 About the authors
 Abstract
 Preface
 1. Introduction
 2. NetCDF Files and Components
 3. Description of the Data
 4. Coordinate Types
 5. Coordinate Systems
 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
 6. Labels and Alternative Coordinates
 7. Data Representative of Cells
 8. Reduction of Dataset Size
 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
 Abstract
 Introduction
 The CF data model
 Revision History
 Bibliography
List of Tables
3.1. Supported 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. Table 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
List of Examples
3.1. Use of standard_name
3.2. Instrument data
3.3. A flag variable, using flag_values
3.4. A flag variable, using flag_masks
3.5. A region variable, using flag_values
3.6. 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. Example 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. Example 5.13, "Multiple forecasts from a single analysis"
6.1. Northward heat transport in Atlantic Ocean
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
B.1. A name table containing three entries
H.1. Example 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. Example 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.
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
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.
Preface
 Home page:

Contains links to: previous draft and current working draft documents; applications for processing CF conforming files; email list for discussion about interpretation, clarification, and proposals for changes or extensions to the current conventions. http://cfconventions.org/
 Revision history:

This document will be updated to reflect agreed changes to the standard and to correct mistakes according to the rules of CF governance. See Revision History for the full revision history.
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. 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 that are ordered monotonically. 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.
 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.
 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.
1.3. 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 "CF1.8
" 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 software 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 dimensionless vertical coordinate used in its mathematical formulation. To achieve the goal of being able to spatially locate all data values, this convention includes the definitions of common dimensionless vertical coordinates in Appendix D, Parametric Vertical Coordinates . These definitions provide a mapping between the dimensionless coordinate values and dimensional values that can be uniquely located with respect to a point on the earth’s surface. The definitions are associated with a coordinate variable via the standard_name
and formula_terms
attributes. For backwards compatibility with COARDS use of these attributes is not required, but is strongly recommended.
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.
1.4. 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 4.3.2, "Dimensionless 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.
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
The netCDF data types string
, char
, byte
, unsigned byte
, short
, unsigned short
,
int
, unsigned int
, int64
, unsigned int64
,
float
or real
, and double
are all acceptable.
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 phrases "an integer type" or "any integer type" are 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
Variable, dimension, attribute and group names should begin with a letter and be composed of letters, digits, and underscores. Note that this is in conformance with the COARDS conventions, but is more restrictive than the netCDF interface which allows use of the hyphen character. The netCDF interface also allows leading underscores in names, but the NUG states that this is reserved for system use.
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 1.4, "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 "CF1.8
".
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.
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 value of the units
attribute is a string that can be recognized by UNIDATA’s Udunits package [UDUNITS], with a few exceptions that are given below. The Udunits package includes a file udunits.dat
, which lists its supported unit names. Note that case is significant in the units
strings.
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".
Units are not required for dimensionless quantities. A variable with no units attribute is assumed to be dimensionless. However, a units attribute specifying a dimensionless unit may optionally be included. The Udunits package defines a few dimensionless units, such as percent
, but is lacking commonly used units such as ppm (parts per million). This convention does not support the addition of new dimensionless units that are not udunits compatible. The conforming unit for quantities that represent fractions, or parts of a whole, is "1". The conforming unit for parts per million is "1e6". Descriptive information about dimensionless quantities, such as seaice concentration, cloud fraction, probability, etc., should be given in the long_name
or standard_name
attributes (see below) rather than the units
.
The units level
, layer
, and sigma_level
are allowed for dimensionless vertical coordinates to maintain backwards compatibility with COARDS. These units are not compatible with Udunits and are deprecated by this standard because conventions for more precisely identifying dimensionless vertical coordinates are introduced (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. 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".
Udunits recognizes the following prefixes and their abbreviations.
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 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 some applications it would be desirable to have a more definitive description of the quantity, which would allow users of data from different sources (some of which might be models and others observational) to determine whether quantities were in fact comparable. For this reason an optional mechanism for uniquely associating each variable with a standard name is provided.
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 3.4).
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
http://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
http://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.
Here are lists of equivalences between the CF standard names and the standard names from the ECMWF GRIB tables, the NCEP GRIB tables, and the PCMDI tables.
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.
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" ;
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:_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. Example 3.5 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:_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. We extend COARDS by providing explicit definitions of dimensionless vertical coordinates. The definitions are associated with a coordinate variable via the standard_name
and formula_terms
attributes. For backwards compatibility with COARDS use of these attributes is not required, but is strongly recommended.
Because identification of a coordinate type by its units is complicated by requiring the use of an external software 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).
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 units
attribute will be a string formatted as per the udunits.dat
file. The recommended unit of latitude is degrees_north
. Also acceptable 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 units attribute
will be a string formatted as per the udunits.dat
file. The recommended unit of longitude is degrees_east
. Also acceptable 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 (a determination which can be made using the udunits routine, utScan) — 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
The units
attribute for dimensional coordinates will be a string formatted as per the udunits.dat
file. The acceptable units for vertical (depth or height) coordinate variables are:

units of pressure as listed in the file
udunits.dat
. For vertical axes the most commonly used of these includebar
,millibar
,decibar
,atmosphere (atm)
,pascal (Pa)
, andhPa
. 
units of length as listed in the file udunits.dat. For vertical axes the most commonly used of these include
meter (metre, m)
, andkilometer (km)
. 
other units listed in the file udunits.dat 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 time must always explicitly include the units
attribute; there is no default value. The units
attribute takes a string value formatted as per the recommendations in the Udunits package [UDUNITS] . The following excerpt from the Udunits documentation explains the time unit encoding by example:
The 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 twodigits (indicating hours) or three or four digits (indicating hours and minutes).
The acceptable units for time are listed in the udunits.dat
file. 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. The reference time string (appearing after the identifier since
) may include date alone; date and time; or date, time, and time zone. The reference time is required. A reference time in year 0 has a special meaning (see Section 7.4, "Climatological Statistics").
Note: 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.
We recommend that the unit year
be used with caution. The Udunits package 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 includes the following definitions for years: a common_year
is 365 days, a leap_year
is 366 days, a Julian_year
is 365.25 days, and a Gregorian_year
is 365.2425 days.
For similar reasons the unit month
, which is defined in udunits.dat
to be exactly year/12
, should also be used with caution.
double time(time) ; time:long_name = "time" ; time:units = "days since 199011 0:0:0" ;
A time coordinate is identifiable from its units string alone. The Udunits routines utScan()
and utIsTime()
can be used to make this determination.
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
In order to calculate a new date and time given a base date, base time and a time increment one must know what calendar to use. For this purpose we recommend that the calendar be specified by the attribute calendar
which is assigned to the time coordinate variable. The values currently defined for calendar
are:
gregorian
orstandard

Mixed Gregorian/Julian calendar as defined by Udunits. This is the default.
proleptic_gregorian

A Gregorian calendar extended to dates before 15821015. That is, 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.
noleap
or365_day

Gregorian calendar without leap years, i.e., all years are 365 days long.
all_leap
or366_day

Gregorian calendar with every year being a leap year, i.e., all years are 366 days long.
360_day

All years are 360 days divided into 30 day months.
julian

Julian calendar.
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 coordinate 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 ;
The mixed Gregorian/Julian calendar used by Udunits is explained in the following excerpt from the udunits(3) man page:
The udunits(3) package uses a mixed Gregorian/Julian calen dar system. Dates prior to 15821015 are assumed to use the Julian calendar, which was introduced by Julius Caesar in 46 BCE and is based on a year that is exactly 365.25 days long. Dates on and after 15821015 are assumed to use the Gregorian calendar, which was introduced on that date and is based on a year that is exactly 365.2425 days long. (A year is actually approximately 365.242198781 days long.) Seem ingly strange behavior of the udunits(3) package can result if a usergiven time interval includes the changeover date. For example, utCalendar() and utInvCalendar() can be used to show that 15821015 *preceded* 15821014 by 9 days.
Due to problems caused by the discontinuity in the default mixed Gregorian/Julian calendar, we strongly recommend that this calendar should only be used when the time coordinate does not cross the discontinuity. For time coordinates that do cross the discontinuity the proleptic_gregorian
calendar should be used instead.
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
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 1.2, "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 two 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, 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, "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 compound
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 attributes as well as by crs_wkt
.
There will be occasions when a given CRS property value is duplicated in both a singleproperty grid
mapping attribute and the crs_wkt
attribute. In such cases the onus is on data producers to
ensure that the property values are consistent. However, in those situations where two values of a
given property are different, then the value specified by the singleproperty attribute shall take
precedence. For example, if the semimajor axis length of the ellipsoid is defined by the grid
mapping attribute semi_major_axis
and also by the crs_wkt
attribute (via the WKT
SPHEROID[…]
element) then the former, being the more specific attribute, takes
precedence. 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".
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 http://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_organisms_in_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. Since a boundary variable is considered to be part of a coordinate variable’s metadata, it is not necessary to provide it with attributes such as long_name
and units
.
Boundary variable attributes which determine the coordinate type (units
, standard_name
, axis
and positive
) or those which affect the interpretation of the array values (units
, calendar
, leap_month
, leap_year
and month_lengths
) must always agree exactly with the same attributes of its associated coordinate, scalar coordinate or auxiliary coordinate variable. To avoid duplication, however, it is recommended that these are not provided to a boundary variable.
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
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)
.  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)
.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. 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 the measure variable should be the same as or a subset of the dimensions of the variable to which they are related, but their order is not restricted. 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.
The COARDS standard offers limited support for climatological time. For compatibility with COARDS, time coordinates should also be recognised as climatological if they have a units
attribute of timeunits relative to midnight on 1 January in year 0 i.e. since 011
in udunits syntax, and provided they refer to the realworld calendar. We do not recommend this convention because (a) it does not provide any information about the intervals used to compute the climatology, and (b) there is no standard for how dates since year 1 will be encoded with units having a reference time in year 0, since this year does not exist; consequently there may be inconsistencies among software packages in the interpretation of the time coordinates. Year 0 may be a valid year in nonrealworld calendars, and therefore cannot be used to signal climatological time in such cases.
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", "200082 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: :Conventions = "CF1.8" ; :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: :Conventions = "CF1.8" ; :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 two methods for reducing dataset size: packing and compression. By packing we mean altering the data in a way that reduces its precision. By compression we mean techniques that store the data more efficiently and result in no precision loss. 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. If the scale_factor
and add_offset
attributes are of the same data type as the associated variable, the unpacked data is assumed to be of the same data type as the packed data. However, if the scale_factor
and add_offset
attributes are of a different data type from the variable (containing the packed data) then the unpacked data should match the type of these attributes, which must both be of type float
or both be of type double
. An additional restriction in this case is that the variable containing the packed data must be of type byte
, short
or int
. It is not advised to unpack an int
into a float
as there is a potential precision loss.
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. 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 array. Thus, the list variable and its dimension have the same name. 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.
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)
.
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 monotonically increasing times 

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

trajectory 
a series of data points along a path through space with monotonically increasing times 

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 monotonically increasing times 

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.
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). 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) 
time(o4) 
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 a coordinate or auxiliary coordinate variable with the attribute cf_role should be included. The only acceptable values of cf_role
for Discrete Geometry CF data sets are timeseries_id
, profile_id
, and trajectory_id
. 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 example A9.2.3.2. 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. See Appendix F for the grid mapping attributes.
The "Type" values are S for string, N for numeric, and D for the type of the data variable. The "Use" values are G for global, Gr for applying to groups, C for variables containing coordinate data, D for variables containing noncoordinate data, M for geometry container variables, and  for variables with a special purpose. "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 
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 
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 
Identifies latitude, longitude, vertical, or time axes. 


S 
C 
Identifies a boundary variable. 


S 
C 
Calendar used for encoding time axes. 


S 
D 
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 
Identifies the roles of variables that identify features in discrete sampling geometries 


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

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

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

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


S 
C, D 
Identifies a variable that defines geometry. 


S 
M 
Indicates the type of geometry present. 


S 
D, M 
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 
Specifies which month is lengthened by a day in leap years for a user defined calendar. 


N 
C 
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 
C, D 
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. 

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

N 
C, D 
Largest valid value of a variable. 


N 
C, D 
Smallest valid value of a variable. 


N 
C, D 
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>
.
<standard_name_table xmlns:xsi="http://www.w3.org/2001/XMLSchemainstance" xsi:noNamespaceSchemaLocation="CFStandardNameTable.xsd">
The content (delimited by the <standard_name_table>
tags) consists of, in order,
<institution>Name of institution here ... </institution> <contact>Email address of contact person ... </contact>
followed by 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>
<?xml version="1.0"?> <standard_name_table> <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 
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)
orap(k)
andb(k)
are components of the hybrid coordinate at levelk
,p0
is a reference pressure, andps(n,j,i)
is the surface pressure at horizontal gridpoint(j,i)
and time(n)
. The choice of whethera(k)
orap(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 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"
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"
Ocean sigma over z coordinate
standard_name = "ocean_sigma_z_coordinate"
 Definition

for k <= nsigma: z(n,k,j,i) = eta(n,j,i) + sigma(k)*(min(depth_c,depth(j,i))+eta(n,j,i)) for k > nsigma: z(n,k,j,i) = zlev(k)
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)
for k
<= nsigma
, and depth(j,i)
is the distance (a positive value) from the
datum to the sea floor at horizontal gridpoint (j,i)
. Above depth depth_c
there are nsigma
layers and below this depth the levels are surfaces of
constant height zlev
(positive upwards) relative to the datum.
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. No standard_name
has been
defined for depth_c
or nsigma
.
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.
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 
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.
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. 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 in this projection are directly related to the scanning angle of the satellite instrument.  Notes:

The algorithm for computing the mapping may be found at http://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.Notes on using the
PROJ
software packages for computing the mapping may be found at https://proj.org/operations/projections/geos.html and https://trac.osgeo.org/geotiff/.The
perspective_point_height
is the distance to the surface of the ellipsoid. Adding the earth major axis gives the distance from the centre of the earth.The
sweep_angle_axis
attribute indicates which axis the instrument sweeps. The value = "y" corresponds to the spinstabilized Meteosat satellites, the value = "x" to the GOESR satellite.The
fixed_angle_axis
attribute indicates which axis the instrument is fixed. The values are opposite tosweep_angle_axis
. Only one of those two attributes is mandatory.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 on a spherical Earth. 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. The Rotated Mercator projection is an Oblique Mercator projection with azimuth = +90.
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:


straight_vertical_longitude_from_pole

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/ups.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.  Notes:

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 
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 
The longitude (degrees_east) to be oriented straight up from the North or
South Pole. Domain: 

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
" and “platform_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 ordered monotonically, 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 ; name_strlen = 23 ; 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 staorage 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" ; time:missing_value = 999.9; 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. In the following example we show how the spatial positions of such a time series should be encoded in CF. 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 ; 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 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" ; time:missing_value = 999.9; float humidity(time) ; humidity:standard_name = “specific_humidity” ; humidity:coordinates = "time lat lon alt precise_lon precise_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 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 ; 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"; 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 ordered monotonically, 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 Example H.8, "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 = "surface_temperature" ; temperature:long_name = "skin temperature" ; temperature:units = "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 = "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 = "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_name = "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 = "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 = "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 ; name_strlen = 23 ; 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 ; name_strlen = 23 ; 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
attribute "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
" and “platform_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 ; 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" ; 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 ordered monotonically. 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 ordered monotonically. 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; 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 = "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 ordered monotonically. 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 ordered monotonically. 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.
Abstract
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 entities 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 entities, 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.
The netCDF data model
The existing CF conventions are for use with netCDF files following the netCDF "classic" data model (figure 1). We first give a brief summary of this explicit data model, since the CF conventions cannot be described without reference to the components of netCDF.
NetCDF classic files contain data in named variables, which can be single numbers (with no dimensions), onedimensional arrays (vectors), or multidimensional arrays, and the dimensions are declared by name in the file. Variables can be of integer, floating point or character data types. Variables may have attributes attached, of any data type. Attributes can have a single value or consist of a onedimensional array. NetCDF files also have "global" file attributes which provide information about the dataset as a whole. NetCDF library software has functions to define dimensions, variables and attributes, and write and read data.
Elements of CFnetCDF
The CFnetCDF elements are listed in table 1 and shown (in blue) with their interrelationships in figure 2. 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 

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 
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 3, figure 4 and figure 5) are called "constructs", a term chosen to differentiate from the CFnetCDF entities previously defined and to be programming languageneutral (i.e. as opposed to "object" or "structure"). The constructs, listed in table 2, are related to CFnetCDF entities (figure 2), which in turn relate to the components of netCDF file (figure 1).
CF construct  Description 

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 
Field ancillary 
Ancillary metadata which varies within the domain 
Cell method 
Describes how data represents variation within cells 
Field construct
The field construct is central to the CF data model and includes all the other constructs (figure 3). A field corresponds to a CFnetCDF data variable with all of its metadata. All CFnetCDF elements are mapped to some component of the CF field construct and the field constructs completely contain all the data and metadata which can be extracted from the file using the CF conventions. Note that the constructs contained by the field construct cannot exist independently, as is indicated by the nature of the class associations shown in figure 3.
The field construct consists of a data array and the definition of its domain, ancillary metadata defined over the same domain, metadata to describe how the cell values represent the variation of the physical quantity within the cells of the domain (figure 3), and 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 3). The only component of the field which is mandatory is the data array. Because the CF conventions do not mention the concept of the domain, it is not regarded as a construct of the data model. Instead, the domain is defined collectively by various other constructs included in the field.
The properties of the field construct correspond to some netCDF
attributes of variables (e.g. the units
, long_name
, and
standard_name
), and some netCDF global file attributes
(e.g. 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 global file 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 global file attributes is not stated in the CF conventions, but for the data model it is necessary because there is no notion of a file. Hence, metadata stored in attributes of the file as a whole have to be transferred to the field construct. If present, the global file 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 featureType are not regarded as separate constructs within the field, because they do not depend on any other construct for their interpretation.
Domain axis construct and the data array
A domain axis construct (figure 4) 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 4) provide information which locate the cells of the domain and which depend on one, more or all of the domain axis constructs. There are two distinct types of coordinate construct: a dimension coordinate construct provides monotonic numeric coordinates for a single domain axis, and an auxiliary coordinate construct provides any type of coordinate information for one or more of the domain axes.
In both cases, the coordinate construct consists of a data array of the coordinate values which spans one, more or all of the domain axis constructs, an optional array of cell bounds recording the extents of each cell, and properties to describe the coordinates (in the same sense as for the field construct). An array of cell bounds spans the same domain axes as its coordinate array, with the addition of an extra dimension whose size is that of the number of vertices of each cell. This extra dimension does not correspond to a domain axis construct since it does not relate to an independent axis of the domain. Note that, for climatological time axes, the bounds are interpreted in a special way indicated by the cell method constructs.
The dimension coordinate construct is able to unambiguously describe cell locations because a domain axis can be associated with at most one dimension coordinate construct, whose data array values must all be nonmissing and strictly monotonically increasing or decreasing. They must also all be of the same numeric data type. If cell bounds are provided, then each cell must have exactly two vertices. 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 then 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.
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. In such cases, onedimensional auxiliary coordinate constructs could be used to store coordinate values. These axes are called "discrete" axes in CFnetCDF.
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 5) 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 5) 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 1).
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
.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" ;
Cell measure construct
A cell measure (figure 3) 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.
Field ancillary constructs
The field ancillary construct (figure 3) 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 3) 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.
Revision History

the section called "Polar Stereographic" : Added
latitude_of_projection_origin
map parameter.

Section 5.7, "Scalar Coordinate Variables" : Added note that use of scalar coordinate variables inhibits interoperability with COARDS conforming applications.

Example 5.13, "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.

Section 7.3, "Cell Methods" : Changed several incorrect occurances of the cell method
"standard deviation"
to"standard_deviation"
.

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

Preface : Changed text to refer to rules of CF governance, and provisional status.

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

Changed document version to 1.1.

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 (Trac ticket #18).

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

Changed document version to 1.2.

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. (Trac ticket #26). 
Changed document version to 1.3.

Fixed defect in Example 4.3, “Atmosphere sigma coordinate”. (Trac ticket #30).

Fixed defect in Chapter 5, Coordinate Systems. (Trac ticket #32).

Fixed defect in wording of Chapter 5, Coordinate Systems. (Trac ticket #35).

Fixed defect related to subsection headings in [dimensionlessvcoord]. (Trac ticket #36).

Changes related to removing ambiguity in Section 7.3, "Cell Methods". (Trac ticket #17).

Changed document version to 1.4.

Added grid mappings Lambert Cylindrical Equal Area, Mercator, and Orthographic to Appendix F, Grid Mappings. (Trac ticket #34).

Fixed defect in Mercator section of Appendix F, Grid Mappings by updating to version 12 of Grid Map Names (see http://cftrac.llnl.gov/trac/wiki/GridMapNames?version=12).

Fixed defect by clarifying that coordinates indicate gridpoint location in Chapter 4, Coordinate Types. (Trac ticket #44).

Fixed defect of outdated Conventions attribute. (Trac ticket #45).
Minor revisions requested by Jonathan Gregory. Revisions 33 and 49 were closed after discussions; the rest had elicited no objections.

Ticket 33, cell_methods for statistical indices

Ticket 49, clarification of flag_meanings attribute

Ticket 58, remove deprecation of "missing_value" attribute

Ticket 57, fix for broken URLs in CF Conventions document

Ticket 56, typo in CF conventions doc

Ticket 51, syntax consistency for dimensionless vertical coordinate definitions

Ticket 47, error in example 7.4

Changed document version to 1.5.

New chapter, ticket 37 Changed document version to 1.6.
Ticket 37. Added Chapter 9, Discrete Sampling Geometries, and a related Appendix H, and revised several other chapters.
In Appendix H (Annotated Examples of Descrete Geometries), updated standard names "station_description" and "station_wmo_id" to "platform_name" and "platform_id".
Redo several changes which had previously been made in an earlier draft of version 1.7:

Ticket 61, two new cell methods in Appendix E.

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

Ticket 65, add range entry in Appendix E.

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

Ticket 93, Added two new dimensionless coordinates to Appendix D.

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

Ticket #71, correction of Vertical perspective projection.

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 141, update affiliation organisations for Jonathan Gregory and Phil Bentley.

Ticket 31, add new attribute
actual_range
.

renamed Appendix G to Revision History, as in Trac Ticket 73.

revised section 3.3 for Trac ticket 123.

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

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

Ticket #149, correction of standard name in example 7.3

Ticket #77, Add sinusoidal projection

Ticket #87, Allow comments in coordinate variables

Ticket #92, Add oblique mercator projection

Ticket #72, Adding the geostationary projection.

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

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 #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 #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 #143, Supplement the definitions of dimensionless vertical coordinates

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

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

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

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

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

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

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

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

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

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

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

a few formatting tweaks

Where appropriate, changed document version from 1.6 to 1.7, and 1.7 (DRAFT) to 1.7.

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

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

Updated use of WKTCRS syntax.

Ticket #164, New Geometries section 7.5.

Ticket #164, Implement suggestions from trac ticket comments.

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, Remove geometry attribute from lat/lon variables in examples.

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

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

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

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

Issues #155, #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 #142: Fix bad reference to an example in section 6.1 "Labels".

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

Issue #136: Missing trajectory dimension in H.22

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

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

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

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

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

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

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

Issue #203: Clarifications to use of groups.

Issue #218: Taxon Names and Identifiers.

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

Issue #223: Axis Order for CRSWKT grid mappings

#230  Correct inconsistency in units or geostationary projection
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 .

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

[NUG] The NetCDF User’s Guide for NetCDF version 4.4.1.1.

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

[OGPEPSG] OGP Surveying & Positioning Committee and EPSG Geodetic Parameter Registry .

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

[SCH02] C Schaer, D Leuenberger, and O Fuhrer. 2002. “ A new terrainfollowing vertical coordiante formulation for atmospheric prediction models ”. 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 .

[W3C] World Wide Web Consortium (W3C) .

[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, https://doi.org/10.5194/gmd1046192017, 2017.