
Records the method used to derive data that represents cell values. 

S 
C, BI 
Identifies the roles of variables that identify features in discrete sampling geometries. Identifies the roles of mesh topology and location index set variables (see Appendix K, Mesh Topology Attributes). 


S 
C 
Identifies a climatology variable. 


S 
G, C, D 
Miscellaneous information about the data or methods used to produce it. 


S 
C 
Section 8.2, "Lossless Compression by Gathering", Section 5.3, "Reduced Horizontal Grid" 
Records dimensions which have been compressed by gathering. 

S 
C, BI 
Indicates the standard name, from the standard name table, of the computed vertical coordinate values, computed according to the formula in the definition. 


S 
G 
Name of the conventions followed by the dataset. 


S 
D, Do 
Indicates that coordinates have been compressed by sampling and identifies the tie point coordinate variables and their associated interpolation variables. 


S 
D, M, Do 
Chapter 5, Coordinate Systems and Domain, Section 6.1, "Labels", Section 6.2, "Alternative Coordinates" 
Identifies auxiliary coordinate variables, label variables, and alternate coordinate variables. 

S 
Do 
Identifies the dimensions that define a domain variable. 


S 
G 
Section 2.6.3, "External variables", Section 7.2, "Cell Measures" 
Identifies variables which are named by 

D 
C, D, BO 
NUG Appendix A, "Attribute Conventions", and Section 2.5.1, "Missing data, valid and actual range of data", and Section 9.6, "Missing Data". 
A value used to represent missing or undefined data. Allowed for auxiliary coordinate variables but not allowed for coordinate variables. 

S 
G 
Specifies the type of discrete sampling geometry to which the data in the scope of this attribute belongs, and implies that all data variables in the scope of this attribute contain collections of features of that type. 


D 
D 
Provides a list of bit fields expressing Boolean or enumerated flags. 


S 
D 
Use in conjunction with 


D 
D 
Provides a list of the flag values.
Use in conjunction with 


S 
C, BO 
Identifies variables that correspond to the terms in a formula. 


S 
C, D, Do 
Identifies a variable that defines geometry. 


S 
M 
Indicates the type of geometry present. 


S 
D, M, Do 
Section 5.6, "Horizontal Coordinate Reference Systems, Grid Mappings, and Projections" 
Identifies a variable that defines a grid mapping. 

S 
G, Gr 
List of the applications that have modified the original data. 


S 
 
Section 9.3, "Representations of collections of features in data variables" 
An attribute which identifies an index variable and names the instance dimension to which it applies. The index variable indicates that the indexed ragged array representation is being used for a collection of features. 

S 
G, D 
Where the original data was produced. 


S 
M 
Identifies a variable that indicates if polygon parts are interior rings (i.e., holes) or not. 


N 
C, BI 
Specifies which month is lengthened by a day in leap years for a user defined calendar. 


N 
C, BI 
Provides an example of a leap year for a user defined calendar. It is assumed that all years that differ from this year by a multiple of four are also leap years. 


S 
D, Do 
Section 5.9, "Mesh Topology Variables", and Appendix K, Mesh Topology Attributes 
Specifies the location type within the mesh topology at which the variable is defined. 

S 
D, Do 
Section 5.9, "Mesh Topology Variables", and Appendix K, Mesh Topology Attributes 
Specifies a variable that defines the subset of locations of a mesh topology at which the variable is defined. 

S 
C, D, Do, BI 
NUG Appendix A, "Attribute Conventions", and Section 3.2, "Long Name" 
A descriptive name that indicates a variable’s content. This name is not standardized. 

S 
D, Do 
Section 5.9, "Mesh Topology Variables", and Appendix K, Mesh Topology Attributes 
Specifies a variable that defines a mesh topology. 

D 
C, D, BO 
Section 2.5.1, "Missing data, valid and actual range of data", and Section 9.6, "Missing Data" 
A value or values used to represent missing or undefined data. Allowed for auxiliary coordinate variables but not allowed for coordinate variables. 

N 
C, BI 
Specifies the length of each month in a nonleap year for a user defined calendar. 


S 
M 
Identifies variables that contain geometry node coordinates. 


S 
M 
Identifies a variable indicating the count of nodes per geometry. 


S 
C 
Identifies a coordinate node variable. 


S 
M 
Identifies a variable providing the count of nodes per geometry part. 


S 
C, BI 
Direction of increasing vertical coordinate value. 


S 
G, D 
References that describe the data or methods used to produce it. 


S 
 
Section 9.3, "Representations of collections of features in data variables" 
An attribute which identifies a count variable and names the sample dimension to which it applies. The count variable indicates that the contiguous ragged array representation is being used for a collection of features. 

N 
C, D, BO 
NUG Appendix A, "Attribute Conventions", and Section 8.1, "Packed Data" 
If present for a variable, the data are to be multiplied by this factor after the data are read by an application.
See also the 

S 
G, D 
Method of production of the original data. 


N 
D 
If a data variable with a standard_name modifier of standard_error has this attribute, it indicates that the values are the stated multiple of one standard error. 


S 
C, D, BI 
A standard name that references a description of a variable"s content in the standard name table. 


S 
G, Gr 
Short description of the file contents. 


S 
C, D, BI 
NUG Appendix A, "Attribute Conventions", and Section 3.1, "Units" 
Units of a variable’s content. 

S 
C, D, BI 
Specifies the interpretation (onscale, difference or unknown) of the unit of temperature appearing in the 


N 
C, D, BO 
Largest valid value of a variable. 


N 
C, D, BO 
Smallest valid value of a variable. 


N 
C, D, BO 
Smallest and largest valid values of a variable. 
Appendix B: Standard Name Table Format
The CF standard name table is an XML document (i.e., its format adheres to the XML 1.0 [XML] recommendation). The XML suite of protocols provides a reasonable balance between human and machine readability. It also provides extensive support for internationalization. See the W3C [W3C] home page for more information.
The document begins with a header that identifies it as an XML file:
<?xml version="1.0"?>
Next is the standard_name_table
itself, which is bracketed by the tags <standard_name_table>
and </standard_name_table>
.
The opening tag has two attributes: xmlns:xsi
that provides a link to the standard XML namespace, and xsi:noNamespaceSchemaLocation
that provides a link to the file that provides the XML schema rules for the content of the Standard Name Table XML file.
<standard_name_table xmlns:xsi="https://www.w3.org/2001/XMLSchemainstance" xsi:noNamespaceSchemaLocation="https://cfconventions.org/Data/schemafiles/cfstandardnametable2.0.xsd">
The content (delimited by the <standard_name_table>
tags) consists of, in order,
<version_number>Version number here ... </version_number> <conventions>Conventions string here ... </conventions> <first_published>Datetime of first publication to the website ... </first_published> <last_modified>Datetime stamp here ... </last_modified> <institution>Name of institution here ... </institution> <contact>Email address of contact person ... </contact>
where the "Conventions string" is composed of the fixed string CFStandardNameTable
immediately followed by the version number.
Next follows a sequence of entry
elements which may optionally be followed by a sequence of alias
elements.
The entry
and alias
elements take the following forms:
<entry id="an_id"> Define the variable whose standard_name attribute has the value "an_id". </entry> <alias id="another_id"> Provide alias for a variable whose standard_name attribute has the value "another_id". </alias>
The value of the id
attribute appearing in the entry
and alias
tags is a case sensitive string, containing no whitespace, which uniquely identifies the entry relative to the table.
This is the value used for a variable’s standard_name
attribute.
The purpose of the entry
elements are to provide definitions for the id
strings.
Each entry
element contains the following elements:
<entry id="an_id"> <canonical_units>Representative units for the variable ... </canonical_units> <description>Description of the variable ... </description> </entry>
Entry
elements may optionally also contain the following elements:
<grib>GRIB parameter code</grib> <amip>AMIP identifier string</amip>
Not all variables have equivalent AMIP or GRIB codes.
ECMWF GRIB codes start with E
, NCEP codes with N
.
Standard codes (in the range 1127) are not prefaced.
When a variable has more than one equivalent GRIB code, the alternatives are given as a blankseparated list.
The alias
elements do not contain definitions.
Rather they contain the value of the id
attribute of an entry
element that contains the sought after definition.
The purpose of the alias
elements are to provide a means for maintaining the table in a backwards compatible fashion.
For example, if more than one id
string was found to correspond to identical definitions, then the redundant definitions can be converted into aliases.
It is not intended that the alias
elements be used to accommodate the use of local naming conventions in the standard_name
attribute strings.
Each alias
element contains a single element:
<alias id="an_id"> <entry_id>Identifier of the defining entry ... </entry_id> </alias>
In exceptional cases the alias
element may contain two elements:
<alias id="an_id"> <entry_id>Identifier of a defining entry ... </entry_id> <entry_id>Identifier of another defining entry ... </entry_id> </alias>
<?xml version="1.0"?> <standard_name_table xmlns:xsi="https://www.w3.org/2001/XMLSchemainstance" xsi:noNamespaceSchemaLocation= "http://cf.conventions.org/Data/schemafiles/cfstandardnametable2.0.xsd"> <version_number>83</version_number> <conventions>CFStandardNameTable83</conventions> <first_published>20231017T15:09:35Z</first_published> <last_modified>20231017T15:09:35Z</last_modified> <institution>Program for Climate Model Diagnosis and Intercomparison</institution> <contact>support@pcmdi.llnl.gov</contact> <entry id="surface_air_pressure"> <canonical_units>Pa</canonical_units> <grib>E134</grib> <amip>ps</amip> <description> The surface called "surface" means the lower boundary of the atmosphere. </description> </entry> <entry id="air_pressure_at_sea_level"> <canonical_units>Pa</canonical_units> <grib>2 E151</grib> <amip>psl</amip> <description> Air pressure at sea level is the quantity often abbreviated as MSLP or PMSL. sea_level means mean sea level, which is close to the geoid in sea areas. </description> </entry> <alias id="mean_sea_level_pressure"> <entry_id>air_pressure_at_sea_level</entry_id> </alias> </standard_name_table>
The definition of a variable with the standard_name
attribute surface_air_pressure
is found directly since the element with id="surface_air_pressure"
is an entry
element which contains the definition.
The definition of a variable with the standard_name
attribute mean_sea_level_pressure is found indirectly by first finding the element with the id="mean_sea_level_pressure"
, and then, since this is an alias element, by searching for the element with id="air_pressure_at_sea_level"
as indicated by the value of the entry_id
tag.
It is possible that new tags may be added in the future. Any applications that parse the standard table should be written so that unrecognized tags are gracefully ignored.
Appendix C: Standard Name Modifiers
In the Units column, u indicates units dimensionally equivalent to those for the unmodified standard name.
Modifier  Units  Description 


u 
The smallest data value which is regarded as a detectable signal. 

1 
The number of discrete observations or measurements from which a data value has been derived. The use of this modifier is deprecated and the standard_name number_of_observations is preferred to describe this type of metadata variable. 

u 
*The uncertainty of the data value.
The standard error includes both systematic and statistical uncertainty.
By default it is assumed that the values supplied are for one standard error.
If the values supplied are for some multiple of the standard error, the 

Flag values indicating the quality or other status of the data values.
The variable should have 
*The definition of this modifier implies that if u is a either unit of temperature, or a unit of temperature multiplied by some other unit, the temperature in u must be interpreted as a temperature difference.
Therefore the units_metadata
attribute, if present, must have the value temperature: difference
, even if the corresponding data variable without the modifier would have units_metadata="temperature: on_scale"
.
See Section 3.1.2, "Temperature units" for explanation.
Appendix D: Parametric Vertical Coordinates
The definitions given here allow an application to compute dimensional coordinate values from the parametric vertical coordinate values (usually dimensionless) and associated variables.
The formulas are expressed for a gridpoint (n,k,j,i)
where i
and j
are the horizontal indices, k
is the vertical index and n
is the time index.
A coordinate variable is associated with its definition by the value of the standard_name
attribute.
The terms in the definition are associated with file variables by the formula_terms
attribute.
The formula_terms
attribute takes a string value, the string being comprised of blankseparated elements of the form "term: variable
", where term
is a caseinsensitive keyword that represents one of the terms in the definition, and variable
is the name of the variable in a netCDF file that contains the values for that term.
The order of elements is not significant.
The gridpoint indices are not formally part of the definitions, but are included to illustrate the indices that might be present in the file variables.
For example, a vertical coordinate whose definition contains a time index is not necessarily time dependent in all netCDF files.
Also, the definitions are given in general forms that may be simplified by omitting certain terms.
A term that is omitted from the formula_terms
attribute should be assumed to be zero.
The variables containing the terms may optionally have standard_name
attributes, with values as indicated in this Appendix.
The standard_name
of the dimensional coordinate values which are computed by the formula may optionally be specified by the computed_standard_name
attribute of the vertical coordinate variable, as indicated in this Appendix.
A computed_standard_name
is uniquely implied by the formula in some cases, while in others it depends on the standard_name
of one or more of the terms, with which it must be consistent.
Atmosphere natural log pressure coordinate
standard_name = "atmosphere_ln_pressure_coordinate"
 Definition

p(k) = p0 * exp(lev(k))
where p(k)
is the pressure at gridpoint (k)
, p0
is a reference pressure, lev(k)
is the dimensionless coordinate at vertical gridpoint (k)
.
The format for the formula_terms
attribute is:
formula_terms = "p0: var1 lev: var2"
The standard_name of p0
is reference_air_pressure_for_atmosphere_vertical_coordinate
.
The computed_standard_name
is air_pressure
.
Atmosphere sigma coordinate
standard_name = "atmosphere_sigma_coordinate"
 Definition

p(n,k,j,i) = ptop + sigma(k)*(ps(n,j,i)ptop)
where p(n,k,j,i)
is the pressure at gridpoint (n,k,j,i)
, ptop
is the pressure at the top of the model, sigma(k)
is the dimensionless coordinate at vertical gridpoint (k)
, and ps(n,j,i)
is the surface pressure at horizontal gridpoint (j,i)
and time (n)
.
The format for the formula_terms attribute is
formula_terms = "sigma: var1 ps: var2 ptop: var3"
The standard_name of ptop
is air_pressure_at_top_of_atmosphere_model
, and of ps
is surface_air_pressure
.
The computed_standard_name
is air_pressure
.
Atmosphere hybrid sigma pressure coordinate
standard_name = "atmosphere_hybrid_sigma_pressure_coordinate"
 Definition

p(n,k,j,i) = a(k)*p0 + b(k)*ps(n,j,i)
or
p(n,k,j,i) = ap(k) + b(k)*ps(n,j,i)
where p(n,k,j,i)
is the pressure at gridpoint (n,k,j,i)
, a(k)
or ap(k)
and b(k)
are components of the hybrid coordinate at level k
, p0
is a reference pressure, and ps(n,j,i)
is the surface pressure at horizontal gridpoint (j,i)
and time (n)
.
The choice of whether a(k)
or ap(k)
is used depends on model formulation; the former is a dimensionless fraction, the latter a pressure value.
In both formulations, b(k)
is a dimensionless fraction.
The format for the formula_terms
attribute is
formula_terms = "a: var1 b: var2 ps: var3 p0: var4"
where a
is replaced by ap
if appropriate.
The hybrid sigmapressure coordinate for level k
is defined as a(k)+b(k)
or ap(k)/p0+b(k)
, as appropriate.
The standard_name
of p0
is reference_air_pressure_for_atmosphere_vertical_coordinate
, and of ps
is surface_air_pressure
.
The computed_standard_name
is air_pressure
.
No standard_name
has been defined for a
, b
or ap
.
Atmosphere hybrid height coordinate
standard_name = "atmosphere_hybrid_height_coordinate"
 Definition

z(n,k,j,i) = a(k) + b(k)*orog(n,j,i)
where z(n,k,j,i)
is the height above the datum (e.g. the geoid, which is approximately mean sea level) at gridpoint (k,j,i)
and time (n)
, orog(n,j,i)
is the height of the surface above the datum at (j,i)
and time (n)
, and a(k)
and b(k)
are the coordinates which define hybrid height level k
.
a(k)
has the dimensions of height and b(i)
is dimensionless.
The format for the formula_terms
attribute is
formula_terms = "a: var1 b: var2 orog: var3"
The standard_name
of orog
may be surface_altitude
(i.e. above the geoid) or surface_height_above_geopotential_datum
.
The computed_standard_name
is altitude
or height_above_geopotential_datum
in these cases respectively.
No standard_name
has been defined for b
.
There is no dimensionless coordinate because a
, which has the standard_name
of atmosphere_hybrid_height_coordinate
, is the best choice for a leveldependent but geographically constant coordinate.
Atmosphere smooth level vertical (SLEVE) coordinate
standard_name = "atmosphere_sleve_coordinate"
 Definition

z(n,k,j,i) = a(k)*ztop + b1(k)*zsurf1(n,j,i) + b2(k)*zsurf2(n,j,i)
where z(n,k,j,i)
is the height above the datum (e.g. the geoid, which is approximately mean sea level) at gridpoint (k,j,i)
and time (n)
, ztop
is the height of the top of the model above the datum, and a(k)
, b1(k)
, and b2(k)
are the dimensionless coordinates which define hybrid level k
.
zsurf1(n,j,i)
and zsurf2(n,j,i)
are respectively the largescale and smallscale components of the topography, and a
, b1
and b2
are all functions of the dimensionless SLEVE coordinate.
See Shaer et al [SCH02] for details.
The format for the formula_terms
attribute is
formula_terms = "a: var1 b1: var2 b2: var3 ztop: var4 zsurf1: var5 zsurf2: var6"
The standard_name
of ztop
may be altitude_at_top_of_atmosphere_model
(i.e. above the geoid) or height_above_geopotential_datum_at_top_of_atmosphere_model
.
The computed_standard_name
is altitude
or height_above_geopotential_datum
in these cases respectively.
No standard_name
has been defined for b1
, zsurf1
, b2
or zsurf2
.
Ocean sigma coordinate
standard_name = "ocean_sigma_coordinate"
 Definition

z(n,k,j,i) = eta(n,j,i) + sigma(k)*(depth(j,i)+eta(n,j,i))
where z(n,k,j,i)
is height (positive upwards) relative to the datum (e.g. mean sea level) at gridpoint (n,k,j,i)
, eta(n,j,i)
is the height of the sea surface (positive upwards) relative to the datum at gridpoint (n,j,i)
, sigma(k)
is the dimensionless coordinate at vertical gridpoint (k)
, and depth(j,i)
is the distance (a positive value) from the datum to the sea floor at horizontal gridpoint (j,i)
.
The format for the formula_terms
attribute is
formula_terms = "sigma: var1 eta: var2 depth: var3"
The standard_name
s for eta
and depth
and the computed_standard_name
must be one of the consistent sets shown in Table D.1.
Ocean scoordinate
standard_name = "ocean_s_coordinate"
 Definition

z(n,k,j,i) = eta(n,j,i)*(1+s(k)) + depth_c*s(k) + (depth(j,i)depth_c)*C(k)
where
C(k) = (1b)*sinh(a*s(k))/sinh(a) + b*[tanh(a*(s(k)+0.5))/(2*tanh(0.5*a))  0.5]
where z(n,k,j,i)
is height (positive upwards) relative to the datum (e.g. mean sea level) at gridpoint (n,k,j,i)
, eta(n,j,i)
is the height of the sea surface (positive upwards) relative to the datum at gridpoint (n,j,i)
, s(k)
is the dimensionless coordinate at vertical gridpoint (k)
, and depth(j,i)
is the distance (a positive value) from the datum to the sea floor at horizontal gridpoint (j,i)
.
The constants a
, b
, and depth_c
control the stretching.
The constants a
and b
are dimensionless, and depth_c
must have units of length.
The format for the formula_terms
attribute is
formula_terms = "s: var1 eta: var2 depth: var3 a: var4 b: var5 depth_c: var6"
The standard_name
s for eta
and depth
and the computed_standard_name
must be one of the consistent sets shown in Table D.1.
No standard_name
has been defined for a
, b
or depth_c
.
Ocean scoordinate, generic form 1
standard_name = "ocean_s_coordinate_g1"
 Definition

z(n,k,j,i) = S(k,j,i) + eta(n,j,i) * (1 + S(k,j,i) / depth(j,i))
where
S(k,j,i) = depth_c * s(k) + (depth(j,i)  depth_c) * C(k)
where z(n,k,j,i)
is height, positive upwards, relative to ocean datum (e.g. mean sea level) at gridpoint (n,k,j,i)
, eta(n,j,i)
is the height of the ocean surface, positive upwards, relative to ocean datum at gridpoint (n,j,i)
, s(k)
is the dimensionless coordinate at vertical gridpoint (k)
with a range of 1 <= s(k) <= 0
, s(0)
corresponds to eta(n,j,i)
whereas s(1)
corresponds to depth(j,i)
; C(k)
is the dimensionless vertical coordinate stretching function at gridpoint (k)
with a range of 1 <= C(k) <= 0
, C(0)
corresponds to eta(n,j,i)
whereas C(1)
corresponds to depth(j,i)
; the constant depth_c
, (positive value), is a critical depth controlling the stretching and depth(j,i)
is the distance from ocean datum to sea floor (positive value) at horizontal gridpoint (j,i)
.
The format for the formula_terms
attribute is
formula_terms = "s: var1 C: var2 eta: var3 depth: var4 depth_c: var5"
The standard_name
s for eta
and depth
and the computed_standard_name
must be one of the consistent sets shown in Table D.1.
No standard_name
has been defined for C
or depth_c
.
Ocean scoordinate, generic form 2
standard_name = "ocean_s_coordinate_g2"
 Definition

z(n,k,j,i) = eta(n,j,i) + (eta(n,j,i) + depth(j,i)) * S(k,j,i)
where
S(k,j,i) = (depth_c * s(k) + depth(j,i) * C(k)) / (depth_c + depth(j,i))
where z(n,k,j,i)
is height, positive upwards, relative to ocean datum (e.g. mean sea level) at gridpoint (n,k,j,i)
, eta(n,j,i)
is the height of the ocean surface, positive upwards, relative to ocean datum at gridpoint (n,j,i)
, s(k)
is the dimensionless coordinate at vertical gridpoint (k)
with a range of 1 <= s(k) <= 0
, S(0)
corresponds to eta(n,j,i)
whereas s(1)
corresponds to depth(j,i)
; C(k)
is the dimensionless vertical coordinate stretching function at gridpoint (k)
with a range of 1 <= C(k) <= 0
, C(0)
corresponds to eta(n,j,i)
whereas C(1)
corresponds to depth(j,i)
; the constant depth_c
, (positive value), is a critical depth controlling the stretching and depth(j,i)
is the distance from ocean datum to sea floor (positive value) at horizontal gridpoint (j,i)
.
The format for the formula_terms
attribute is
formula_terms = "s: var1 C: var2 eta: var3 depth: var4 depth_c: var5"
The standard_name
s for eta
and depth
and the computed_standard_name
must be one of the consistent sets shown in Table D.1.
No standard_name
has been defined for C
or depth_c
.
Ocean sigma over z coordinate
The description of this type of parametric vertical coordinate is defective in version 1.8 and earlier versions of the standard, in that it does not state what values the vertical coordinate variable should contain. Therefore, in accordance with the rules, all versions of the standard before 1.9 are deprecated for datasets that use the "ocean sigma over z" coordinate.
standard_name = "ocean_sigma_z_coordinate"
 Definition

for levels k where sigma(k) has a defined value and zlev(k) is not defined:
z(n,k,j,i) = eta(n,j,i) + sigma(k)*(min(depth_c,depth(j,i))+eta(n,j,i))
for levels k where zlev(k) has a defined value and sigma(k) is not defined:
z(n,k,j,i) = zlev(k)
where z(n,k,j,i)
is height, positive upwards, relative to ocean datum (e.g. mean sea level) at gridpoint (n,k,j,i)
, eta(n,j,i)
is the height of the ocean surface, positive upwards, relative to ocean datum at gridpoint (n,j,i)
, and depth(j,i)
is the distance from ocean datum to sea floor (positive value) at horizontal gridpoint (j,i)
.
The parameter sigma(k)
is defined only for the nsigma
layers nearest the ocean surface, while zlev(k)
is defined for the nlayer  nsigma
deeper layers, where 0 <= nsigma <= nlayer
and nlayer
is the size of the dimension of the vertical coordinate variable.
Both sigma
and zlev
must have this dimension.
For any k
, whichever of sigma(k)
or zlev(k)
is undefined must contain missing data, while the other must not.
The format for the formula_terms
attribute is
formula_terms = "sigma: var1 eta: var2 depth: var3 depth_c: var4 nsigma: var5 zlev: var6"
The standard_name
s for eta
, depth
, zlev
and the computed_standard_name
must be one of the consistent sets shown in Table D.1.
The standard_name
for sigma
is ocean_sigma_coordinate
.
No standard_name
has been defined for depth_c
or nsigma
.
The nsigma
parameter is deprecated and optional in formula_terms
; if supplied, it must equal the number of elements of zlev
which contain missing data.
The standard_name
for the vertical coordinate variable is ocean_sigma_z_coordinate
.
This variable should contain sigma(k)*depth_c
for the layers where sigma
is defined and zlev(k)
for the other layers, with units of length.
The layers must be arranged so that the vertical coordinate variable contains a strictly monotonic set of indicative values for the heights of the levels relative to the datum, either increasing or decreasing, and the direction must be indicated by the positive
attribute, in the usual way for a vertical coordinate variable.
Ocean double sigma coordinate
standard_name = "ocean_double_sigma_coordinate"
 Definition

for k <= k_c: z(k,j,i)= sigma(k)*f(j,i) for k > k_c: z(k,j,i)= f(j,i) + (sigma(k)1)*(depth(j,i)f(j,i)) f(j,i)= 0.5*(z1+ z2) + 0.5*(z1z2)* tanh(2*a/(z1z2)*(depth(j,i)href))
where z(k,j,i)
is height (positive upwards) relative to the datum (e.g. mean sea level) at gridpoint (k,j,i)
, sigma(k)
is the dimensionless coordinate at vertical gridpoint (k)
for k <= k_c
, and depth(j,i)
is the distance (a positive value) from the datum to sea floor at horizontal gridpoint (j,i)
.
z1
, z2
, a
, and href
are constants with units of length.
The format for the formula_terms
attribute is
formula_terms = "sigma: var1 depth: var2 z1: var3 z2: var4 a: var5 href: var6 k_c: var7"
The standard_name
for depth
and the computed_standard_name
must be one of the consistent sets shown in Table D.1.
No standard_name
has been defined for z1
, z2
, a
, href
or k_c
.
option  standard_name of computed dimensional coordinate  formula term name  standard_name of formula term 

1 
altitude 
zlev 
altitude 
eta 
sea_surface_height_above_geoid 

depth 
sea_floor_depth_below_geoid 

2 
height_above_geopotential_ datum 
zlev 
height_above_geopotential_datum 
eta 
sea_surface_height_above_ geopotential_datum 

depth 
sea_floor_depth_below_ geopotential_datum 

3 
height_above_reference_ ellipsoid 
zlev 
height_above_reference_ellipsoid 
eta 
sea_surface_height_above_ reference_ellipsoid 

depth 
sea_floor_depth_below_ reference_ellipsoid 

4 
height_above_mean_sea_ level 
zlev 
height_above_mean_sea_level 
eta 
sea_surface_height_above_mean_ sea_level 

depth 
sea_floor_depth_below_mean_ sea_level 
Appendix E: Cell Methods
In the Units column, u indicates the units of the physical quantity before the method is applied.
cell_methods 
Units  Description 


u 
The data values are representative of points in space or time (instantaneous). This is the default method for a quantity that is intensive with respect to the specified dimension. 

u 
The data values are representative of a sum or accumulation over the cell. This is the default method for a quantity that is extensive with respect to the specified dimension. 

u 
Maximum 

u 
Maximum absolute value 

u 
Median 

u 
Average of maximum and minimum 

u 
Minimum 

u 
Minimum absolute value 

u 
Mean (average value) 

u 
Mean absolute value 

u 
Mean of the upper group of data values defined by the upper tenth of their distribution 

u 
Mode (most common value) 

u 
*Absolute difference between maximum and minimum 

u 
Root mean square (RMS) 

u 
*Standard deviation 

u^{2} 
Sum of squares 

u^{2} 
*Variance 
*The definition of this method implies that if u is a either a unit of temperature, or a unit of temperature multiplied by some other unit, the temperature in u must be interpreted as a temperature difference.
Therefore the units_metadata
attribute, if present, must have the value temperature: difference
.
See Section 3.1.2, "Temperature units" for explanation.
Appendix F: Grid Mappings
Each recognized grid mapping is described in one of the sections below.
Each section contains: the valid name that is used with the grid_mapping_name
attribute; a list of the specific attributes that may be used to assign values to the mapping’s parameters; the standard names used to identify the coordinate variables that contain the mapping’s independent variables; and references to the mapping’s definition or other information that may help in using the mapping.
Since the attributes used to set a mapping’s parameters may be shared among several mappings, their definitions are contained in a table in the final section.
The attributes which describe the ellipsoid and prime meridian may be included, when applicable, with any grid mapping.
These are:

earth_radius

inverse_flattening

longitude_of_prime_meridian

prime_meridian_name

reference_ellipsoid_name

semi_major_axis

semi_minor_axis
In general we have used the FGDC "Content Standard for Digital Geospatial Metadata" [FGDC] as a guide in choosing the values for grid_mapping_name
and the attribute names for the parameters describing map projections.
Albers Equal Area
grid_mapping_name = albers_conical_equal_area
 Map parameters:


standard_parallel
 There may be 1 or 2 values. 
longitude_of_central_meridian

latitude_of_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software package for computing the mapping may be found at https://proj.org/operations/projections/aea.html and http://geotiff.maptools.org/proj_list/albers_equal_area_conic.html.
Azimuthal equidistant
grid_mapping_name = azimuthal_equidistant
 Map parameters:


longitude_of_projection_origin

latitude_of_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software package for computing the mapping may be found at http://geotiff.maptools.org/proj_list/azimuthal_equidistant.html and https://proj.org/operations/projections/aeqd.html.
Geostationary projection
grid_mapping_name = geostationary
 Map parameters:


latitude_of_projection_origin

longitude_of_projection_origin

perspective_point_height

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0) 
sweep_angle_axis

fixed_angle_axis

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_angular_coordinate
andprojection_y_angular_coordinate
, respectively. It is assumed that the yaxis is aligned to the Earth’s N/S axis, whereas the xaxis aligns with the E/W axis. CF specified the standard namesprojection_x_coordinate
andprojection_y_coordinate
for these coordinates prior to version 1.9, but that use is deprecated. In the case of this projection, the projection coordinates are the scanning angle of the satellite instrument.  Notes:

The geostationary projection assumes a hypothetical view of the Earth from a perspective above the Earth where the azimuth and elevation viewing angles are described using a hypothetical gimbal model. This model is independent of the physical scan principles of any observing instrument. The model consists conceptually of a set of two rotating circles with a colocated centre, whose axes of rotation are perpendicular to each other. The axis of the outer circle is stationary, while the axis of the inner circle moves about the stationary axis. This means that a given viewing angle described using this model is the result of matrix multiplications, which is not commutative, so that order of operations is essential in achieving accurate results. The two axes are conventionally called the sweepangle and fixedangle axes; we adhere to this terminology, although some find these terms confusing, for the sake of interoperability with existing implementations.
The algorithm for computing the mapping may be found at https://www.cgmsinfo.org/documents/pdf_cgms_03.pdf. This document assumes the point of observation is directly over the equator, and that the
sweep_angle_axis
is y.Explanatory diagrams for the projection may be found on the PROJ website, as well as notes on using the PROJ software for computing the mapping.
The
perspective_point_height
is the distance to the surface of the ellipsoid.The
sweep_angle_axis
attribute indicates the axis on which the view sweeps. It corresponds to the outergimbal (stable) axis of the gimbal view model. For example, the value = "y" corresponds to the Meteosat satellites, the value = "x" to the GOES satellites.The
fixed_angle_axis
attribute indicates the axis on which the view is fixed. It corresponds to the innergimbal axis of the gimbal view model, whose axis of rotation moves about the outergimbal axis. Iffixed_angle_axis
is "x",sweep_angle_axis
is "y", and vice versa. Only one of those the attributesfixed_angle_axis
orsweep_angle_axis
is mandatory, as they can be used to infer each other. Note also that the values "x" and "y" are not casesensitive.The use of
projection_x_coordinate
andprojection_y_coordinate
was deprecated in version 1.9 of the CF Conventions. The initial definition of this projection used these standard names to identify the projection coordinates even though their canonical units (meters) do not match those required for this projection (radians).
Lambert azimuthal equal area
grid_mapping_name = lambert_azimuthal_equal_area
 Map parameters:


longitude_of_projection_origin

latitude_of_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software package for computing the mapping may be found at https://proj.org/operations/projections/laea.html and http://geotiff.maptools.org/proj_list/lambert_azimuthal_equal_area.html
Lambert conformal
grid_mapping_name = lambert_conformal_conic
 Map parameters:


standard_parallel
 There may be 1 or 2 values. 
longitude_of_central_meridian

latitude_of_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software package for computing the mapping may be found at https://proj.org/operations/projections/lcc.html. and http://geotiff.maptools.org/proj_list/lambert_conic_conformal_1sp.html ("Lambert Conic Conformal (1SP)" or EPSG 9801) or http://geotiff.maptools.org/proj_list/lambert_conic_conformal_2sp.html ("Lambert Conic Conformal (2SP)" or EPSG 9802). For the 1SP variant, latitude_of_projection_origin=standard_parallel and the PROJ scale factor is 1.
Lambert Cylindrical Equal Area
grid_mapping_name = lambert_cylindrical_equal_area
 Map parameters:


longitude_of_central_meridian

Either
standard_parallel
orscale_factor_at_projection_origin
(deprecated) 
false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software packages for computing the mapping may be found at https://proj.org/operations/projections/cea.html and http://geotiff.maptools.org/proj_list/cylindrical_equal_area.html ("Lambert Cylindrical Equal Area" or EPSG 9834 or EPSG 9835). Detailed formulas can be found in [Snyder] pages 7685.
LatitudeLongitude
grid_mapping_name = latitude_longitude
This grid mapping defines the canonical 2D geographical coordinate system based upon latitude and longitude coordinates. It is included so that the figure of the Earth can be described.
 Map parameters:

None.
 Map coordinates:

The rectangular coordinates are longitude and latitude identified by the usual conventions (Section 4.1, "Latitude Coordinate" and Section 4.2, "Longitude Coordinate").
Mercator
grid_mapping_name = mercator
 Map parameters:


longitude_of_projection_origin

Either
standard_parallel
(EPSG 9805) orscale_factor_at_projection_origin
(EPSG 9804) 
false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software packages for computing the mapping may be found at https://proj.org/operations/projections/merc.html and http://geotiff.maptools.org/proj_list/mercator_1sp.html ("Mercator (1SP)" or EPSG 9804) or http://geotiff.maptools.org/proj_list/mercator_2sp.html ("Mercator (2SP)" or EPSG 9805).More information on formulas available in [OGPEPSG_GN7_2].
Oblique Mercator
grid_mapping_name = oblique_mercator
 Map parameters:


azimuth_of_central_line

latitude_of_projection_origin

longitude_of_projection_origin

scale_factor_at_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software package for computing the mapping may be found at https://proj.org/operations/projections/omerc.html and http://geotiff.maptools.org/proj_list/oblique_mercator.html.
Orthographic
grid_mapping_name = orthographic
 Map parameters:


longitude_of_projection_origin

latitude_of_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software packages for computing the mapping may be found at https://proj.org/operations/projections/ortho.html and http://geotiff.maptools.org/proj_list/orthographic.html ("Orthographic" or EPSG 9840).More information on formulas available in [OGPEPSG_GN7_2].
Polar stereographic
grid_mapping_name = polar_stereographic
 Map parameters:


longitude_of_projection_origin
orstraight_vertical_longitude_from_pole
(deprecated) 
latitude_of_projection_origin
 Either +90. or 90. 
Either
standard_parallel
(EPSG 9829) orscale_factor_at_projection_origin
(EPSG 9810) 
false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software package for computing the mapping may be found at https://proj.org/operations/projections/stere.html and http://geotiff.maptools.org/proj_list/polar_stereographic.html.
The standard_parallel variant corresponds to EPSG Polar Stereographic (Variant B) (EPSG dataset coordinate operation method code 9829), while the scale_factor_at_projection_origin variant corresponds to EPSG Polar Stereographic (Variant A) (EPSG dataset coordinate operation method code 9810). As PROJ requires the standard parallel, [Snyder] formula 217 can be used to compute it from the scale factor if needed.
Rotated pole
grid_mapping_name = rotated_latitude_longitude
 Map parameters:


grid_north_pole_latitude

grid_north_pole_longitude

north_pole_grid_longitude
 This parameter is optional (default is 0).

 Map coordinates:

The rotated latitude and longitude coordinates are identified by the
standard_name
attribute valuesgrid_latitude
andgrid_longitude
respectively.
Sinusoidal
grid_mapping_name = sinusoidal
 Map parameters:


longitude_of_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Notes on using the
PROJ
software package for computing the mapping may be found at https://proj.org/operations/projections/sinu.html and http://geotiff.maptools.org/proj_list/sinusoidal.html. Detailed formulas can be found in [Snyder], pages 243248.
Stereographic
grid_mapping_name = stereographic
 Map parameters:


longitude_of_projection_origin

latitude_of_projection_origin

scale_factor_at_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Formulas for the mapping and its inverse along with notes on using the
PROJ
software package for doing the calcuations may be found at https://proj.org/operations/projections/stere.html and http://geotiff.maptools.org/proj_list/stereographic.html. See the section "Polar stereographic" for the special case when the projection origin is one of the poles.
Transverse Mercator
grid_mapping_name = transverse_mercator
 Map parameters:


scale_factor_at_central_meridian

longitude_of_central_meridian

latitude_of_projection_origin

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valuesprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

Formulas for the mapping and its inverse along with notes on using the
PROJ
software package for doing the calcuations may be found at https://proj.org/operations/projections/tmerc.html and http://geotiff.maptools.org/proj_list/transverse_mercator.html.
Vertical perspective
grid_mapping_name = vertical_perspective
 Map parameters:


latitude_of_projection_origin

longitude_of_projection_origin

perspective_point_height

false_easting
 This parameter is optional (default is 0) 
false_northing
 This parameter is optional (default is 0)

 Map coordinates:

The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute valueprojection_x_coordinate
andprojection_y_coordinate
respectively.  Notes:

A general description of vertical perspective projection is given in [Snyder], pages 169181.
The corresponding projection in PROJ is nsper. This should not be confused with the PROJ geos projection.
In the following table the "Type" values are S for string and N for numeric.
Attribute  Type  Description 


N 
Specifies a horizontal angle measured in degrees clockwise from North. Used by certain projections (e.g., Oblique Mercator) to define the orientation of the map projection relative to a reference direction. 

S 
This optional attribute may be used to specify multiple coordinate system properties in wellknown text (WKT) format.
The syntax must conform to the WKT format as specified in reference [OGC_WKTCRS].
Use of the 

N 
Used to specify the radius, in metres, of the spherical figure used to approximate the shape of the Earth. This attribute should be specified for those projected coordinate reference systems in which the XY cartesian coordinates have been derived using a spherical Earth approximation. If the cartesian coordinates were derived using an ellipsoid, this attribute should not be defined. Example: "6371007", which is the radius of the GRS 1980 Authalic Sphere. 

N 
Applied to all abscissa values in the rectangular coordinates for a map projection in order to eliminate negative numbers.
Expressed in the unit of the coordinate variable identified by the standard name 

N 
Applied to all ordinate values in the rectangular coordinates for a map projection in order to eliminate negative numbers.
Expressed in the unit of the coordinate variable identified by the standard name 

S 
Indicates the axis on which the view is fixed in a hypothetical gimbal view model of the Earth, as used in the geostationary grid mapping.
It corresponds to the innergimbal axis of the gimbal view model, whose axis of rotation moves about the outergimbal axis.
This value can adopt two values, "x" or "y", corresponding with the Earth’s EW or NS axis, respectively.
The counterpart to this attribute is 

S 
The name of the geographic coordinate reference system. Corresponds to a OGC WKT GEOGCS node name. 

S 
The name of the estimate or model of the geoid being used as a datum, e.g. GEOID12B.
Corresponds to an OGC WKT VERT_DATUM name.
The geoid is the surface of constant geopotential that the ocean would follow if it were at rest.
This attribute and 

S 
The name of an estimated surface of constant geopotential being used as a datum, e.g. NAVD88.
Such a surface is often called an equipotential surface in geodesy.
Corresponds to an OGC WKT VERT_DATUM name.
This attribute and 

S 
The name used to identify the grid mapping. 

N 
True latitude (degrees_north) of the north pole of the rotated grid. 

N 
True longitude (degrees_east) of the north pole of the rotated grid. 

S 
The name of the geodetic (horizontal) datum, which corresponds to the procedure used to measure positions on the surface of the Earth. Valid datum names and their associated parameters are given in https://github.com/cfconvention/cfconventions/wiki/MappingfromCFGridMappingAttributestoCRSWKTElements (horiz_datum.csv, OGC_DATUM_NAME column) and are obtained by transforming the EPSG name using the following rules (used by OGR and Cadcorp): convert all non alphanumeric characters (including +) to underscores, then strip any leading, trailing or repeating underscores. This is to ensure that named datums can be correctly identified for precise datum transformations (see https://github.com/cfconvention/cfconventions/wiki/OGCWKTCoordinateSystemIssues for more details). Corresponds to a OGC WKT DATUM node name. 

N 
Used to specify the inverse flattening (1/f) of the ellipsoidal figure associated with the geodetic datum and used to approximate the shape of the Earth. The flattening (f) of the ellipsoid is related to the semimajor and semiminor axes by the formula f = (ab)/a. In the case of a spherical Earth this attribute should be omitted or set to zero. Example: 298.257222101 for the GRS 1980 ellipsoid. (Note: By convention the dimensions of an ellipsoid are specified using either the semimajor and semiminor axis lengths, or the semimajor axis length and the inverse flattening. If all three attributes are specified then the supplied values must be consistent with the aforementioned formula.) 

N 
The latitude (degrees_north) chosen as the origin of rectangular coordinates for a map projection.
Domain: 

N 
The line of longitude (degrees_east) at the center of a map projection generally used as the basis for constructing the projection.
Domain: 

N 
Specifies the longitude, with respect to Greenwich, of the prime meridian associated with the geodetic datum.
The prime meridian defines the origin from which longitude values are determined.
Not to be confused with the projection origin longitude (cf. 

N 
The longitude (degrees_east) chosen as the origin of rectangular coordinates for a map projection.
Domain: + 

N 
Longitude (degrees) of the true north pole in the rotated grid. 

N 
Records the height, in metres, of the map projection perspective point above the ellipsoid (or sphere). Used by perspectivetype map projections, for example the Vertical Perspective Projection, which may be used to simulate the view from a Meteosat satellite. 

S 
The name of the prime meridian associated with the geodetic datum. Valid names are given in https://github.com/cfconvention/cfconventions/wiki/MappingfromCFGridMappingAttributestoCRSWKTElements (prime_meridian.csv). Corresponds to a OGC WKT PRIMEM node name. 

S 
The name of the projected coordinate reference system. Corresponds to a OGC WKT PROJCS node name. 

S 
The name of the reference ellipsoid. Valid names are given in https://github.com/cfconvention/cfconventions/wiki/MappingfromCFGridMappingAttributestoCRSWKTElements (ellipsoid.csv). Corresponds to a OGC WKT SPHEROID node name. 

N 
A multiplier for reducing a distance obtained from a map by computation or scaling to the actual distance along the central meridian.
Domain: 

N 
A multiplier for reducing a distance obtained from a map by computation or scaling to the actual distance at the projection origin.
Domain: 

N 
Specifies the length, in metres, of the semimajor axis of the ellipsoidal figure associated with the geodetic datum and used to approximate the shape of the Earth.
Commonly denoted using the symbol a.
In the case of a spherical Earth approximation this attribute defines the radius of the Earth.
See also the 

N 
Specifies the length, in metres, of the semiminor axis of the ellipsoidal figure associated with the geodetic datum and used to approximate the shape of the Earth. Commonly denoted using the symbol b. In the case of a spherical Earth approximation this attribute should be omitted (the preferred option) or else set equal to the value of the semi_major_axis attribute. See also the inverse_flattening attribute. 

N 
Specifies the line, or lines, of latitude at which the developable map projection surface (plane, cone, or cylinder) touches the reference sphere or ellipsoid used to represent the Earth.
Since there is zero scale distortion along a standard parallel it is also referred to as a "latitude of true scale".
In the situation where a conical developable surface intersects the reference ellipsoid there are two standard parallels, in which case this attribute can be used as a vector to record both latitude values, with the additional convention that the standard parallel nearest the pole (N or S) is provided first.
Domain: 

N 
Deprecated. Has the same meaning as 

S 
Indicates the axis on which the view sweeps in a hypothetical gimbal view model of the Earth, as used in the geostationary grid mapping.
It corresponds to the outergimbal axis of the gimbal view model, about whose axis of rotation the gimbalgimbal axis moves.
This value can adopt two values, "x" or "y", corresponding with the Earth’s EW or NS axis, respectively.
The counterpart to this attribute is 

N 
This indicates a list of up to 7 Bursa Wolf transformation parameters., which can be used to approximate a transformation from the horizontal datum to the WGS84 datum. More precise datum transformations can be done with datum shift grids. Represented as a doubleprecision array, with 3, 6 or 7 values (if there are less than 7 values the remaining are considered to be zero). Corresponds to a OGC WKT TOWGS84 node. 
Notes:

The various
*_name
attributes are optional but recommended when known as they allow for a better description and interoperability with WKT definitions. 
reference_ellipsoid_name
,prime_meridian_name
,horizontal_datum_name
andgeographic_crs_name
must be all defined if any one is defined, and ifprojected_crs_name
is defined thengeographic_crs_name
must be also.
Appendix G: Revision History
The content in this appendix has moved to Revision History.
Appendix H: Annotated Examples of Discrete Geometries
H.1. Point Data
To represent data at scattered locations and times with no implied relationship among of coordinate positions, both data and coordinates must share the same (sample) instance dimension.
Because each feature contains only a single data element, there is no need for a separate element dimension.
The representation of point features is a special, degenerate case of the standard four representations.
The coordinates
attribute is used on the data variables to unambiguously identify the relevant space and time auxiliary coordinate variables.
dimensions: obs = 1234 ; variables: double time(obs) ; time:standard_name = “time”; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; float lon(obs) ; lon:standard_name = "longitude"; lon:long_name = "longitude of the observation"; lon:units = "degrees_east"; float lat(obs) ; lat:standard_name = "latitude"; lat:long_name = "latitude of the observation" ; lat:units = "degrees_north" ; float alt(obs) ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m"; alt:positive = "up"; alt:axis = "Z"; float humidity(obs) ; humidity:standard_name = "specific_humidity" ; humidity:coordinates = "time lat lon alt" ; float temp(obs) ; temp:standard_name = "air_temperature" ; temp:units = "Celsius" ; temp:coordinates = "time lat lon alt" ; attributes: :featureType = "point";
In this example, the humidity(i)
and temp(i)
data are associated with the coordinate values time(i)
, lat(i)
, lon(i)
, and alt(i)
.
The obs
dimension may optionally be the netCDF unlimited dimension of the netCDF file.
H.2. Time Series Data
Data may be taken over periods of time at a set of discrete point, spatial locations called stations (see also discussion in 9.1). The set of elements at a particular station is referred to as a timeSeries feature and a data variable may contain a collection of such features. The instance dimension in the case of timeSeries specifies the number of time series in the collection and is also referred to as the station dimension. The instance variables, which have just this dimension, including latitude and longitude for example, are also referred to as station variables and are considered to contain information describing the stations. The station variables may contain missing values, allowing one to reserve space for additional stations that may be added at a later time, as discussed in section 9.6. In addition,

It is strongly recommended that there should be a station variable (which may be of any type) with the attribute
cf_role=”timeseries_id”
, whose values uniquely identify the stations. 
It is recommended that there should be station variables with standard_name attributes "
platform_name
", "surface_altitude
" andplatform_id
when applicable.
All the representations described in section 9.3 can be used for time series.
The global attribute featureType=”timeSeries”
(caseinsensitive) must be included.
H.2.1. Orthogonal multidimensional array representation of time series
If the time series instances have the same number of elements and the time values are identical for all instances, you may use the orthogonal multidimensional array representation.
This has either a onedimensional coordinate variable, time(time), provided the time values are in strict monotonically increasing order, or a onedimensional auxiliary coordinate variable, time(o), where o is the element dimension.
In the former case, listing the time variable in the coordinates
attributes of the data variables is optional.
dimensions: station = 10 ; // measurement locations time = UNLIMITED ; variables: float humidity(station,time) ; humidity:standard_name = "specific humidity" ; humidity:coordinates = "lat lon alt station_name" ; humidity:_FillValue = 999.9f; double time(time) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; float lon(station) ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat(station) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(station) ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m"; alt:positive = "up"; alt:axis = "Z"; string station_name(station) ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id"; attributes: :featureType = "timeSeries";
In this example, humidity(i,o)
is element o
of time series i
, and associated with the coordinate values time(o)
, lat(i)
, and lon(i)
.
Either the instance (station
) or the element (time
) dimension may optionally be the netCDF unlimited dimension.
H.2.2. Incomplete multidimensional array representation of time series
Much of the simplicity of the orthogonal multidimensional representation can be preserved even in cases where individual time series have different time coordinate values. All time series must be allocated the amount of storage needed by the longest, so the use of this representation will trade off simplicity against storage space in some cases.
dimensions: station = UNLIMITED ; obs = 13 ; name_strlen = 23 ; variables: float lon(station) ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat(station) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(station) ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m"; alt:positive = "up"; alt:axis = "Z"; char station_name(station, name_strlen) ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id"; int station_info(station) ; station_info:long_name = "any kind of station info" ; float station_elevation(station) ; station_elevationalt:long_name = "height above the geoid" ; station_elevationalt:standard_name = "surface_altitude" ; station_elevationalt:units = "m"; double time(station, obs) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; time:missing_value = 999.9; float humidity(station, obs) ; humidity:standard_name = “specific_humidity” ; humidity:coordinates = "time lat lon alt station_name" ; humidity:_FillValue = 999.9f; float temp(station, obs) ; temp:standard_name = “air_temperature” ; temp:units = "Celsius" ; temp:coordinates = "time lat lon alt station_name" ; temp:_FillValue = 999.9f; attributes: :featureType = "timeSeries";
In this example, the humidity(i,o)
and temp(i,o)
data for element o
of time series i
are associated with the coordinate values time(i,o)
, lat(i)
, lon(i)
and alt(i)
.
Either the instance (station
) dimension or the element (obs
) dimension could be the unlimited dimension of a netCDF file.
Any unused elements of the data and auxiliary coordinate variables must contain the missing data flag value(section 9.6).
H.2.3. Single time series, including deviations from a nominal fixed spatial location
When the intention of a data variable is to contain only a single time series, the preferred encoding is a special case of the multidimensional array representation.
dimensions: time = 100233 ; variables: float lon ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m"; alt:positive = "up"; alt:axis = "Z"; string station_name ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id"; double time(time) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; float humidity(time) ; humidity:standard_name = “specific_humidity” ; humidity:coordinates = "time lat lon alt station_name" ; humidity:_FillValue = 999.9f; float temp(time) ; temp:standard_name = “air_temperature” ; temp:units = "Celsius" ; temp:coordinates = "time lat lon alt station_name" ; temp:_FillValue = 999.9f; attributes: :featureType = "timeSeries";
While an idealized time series is defined at a single, stable point location, there are examples of time series, such as cabled ocean surface mooring measurements, in which the precise position of the observations varies slightly from a nominal fixed point. It is quite common that the deployment position of a station changes after maintenance or repositioning after it drifts. In the following example we show how the spatial positions of such a time series should be encoded in CF. In addition, this example shows how lossless compression by gathering Section 8.2, "Lossless Compression by Gathering" has been applied to the deployment coordinate variables, which otherwise would contain a lot of missing or repetitive data. Note that although this example shows only a single time series, the technique is applicable to all of the representations.
dimensions: time = 100233 ; name_strlen = 23 ; deployment = 5 ; variables: float lon ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; lon:axis = “X”; float lat ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; lat: axis = “Y” ; float precise_lon (time); precise_lon:standard_name = "longitude"; precise_lon:long_name = "station longitude"; precise_lon:units = "degrees_east"; float precise_lat (time); precise_lat:standard_name = "latitude"; precise_lat:long_name = "station latitude" ; precise_lat:units = "degrees_north" ; float deploy_lon (deployment); deploy_lon:standard_name = "deployment_longitude"; deploy_lon:long_name = station longitude"; deploy_lon:units = "degrees_east"; float deploy_lat (deployment); deploy_lat:standard_name = "deployment_latitude"; deploy_lat:long_name = station latitude"; deploy_lat:units = "degrees_north"; int deployment (deployment) ; deployment:long_name = "index of the first time after (re)deployment" ; deployment:compress="time"; float alt ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m"; alt:positive = "up"; alt:axis = "Z"; char station_name(name_strlen) ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id"; double time(time) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; float humidity(time) ; humidity:standard_name = “specific_humidity” ; humidity:coordinates = "time lat lon alt precise_lon precise_lat deploy_lon deploy_lat station_name" ; humidity:_FillValue = 999.9f; float temp(time) ; temp:standard_name = “air_temperature” ; temp:units = "Celsius" ; temp:coordinates = "time lat lon alt precise_lon precise_lat deploy_lon deploy_lat station_name" ; temp:_FillValue = 999.9f; attributes: :featureType = "timeSeries";
H.2.4. Contiguous ragged array representation of time series
When the time series have different lengths and the data values for entire time series are available to be written in a single operation, the contiguous ragged array representation is efficient.
dimensions: station = 23 ; obs = 1234 ; variables: float lon(station) ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat(station) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(station) ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m"; alt:positive = "up"; alt:axis = "Z"; string station_name(station) ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id"; int station_info(station) ; station_info:long_name = "some kind of station info" ; int row_size(station) ; row_size:long_name = "number of observations for this station " ; row_size:sample_dimension = "obs" ; double time(obs) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; float humidity(obs) ; humidity:standard_name = “specific_humidity” ; humidity:coordinates = "time lat lon alt station_name" ; humidity:_FillValue = 999.9f; float temp(obs) ; temp:standard_name = “air_temperature” ; temp:units = "Celsius" ; temp:coordinates = "time lat lon alt station_name" ; temp:_FillValue = 999.9f; attributes: :featureType = "timeSeries";
The data humidity(o)
and temp(o)
are associated with the coordinate values time(o)
, lat(i)
, lon(i)
, and alt(i)
, where i
indicates which time series.
Time series i
comprises the data elements from
rowStart(i) to rowStart(i) + row_size(i)  1
where
rowStart(i) = 0 if i = 0 rowStart(i) = rowStart(i1) + row_size(i1) if i > 0
The variable, row_size
, is the count variable containing the length of each time series feature.
It is identified by having an attribute with name sample_dimension
whose value is name of the sample dimension (obs
in this example).
The sample dimension could optionally be the netCDF unlimited dimension.
The variable bearing the sample_dimension
attribute must have the instance dimension (station
in this example) as its single dimension, and must have an integer type.
This variable implicitly partitions into individual instances all variables that have the sample dimension.
The auxiliary coordinate variables lat
, lon
, alt
and station_name
are station variables.
H.2.5. Indexed ragged array representation of time series
When time series with different lengths are written incrementally, the indexed ragged array representation is efficient.
dimensions: station = 23 ; obs = UNLIMITED ; name_strlen = 23 ; variables: float lon(station) ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat(station) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(station) ; alt:long_name = "vertical distance above the surface" ; alt:standard_name = "height" ; alt:units = "m"; alt:positive = "up"; alt:axis = "Z"; char station_name(station, name_strlen) ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id"; int station_info(station) ; station_info:long_name = "some kind of station info" ; int stationIndex(obs) ; stationIndex:long_name = "which station this obs is for" ; stationIndex:instance_dimension= "station" ; double time(obs) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; float humidity(obs) ; humidity:standard_name = “specific_humidity” ; humidity:coordinates = "time lat lon alt station_name" ; humidity:_FillValue = 999.9f; float temp(obs) ; temp:standard_name = “air_temperature” ; temp:units = "Celsius" ; temp:coordinates = "time lat lon alt station_name" ; temp:_FillValue = 999.9f; attributes: :featureType = "timeSeries";
The humidity(o)
and temp(o)
data are associated with the coordinate values time(o)
, lat(i)
, lon(i)
, and alt(i)
, where i = stationIndex(o)
is a zerobased index indicating which time series.
Thus, time(0)
, humidity(0)
and temp(0)
belong to the element of the station
dimension that is indicated by stationIndex(0)
; time(1)
, humidity(1)
and temp(1)
belong to element stationIndex(1)
of the station
dimension, etc.
The variable, stationIndex
, is identified as the index variable by having an attribute with name of instance_dimension
whose value is the instance dimension (station
in this example).
The variable bearing the instance_dimension
attribute must have the sample dimension (obs
in this example) as its single dimension, and must have an integer type.
This variable implicitly assigns the station to each value of any variable having the sample dimension.
The sample dimension need not be the netCDF unlimited dimension, though it commonly is.
H.3. Profile Data
A series of connected observations along a vertical line, like an atmospheric or ocean sounding, is called a profile.
For each profile, there is a single time, lat and lon.
A data variable may contain a collection of profile features.
The instance dimension in the case of profiles specifies the number of profiles in the collection and is also referred to as the profile dimension.
The instance variables, which have just this dimension, including latitude and longitude for example, are also referred to as profile variables and are considered to be information about the profiles.
It is strongly recommended that there always be a profile variable (of any data type) with cf_role
attribute " profile_id
", whose values uniquely identify the profiles.
The profile variables may contain missing values.
This allows one to reserve space for additional profiles that may be added at a later time, as discussed in section 9.6.
All the representations described in section 9.1.3 can be used for profiles.
The global attribute featureType=”profile”
(caseinsensitive) should be included if all data variables in the file contain profiles.
H.3.1. Orthogonal multidimensional array representation of profiles
If the profile instances have the same number of elements and the vertical coordinate values are identical for all instances, you may use the orthogonal multidimensional array representation.
This has either a onedimensional coordinate variable, z(z)
, provided the vertical coordinate values are in strict monotonic order, or a onedimensional auxiliary coordinate variable, alt(o)
, where o
is the element dimension.
In the former case, listing the vertical coordinate variable in the coordinates attributes of the data variables is optional.
dimensions: z = 42 ; profile = 142 ; variables: int profile(profile) ; profile:cf_role = "profile_id"; double time(profile); time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(profile); lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(profile); lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float z(z) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float pressure(profile, z) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat z" ; float temperature(profile, z) ; temperature:standard_name = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "Celsius" ; temperature:coordinates = "time lon lat z" ; float humidity(profile, z) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat z" ; attributes: :featureType = "profile";
The pressure(i,o)
, temperature(i,o)
, and humidity(i,o)
data for element o
of profile i
are associated with the coordinate values time(i)
, lat(i)
, and lon(i)
.
The vertical coordinate for element o
in each profile is altitude z(o)
.
Either the instance (profile
) or the element (z
) dimension could be the netCDF unlimited dimension.
H.3.2. Incomplete multidimensional array representation of profiles
If there are the same number of levels in each profile, but they do not have the same set of vertical coordinates, one can use the incomplete multidimensional array representation, which the vertical coordinate variable is twodimensional e.g. replacing z(z)
in "Atmospheric sounding profiles for a common set of vertical coordinates stored in the orthogonal multidimensional array representation." with alt(profile,z)
.
This representation also allows one to have a variable number of elements in different profiles, at the cost of some wasted space.
In that case, any unused elements of the data and auxiliary coordinate variables must contain missing data values (section 9.6).
H.3.3. Single profile
When a single profile is stored in a file, there is no need for the profile dimension; the data arrays are onedimensional. This is a special case of the orthogonal multidimensional array representation (9.3.1).
dimensions: z = 42 ; variables: int profile ; profile:cf_role = "profile_id"; double time; time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon; lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat; lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float z(z) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float pressure(z) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat z" ; float temperature(z) ; temperature:standard_name = "air_temperature" ; temperature:units = "degree_celsius" ; temperature:coordinates = "time lon lat z" ; float humidity(z) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat z" ; attributes: :featureType = "profile";
The pressure(o)
, temperature(o)
, and humidity(o)
data is associated with the coordinate values time
, z(o)
, lat
, and lon
.
The profile variables time
, lat
and lon
, shown here as scalar, could alternatively be onedimensional time(profile)
, lat(profile)
, lon(profile)
if a sizeone profile dimension were retained in the file.
H.3.4. Contiguous ragged array representation of profiles
When the number of vertical levels for each profile varies, and one can control the order of writing, one can use the contiguous ragged array representation. The canonical use case for this is when rewriting raw data, and you expect that the common read pattern will be to read all the data from each profile.
dimensions: obs = UNLIMITED ; profile = 142 ; variables: int profile(profile) ; profile:cf_role = "profile_id"; double time(profile); time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(profile); lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(profile); lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; int rowSize(profile) ; rowSize:long_name = "number of obs for this profile " ; rowSize:sample_dimension = "obs" ; float z(obs) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float pressure(obs) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat z" ; float temperature(obs) ; temperature:standard_name = "air_temperature" ; temperature:units = "degree_celsius" ; temperature:coordinates = "time lon lat z" ; float humidity(obs) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat z" ; attributes: :featureType = "profile";
The pressure(o)
, temperature(o)
, and humidity(o)
data is associated with the coordinate values time(i)
, z(o)
, lat(i)
, and lon(i)
, where i
indicates which profile.
All elements for one profile are contiguous along the sample dimension.
The sample dimension (obs
) may be the unlimited dimension or not.
All variables that have the instance dimension (profile
) as their single dimension are considered to be information about the profiles.
The count variable (row_size
) contains the number of elements for each profile, and is identified by having an attribute with name sample_dimension
whose value is the sample dimension being counted.
It must have the profile dimension as its single dimension, and must have an integer type.
The elements are associated with the profile using the same algorithm as in H.2.4.
H.3.5. Indexed ragged array representation of profiles
When the number of vertical levels for each profile varies, and one cannot write them contiguously, one can use the indexed ragged array representation. The canonical use case is when writing realtime data streams that contain reports from many profiles, arriving randomly. If the sample dimension is the unlimited dimension, this allows data to be appended to the file.
dimensions: obs = UNLIMITED ; profile = 142 ; variables: int profile(profile) ; profile:cf_role = "profile_id"; double time(profile); time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(profile); lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(profile); lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; int parentIndex(obs) ; parentIndex:long_name = "index of profile " ; parentIndex:instance_dimension= "profile" ; float z(obs) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float pressure(obs) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat z" ; float temperature(obs) ; temperature:standard_name = "air_temperature" ; temperature:units = "degree_celsius" ; temperature:coordinates = "time lon lat z" ; float humidity(obs) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat z" ; attributes: :featureType = "profile";
The pressure(o)
, temperature(o)
, and humidity(o)
data are associated with the coordinate values time(i)
, z(o)
, lat(i)
, and lon(i)
, where i
indicates which profile.
The sample dimension (obs
) may be the unlimited dimension or not.
The profile index variable (parentIndex
) is identified by having an attribute with name of instance_dimension
whose value is the profile dimension name.
It must have the sample dimension as its single dimension, and must have an integer type.
Each value in the profile index variable is the zerobased profile index that the element belongs to.
The elements are associated with the profiles using the same algorithm as in H.2.5.
H.4. Trajectory Data
Data may be taken along discrete paths through space, each path constituting a connected set of points called a trajectory, for example along a flight path, a ship path or the path of a parcel in a Lagrangian calculation.
A data variable may contain a collection of trajectory features.
The instance dimension in the case of trajectories specifies the number of trajectories in the collection and is also referred to as the trajectory dimension.
The instance variables, which have just this dimension, are also referred to as trajectory variables and are considered to be information about the trajectories.
It is strongly recommended that there always be a trajectory variable (of any data type) with the attribute cf_role=”trajectory_id”
attribute, whose values uniquely identify the trajectories.
The trajectory variables may contain missing values.
This allows one to reserve space for additional trajectories that may be added at a later time, as discussed in section 9.6.
All the representations described in section 9.3 can be used for trajectories.
The global attribute featureType=”trajectory”
(caseinsensitive) should be included if all data variables in the file contain trajectories.
H.4.1. Multidimensional array representation of trajectories
When storing multiple trajectories in the same file, and the number of elements in each trajectory is the same, one can use the multidimensional array representation. This representation also allows one to have a variable number of elements in different trajectories, at the cost of some wasted space. In that case, any unused elements of the data and auxiliary coordinate variables must contain missing data values (section 9.6).
dimensions: obs = 1000 ; trajectory = 77 ; variables: string trajectory(trajectory) ; trajectory:cf_role = "trajectory_id"; trajectory:long_name = "trajectory name" ; int trajectory_info(trajectory) ; trajectory_info:long_name = "some kind of trajectory info" double time(trajectory, obs) ; time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(trajectory, obs) ; lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(trajectory, obs) ; lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float z(trajectory, obs) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float O3(trajectory, obs) ; O3:standard_name = “mass_fraction_of_ozone_in_air”; O3:long_name = "ozone concentration" ; O3:units = "1e9" ; O3:coordinates = "time lon lat z" ; float NO3(trajectory, obs) ; NO3:standard_name = “mass_fraction_of_nitrate_radical_in_air”; NO3:long_name = "NO3 concentration" ; NO3:units = "1e9" ; NO3:coordinates = "time lon lat z" ; attributes: :featureType = "trajectory";
The NO3(i,o)
and O3(i,o)
data for element o
of trajectory i
are associated with the coordinate values time(i,o)
, lat(i,o)
, lon(i,o)
, and z(i,o)
.
Either the instance (trajectory) or the element (obs
) dimension could be the netCDF unlimited dimension.
All variables that have trajectory as their only dimension are considered to be information about that trajectory.
If the trajectories all have the same set of times, the time auxiliary coordinate variable could be onedimensional time(obs)
, or replaced by a onedimensional coordinate variable time(time)
, where the size of the time dimension is now equal to the number of elements of each trajectory.
In the latter case, listing the time coordinate variable in the coordinates attribute is optional.
H.4.2. Single trajectory
When a single trajectory is stored in the data variable, there is no need for the trajectory dimension and the arrays are onedimensional. This is a special case of the multidimensional array representation.
dimensions: time = 42; name_strlen = 23 ; variables: char trajectory(name_strlen) ; trajectory:cf_role = "trajectory_id"; double time(time) ; time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(time) ; lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(time) ; lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float z(time) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float O3(time) ; O3:standard_name = “mass_fraction_of_ozone_in_air”; O3:long_name = "ozone concentration" ; O3:units = "1e9" ; O3:coordinates = "time lon lat z" ; float NO3(time) ; NO3:standard_name = “mass_fraction_of_nitrate_radical_in_air”; NO3:long_name = "NO3 concentration" ; NO3:units = "1e9" ; NO3:coordinates = "time lon lat z" ; attributes: :featureType = "trajectory";
The NO3(o)
and O3(o)
data are associated with the coordinate values time(o)
, z(o)
, lat(o)
, and lon(o)
.
In this example, the time coordinate is ordered, so time values are contained in a coordinate variable i.e. time(time)
and time
is the element dimension.
The time
dimension may be unlimited or not.
Note that structurally this looks like unconnected point data as in example 9.5.
The presence of the featureType = "trajectory"
global attribute indicates that in fact the points are connected along a trajectory.
H.4.3. Contiguous ragged array representation of trajectories
When the number of elements for each trajectory varies, and one can control the order of writing, one can use the contiguous ragged array representation. The canonical use case for this is when rewriting raw data, and you expect that the common read pattern will be to read all the data from each trajectory.
dimensions: obs = 3443; trajectory = 77 ; variables: string trajectory(trajectory) ; trajectory:cf_role = "trajectory_id"; int rowSize(trajectory) ; rowSize:long_name = "number of obs for this trajectory " ; rowSize:sample_dimension = "obs" ; double time(obs) ; time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(obs) ; lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(obs) ; lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float z(obs) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float O3(obs) ; O3:standard_name = “mass_fraction_of_ozone_in_air”; O3:long_name = "ozone concentration" ; O3:units = "1e9" ; O3:coordinates = "time lon lat z" ; float NO3(obs) ; NO3:standard_name = “mass_fraction_of_nitrate_radical_in_air”; NO3:long_name = "NO3 concentration" ; NO3:units = "1e9" ; NO3:coordinates = "time lon lat z" ; attributes: :featureType = "trajectory";
The O3(o)
and NO3(o)
data are associated with the coordinate values time(o)
, lat(o)
, lon(o)
, and alt(o)
.
All elements for one trajectory are contiguous along the sample dimension.
The sample dimension (obs
) may be the unlimited dimension or not.
All variables that have the instance dimension (trajectory
) as their single dimension are considered to be information about that trajectory.
The count variable (row_size
) contains the number of elements for each trajectory, and is identified by having an attribute with name sample_dimension
whose value is the sample dimension being counted.
It must have the trajectory dimension as its single dimension, and must have an integer type.
The elements are associated with the trajectories using the same algorithm as in H.2.4.
H.4.4. Indexed ragged array representation of trajectories
When the number of elements at each trajectory vary, and the elements cannot be written in order, one can use the indexed ragged array representation. The canonical use case is when writing realtime data streams that contain reports from many trajectories. The data can be written as it arrives; if the flatsample dimension is the unlimited dimension, this allows data to be appended to the file.
dimensions: obs = UNLIMITED ; trajectory = 77 ; name_strlen = 23 ; variables: char trajectory(trajectory, name_strlen) ; trajectory:cf_role = "trajectory_id"; int trajectory_index(obs) ; trajectory_index:long_name = "index of trajectory this obs belongs to " ; trajectory_index:instance_dimension= "trajectory" ; double time(obs) ; time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(obs) ; lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(obs) ; lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float z(obs) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float O3(obs) ; O3:standard_name = “mass_fraction_of_ozone_in_air”; O3:long_name = "ozone concentration" ; O3:units = "1e9" ; O3:coordinates = "time lon lat z" ; float NO3(obs) ; NO3:standard_name = “mass_fraction_of_nitrate_radical_in_air”; NO3:long_name = "NO3 concentration" ; NO3:units = "1e9" ; NO3:coordinates = "time lon lat z" ; attributes: :featureType = "trajectory";
The O3(o)
and NO3(o)
data are associated with the coordinate values time(o)
, lat(o)
, lon(o)
, and alt(o)
.
All elements for one trajectory will have the same trajectory index value.
The sample dimension (obs
) may be the unlimited dimension or not.
The index variable (trajectory_index
) is identified by having an attribute with name of instance_dimension
whose value is the trajectory dimension name.
It must have the sample dimension as its single dimension, and must have an integer type.
Each value in the trajectory_index
variable is the zerobased trajectory index that the element belongs to.
The elements are associated with the trajectories using the same algorithm as in H.2.5.
H.5. Time Series of Profiles
When profiles are taken repeatedly at a station, one gets a time series of profiles (see also section H.2 for discussion of stations and time series). The resulting collection of profiles is called a timeSeriesProfile. A data variable may contain a collection of such timeSeriesProfile features, one feature per station. The instance dimension in the case of a timeSeriesProfile is also referred to as the station dimension. The instance variables, which have just this dimension, including latitude and longitude for example, are also referred to as station variables and are considered to contain information describing the stations. The station variables may contain missing values. This allows one to reserve space for additional stations that may be added at a later time, as discussed in section 9.6. In addition,

It is strongly recommended that there should be a station variable (which may be of any type) with
cf_role
attributetimeseries_id
, whose values uniquely identify the stations. 
It is recommended that there should be station variables with standard_name attributes
platform_name
,surface_altitude
andplatform_id
when applicable.
TimeSeriesProfiles are more complicated than timeSeries because there are two element dimensions (profile and vertical).
Each time series has a number of profiles from different times as its elements, and each profile has a number of data from various levels as its elements.
It is strongly recommended that there always be a variable (of any data type) with the profile dimension and the cf_role
attribute profile_id
, whose values uniquely identify the profiles.
H.5.1. Multidimensional array representations of time series profiles
When storing time series of profiles at multiple stations in the same data variable, if there are the same number of time points for all timeSeries, and the same number of vertical levels for every profile, one can use the multidimensional array representation:
dimensions: station = 22 ; profile = 3002 ; z = 42 ; variables: float lon(station) ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat(station) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; string station_name(station) ; station_name:cf_role = "timeseries_id" ; station_name:long_name = "station name" ; int station_info(station) ; station_info:long_name = "some kind of station info" ; float alt(station, profile , z) ; alt:standard_name = “altitude”; alt:long_name = "height above mean sea level" ; alt:units = "km" ; alt:positive = "up" ; alt:axis = "Z" ; double time(station, profile ) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; time:missing_value = 999.9; float pressure(station, profile , z) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat alt station_name" ; float temperature(station, profile , z) ; temperature:standard_name = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "Celsius" ; temperature:coordinates = "time lon lat alt station_name" ; float humidity(station, profile , z) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat alt station_name" ; attributes: :featureType = "timeSeriesProfile";
The pressure(i,p,o)
, temperature(i,p,o)
, and humidity(i,p,o)
data for element o
of profile p
at station i
are associated with the coordinate values time(i,p)
, z(i,p,o)
, lat(i)
, and lon(i)
.
Any of the three dimensions could be the netCDF unlimited dimension, if it might be useful to be able enlarge it.
If all of the profiles at any given station have the same set of vertical coordinates values, the vertical auxiliary coordinate variable could be dimensioned alt(station, z)
.
If all the profiles have the same set of vertical coordinates, the vertical auxiliary coordinate variable could be onedimensional alt(z)
, or replaced by a onedimensional coordinate variable z(z)
, provided the values are in strict monotonic order.
In the latter case, listing the vertical coordinate variable in the coordinates attribute is optional.
If the profiles are taken at all stations at the same set of times, the time auxiliary coordinate variable could be onedimensional time(profile)
, or replaced by a onedimensional coordinate variable time(time)
, where the size of the time
dimension is now equal to the number of profiles at each station.
In the latter case, listing the time coordinate variable in the coordinates attribute is optional.
If there is only a single set of levels and a single set of times, the multidimensional array representation is formally orthogonal:
dimensions: station = 10 ; // measurement locations pressure = 11 ; // pressure levels time = UNLIMITED ; variables: float humidity(time,pressure,station) ; humidity:standard_name = “specific_humidity” ; humidity:coordinates = "lat lon" ; double time(time) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; float lon(station) ; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat(station) ; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float pressure(pressure) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure" ; pressure:units = "hPa" ; pressure:axis = "Z" ;
humidity(p,o,i)
is associated with the coordinate values time(p)
, pressure(o)
, lat(i)
, and lon(i)
.
The number of profiles equals the number of times.
At the cost of some wasted space, the multidimensional array representation also allows one to have a variable number of profiles for different stations, and varying numbers of levels for different profiles. In these cases, any unused elements of the data and auxiliary coordinate variables must contain missing data values (section 9.6).
H.5.2. Time series of profiles at a single station
If there is only one station in the data variable, there is no need for the station dimension:
dimensions: profile = 30 ; z = 42 ; name_strlen = 23 ; variables: float lon ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; char station_name(name_strlen) ; station_name:cf_role = "timeseries_id" ; station_name:long_name = "station name" ; int station_info; station_info:long_name = "some kind of station info" ; float alt(profile , z) ; alt:standard_name = “altitude”; alt:long_name = "height above mean sea level" ; alt:units = "km" ; alt:axis = "Z" ; alt:positive = "up" ; double time(profile ) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; time:missing_value = 999.9; float pressure(profile , z) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat alt station_name" ; float temperature(profile , z) ; temperature:standard_name = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "Celsius" ; temperature:coordinates = "time lon lat alt station_name" ; float humidity(profile , z) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat alt station_name" ; attributes: :featureType = "timeSeriesProfile";
The pressure(p,o)
, temperature(p,o)
, and humidity(p,o)
data for element o
of profile p
are associated with the coordinate values time(p)
, alt(p,o)
, lat
, and lon
.
If all the profiles have the same set of vertical coordinates, the vertical auxiliary coordinate variable could be onedimensional alt(z)
, or replaced by a onedimensional coordinate variable z(z)
, provided the values are in strict monotonic order.
In the latter case, listing the vertical coordinate variable in the coordinates attribute is optional.
H.5.3. Ragged array representation of time series profiles
When the number of profiles and levels for each station varies, one can use a ragged array representation. Each of the two element dimensions (time and vertical) could in principle be stored either contiguous or indexed, but this convention supports only one of the four possible choices. This uses the contiguous ragged array representation for each profile (9.5.43.3), and the indexed ragged array representation to organise the profiles into time series (9.3.54). The canonical use case is when writing realtime data streams that contain profiles from many stations, arriving randomly, with the data for each entire profile written all at once.
dimensions: obs = UNLIMITED ; profiles = 1420 ; stations = 42; variables: float lon(station) ; lon:standard_name = "longitude"; lon:long_name = "station longitude"; lon:units = "degrees_east"; float lat(station) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(station) ; alt:long_name = "altitude above MSL" ; alt:units = "m" ; string station_name(station) ; station_name:long_name = "station name" ; station_name:cf_role = "timeseries_id"; int station_info(station) ; station_info:long_name = "some kind of station info" ; int profile(profile) ; profile:cf_role = "profile_id"; double time(profile); time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; int station_index(profile) ; station_index:long_name = "which station this profile is for" ; station_index:instance_dimension = "station" ; int row_size(profile) ; row_size:long_name = "number of obs for this profile " ; row_size:sample_dimension = "obs" ; float z(obs) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:axis = "Z" ; z:positive = "up" ; float pressure(obs) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat z station_name" ; float temperature(obs) ; temperature:standard_name = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "Celsius" ; temperature:coordinates = "time lon lat z station_name" ; float humidity(obs) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat z station_name" ; attributes: :featureType = "timeSeriesProfile";
The pressure(o)
, temperature(o)
, and humidity(o)
data for element o
of profile p
at station i
are associated with the coordinate values time(p)
, z(o)
, lat(i)
, and lon(i)
.
The index variable (station_index
) is identified by having an attribute with name of instance_dimension whose value is the instance dimension name (station
in this example).
The index variable must have the profile dimension as its sole dimension, and must have an integer type.
Each value in the index variable is the zerobased station index that the profile belongs to i.e. profile p
belongs to station i=station_index(p)
, as in section H.2.5.
The count variable (row_size
) contains the number of elements for each profile, which must be written contiguously.
The count variable is identified by having an attribute with name sample_dimension
whose value is the sample dimension (obs
in this example) being counted.
It must have the profile dimension as its sole dimension, and must have an integer type.
The number of elements in profile p
is recorded in row_size(p)
, as in section H.2.4.
The sample dimension need not be the netCDF unlimited dimension, though it commonly is.
H.6. Trajectory of Profiles
When profiles are taken along a trajectory, one gets a collection of profiles called a trajectoryProfile.
A data variable may contain a collection of such trajectoryProfile features, one feature per trajectory.
The instance dimension in the case of a trajectoryProfile is also referred to as the trajectory dimension.
The instance variables, which have just this dimension, are also referred to as trajectory variables and are considered to contain information describing the trajectories.
The trajectory variables may contain missing values.
This allows one to reserve space for additional trajectories that may be added at a later time, as discussed in section 9.6.
TrajectoryProfiles are more complicated than trajectories because there are two element dimensions.
Each trajectory has a number of profiles as its elements, and each profile has a number of data from various levels as its elements.
It is strongly recommended that there always be a variable (of any data type) with the profile dimension and the cf_role
attribute profile_id
, whose values uniquely identify the profiles.
H.6.1. Multidimensional array representation of trajectory profiles
If there are the same number of profiles for all trajectories, and the same number of vertical levels for every profile, one can use the multidimensional representation:
dimensions: trajectory = 22 ; profile = 33; z = 42 ; variables: int trajectory (trajectory ) ; trajectory:cf_role = "trajectory_id" ; float lon(trajectory, profile) ; lon:standard_name = "longitude"; lon:units = "degrees_east"; float lat(trajectory, profile) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(trajectory, profile , z) ; alt:standard_name = “altitude”; alt:long_name = "height above mean sea level" ; alt:units = "km" ; alt:positive = "up" ; alt:axis = "Z" ; double time(trajectory, profile ) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; time:missing_value = 999.9; float pressure(trajectory, profile , z) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat alt" ; float temperature(trajectory, profile , z) ; temperature:standard_name = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "Celsius" ; temperature:coordinates = "time lon lat alt" ; float humidity(trajectory, profile , z) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat alt" ; attributes: :featureType = "trajectoryProfile";
The pressure(i,p,o)
, temperature(i,p,o)
, and humidity(i,p,o)
data for element o
of profile p
along trajectory i
are associated with the coordinate values time(i,p)
, alt(i,p,o)
, lat(i,p)
, and lon(i,p)
.
Any of the three dimensions could be the netCDF unlimited dimension, if it might be useful to be able enlarge it.
If all of the profiles along any given trajectory have the same set of vertical coordinates values, the vertical auxiliary coordinate variable could be dimensioned alt(trajectory, z)
.
If all the profiles have the same set of vertical coordinates, the vertical auxiliary coordinate variable could be onedimensional alt(z)
, or replaced by a onedimensional coordinate variable z(z)
, provided the values are in strict monotonic order.
In the latter case, listing the vertical coordinate variable in the coordinates attribute is optional.
If the profiles are taken along all the trajectories at the same set of times, the time auxiliary coordinate variable could be onedimensional time(profile)
, or replaced by a onedimensional coordinate variable time(time)
, where the size of the time dimension is now equal to the number of profiles along each trajectory.
In the latter case, listing the time coordinate variable in the coordinates attribute is optional.
At the cost of some wasted space, the multidimensional array representation also allows one to have a variable number of profiles for different trajectories, and varying numbers of levels for different profiles. In these cases, any unused elements of the data and auxiliary coordinate variables must contain missing data values (section 9.6).
H.6.2. Profiles along a single trajectory
If there is only one trajectory in the data variable, there is no need for the trajectory dimension:
dimensions: profile = 33; z = 42 ; variables: int trajectory; trajectory:cf_role = "trajectory_id" ; float lon(profile) ; lon:standard_name = "longitude"; lon:units = "degrees_east"; float lat(profile) ; lat:standard_name = "latitude"; lat:long_name = "station latitude" ; lat:units = "degrees_north" ; float alt(profile, z) ; alt:standard_name = “altitude”; alt:long_name = "height above mean sea level" ; alt:units = "km" ; alt:positive = "up" ; alt:axis = "Z" ; double time(profile ) ; time:standard_name = "time"; time:long_name = "time of measurement" ; time:units = "days since 19700101 00:00:00" ; time:missing_value = 999.9; float pressure(profile, z) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat alt" ; float temperature(profile, z) ; temperature:standard_name = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "Celsius" ; temperature:coordinates = "time lon lat alt" ; float humidity(profile, z) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat alt" ; attributes: :featureType = "trajectoryProfile";
The pressure(p,o)
, temperature(p,o)
, and humidity(p,o)
data for element o
of profile p
are associated with the coordinate values time(p)
, alt(p,o)
, lat(p)
, and lon(p)
.
If all the profiles have the same set of vertical coordinates, the vertical auxiliary coordinate variable could be onedimensional alt(z)
, or replaced by a onedimensional coordinate variable z(z)
, provided the values are in strict monotonic order.
In the latter case, listing the vertical coordinate variable in the coordinates attribute is optional.
H.6.3. Ragged array representation of trajectory profiles
When the number of profiles and levels for each trajectory varies, one can use a ragged array representation. Each of the two element dimensions (along a trajectory, within a profile) could in principle be stored either contiguous or indexed, but this convention supports only one of the four possible choices. This uses the contiguous ragged array representation for each profile (9.3.3), and the indexed ragged array representation to organise the profiles into time series (9.3.4). The canonical use case is when writing realtime data streams that contain profiles from many trajectories, arriving randomly, with the data for each entire profile written all at once.
dimensions: obs = UNLIMITED ; trajectory = 22 ; profile = 142 ; variables: int trajectory(trajectory) ; cf_role = "trajectory_id" ; double time(profile); time:standard_name = "time"; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(profile); lon:standard_name = "longitude"; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(profile); lat:standard_name = "latitude"; lat:long_name = "latitude" ; lat:units = "degrees_north" ; int row_size(profile) ; row_size:long_name = "number of obs for this profile " ; row_size:sample_dimension = "obs" ; int trajectory_index(profile) ; trajectory_index:long_name = "which trajectory this profile is for" ; trajectory_index:instance_dimension= "trajectory" ; float z(obs) ; z:standard_name = “altitude”; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ; z:axis = "Z" ; float pressure(obs) ; pressure:standard_name = "air_pressure" ; pressure:long_name = "pressure level" ; pressure:units = "hPa" ; pressure:coordinates = "time lon lat z" ; float temperature(obs) ; temperature:standard_name = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "Celsius" ; temperature:coordinates = "time lon lat z" ; float humidity(obs) ; humidity:standard_name = "relative_humidity" ; humidity:long_name = "relative humidity" ; humidity:units = "%" ; humidity:coordinates = "time lon lat z" ; attributes: :featureType = "trajectoryProfile";
The pressure(o)
, temperature(o)
, and humidity(o)
data for element o
of profile p
along trajectory i
are associated with the coordinate values time(p)
, z(o)
, lat(p)
, and lon(p)
.
The index variable (trajectory_index
) is identified by having an attribute with name of instance_dimension
whose value is the instance dimension name (trajectory in this example).
The index variable must have the profile dimension as its sole dimension, and must have an integer type.
Each value in the index variable is the zerobased trajectory index that the profile belongs to i.e. profile p
belongs to trajectory i=trajectory_index(p)
, as in section H.2.5.
The count variable (row_size
) contains the number of elements for each profile, which must be written contiguously.
The count variable is identified by having an attribute with name sample_dimension
whose value is the sample dimension (obs
in this example) being counted.
It must have the profile dimension as its sole dimension, and must have an integer type.
The number of elements in profile p
is recorded in row_size(p)
, as in section H.2.4.
The sample dimension need not be the netCDF unlimited dimension, though it commonly is.
Appendix I: The CF data model
The CF conventions are designed to promote the creation, processing, and sharing of climate and forecasting data using Network Common Data Form (netCDF) files and libraries. This appendix contains the explicit data model for CF to provide an interpretation of the conceptual structure of CF which is consistent, comprehensive, and as far as possible independent of the netCDF encoding. An explicit comprehensive data model promotes the CF conventions being better understood, provides guidance during the development of future extensions to the CF conventions, and helps software developers to design CFcompliant dataprocessing applications and to build interfaces to other explicit data models.
Introduction
A data model is an abstract interpretation of the data, that identifies the elements of the dataset and their scientific intent, and describes how they are related to one another and to the real or model world from which the data were derived. A data model is necessary because it imposes the rules, constraints, and relationships connecting metadata to the data that are needed to imagine how the quantities included in the dataset should be combined and processed scientifically.
The CF data model was first created for CF version 1.6 and published externally in journal Geoscientific Model Development (GMD) [CFDM], and that version also includes further discussions on the background and motivation, as well as on the relationships between the CF data model and other data models. The data model was transcribed from the GMD paper into the CF conventions at version 1.9, also incorporating the modifications required to represent new features introduced at versions 1.7, 1.8 and 1.9.
Design criteria of the CF data model
The primary requirement of the data model is that it should be able to describe all existing and conceivable CFcompliant datasets.
The data model should comprise a minimal set of elements that are sufficient for accommodating all aspects of the CF conventions. The elements of the data model are restricted to those that are explicitly mentioned in CF, but there do not have to be as many elements in the data model as there are elements described by CF, because a single data model element can incorporate more than one CF entity. For example, in CF, coordinates and coordinate bounds are distinct elements, but coordinate bounds cannot exist without coordinates. Therefore, it makes sense in the data model to group them into a single element.
Similarly, while it is possible to introduce additional elements not presently needed or used by CF, this would not be desirable because it would increase the likelihood of the data model becoming outdated or inconsistent with future versions of CF.
The CF data model should also be independent of the encoding. This means that it should not be constrained by the parts of the CF conventions which describe explicitly how to store (i.e. encode) metadata in a netCDF file. The virtue of this is that should netCDF ever fail to meet the community needs, the groundwork for applying CF to other file formats will already exist.
Elements of CFnetCDF
The CFnetCDF elements are listed in Table I.1 and shown (in blue) with their interrelationships in Figure I.1. The CF data model has been derived from these CFnetCDF elements and relationships with the aims of removing aspects specific to the netCDF encoding, and reducing the number of elements, whilst retaining the ability to describe the CF conventions fully, in order to meet the design criteria.
CFnetCDF element  Description 

Domain variable 
Discrete locations in multidimensional space 
Data variable 
Scientific data discretised within a domain 
Dimension 
Independent axis of the domain 
Coordinate variable 
Unique coordinates for a single axis 
Auxiliary coordinate variable 
Additional or alternative coordinates for any axes 
Scalar coordinate variable 
Coordinate for an implied size one axis 
Grid mapping variable 
Horizontal coordinate system 
Boundary variable 
Cell vertices 
Cell measure variable 
Cell areas or volumes 
Ancillary data variable 
Metadata that depends on the domain 
Mesh topology variable 
One or more related domains with cell connectivity 
Location index set variable 
A domain with cell connectivity 
Formula terms attribute 
Vertical coordinate system 
Feature type attribute 
Characteristics of discrete sampling geometry 
Cell methods attribute 
Description of variation within cells 
The CF data model
The elements of the CF data model (Figure I.2, Figure I.3 and Figure I.4) are called "constructs", a term chosen to differentiate from the CFnetCDF elements previously defined and to be programming languageneutral (i.e. as opposed to "object" or "structure"). The constructs, listed in Table I.2, are related to CFnetCDF elements (Figure I.1), which in turn relate to the components of netCDF file.
CF construct  Description 

Domain 
Discrete locations in multidimensional space 
Field 
Scientific data discretised within a domain 
Domain axis 
Independent axes of the domain 
Dimension coordinate 
Cell locations 
Auxiliary coordinate 
Cell locations 
Coordinate reference 
Domain coordinate systems 
Domain ancillary 
Cell locations in alternative coordinate systems 
Cell measure 
Cell size or shape 
Domain topology 
Geospatial topology of domain cells 
Cell connectivity 
Connectivity of domain cells 
Field ancillary 
Ancillary metadata which varies within the domain 
Cell method 
Describes how data represents variation within cells 
The field construct and domain construct are central to the CF data model in that all the other constructs are included in one or other of them (Figure I.2). The constructs contained by the field and domain constructs cannot exist independently, with the exception of the domain construct itself that may be part of a field construct or exist on its own, as is indicated by the nature of the class associations shown in Figure I.2. All CFnetCDF elements are mapped to field constructs, domain constructs or their components; and the field and domain constructs completely contain all the data and metadata which can be extracted from the file using the CF conventions.
Field construct
A field construct (Figure I.2) corresponds to a CFnetCDF data variable with all of its metadata. The field construct consists of

A data array.

A domain construct containing metadata defining the domain that provides measurement locations and cell properties for the data.

Field ancillary constructs containing ancillary metadata defined over the same domain.

Cell method constructs containing metadata to describe how the cell values represent the variation of the physical quantity within the cells of the domain.

Properties to describe aspects of the data that are independent of the domain.
All of the constructs contained by the field construct are optional (as indicated by "0.." in Figure I.2). The only component of the field which is mandatory is the data array.
The properties of the field construct correspond to some netCDF attributes of variables (e.g. units
, long_name
, and standard_name
); and some netCDF group attributes, which include global attributes in the root group, such as history
and institution
.
The term "property" is used, rather than "attribute", because not all CFnetCDF attributes are properties in this sense—some CFnetCDF attributes are used to point to (i.e. reference) other netCDF variables and so only describe the data indirectly (e.g. the coordinates attribute), and others have structural functions in the CFnetCDF file (e.g. the Conventions attribute).
In the data model, netCDF group attributes apply to every data variable in the file, except where they are overridden by netCDF data variable attributes with the same name.
This interpretation of group attributes is not stated in the CF conventions, but for the data model it is necessary because there is no notion of a group.
Hence, metadata stored in attributes of the group as a whole have to be transferred to the field construct.
If present, the global file attribute (i.e. root group attribute) featureType
applies to every data variable in the file with a discrete sampling geometry.
Hence, the feature type is regarded as a property of the field construct.
The standard_name
property constrains the units
property (i.e. only certain units are consistent with each standard name) and in some cases also the dimensions that a data variable must have.
These constraints, however, do not supply any further information—they are just for self consistency.
Similarly the featureType
property imposes some requirements on the axes the domain must have.
Following the aim of constructing a minimal data model, the standard name and feature type are not regarded as separate constructs within the field, because they do not depend on any other construct for their interpretation.
Domain construct
The domain construct (Figure I.2) describes a domain comprising measurement locations and cell properties. The domain construct is the only metadata construct that may also exist independently of a field construct. The domain construct contains properties to describe the domain (in the same sense as for the field construct) and relates the following metadata constructs

Domain axis constructs.

Dimension coordinate and auxiliary coordinate constructs.

Coordinate reference constructs.

Domain ancillary constructs.

Cell measure constructs.

Domain topology constructs.

Cell connectivity constructs.
All of the constructs contained by the domain construct are optional (as indicated by "0.." in Figure I.2).
In CFnetCDF, domain information is stored either implicitly via data variable attributes (such as coordinates
), or explicitly in a domain variable.
In the latter case, the domain exists without reference to a data array.

implicitly via data variable attributes (such as
coordinates
); 
explicitly in a domain variable;

explicitly in a mesh topology variable, in which case the domain may be one of multiple domains defined by the same variable (for instance, a single mesh topology variable could contain different domains defined respectively at node, edge, and face mesh elements);

explicitly in a location index set variable that references a subset of another domain defined by a mesh topology variable.
For the explicit cases, the domain exists without reference to a data array.
Domain axis construct and the data array
A domain axis construct (Figure I.3) comprises a positive integer which specifies the number of cells lying along an independent axis of the domain. In CFnetCDF, it is usually defined either by a netCDF dimension or by a scalar coordinate variable, which implies a domain axis of size one. The field construct’s data array spans the domain axis constructs of the domain, except that the sizeone axes may optionally be omitted, because their presence makes no difference to the order of the elements. Hence, the data array may be zerodimensional (i.e. scalar) if there are no domain axis constructs of size greater than one.
When a collection of discrete sampling geometry (DSG) features has been combined in a data variable using the incomplete orthogonal or ragged representations to save space, the axis size has to be inferred, but this is an aspect of unpacking the data, rather than its conceptual description. In practice, the unpacked data array may be dominated by missing values (as could occur, for example, if all features in a collection of time series had no common time coordinates), in which case it may be preferable to view the collection as if each DSG feature were a separate variable, each one corresponding to a different field construct.
Coordinates: dimension coordinate and auxiliary constructs
Coordinate constructs (Figure I.3) provide information which locate the cells of the domain and which depend on a subset of the domain axis constructs. A coordinate construct consists of an optional data array of the coordinate values spanning the subset of the domain axis constructs, properties to describe the coordinates (in the same sense as for the field construct), an optional data array of cell bounds recording the extents of each cell, and any extra arrays needed to interpret the cell bounds values. The data array of the coordinate values is required, execpt for the special cases described below.
There are two distinct types of coordinate construct: dimension coordinate constructs unambiguously describe cell locations for a single domain axis, thus providing independent variables on which the field construct’s data depend; and auxiliary coordinate constructs provide any type of coordinate information for one or more of the domain axes.
A dimension coordinate construct contains numeric coordinates for a single domain axis that are nonmissing and strictly monotonically increasing or decreasing. CFnetCDF coordinate variables and numeric scalar coordinate variables correspond to dimension coordinate constructs.
Auxiliary coordinate constructs have to be used, instead of dimension coordinate constructs, when a single domain axis requires more than one set of coordinate values, when coordinate values are not numeric, strictly monotonic, or contain missing values, or when they vary along more than one domain axis construct simultaneously. CFnetCDF auxiliary coordinate variables and nonnumeric scalar coordinate variables correspond to auxiliary coordinate constructs.
When cell bounds are provided, each cell comprises one or more parts, and each part is either a collection of points, a line defined by a connected series of points, or a polygonal area (i.e. the region enclosed by a connected series of points, where the first and last points are connected as well). All parts of all the cells must be of the same one of these three kinds, which are called "geometry types". The bounds array spans the domain axis constructs of the coordinate construct, with the addition of two trailing ragged dimensions. The first extra dimension indexes the parts of each cell and the second indexes the points that describe each part.
If cell bounds are provided for a dimension coordinate construct then each cell must have exactly two vertices forming a line geometry. For climatological time coordinates the actual cell extent comprises multiple time segments equivalent to multiple line geometry parts, but the bounds require just two points to define each cell, namely the earliest and latest times of the sequence. The cell method constructs indicate how the multiple time segments should be inferred from these climatological bounds.
If a polygonal cell is composed of multiple parts it may have holes, i.e. polygon regions that are to be omitted from, as opposed to included in, the cell extent. When such holes are present an "interior ring" array is required that records whether each polygon is to be included or excluded from the cell, and is supplied by an interior ring variable in CFnetCDF. The interior ring array spans the domain axis constructs of the coordinate construct, with the addition of an extra ragged dimension that indexes the parts for each cell. For example, a cell describing the land area surrounding a lake would require two polygon parts: one defines the outer boundary of the land area; the other, recorded as an interior ring, is the lake boundary, defining the inner boundary of the land area.
If a domain axis construct does not correspond to a continuous physical quantity, then it is not necessary for it to be associated with a dimension coordinate construct. For example, this is the case for an axis that runs over ocean basins or area types, or for a domain axis that indexes a time series at scattered points. These axes are discrete axes in CFnetCDF. In such cases cells may be described with onedimensional auxiliary coordinate constructs for which, provided that there is a cell bounds array to describe the cell extents, the coordinate array is optional, since coordinates are not always well defined for such cells. A CFnetCDF geometry container variable or mesh topology variable is used to store cell bounds without coordinates for a discrete axis.
In CFnetCDF, when a geometry container variable is present it explicitly describes the geometry type and identifies the node coordinate variables that contain the cell vertices. The geometry container variable also identifies a node count variable that contains the number of nodes per cell when more than one cell is present, and a part node count variable that contains the number of nodes per cell part when cells are composed of multipart lines, multipart polygons, or polygons with holes. When a geometry container variable is not present then the bounds contain exactly one part and their geometry type is implied by convention: for multidimensional auxiliary coordinates each cell is a single polygon, and for all other types of coordinate each cell is a single line segment defined by two points. In the case of climatological time coordinates, the two points of the cell bounds, in conjunction with the cell methods, imply the existence of multiple line parts, different subsets of which are associated with the different cell methods required to define the climatology. For example, when the field construct’s data are multiannual averages of monthly minima, the implied cell parts define the individual months over which the original data was minimised; and all of the implied parts taken together define the exact temporal extent of the average of the monthly minima.
Coordinate reference construct
The domain may contain various coordinate systems, each of which is constructed from a subset of the dimension and auxiliary coordinate constructs. For example, the domain of a fourdimensional field construct may contain horizontal (yx), vertical (z), and temporal (t) coordinate systems. There may be more than one of each of these, if there is more than one coordinate construct applying to a particular spatiotemporal dimension (for example, there could be both latitudelongitude and yx projection coordinate systems).
A coordinate system may be constructed implicitly from any subset of the coordinate constructs, yet a coordinate construct does not need to be explicitly or exclusively associated with any coordinate system. A coordinate system of the field construct can be explicitly defined by a coordinate reference construct (Figure I.4) which relates the coordinate values of the coordinate system to locations in a planetary reference frame and consists of the following:

The dimension coordinate and auxiliary coordinate constructs that define the coordinate system to which the coordinate reference construct applies. Note that the coordinate values are not relevant to the coordinate reference construct, only their properties.

A definition of a datum specifying the zeroes of the dimension and auxiliary coordinate constructs which define the coordinate system. The datum may be explicitly indicated via properties, or it may be implied by the metadata of the contained dimension and auxiliary coordinate constructs. For example, in a twodimensional geographical latitudelongitude coordinate system based upon a spherical Earth, the datum is assumed to be 0^{o}N, 0^{o}E. Note that the datum may contain the definition of a geophysical surface which corresponds to the zero of a vertical coordinate construct, and this may be required for both horizontal and vertical coordinate systems.

A coordinate conversion, which defines a formula for converting coordinate values taken from the dimension or auxiliary coordinate constructs to a different coordinate system. A term of the conversion formula can be a scalar or vector parameter which does not depend on any domain axis constructs, may have units (such as a reference pressure value), or may be a descriptive string (such as the projection name "mercator"), or it can be a domain ancillary construct (such as one containing spatially varying orography data).
For yx coordinates, the coordinate conversion is either a map projection, which converts between Cartesian coordinates and spherical or ellipsoidal coordinates on the vertical datum, or a conversion between different spherical coordinate systems (as in the case of rotated pole coordinates). In the case of z coordinates, the conversion is between a coordinate construct with parameterised values (such as ocean sigma coordinates) and a coordinate construct with dimensional values (such as depths), again with respect to the vertical datum. The coordinate conversion is not required if no other coordinate systems are described.
Some parts of the coordinate reference construct may not be relevant to a given coordinate construct which it contains. The relevant parts are determined by an application using the coordinate reference construct. For example, for a coordinate reference construct which contained coordinate constructs for yx projection and latitude and longitude coordinates, a datum comprising a reference ellipsoid would apply to all of them, but projection parameters would only apply to the projection coordinates.
In CFnetCDF, coordinate system information that is not found in coordinate or auxiliary coordinate variables is stored in a grid mapping variable or the formula_terms attribute of a coordinate variable, for horizontal or vertical coordinate variables, respectively. Although these two cases are arranged differently in CFnetCDF, each one contains, sometimes implicitly, a datum or a coordinate conversion formula (or both) and is therefore regarded as a coordinate reference construct by the data model. A grid mapping name or the standard name of a parametric vertical coordinate corresponds to a stringvalued scalar parameter of a coordinate conversion formula. A grid mapping parameter which has more than one value (as is possible with the "standard parallel" attribute) corresponds to a vector parameter of a coordinate conversion formula. A data variable referenced by a formula_terms attribute corresponds to the term of a coordinate conversion formula—either a domain ancillary construct or, if it is zerodimensional, a scalar parameter.
formula_terms
attribute of a CFnetCDF coordinate variable. The coordinate reference construct is composed of generic coordinate constructs, a datum, and a coordinate conversion formula. The coordinate conversion formula is usually defined by a named formula in the CF conventions. A domain ancillary construct term of a coordinate conversion formula is defined by a CFnetCDF data variable or a CFnetCDF generic coordinate variable.Domain ancillary construct
A domain ancillary construct (Figure I.4) provides information which is needed for computing the location of cells in an alternative coordinate system. It is the value of a term of a coordinate conversion formula that contains a data array which is either scalar or which depends on one, more or all of the domain axis constructs.
It also contains an optional array of cell bounds recording the extents of each cell (only applicable if the array contains coordinate data) and properties to describe the data (in the same sense as for the field construct). An array of cell bounds spans the same domain axes as the data array, with the addition of an extra dimension whose size is that of the number of vertices of each cell.
CFnetCDF variables named by the formula_terms
attribute of a CFnetCDF coordinate variable correspond to domain ancillary constructs.
These CFnetCDF variables may be coordinate, scalar coordinate, or auxiliary coordinate variables, or they may be data variables.
For example, in a coordinate conversion for converting between ocean sigma and height coordinate systems, the value of the "depth" term for horizontally varying distance from ocean datum to sea floor would correspond to a domain ancillary construct.
In the case of a named term being a type of coordinate variable, that variable will correspond to an independent domain ancillary construct in addition to the coordinate construct; that is, a single CFnetCDF variable is translated into two constructs (see Example I.1).
float eta(eta) ; eta:long_name = "eta at full levels" ; eta:positive = "down" ; eta:standard_name = "atmosphere_hybrid_sigma_pressure_coordinate" ; eta:formula_terms = "a: A b: B ps: PS p0: P0" ; float A(eta) ; A:units = "Pa" ; float B(eta) ; B:units = "1" ; float PS(lat, lon) ; PS:units = "Pa" ; float P0 ; P0:units = "Pa" ; float temp(eta, lat, lon) ; temp:standard_name = "air_temperature" ; temp:units = "K"; temp:coordinates = "A B" ;
The netCDF variable A
corresponds to an auxiliary coordinate construct (since it is referenced by the coordinates
attribute) as well as a domain ancillary construct (since it is referenced by the formula_terms
attribute).
Similarly for the netCDF variable B
.
Cell measure construct
A cell measure (Figure I.2) construct provides information about the size or shape of the cells and depending on one, more or all of the domain axis constructs. Cell measure constructs have to be used when the size or shape of the cells cannot be deduced from the dimension or auxiliary coordinate constructs without special knowledge that a generic application cannot be expected to have.
The cell measure construct consists of a numeric array of the metric data which span one, more or all of the domain axis constructs, and properties to describe the data (in the same sense as for the field construct). The properties must contain a "measure" property, which indicates which metric of the space it supplies, e.g. cell horizontal areas, and a units property consistent with the measure property, e.g. m2. It is assumed that the metric does not depend on axes of the domain which are not spanned by the array, along which the values are implicitly propagated. CFnetCDF cell measure variables correspond to cell measure constructs.
Domain topology construct
A domain topology construct defines the geospatial topology of cells arranged in two or three dimensions in real space but indexed by a single (discrete) domain axis construct, and at most one domain topology construct may be associated with any such domain axis. The topology describes topological relationships between the cells  spatial relationships which do not depend on the cell locations  and is represented by an undirected graph, i.e. a mesh in which pairs of nodes are connected by links. Each node has a unique arbitrary identity that is independent of its spatial location, and different nodes may be spatially colocated.
The topology may only describe cells that have a common spatial dimensionality, one of:

Point: A point is zerodimensional and has no boundary vertices.

Edge: An edge is onedimensional and corresponds to a line connecting two boundary vertices.

Face: A face is twodimensional and corresponds to a surface enclosed by a set of edges.
Each type of cell implies a restricted topology for which only some kinds of mesh are allowed. For point cells, every node corresponds to exactly one cell; and two cells have a topological relationship if and only if their nodes are connected by a mesh link. For edge and face cells, every node corresponds to a boundary vertex of a cell; the same node can represent vertices in multiple cells; every link in the mesh connects two cell boundary vertices; and two cells have a topological relationship if and only if they share at least one node.
For example, the mesh depicted in Figure I.5 may be used with any of three domain topology constructs for domains comprising two face cells (one triangle and one quadrilateral), six edge cells, and five point cells respectively.
A domain topology construct contains an array defining the mesh, and properties to describe it. There must be a property indicating the spatial dimensionality of the cells. The array values comprise the node identities, and all array elements that refer to the same node must contain the same value, which must differ from any other value in the array. The array spans the domain axis construct and also has a ragged dimension, whose function depends on the spatial dimensionality of the cells.
For each point cell, the first element along the ragged dimension contains the node identity of the cell, and the following elements contain in arbitrary order the identities of all the cells to which it is connected by a mesh link.
For each edge or face cell, the elements along the ragged dimension contain the node identities of the boundary vertices of the cell, in the same order that the boundary vertices are stored by the auxiliary coordinate constructs. Each boundary vertex except the last is connected by a mesh link to the next vertex along the ragged dimension, and the last vertex is connected to the first.
When a domain topology construct is present it is considered to be definitive and must be used in preference to the topology implied by inspection of any other constructs, which is not guaranteed to be the same.
In CFnetCDF a domain topology construct can only be provided for a UGRID mesh topology variable. The information in the construct array is supplied by the UGRID "edge_nodes_connectivity" variable (for edge cells) or "face_nodes_connectivity" variable (for face cells). The topology for node cells may be provided by any of these three UGRID variables. The integer indices contained in the UGRID variable may be used as the mesh node identities, although the CF data model attaches no significance to the values other than the fact that some values are the same as others. The spatial dimensionality property is provided by the "location" attribute of a variable that references the UGRID mesh topology variable, i.e. a data variable or a UGRID location index set variable.
A single UGRID mesh topology defines multiple domain constructs and defines how they relate to each other. For instance, when "face_node_connectivity" and "edge_node_connectivity" variables are both present there are three implied domain constructs  one each for face, edge and point cells  all of which have the same mesh and so are explicitly linked (e.g. it is known which edge cells define each face cell). The CF data model has no mechanism for explicitly recording such relationships between multiple domain constructs. Whether or not two domains have the same mesh may be reliably deternined by inspection, thereby allowing the creation of netCDF datasets containing UGRID mesh topology variables.
The restrictions on the type of mesh that may be used with a given cell spatial dimensionality excludes some meshes which can be described by an undirected graph, but is consistent with UGRID encoding within CFnetCDF. UGRID also describes meshes for threedimensional volume cells that correspond to a volume enclosed by a set of faces, but how the nodes relate to volume boundary vertices is undefined and so volume cells are currently omitted from the CF data model.
Cell connectivity construct
A cell connectivity construct defines explicitly how cells arranged in two or three dimensions in real space but indexed by a single domain (discrete) axis are connected. Connectivity can only be provided when the domain axis construct also has a domain topology construct, and two cells can only be connected if they also have a topological relationship. For instance, the connectivity of twodimensional face cells could be characterised by whether or not they have shared edges, where the edges are defined by connected nodes of the domain topology construct.
The cell connectivity construct consists of an array recording the connectivity, and properties to describe the data. There must be a property indicating the condition by which the connectivity is derived from the domain topology. The array spans the domain axis construct with the addition of a ragged dimension. For each cell, the first element along the ragged dimension contains the unique identity of the cell, and the following elements contain in arbitrary order the identities of all the other cells to which the cell is connected. Note that the connectivity array for point cells is, by definition, equivalent to the array of the domain topology construct.
When cell connectivity constructs are present, they are considered to define the connectivity of the cells. Exactly the same connectivity information could be derived from the domain topology construct. Connectivity information inferred from inspection of any other constructs is not guaranteed to be the same.
In CFnetCDF a cell topology construct can only be provided by a UGRID mesh topology variable. The construct array is supplied either indirectly by any of the UGRID variables that are used to define a domain topology construct, or directly by the UGRID "face_face_connectivity" variable (for face cells). In the direct case, the integer indices contained in the UGRID variable may be used as the cell identities, although the CF data model attaches no significance to the values other than the fact that some values are the same as others.
Restricting the types of connectivity to those implied by the geospatial topology of the cells precludes connectivity derived from any other sources, but is consistent with UGRID encoding within CFnetCDF.
Field ancillary constructs
The field ancillary construct (Figure I.2) provides metadata which are distributed over the same sampling domain as the field itself. For example, if a data variable holds a variable retrieved from a satellite instrument, a related ancillary data variable might provide the uncertainty estimates for those retrievals (varying over the same spatiotemporal domain).
The field ancillary construct consists of an array of the ancillary data which is either scalar or which depends on one, more or all of the domain axis constructs, and properties to describe the data (in the same sense as for the field construct). It is assumed that the data do not depend on axes of the domain which are not spanned by the array, along which the values are implicitly propagated. CFnetCDF ancillary data variables correspond to field ancillary constructs. Note that a field ancillary construct is constrained by the domain definition of the parent field construct but does not contribute to the domain’s definition, unlike, for instance, an auxiliary coordinate construct or domain ancillary construct.
Cell method construct
The cell method constructs (Figure I.2) describe how the cell values represent the variation of the physical quantity within its cells—the structure of the data at a higher resolution. A single cell method construct consists of a set of axes (see below), a "method" property which describes how a value of the field construct’s data array describes the variation of the quantity within a cell over those axes (e.g. a value might represent the cell area average), and properties serving to indicate more precisely how the method was applied (e.g. recording the spacing of the original data, or the fact the method was applied only over El Niño years).
The field construct may contain an ordered sequence of cell method constructs describing multiple processes which have been applied to the data, e.g. a temporal maximum of the areal mean has two components—a mean and a maximum, each acting over different sets of axes.
It is an ordered sequence because the methods specified are not necessarily commutative.
There are properties to indicate climatological time processing, e.g. multiannual means of monthly maxima, in which case multiple cell method constructs need to be considered together to define a special interpretation of boundary coordinate array values.
The cell_methods
attribute of a CFnetCDF data variable corresponds to one or more cell method constructs.
The axes over which a cell method applies are either a subset of the domain axis constructs or a collection of strings which identify axes that are not part of the domain.
The latter case is particularly useful when the coordinate range for an axis cannot be precisely defined, making it impossible to define a domain axis construct.
For example, a climatological time mean might be based on data which are not available over the same time periods at every horizontal location—the useful information that the data have been temporally averaged can be recorded without specifying the range of times.
The strings which identify such axes are well defined in that they must be standard names (e.g. time, longitude) or the special string area
, indicating a combination of horizontal axes.
Appendix J: Coordinate Interpolation Methods
The general description of the compression by coordinate subsampling is given in section Section 8.3, "Lossy Compression by Coordinate Subsampling". This appendix provides details on the available methods for compression by coordinate subsampling.
The definitions and guidance given here allow an application to compress an existing data set using coordinate subsampling, while letting the creator of the compressed dataset control the accuracy of the reconstituted coordinates through the degree of subsampling, the choice of interpolation method and by setting the computational precision.
Furthermore, the definitions given here allow an application to uncompress coordinate and auxiliary coordinate variables that have been compressed using coordinate subsampling. The key element of this process is the reconstitution of the full resolution coordinates in the domain of the data by interpolation between the subsampled coordinates, the tie points, stored in the compressed dataset.
The appendix is organised in a sections on Section J.1, "Common Definitions and Notation", Section J.2, "Common Conversions and Formulas", Section J.3, "Interpolation Methods" and finally two sections with step procedures Section J.4, "Coordinate Compression Steps" and Section J.5, "Coordinate Uncompression Steps".
Common Definitions and Notation
The coordinate interpolation methods are named to indicate the number of dimensions they interpolate as well as the type of interpolation provided.
For example, the interpolation method named linear
provides linear interpolation in one dimension and the method named bi_linear
provides linear interpolation in two dimensions.
Equivalently, the interpolation method named quadratic
provides quadratic interpolation in one dimension and the interpolation method named bi_quadratic
provides quadratic interpolation in two dimensions.
When an interpolation method is referred to as linear or quadratic, it means that the method is linear or quadratic in the indices of the interpolated dimensions.
For convenience, an interpolation argument s
is introduced, calculated as a function of the index in the target domain of the coordinate value to be reconstituted.
In the case of onedimensional interpolation the variable is computed as:
s = s(ia, ib, i) = (i  ia)/(ib  ia)
where ia
and ib
are the indices in the target domain of the tie points A
and B
and i
is the index in the target domain of the coordinate value to be reconstituted.
Note that the value of s
varies from 0.0
at the tie point A
to 1.0
at tie point B
.
For example, if ia = 100
and ib = 110
and the index in the target domain of the coordinate value to be reconstituted is i = 105
, then s = (105  100)/(110  100) = 0.5
.
In the case of twodimensional interpolation, the interpolation arguments are similarly computed as:
s1 = s(ia1, ib1, i1) = (i1  ia1)/(ib1  ia1) s2 = s(ia2, ic2, i2) = (i2  ia2)/(ic2  ia2)
where ia1
and ib1
are the first dimension indices in the target domain of the tie points A
and B
respectively, ia2
and ic2
are the second dimension indices in the target domain of the tie points A
and C
respectively and the indices i1
and i2
are the first and second dimension indices respectively in the target domain of the coordinate value to be reconstituted.
The target domain is segmented into smaller interpolation subareas as described in Section 8.3.1, "Tie Points and Interpolation Subareas".
For onedimensional interpolation, an interpolation subarea is defined by two tie points, one at each end of the interpolation subarea. However, the tie points may be inside or outside the interpolation subareas as shown in Figure J.1. When interpolation methods are applied for a given interpolation subarea, it must be ensured that reconstituted coordinate points are only generated inside the interpolation subarea being processed, even if some of the tie point coordinates lie outside of that interpolation subarea. See also description in Section 8.3.1, "Tie Points and Interpolation Subareas".
A
.For twodimensional interpolation, an interpolation subarea is defined by four tie points, one at each corner of a rectangular area aligned with the domain axes, see Figure J.2.
For the reconstitution of the uncompressed coordinate and auxiliary coordinate variables the interpolation method can be applied independently for each interpolation subarea, making it possible to parallelize the computational process.
The following notation is used:
A variable staring with v
denotes a vector and v.x
, v.y
and v.z
refer to the three coordinates of that vector.
A variable staring with ll
denotes a latitudelongitude coordinate pair and ll.lat
and ll.lon
refer to the latitude and longitude coordinates.
For onedimensional interpolation, i
is an index in the interpolated dimension, tpi
is an index in the subsampled dimension and is
is an index in the interpolation subarea dimensions.
For twodimensional interpolation, i1
and i2
are indices in the interpolated dimensions, tpi1
and tpi2
are indices in the subsampled dimensions and is1
and is2
are indices in the interpolation subarea dimensions.
Dimension 1 is the dimension with index values increasing from tie point A
to tie point B
, dimension 2 is the dimension with index values increasing from tie point A
to tie point C
.
Note that, for simplicity of notation, the descriptions of the interpolation methods in most places leave out the indices of tie point related variables and refer to these with a
and b
in the onedimensional case and with a
, b
, c
and d
in the twodimensional case.
In the twodimensional case, a = tp(tpi2, tpi1)
, b = tp(tpi2, tpi1+1)
, c = tp(tpi2+1, tpi1)
and d = tp(tpi2+1, tpi1+1)
would reflect the way the tie point data would be stored in the data set, see also Figure J.2.
Common Conversions and Formulas
Description  Formula  


Square Root 


Inverse Tangent of 


Conversion from geocentric 


Conversion from threedimensional cartesian vector 


Conversion from 


Conversion from threedimensional cartesian vector 


Vector Sum 


Vector Difference 


Vector multiplied by Scalar 


Vector Cross Product 


Vector Dot Product 

Interpolation Methods
Linear Interpolation
Name
interpolation_name = "linear"
Description
General purpose onedimensional linear interpolation method for one or more coordinates
Interpolation parameter terms
None.
Coordinate compression calculations
None.
Coordinate uncompression calculations
The coordinate value u(i)
at index i
between tie points A
and B
is calculated from:
u(i) = fl(ua, ub, s(i)) = ua + s*(ubua)
where ua
and ub
are the coordinate values at tie points A
and B
respectively.
Bilinear Interpolation
Name
interpolation_name = "bi_linear"
Description
General purpose twodimensional linear interpolation method for one or more coordinates.
Interpolation parameter terms
None.
Coordinate compression calculations
None.
Coordinate uncompression calculations
The interpolation function fl() defined for linear interpolation above is first applied twice in the interpolated dimension 2, once between tie points A
and C
and once between tie points B
and D
.
It is then applied once in the interpolated dimension 1, between the two resulting coordinate points, yielding the interpolated coordinate value u(i2, i1)
:
uac = fl(ua, uc, s(ia2, ic2, i2)) ubd = fl(ub, ud, s(ia2, ic2, i2)) u(i2, i1) = fl(uac, ubd, s(ia1, ib1, i1))
Quadratic Interpolation
Name
interpolation_name = "quadratic"
Description
General purpose onedimensional quadratic interpolation method for one coordinate.
Interpolation parameter terms
Optionally the term w
, specifying a numerical variable spanning the interpolation subarea dimension.
Coordinate compression calculations
The expression
w = fw(ua, ub, u(i), s(i)) = (u  (1  s) * ua  s * ub)/(4 * (1  s) * s)
enables the creator of the dataset to calculate the coefficient w
from the coordinate values ua
and ub
at tie points A
and B
respectively, and the coordinate value u(i)
at index i
between the tie points A
and B
.
If the number of points in the interpolation subarea (ib  ia + 1)
is odd, then the data point at index i = (ib + ia)/2
shall be selected for this calculation, otherwise the data point at index i = (ib + ia  1)/2
shall be selected.
Coordinate uncompression calculations
The coordinate value u(i)
at index i
between tie points A
and B
is calculated from:
u(i) = fq(ua, ub, w, s(i)) = ua + s * (ub  ua + 4 * w * (1  s))
where ua
and ub
are the coordinate values at tie points A
and B
respectively and the coefficient w
is available as a term in the interpolation_parameters
, or otherwise defaults to 0.0
.
Quadratic Interpolation of Geographic Coordinates Latitude and Longitude
Name
interpolation_name = "quadratic_latitude_longitude"
Description
A onedimensional quadratic method for interpolation of the geographic coordinates latitude and longitude, typically used for remote sensing products with geographic coordinates on the reference ellipsoid.
Requires a pair of latitude and longitude tie point variables, as defined unambiguously in Section 4.1, "Latitude Coordinate" and Section 4.2, "Longitude Coordinate". For each interpolation subarea, none of the tie points defining the interpolation subarea are permitted to coincide.
By default, interpolation is performed directly in the latitude and longitude coordinates, but may be performed in threedimensional cartesian coordinates where required for achieving the desired accuracy.
This must be indicated by setting the location_use_3d_cartesian
flag within the interpolation parameter interpolation_subarea_flags
for each interpolation subarea where interpolation in threedimensional cartesian coordinates is required.
The quadratic interpolation coefficients cea = (ce, ca)
, stored as interpolation parameters in the product, describe a point P
between the tie points A
and B
, which is equivalent of an additional tie point in the sense that the method will accurately reconstitute the point P
in the same way as it accurately reconstitutes the tie points A
and B
.
See Figure J.3 and Figure J.4.
Although equivalent to a tie point, the coefficients ce
and ca
have two advantages over tie points.
Firstly, they can often be stored as a lower precision floating point number compared to the tie points, as ce
and ca
only describes the position of P
relative to the midpoint M
between the tie points A
and B
.
Secondly, if any of ce
and ca
do not contribute significantly to the accuracy of the reconstituted points, it can be left out of the data set and its value will default to zero during uncompression.
The coefficients may be represented in three different ways:

For storage in the dataset as the nondimensional coefficients
cea = (ce, ca)
, referred to as the parametric representation. The componentce
is the offset projected on the line from tie pointB
to tie pointA
and expressed as a fraction of the distance betweenA
andB
. The componentca
is the offset projected on the line perpendicular to the line from tie pointB
to tie pointA
and perpendicular to the plane spanned byva
andvb
, the vector representations of the two tie points, and expressed as a fraction of the length ofA x B
. 
For interpolation in threedimensional cartesian coordinates as the coefficients
cv = (cv.x, cv.y, cv.z)
, expressing the offset components along the threedimensional cartesian axes X, Y and Z respectively. 
For interpolation in geographic coordinates latitude and longitude as the coefficients
cll = (cll.lat, cll.lon)
, expressing the offset components along the longitude and latitude directions respectively.
The functions fq()
and fw()
referenced in the following are defined in Quadratic Interpolation.
Interpolation parameter terms
Optionally, any subset of terms ce, ca
, each specifying a numerical variable spanning the interpolation subarea dimension.
The mandatory term interpolation_subarea_flags
, specifying a flag variable spanning the interpolation subarea dimension and including location_use_3d_cartesian
in the flag_meanings
attribute.
Coordinate compression calculations
First calculate the tie point vector representations from the tie point latitudelongitude representations:
va = fll2v(lla) vb = fll2v(llb)
Then calculate the threedimensional cartesian representation of the interpolation coefficients from the tie points va
and vb
as well as the point vp(i)
at index i
between the tie points A
and B
.
If the number of points in an interpolation subarea (ib  ia + 1)
is odd, then the data point at index i = (ib + ia)/2
shall be selected for this calculation, otherwise the data point at index i = (ib + ia  1)/2
shall be selected.
The threedimensional cartesian interpolation coefficients are found from:
cv = fcv(va, vb, vp(i), s(i)) = (fw(va.x, vb.x, vp(i).x, s(i)), fw(va.y, vb.y, vp(i).y, s(i)), fw(va.z, vb.z, vp(i).z, s(i)))
Finally, for storage in the dataset, convert the coefficients to the parametric representation:
cea(is) = (ce(is), ca(is)) = fcv2cea(va, vb, cv) = (fdot(cv, fminus(va, vb))/gsqr, fdot(cv, fcross(va, vb))/(rsqr*gsqr))
where
vr = fmultiply(0.5, fplus(va, vb)) rsqr = fdot(vr, vr) vg = fminus(va, vb) gsqr = fdot(vg, vg)
The interpolation parameter term interpolation_subarea_flags(is)
shall have the flag location_use_3d_cartesian
set if the interpolation subarea intersects the longitude = 180.0
or if the interpolation subarea extends into latitude > latitude_limit
or latitude < latitude_limit
.
The value of latitude_limit
is set by the data set creator and defines the high latitude areas where interpolation in threedimensional cartesian coordinates is required for reasons of coordinate reconstitution accuracy.
The latitude_limit
is used solely for setting the flag location_use_3d_cartesian
, and is not required in a compressed dataset.
Coordinate uncompression calculations
First calculate the tie point vector representations from the tie point latitudelongitude representations:
va = fll2v(lla) vb = fll2v(llb)
Then calculate the threedimensional cartesian representation of the interpolation coefficients from the parametric representation stored in the dataset using:
cv = fcea2cv(va, vb, cea(is)) = fplus(fmultiply(ce, fminus(va, vb)), fmultiply(ca, fcross(va, vb)), fmultiply(cr, vr))
where
vr = fmultiply(0.5, fplus(va, vb)) rsqr = fdot(vr, vr) cr = sqrt(1  ce(is)*ce(is)  ca(is)*ca(is))  sqrt(rsqr)
If the flag location_use_3d_cartesian
of the interpolation parameter term interpolation_subarea_flags(is2, is1)
is set, use the following expression to reconstitute any point llp(i)
between the tie points A
and B
using interpolation in threedimensional cartesian coordinates:
vp(i) = fqv(va, vb, cv, s(i)) = (fq(va.x, vb.x, cv.x, s(i)), fq(va.y, vb.y, cv.y, s(i)), fq(va.z, vb.z, cv.z, s(i))) llp(i) = fv2ll(vp(i))
Otherwise, first calculate latitudelongitude representation of the interpolation coefficients:
cll = fcll(lla, llb, llab) = (fw(lla.lat, llb.lat, llab.lat, 0.5), fw(lla.lon, llb.lon, llab.lon, 0.5))
where
llab = fv2ll(fqv(va, vb, cv, 0.5))
Then use the following expression to reconstitute any point llp(i)
between the tie points A
and B
using interpolation in latitudelongitude coordinates:
llp(i) = (llp(i).lat, llp(i).lon) = fqll(lla, llb, cll, s(i)) = (fq(lla.lat, llb.lat, cll.lat, s(i)), fq(lla.lon, llb.lon, cll.lon, s(i)))
ce = 0
and the alignment coefficient ca = 0
, the method reconstitutes the points at regular intervals along a great circle between tie points A
and B
.ce > 0
and the alignment coefficient ca > 0
, the method reconstitutes the points at intervals of expanding size (ce
) along an arc with an alignment offset (ca
) from the great circle between tie points A
and B
.Biquadratic Interpolation of Geographic Coordinates Latitude and Longitude
Name
interpolation_name = "bi_quadratic_latitude_longitude"
Description
A twodimensional quadratic method for interpolation of the geographic coordinates latitude and longitude, typically used for remote sensing products with geographic coordinates on the reference ellipsoid.
Requires a pair of latitude and longitude tie point variables, as defined unambiguously in Section 4.1, "Latitude Coordinate" and Section 4.2, "Longitude Coordinate". For each interpolation subarea, none of the tie points defining the interpolation subarea are permitted to coincide.
The functions fcv()
, fcv2cea()
, fcea2cv()
, fcll()
, fqv()
and fqll()
referenced in the following are defined in Quadratic Interpolation of Geographic Coordinates Latitude and Longitude.
As for that method, interpolation is performed directly in the latitude and longitude coordinates or in threedimensional cartesian coordinates, where required for achieving the desired accuracy.
Similarly, it shares the three different representations of the quadratic interpolation coefficients, the parametric representation cea = (ce, ca)
for storage in the dataset, cll = (cll.lat, cll.lon)
for interpolation in geographic coordinates latitude and longitude and cv = (cv.x, cv.y, cv.z)
for interpolation in threedimensional cartesian coordinates.
The parametric representation of the interpolation coefficients, stored in the interpolation parameters ce1
, ca1
, ce2
, ca2
, ce3
and ca3
, is equivalent to five additional tie points for the interpolation subarea as shown in Figure J.5, which also shows the orientation and indices of the parameters.
Interpolation parameter terms
Optionally, any subset of terms ce1
and ca1
, each specifying a numerical variable spanning the subsampled dimension 2 and the interpolation subarea dimension 1.
Optionally, any subset of terms ce2
and ca2
, each specifying a numerical variable spanning the interpolation subarea dimension 2 and the subsampled dimension 1.
Optionally, any subset of terms ce3
and ca3
, each specifying a numerical variable spanning the interpolation subarea dimension 2 and the interpolation subarea dimension 1.
The mandatory term interpolation_subarea_flags
, specifying a flag variable spanning the interpolation subarea dimension 2 and the interpolation subarea dimension 1 and including location_use_3d_cartesian
in the flag_meanings
attribute.
Coordinate compression calculations
First calculate the tie point vector representations from the tie point latitudelongitude representations:
va = fll2v(lla) vb = fll2v(llb) vc = fll2v(llc) vd = fll2v(lld)
Then calculate the threedimensional cartesian representation of the interpolation coefficients sets from the tie points as well as a point vp(i2, i1)
between the tie points.
If the number of points in the first dimension of the interpolation subarea (ib1  ia1 + 1)
is odd, then the data point at index i1 = (ib1 + ia1)/2
shall be selected for this calculation, otherwise the data point at index i1 = (ib1 + ia1  1)/2
shall be selected.
If the number of points in the second dimension of the interpolation subarea (ic2  ia2 + 1)
is odd, then the data point at index i2 = (ic2 + ica)/2
shall be selected for this calculation, otherwise the data point at index i2 = (ic2 + ia2  1)/2
shall be selected.
Using the selected (i2, i1)
, the threedimensional cartesian interpolation coefficients are found from:
s1 = s(ia1, ib1, i1) s2 = s(ia2, ic2, i2) vac = fll2v(ll(i2, ia1)) vbd = fll2v(ll(i2, ib1)) cv_ac = fcv(va, vc, vac, s2) cv_bd = fcv(vb, vd, vbd, s2) cv_ab = fcv(va, vb, fll2v(ll(ia2, i1)), s1) cv_cd = fcv(vc, vd, fll2v(ll(ic2, i1)), s1) cv_zz = fcv(vac, vbd, fll2v(ll(i2, i1)), s1) vz = fqv(vac, vbd, cv_zz, 0.5) vab = fqv(va, vb, cv_ab, 0.5) vcd = fqv(vc, vd, cv_cd, 0.5) cv_z = fcv(vab, vcd, vz, s2)
Finally, before storing them in the dataset’s interpolation parameters, convert the coefficients to the parametric representation:
cea1(tpi2, is1) = fcv2cea(va, vb, cv_ab) cea1(tpi2+1, is1) = fcv2cea(vc, vd, cv_cd) cea2(is2, tpi1) = fcv2cea(va, vc, cv_ac) cea2(is2, tpi1+1) = fcv2cea(vb, vd, cv_bd) cea3(is2, is1) = fcv2cea(vab, vcd, cv_z)
The interpolation parameter term interpolation_subarea_flags(is2, is1)
shall have the flag location_use_3d_cartesian
set if the interpolation subarea intersects the longitude = 180.0
or if the interpolation subarea extends into latitude > latitude_limit
or latitude < latitude_limit
.
The value of latitude_limit
is set by the data set creator and defines the high latitude areas where interpolation in threedimensional cartesian coordinates is required for reasons of coordinate reconstitution accuracy.
The latitude_limit
is used solely for setting the flag location_use_3d_cartesian
, and is not required in a compressed dataset.
Coordinate uncompression calculations
First calculate the tie point vector representations from the tie point latitudelongitude representations:
va = fll2v(lla) vb = fll2v(llb) vc = fll2v(llc) vd = fll2v(lld)
Then calculate the threedimensional cartesian representation of the interpolation coefficient sets from the parametric representation stored in the dataset:
cv_ac = fcea2cv(va, vc, cea2(is2, tpi1)) cv_bd = fcea2cv(vb, vd, cea2(is2, tpi1 + 1)) vab = fqv(va, vb, fcea2cv(va, vb, cea1(tpi2, is1)), 0.5) vcd = fqv(vc, vd, fcea2cv(vc, vd, cea1(tpi2 + 1, is1)), 0.5) cv_z = fcea2cv(vab, vcd, cea3(is2, is1))
If the flag location_use_3d_cartesian
of the interpolation parameter term interpolation_subarea_flags
is set, use the following expression to reconstitute any point llp(i2, i1)
between the tie points A
and B
using interpolation in threedimensional cartesian coordinates:
llp(i2, i1) = fv2ll(fqv(vac, vbd, cv_zz, s(ia1, ib1, i1)))
where
s2 = s(ia2, ic2, i2) vac = fqv(va, vc, cv_ac, s2) vbd = fqv(vb, vd, cv_bd, s2) vz = fqv(vab, vcd, cv_z, s2) cv_zz = fcv(vac, vbd, vz, 0.5)
Otherwise, first calculate latitudelongitude representation of the interpolation coefficients:
llc_ac = fcll(lla, llc, fv2ll(fqv(va, vc, cv_ac, 0.5))) llc_bd = fcll(llb, lld, fv2ll(fqv(vb, vd, cv_bd, 0.5))) llab = fv2ll(vab) llcd = fv2ll(vcd) llc_z = fcll(llab, llcd, fv2ll(fqv(vab, vcd, cv_z, 0.5)))
Then use the following expression to reconstitute any point llp(i2, i1)
in the interpolation subarea using interpolation in latitudelongitude coordinates:
llp(i2, i1) = fqll(llac, llbd, cl_zz, s(ia1, ib1, i1))
where
s2 = s(ia2, ic2, i2) llac = fqll(lla, llc, llc_ac, s2) llbd = fqll(llb, lld, llc_bd, s2) llz = fqll(llab, llcd, llc_z, s2) cl_zz = fcll(llac, llbd, llz)
cea = (ce, ca)
, stored in the interpolation parameters ce1
, ca1
, ce2
, ca2
, ce3
and ca3
, is equivalent to five additional tie points for the interpolation subarea. Shown with parameter orientation and indices.Coordinate Compression Steps
Step  Description  Link 

1 
Identify the coordinate and auxillary coordinate variables for which tie point and interpolation variables are required. 

2 
Identify nonoverlapping subsets of the coordinate variables to be interpolated by the same interpolation method.
For each coordinate variable subset, create an interpolation variable and specify the selected interpolation method using the 

3 
For each coordinate variable subset, add the coordinates variable subset and the corresponding interpolation variable name to the the 

4 
For each coordinate variable subset, identify the set of interpolated dimensions and the set of noninterpolated dimensions. 
Section 8.3.4, "Subsampled, Interpolated and NonInterpolated Dimensions" 
5 
For each set of the interpolated dimensions, identify the continuous areas and select the interpolation subareas and the tie points, taking into account the required coordinate reconstitution accuracy when selecting the density of tie points. 

6 
For each of the interpolated dimensions, add the interpolated dimension, the corresponding subsampled dimension and, if required by the selected interpolation method, its corresponding interpolation subarea dimension to the 
Section 8.3.5, "Tie Point Mapping Attribute" 
7 
For each of the interpolated dimensions, record the location of each identified tie point in a tie point index variable.
For each interpolated dimension, add the tie point index variable name to the 
Section 8.3.5, "Tie Point Mapping Attribute" 
8 
For each of the target coordinate and auxillary coordinate variables, create the corresponding tie point coordinate variable and copy the coordinate values from the target domain coordinate variables to the tie point variables for the target domain indices identified by the tie point index variable. Repeat this step for each combination of indices of the noninterpolated dimensions. 
Section 8.3.5, "Tie Point Mapping Attribute" 
9 
For each of the target coordinate and auxillary coordinate variable having a 

10 
If required by the selected interpolation method, follow the steps defined for the method in Section J.3, "Interpolation Methods" to create any required interpolation parameter variables.
As relevant, create the 
Section 8.3.3, "Interpolation Variable" 
11 
Optionally, check the consistency of the original coordinates and the reconstructed coordinates and add a 
Coordinate Uncompression Steps
Step  Description  Link 

1 
From the 

2 
For each coordinate variable subset, identify the interpolation method from the


3 
For each coordinate variable subset, identify the set of interpolated dimensions and the set of noninterpolated dimensions from the 
Section 8.3.5, "Tie Point Mapping Attribute" 
4 
From the 
Section 8.3.5, "Tie Point Mapping Attribute" 
5 
From the tie point index variables referenced in the 
Section 8.3.5, "Tie Point Mapping Attribute" 
6 
For each of the interpolated dimensions, identify pairs of adjacent indices in the tie point index variable with index values differing by more than one, each index pair defining the extend of an interpolation subarea in that dimension. A full interpolation subarea is defined by one such index pair per interpolated dimension, with combinations of one index from each pair defining the interpolation subarea tie points. 

7 
As required by the selected interpolation method, identify the interpolation parameter variables from the interpolation variable attribute 

8 
For each of the tie point coordinate and auxillary coordinate variables, create the corresponding target coordinate variable. For each interpolation subarea, apply the interpolation method, as described in Section J.3, "Interpolation Methods", to reconstitute the target domain coordinate values and store these in the target domain coordinate variables. Repeat this step for each combination of indices of the noninterpolated dimensions. 
Section 8.3.5, "Tie Point Mapping Attribute" 
9 
For each of the tie point coordinate and auxillary coordinate variables having a 

10 
If auxiliary coordinate variables have been reconstituted, then, if not already present, add a 
Appendix K: Mesh Topologies
The CF attributes listed here may be used to define mesh topologies (Section 5.9, "Mesh Topology Variables"). This list is intended as a summary of the attributes that have been standardized via the UGRID conventions [UGRID], which should be consulted for further details. UGRID attributes that are not currently recognised by the CF convensions are included in the list.
The "Type" values are S for string and I for integer. The "Use" values are MT for mesh topology variables, LIS for location index set variables, D for data variables, Do for domain variables, and Con for connectivity index variables.
Attribute  Type  Use  Description 


S 
MT 
Specifies an index variable identifying the nodes that define where boundary condtions have been provided. Not currently recognised by the CF conventions. 

S 
MT, LIS 
Specifies the roles of mesh topology or location index set variables. 

S 
LIS 
Specifies the auxiliary coordinate variables associated with the characteristic locations of the subset of mesh topology locations. 

S 
MT 
Specifies the auxiliary coordinate variables associated with the characteristic location of the edges (commonly the midpoint). 

S 
MT 
Specifies the dimension used to index the nodes in the edge connectivity variable. 

S 
MT 
Specifies an index variable identifying all faces that share the same edge, i.e. are neighbours to an edge. 

S 
MT 
Specifies an index variable identifying for every edge the indices of its begin and end nodes. 

S 
MT 
Specifies the auxiliary coordinate variables associated with the characteristic location of faces. 

S 
MT 
Specifies the dimension used to index the edges in the face connectivity variable. 

S 
MT 
Specifies an index variable identifying for every face the indices of its edges. 

S 
MT 
Specifies an index variable identifying all faces that share an edge with each face, i.e. are neighbours. 

S 
MT 
Specifies an index variable identifying for every face the indices of its corner nodes. 

S 
D, Do, LIS 
Specifies the location within the mesh topology at which the variable is defined. 

S 
D, Do 
Specifies a variable that defines the subset of locations of a mesh topology at which the variable is defined. 

S 
D, Do, LIS 
Specifies a variable that defines a mesh topology. 

S 
MT 
Specifies the auxiliary coordinate variables representing the node locations (latitude, longitude, or other spatial coordinates, and optional elevation or other coordinates). 

I 
LIS, Con 
Indicates whether 0 or 1based indexing is used to identify connected geometric elements; connectivity indices are 0based by default. 

I 
MT 
Indicates the highest dimensionality of the geometric elements. 

S 
MT 
Specifies the auxiliary coordinate variables associated with the characteristic location of volumes. Not currently recognised by the CF conventions. 

S 
MT 
Specifies the dimension used to index the faces in the volume connectivity variable. Not currently recognised by the CF conventions. 

S 
MT 
Specifies an index variable identifying for every volume the indices of its edges. 

S 
MT 
Specifies an index variable identifying for every volume the indices of its faces. Not currently recognised by the CF conventions. 

S 
MT 
Specifies an index variable identifying for every volume the indices of its corner nodes. Not currently recognised by the CF conventions. 

S 
MT 
Specifies a flag variable that specifies for every volume its shape. Not currently recognised by the CF conventions. 

S 
MT 
Specifies an index variable identifying all volumes that share a face with each volume, i.e. are neighbours. Not currently recognised by the CF conventions. 
Revision History
Working version (most recent first)

Issue #237: Clarify that the character set given in section 2.3 for variable, dimension, attribute and group names is a recommendation, not a requirement.

Issue #515: Clarify the recommendation to use the convention of 4.3.3 for parametric vertical coordinates, because the previous wording caused confusion.

Issue #511: Appendix B: New element in XML file header to record the "first published date"

Issue #509: In exceptional cases allow a standard name to be aliased into two alternatives

Issue #501: Clarify that data variables and variables containing coordinate data are highly recommended to have
long_name
orstandard_name
attributes, thatcf_role
is used only for discrete sampling geometries and UGRID mesh topologies, and that CF does not prohibit CF attributes from being used in ways that are not defined by CF but that in such cases their meaning is not defined by CF. 
Issue #477: Period and hyphen allowed in attribute names

Issue #500: Appendix B: Added a
conventions
string to the standard name xml file format definition
Version 1.11 (05 December 2023)

Issue #481: Introduce
units_metadata
attribute and clarify some other aspects ofunits

Issue #147: Clarify the use of compressed dimensions in related variables

Issue #486: Fix PDF formatting problems and invalid references

Issue #490: Simple correction to Example 6.1.2

Issue #457: Creation date of the draft Conventions document

Issue #445: Updates concerning the Polar Stereographic Grid Mapping

Issue #468: Update section 2.3 to clarify recommended character set

Issue #147: Clarify the use of compressed dimensions in related variables

Issue #483: Add a missing author

Issue #463: Convert URLs with HTTP protocol to HTTPS if available, fixed a few dead links

Issue #383: Link to the CF website and deleted the Preface section

Issue #472: Fix incorrect formating for some <= symbols

Issue #458: Fix broken link to Unidata documentation.

Issue #423: Always use "strictly monotonic" when describing coordinate variables

Issue #420: Add List of Figures

Issue #210: Correct errors in examples H9H11

Issue #374: Clarify rules for packing and unpacking in Section 8.1

Issue #449: Typo in enddate in Example 7.12

Issue #266: Updates to some links in the bibliography

Issue #286: Some labels of examples contain "Example" so that their label in the list of examples contains "Example" (affects four examples); corrected captions of three tables and five examples

Issue #418: Add missing examples to TOE (table of examples); corrected captions of three tables and three examples

Issue #367: Delete obsolete references in section 3.3 for mappings of CF standard names to GRIB and PCMDI tables

Issue #405: Update ch. 4.4 text on reference time vs. UDUNIT

Issue #406: Remove duplicate section 8.2 in the conformance document

Issue #391: Correct link to Snyder and typo in the bibliography

Issue #437: Correct link to NUG in the bibliography

Issue #428: Recording deployment positions

Issue #430: Clarify the function of the
cf_role
attribute 
Pull request #408: Deleted a sentence on "rotated Mercator" under
Oblique Mercator
grid mapping in Appendix F 
Issue #265: Clarification of the requirements on bounds variable attributes

Issue #260: Clarify use of dimensionless units

Issue #410: Delete "on a spherical Earth" from the definition of the
latitude_longitude
grid mapping in Appendix F 
Issue #153: Reference UGRID conventions in CF
Version 1.10 (31 August 2022)

Pull request #378: Fixed missing semicolon in example 7.16

Issue #366: Clarify the intention of standard names

Issue #352: Correct errors in description of lossy compression by coordinate subsampling

Issue #345: Reformat the revision history

Issue #349: Delete unnecessary Conventions attribute in two examples

Issue #162: Delete incorrect missing_data attributes of time coordinate variables in two examples

Issue #129: timeSeries featureType with a forecast/reference time dimension?
Version 1.9 (10 September 2021)

Issue #327: Lossy compression by coordinate subsampling, including new Appendix J ("Coordinate Subsampling Methods")

Issue #323: Update data model figures for the Domain

Issue #319: Restrict "gregorian" label to only dates in the Gregorian calendar

Issue #298: Interpretation of negative years in the units attribute

Issue #314: Correction to the definition of "ocean sigma over z coordinate" in Appendix D

Issue #313: Clarification of the handling of leap seconds

Issue #304: Clarify formula terms definitions

Issue #301: Introduce the CF domain variable.

Issue #288: Remove unnecessary line from table in section 9.3.1

Issue #284: Fix the mention of example 6.1.2 in the example list

Issue #273: State the principles for design of the CF conventions

Issue #295: Correction of figures and their description

Issue #243: Rewording changes relating to the new integer types

Issue #222: Allow CRS WKT to represent the CRS without requiring reader to compare with grid mapping parameters

Issue #193: Figures to clarify the order of the vertices of cell bounds

Issue #271: Extend the CF data model for geometries

Issue #272: Remove unnecessary netCDF dimensions from some examples

Issue #258: Clarification of geostationary projection items

Issue #216: New text describing usage of ancillary variables as status/quality flags

Issue #159: Incorporate the CF data model into the conventions in new Appendix I

Issue #253: Update PROJ links in Appendix F

Pull request #236: Fixed the link in the COARDS reference

Issue #243: Add new integer types to CF

Issue #238: Clarifications to ancillary variables text and examples

Issue #230: Correct inconsistency in units of geostationary projection
Version 1.8 (11 February 2020)

Issue #223: Axis Order for CRSWKT grid mappings

Issue #212: Inconsistent usage of false_easting and false_northing in grid mappings definitions and in examples

Issue #218: Taxon Names and Identifiers.

Issue #203: Clarifications to use of groups.

Issue #213: Missing `s`s in grid mapping description texts.

Pull request #202: Fix Section 7 examples numbering in the list of examples

Issue #198: Clarification of use of standard region names in "region" variables.

Issue #179: Don’t require longitude and Latitude for projected coordinates.

Issue #139: Added support for variables of type string.

Issue #186: Minor corrections to Example 5.10, Section 9.5 & Appendix F

Issue #136: Missing trajectory dimension in H.22

Issue #128: Add definition of 'name_strlen' dimension where missing in Appendix H CDL examples.

Pull request #142: Fix bad reference to an example in section 6.1 "Labels".

Issue #155, Issue #156: Allow alternate grid mappings for geometry containers. When node_count attribute is missing, require the dimension of the node coordinate variables to be one of the dimensions of the data variable.

Pull request #146: Typos (plural dimensions) in section H

Ticket #164: Add bounds attribute to first geometry CDL example.

Ticket #164: Replace axis with bounds for coordinate variables related to geometry node variables.

Ticket #164: Add Tim Whiteaker and Dave Blodgett as authors.

Ticket #164: Remove geometry attribute from lat/lon variables in examples.

Ticket #164: If coordinates attribute is carried by geometry container, require coordinate variables which correspond to node coordinate variables to have the corresponding axis attribute.

Ticket #164: Implement suggestions from trac ticket comments.

Ticket #164: New Geometries section 7.5.
Version 1.7 (7 August 2017)

Updated use of WKTCRS syntax.

Trivial updates to links for COARDS and UDUNITS in the bibliography.

Updated the links and references to NUG (The NetCDF User Guide), to refer to the current version.

A few formatting tweaks.

Ticket #140: Added 3 paragraphs and an example to Chapter 7, Section 7.1.

Ticket #100: Clarifications to the preamble of sections 4 and 5.

Ticket #70: Connecting coordinates to Grid Mapping variables: revisions in Section 5.6 and Examples 5.10 and 5.12

Ticket #104: Clarify the interpretation of scalar coordinate variables, changes in sections 5.7 and 6.1

Ticket #102: additional cell_methods, changes in Appendix E and section 7.3

Ticket #80: added attributes to AppF Table F1, changes in section 5.6 and 5.6.1.

Ticket #86: Allow coordinate variables to be scaled integers, affects two table rows in Appendix A.

Ticket #138: Clarification of false_easting / false_northing (Table F.1)

Ticket #76: More than one name in Conventions attribute (section 2.6.1)

Ticket #109: resolve inconsistency of positive and standard_name attributes (section 4.3)

Ticket #75: fix documentation and definitions of 3 grid mapping definitions

Ticket #143: Supplement the definitions of dimensionless vertical coordinates

Ticket #85: Added sentence to bottom of first para in Section 9.1 "Features and feature types". Added Links column in Section 9.1. Replaced first para in Section 9.6. "Missing Data". Added verbiage to Section 2.5.1, "Missing data…". Added sentence to Appendix A "Description" "missing_value" and "Fill_Value".

Ticket #145: Add new sentence to bottom of Section 7.2, Add new Section 2.6.3, "External variables". Add "External variable" attribute to Appendix A.

Ticket #74: Removed "sea_water_speed" from flag values example and added Note at bottom of Example 3.3 in Chapter 3. Also added a sentence to Appendix C Standard Name Modifiers "number of observations" and and a sentence to "status_flag_modifiers"

Ticket #103: Corrections to Appendices A and H, finish the ticket with remaining changes to Appendix H.

Ticket #72: Adding the geostationary projection.

Ticket #92: Add oblique mercator projection

Ticket #87: Allow comments in coordinate variables

Ticket #77: Add sinusoidal projection

Ticket #149: correction of standard name in example 7.3

Ticket #148: Added maximum_absolute_value, minimum_absolute_value and mean_absolute_value to cell methods in Appendix E

Ticket #118: Add geoid_name and geopotential_datum_name to the list of Grid Mapping Attributes.

Ticket #123: revised section 3.3

Ticket #73: renamed Appendix G to Revision History

Ticket #31, add new attribute
actual_range
. 
Ticket #141, update affiliation organisations for Jonathan Gregory and Phil Bentley.

Ticket #103 updated Type and Use values for some attributes in Appendix A, Attributes and added "special purpose" value. In Appendix H, Annotated Examples of Discrete Geometries, updated coordinate values for the variables in some examples to correct omissions.

Ticket #71, correction of Vertical perspective projection.

Ticket #67, remove deprecation of "missing_value" from Appendix A, Attributes.

Ticket #93: Added two new dimensionless coordinates to Appendix D.

Ticket #69. Added Section 5.6.1, Use of the CRS Wellknown Text Format and related changes.

Ticket #65: add range entry in Appendix E.

Ticket #64: section 7.3 editorial correction, replace "cell_bounds" with "bounds".

Ticket #61: two new cell methods in Appendix E.
Version 1.6 (5 December 2011)

Ticket #37: Added Chapter 9, Discrete Sampling Geometries, and a related Appendix H, and revised several other chapters.

In Appendix H (Annotated Examples of Discrete Geometries), updated standard names "station_description" and "station_wmo_id" to "platform_name" and "platform_id".
Version 1.5 (25 October 2010)

Ticket #47: error in example 7.4

Ticket #51: syntax consistency for dimensionless vertical coordinate definitions

Ticket #56: typo in CF conventions doc

Ticket #57: fix for broken URLs in CF Conventions document

Ticket #58: remove deprecation of "missing_value" attribute

Ticket #49: clarification of flag_meanings attribute

Ticket #33: cell_methods for statistical indices

Ticket #45: Fixed defect of outdated Conventions attribute.

Ticket #44: Fixed defect by clarifying that coordinates indicate gridpoint location in Chapter 4, Coordinate Types.

Fixed defect in Mercator section of Appendix F, Grid Mappings by updating to version 12 of Grid Map Names.

Ticket #34: Added grid mappings Lambert Cylindrical Equal Area, Mercator, and Orthographic to Appendix F, Grid Mappings.
Version 1.4 (27 February 2009)

Ticket #17: Changes related to removing ambiguity in Section 7.3, "Cell Methods".

Ticket #36: Fixed defect related to subsection headings in Appendix D, Parametric Vertical Coordinates.

Ticket #35: Fixed defect in wording of Chapter 5, Coordinate Systems and Domain.

Ticket #32: Fixed defect in Chapter 5, Coordinate Systems and Domain.

Ticket #30: Fixed defect in Example 4.3, “Atmosphere sigma coordinate”.
Version 1.3 (4 May 2008)

Ticket #26: Section 3.5, "Flags", Appendix A, Attributes, Appendix C, Standard Name Modifiers : Enhanced the Flags definition to support bit field notation using a
flag_masks
attribute.
Version 1.2 (4 May 2008)

Ticket #25: Table 3.1, "Supported Units" : Corrected Prefix for Factor "1e2" from "deci" to "centi".

Ticket #18: Section 5.6, "Horizontal Coordinate Reference Systems, Grid Mappings, and Projections", Appendix F, Grid Mappings : Additions and revisions to CF grid mapping attributes to support the specification of coordinate reference system properties
Version 1.1 (17 January 2008)

17 January 2008: Chapter 4, Coordinate Types, Chapter 5, Coordinate Systems and Domain: Made changes regarding use of the axis attribute to identify horizontal coordinate variables.

17 January 2008: Changed text to refer to rules of CF governance, and provisional status.

21 March 2006: Added the section called "Atmosphere natural log pressure coordinate".

21 March 2006: Added the section called "Azimuthal equidistant".

25 November 2005: the section called "Atmosphere hybrid height coordinate" : Fixed definition of atmosphere hybrid height coordinate.

22 October 2004: Added "Lambert conformal projection".

20 September 2004: Section 7.3, "Cell Methods" : Changed several incorrect occurrences of the cell method
"standard deviation"
to"standard_deviation"
. 
1 July 2004: "Multiple forecasts from a single analysis" : Added
positive
attribute to the scalar coordinate p500 to make it unambiguous that the pressure is a vertical coordinate value. 
1 July 2004: Section 5.7, "Scalar Coordinate Variables" : Added note that use of scalar coordinate variables inhibits interoperability with COARDS conforming applications.

14 June 2004: the section called "Polar Stereographic" : Added
latitude_of_projection_origin
map parameter. 
14 June 2004: Added the section called “Lambert azimuthal equal area”.
Bibliography
References

[COARDS] Conventions for the standardization of NetCDF Files. Sponsored by the "Cooperative Ocean/Atmosphere Research Data Service," a NOAA/university cooperative for the sharing and distribution of global atmospheric and oceanographic research data sets. May 1995.

[FGDC] Content Standard for Digital Geospatial Metadata. Federal Geographic Data Committee, FGDCSTD0011998.

[IEEE_754] IEEE Standard for FloatingPoint Arithmetic, in IEEE Std 7542019 (Revision of IEEE 7542008), 22 July 2019.

[NetCDF] NetCDF Software Package. UNIDATA Program Center of the University Corporation for Atmospheric Research.

[NUG] The NetCDF User’s Guide.

[OGC_WKTCRS] OGC Wellknown text representation of coordinate reference systems. OGC document 12063. 1st May 2015.

[OGPEPSG_GN7_2] OGP Surveying and Positioning Guidance Note 7, part 2: Coordinate Conversions and Transformations including Formulas.

[SCH02] A new terrainfollowing vertical coordinate formulation for atmospheric prediction models. C Schaer, D Leuenberger, and O Fuhrer. 2002. Monthly Weather Review. 130. 24592480.

[Snyder] Map Projections: A Working Manual. USGS Professional Paper 1395.

[UDUNITS] UDUNITS Software Package. UNIDATA Program Center of the University Corporation for Atmospheric Research.

[XML] Extensible Markup Language (XML) 1.0. T. Bray, J. Paoli, and C.M. SperbergMcQueen. 10 February 1998.

[CFDM] A data model of the Climate and Forecast metadata conventions (CF1.6) with a software implementation (cfpython v2.1). Hassell, D., Gregory, J., Blower, J., Lawrence, B. N., and Taylor, K. E.: Geosci. Model Dev., 10, 46194646, 2017.

[UGRID] UGRID Conventions for storing unstructured (or flexible mesh) data in netCDF files