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.
Table of Contents
List of Tables
List of Examples
standard_name
flag_values
flag_masks
flag_masks
and
flag_values
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://wwwpcmdi.llnl.gov/cf/
This document will be updated to reflect agreed changes to the standard and to correct mistakes according to the rules of CF governance . See Appendix G, Revision History for the full revision history. Changes with provisional status use the following markup style: new text , deleted text , and [a comment] .
Table of Contents
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.
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.
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).
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.
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 chapter 10 of the NUG chapter 10 of the NUG ). All examples in this document use CDL syntax.
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.
We use this term precisely as it is defined in section
2.3.1 of the NUG
2.3.1 of the NUG
. 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.
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.
A dimension of a netCDF variable that has an associated latitude coordinate variable.
A dimension of a netCDF variable that has an associated longitude coordinate variable.
An auxiliary coordinate variable that is multidimensional.
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.
A scalar variable that contains coordinate data. Functionally equivalent to either a size one coordinate variable or a size one auxiliary coordinate variable.
A dimension of a netCDF variable that is used to identify a location in time and/or space.
A dimension of a netCDF variable that has an associated time coordinate variable.
A dimension of a netCDF variable that has an associated vertical coordinate variable.
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. 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.
We recommend that the NUG defined attribute
Conventions
be given the string value
"
CF1.3
"
"
CF1.4
"
"
CF1.5
"
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,
Dimensionless 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.
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.
Table of Contents
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.
The netCDF data types
char
,
byte
,
short
,
int
,
float
or
real
, and
double
are all acceptable. The
char
type is not intended for numeric data. One
byte numeric data should be stored using the
byte
data type. All integer types are treated by
the netCDF interface as signed. It is possible
to treat the
byte
type as unsigned by using the
NUG convention of indicating the unsigned range
using the
valid_min
,
valid_max
,
or
valid_range
attributes.
NetCDF does not support a character string type, so these must be represented as character arrays. In this document, a one dimensional array of character data is simply referred to as a "string". An ndimensional array of strings must be implemented as a character array of dimension (n,max_string_length), with the last (most rapidly varying) dimension declared large enough to contain the longest string in the array. All the strings in a given array are therefore defined to be equal in length. For example, an array of strings containing the names of the months would be dimensioned (12,9) in order to accommodate "September", the month with the longest name.
Variable, dimension and attribute 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.
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 a 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.
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 .
The NUG conventions
(
NUG section 8.1
NUG section 8.1
) provide the
_FillValue
,
missing_value
,
valid_min
,
valid_max
, and
valid_range
attributes
to indicate missing data.
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
strongly
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 (
NUG section 7.16
NUG section 7.16
).
The
missing_value
attribute is considered deprecated by
the NUG and we do not recommend its use. However for backwards compatibility
with COARDS this standard continues to recognize the use of the
missing_value
attribute to indicate undefined or missing data.
The missing values of a variable with
scale_factor
and/or
add_offset
attributes
(see section
Section 8.1, “Packed Data”
) are interpreted
relative to the variable's external values
, i.e., the values stored in the netCDF file.
(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 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.
We recommend that netCDF files that
follow these conventions indicate
this by setting the NUG defined global
attribute
Conventions
to the string value
"
CF1.3
"
"
CF1.4
"
"
CF1.5
"
. The string is interpreted as a
directory name relative to a directory
that is a repository of documents
describing sets of disciplinespecific
conventions. The conventions directory
name is currently interpreted relative to
the directory
pub/netcdf/Conventions/
on the host machine
ftp.unidata.ucar.edu
. The
web based versions of this
document are linked from the
netCDF Conventions web page
.
netCDF Conventions web page
.
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.
Table of Contents
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.
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.
Table 3.1. Supported Units
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 
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.
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 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:
The name used to identify the physical quantity. A standard name contains no whitespace and is case sensitive.
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 either the standard name modifier (see below and
Appendix C,
Standard Name Modifiers
) or by the
cell_methods
attribute (see
Section 7.3, “Cell Methods”
and
Appendix E,
Cell Methods
).
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.
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://cfpcmdi.llnl.gov/documents/cfstandardnames/standardnametable/current/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://cfpcmdi.llnl.gov/documents/cfstandardnames/standardnametable/current/standardnametable
, 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
.
Example 3.1. Use of
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 .
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.
Example 3.2. Instrument data
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" ;
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.
Example 3.3. A flag variable
, using
flag_values
byte current_speed_qc(time, depth, lat, lon) ; current_speed_qc:long_name = "Current Speed Quality" ; current_speed_qc:standard_name = "sea_water_speed status_flag" ; current_speed_qc:_FillValue = 128b ; current_speed_qc:valid_range = 0b, 2b 127b, 127b ; current_speed_qc:flag_values = 0b, 1b, 2b ; current_speed_qc:flag_meanings = "quality_good sensor_nonfunctional outside_valid_range" ;
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.
Example 3.4.
A flag variable, using
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" ;
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.
Example 3.5.
A flag variable, using
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.
The remaining bits (Bit 2 and Bit 3) are decoded as follows:
Table 3.3. Flag Variable Bit 2 and Bit 3 (from Example)
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.
Table of Contents
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.
Coordinate types other than latitude, longitude, vertical, and time
are allowed. 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.
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
.
Example 4.1. Latitude axis
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.
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
.
Example 4.2. Longitude axis
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.
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 auxillary 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 of
up
or
down
(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
.
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 include
include
bar
,
millibar
,
decibar
,
atmosphere (atm)
,
pascal (Pa)
, and
hPa
.
units of length as listed in the file udunits.dat. For vertical axes the most commonly used of these include
meter (metre, m)
, and
kilometer (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.
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.
For dimensionless vertical coordinates we extend the COARDS standard by making use of the
standard_name
attribute to associate a coordinate with its definition from
Appendix D,
Dimensionless Vertical Coordinates
. The definition provides a mapping between the dimensionless coordinate values and dimensional values that can positively and uniquely indicate the location of the data. A new attribute,
formula_terms
, is used to associate terms in the definitions with variables in a netCDF file. To maintain backwards compatibility with COARDS the use of these attributes is not required, but is strongly recommended.
Example 4.3. Atmosphere sigma coordinate
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" ;
In this example the
standard_name
value
atmosphere_sigma_coordinate
identifies the following
definition from
Appendix D,
Dimensionless 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)
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.
Example 4.4. Time axis
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
.
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
or
standard
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
or
365_day
Gregorian calendar without leap years, i.e., all years are 365 days long.
all_leap
or
366_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.
Example 4.5. Perpetual time axis
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.
Example 4.6. Paleoclimate time axis
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.
Table of Contents
A variable's spatiotemporal dimensions are used to locate data values in time and space. This is accomplished by associating these dimensions with the relevant set of latitude, longitude, vertical, and time coordinates. This section presents two methods for making that association: the use of coordinate variables , and the use of auxiliary coordinate variables .
All of a variable's dimensions that are latitude, longitude, vertical, or time dimensions (see Section 1.2, “Terminology” ) must have corresponding coordinate variables, i.e., onedimensional variables 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 ].
All of a variable's spatiotemporal dimensions that are not latitude,
longitude, vertical, or time dimensions are required to be associated
with the relevant latitude, longitude, vertical, or time coordinates
via the new
coordinates
attribute of the 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
(an exception is label coordinates (
Section 6.1, “Labels”
) which
contain a dimension for maximum string length). 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.
The use of coordinate variables is required whenever they are applicable.
That is, auxiliary coordinate variables may not be used as the only way
to identify latitude and longitude coordinates that could be identified
using coordinate variables. 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. The
axis
attribute
is not allowed for auxiliary coordinate variables. 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
(see
Chapter 4,
Coordinate Types
).
If the coordinate variables for a horizontal grid are not longitude
and latitude, it is recommended that they be supplied
in addition
to the required coordinates.
For example, the Cartesian coordinates of a map projection should be
supplied as coordinate variables in addition to the required
twodimensional latitude and longitude variables that are identified
via the
coordinates
attribute.
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.
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.
Example 5.1. Independent coordinate variables
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)
.
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.
Example 5.2. Twodimensional coordinate variables
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.
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.
Example 5.3. Reduced horizontal grid
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.
To represent data at scattered points it is convenient to use a variable with one dimension to represent the measurement locations. Auxiliary coordinate variables are used to associate a single spatial dimension with multiple independent coordinates.
Example 5.4. Timeseries of station data
dimensions: station = 10 ; // measurement locations pressure = 11 ; // pressure levels time = UNLIMITED ; variables: float humidity(time,pressure,station) ; humidity:long_name = "specific humidity" ; humidity:coordinates = "lat lon" ; double time(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:long_name = "pressure" ; pressure:units = "hPa" ;
humidity(n,k,i)
is associated with the coordinate values
time(n)
,
pressure(k)
,
lat(i)
, and
lon(i)
.
A possible representation of the spatiotemporal locations of measurements along a flight path is to use time to parameterize the trajectory and use auxiliary coordinate variables to provide the spatial locations.
Example 5.5. Trajectories
dimensions: time = 1000 ; variables: float O3(time) ; O3:long_name = "ozone concentration" ; O3:units = "1e9" ; O3:coordinates = "lon lat z" ; double time(time) ; time:long_name = "time" ; time:units = "days since 19700101 00:00:00" ; float lon(time) ; lon:long_name = "longitude" ; lon:units = "degrees_east" ; float lat(time) ; lat:long_name = "latitude" ; lat:units = "degrees_north" ; float z(time) ; z:long_name = "height above mean sea level" ; z:units = "km" ; z:positive = "up" ;
O3(n)
is associated with the coordinate
values
time(n)
,
z(n)
,
lat(n)
, and
lon(n)
.
When the coordinate variables for a horizontal grid are not longitude
and latitude, it is required that the true latitude and longitude
coordinates be supplied via the
coordinates
attribute.
If in addition it is desired to describe the mapping between the
given coordinate variables and the true latitude and longitude
coordinates, the attribute
grid_mapping
may be
used to supply this description. 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 which is the
name of another variable in the file that provides the description
of the mapping via a collection of attached attributes. This variable
is called
a grid mapping variable
and 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
.
When the coordinate variables for a horizontal grid are longitude
and latitude, a grid mapping variable with
grid_mapping_name
of
latitude_longitude
may be used to specify the
ellipsoid and prime meridian.
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
.
Example 5.6. Rotated pole grid
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" ; rlon: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
.
Example 5.7. Lambert conformal projection
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
.
Example 5.8. Latitude and longitude on a spherical Earth
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 ;
Example 5.9. Latitude and longitude on the WGS 1984 datum
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 ;
Example 5.10. British National Grid
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" ; double lat(y, x) ; double lon(y, x) ; float temp(y, x) ; temp:long_name = "temperature" ; temp:units = "K" ; temp:coordinates = "lat lon" ; temp:grid_mapping = "crs" ; int crs ; crs:grid_mapping_name = "transverse_mercator"; crs:semi_major_axis = 6377563.396 ; crs:semi_minor_axis = 6356256.910 ; crs:inverse_flattening = 299.3249646 ; crs:latitude_of_projection_origin = 49.0 ; crs:longitude_of_projection_origin = 2.0 ; crs:false_easting = 400000.0 ; crs:false_northing = 100000.0 ; crs:scale_factor_at_projection_origin = 0.9996012717 ;
When a variable has an associated coordinate which is
singlevalued, that coordinate may be represented as a
scalar variable. Since there is no associated dimension
these scalar coordinate variables should be attached to
a data variable via the
coordinates
attribute.
Under COARDS the method of providing a single valued coordinate was to add a dimension of size one to the variable, and supply the corresponding coordinate variable. The new scalar coordinate variable is a convenience feature which avoids adding size one dimensions to variables. Scalar coordinate variables have the same information content and can be used in the same contexts as a size one coordinate variable. 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.
Example 5.11. Multiple forecasts from a single analysis
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".
Table of Contents
The previous section contained several examples in which measurements from scattered sites were grouped using a single dimension. Coordinates of the site locations can be provided using auxiliary coordinate variables, but it is often desirable to identify measurement sites by name, or some other unique string. Other purposes for string identifiers are also described in Section 6.1.1, “Geographic Regions” , and Section 7.3.3, “ Statistics applying to portions of cells ” .
The list of string identifiers plays an analogous role to a coordinate variable, hence we have chosen to use the
coordinates
attribute to provide the name of the variable that contains the string array. An application processing the variables listed in the
coordinates
attribute can recognize a labeled axis by checking whether or not a given variable contains character data. If a character variable has only one dimension (the length of the string), it is regarded as a stringvalued scalar coordinate variable, analogous to a numeric scalar coordinate variable (see
Chapter 5,
Coordinate Systems
.)
Example 6.1. Several parcel trajectories
Consider a set of ocean floats that follow parcel trajectories and simultaneously measure temperature at fixed times. We wish to identify the floats by name. The temperature data is a function of parcel (i.e.,
float
) and time. The location of each sample is also a function of parcel and time, so the position information is stored in a multidimensional coordinate variable.
dimensions: parcel = 15 ; // number of trajectories times = 20 ; max_len_parcel_name = 64 ; // max length of trajectory name variables: float temperature(parcel,times) ; temperature:coordinates = "parcel_name lat lon" ; float times(times) ; char parcel_name(parcel,max_len_parcel_name) ; float lon(parcel,times) ; float lat(parcel,times) ;
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
.
Example 6.2. Northward heat transport in Atlantic Ocean
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 ; strlen = 64 ; 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" ; char geo_region(lbl,strlen) ; geo_region:standard_name="region" data: geo_region = "atlantic_ocean" ; lat = 10., 20., 30., 40., 50. ;
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.
Example 6.3. Model level numbers
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";
Table of Contents
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” .
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
.
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.
For a coordinate variable such as
lat(lat)
with associated boundary variable
latbnd(x,2)
, the
interval endpoints must be ordered consistently with
the associated coordinate, e.g., for an increasing
coordinate,
lat(1)
>
lat(0)
implies
latbnd(i,1)
>=
latbnd(i,0)
for all
i
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)
and
lat(i+1)
are contiguous,
then
latbnd(i+1,0)
=
latbnd(i,1)
.
In the case where the horizontal grid is described
by twodimensional auxiliary coordinate
variables in latitude
lat(n,m)
and longitude
lon(n,m)
, and the associated cells are foursided,
then the boundary variables are given in the form
latbnd(n,m,4)
and
lonbnd(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
sides
i1
and
j1
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)
In all other cases, the bounds should be dimensioned
(...,n,p)
, where
(...,n)
are the dimensions of the auxiliary coordinate variables, and
p
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.
Example 7.1. Cells on a latitude axis
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.
Example 7.2. Cells in a nonrectangular grid
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.
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.
Example 7.3. Cell areas for a spherical geodesic grid
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="area"; cell_area:units = "m2" float lon_vertices(cell,nv) ; float lat_vertices(cell,nv) ;
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".
The token name
can be a dimension of the variable, a scalar
coordinate variable, or a valid standard name.
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
,
maximum
,
minimum
,
mid_range
,
standard_deviation
,
variance
,
mode
,
and
median
.
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
cell_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
cell_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.
Example 7.4. Methods applied to a timeseries
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 (station,time) (time,station) ; pressure:long_name = "pressure"; pressure:units = "kPa"; pressure:cell_methods = "time: point"; float maxtemp (station,time) (time,station) ; maxtemp:long_name = "temperature"; maxtemp:units = "K"; maxtemp:cell_methods = "time: maximum"; float ppn (station,time) (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
.
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
would
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
.
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
cell_bounds
attribute).
Example 7.5. Surface air temperature variance
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.
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.).
Example 7.6. Mean surface temperature over land and sensible heat flux averaged separately over land and sea.
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 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.
Example 7.7. Thickness of seaice and snow on seaice averaged over sea area.
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.
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.
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.
within years
time: method2
over years
method1 is applied to the time intervals (mdHMS0mdHMS1) within individual years and method2 is applied over the range of years (y0y1).
within days
time: method2
over days
method1 is applied to the time intervals (HMS0HMS1) within individual days and method2 is applied over the days in the interval (ymd0ymd1).
within days
time: method2
over days
time: method3
over 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.
Example 7.8. Climatological seasons
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" ;
Example 7.9. Decadal averages for January
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" ;
Example 7.10. Temperature for each hour of the average day
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" ;
Example 7.11. Extreme statistics and spelllengths
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.;
Example 7.12. Temperature for each hour of the typical climatological day
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" ;
Example 7.13. Monthlymaximum daily precipitation totals
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" ;
Table of Contents
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.
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”
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.
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.
Example 8.1. Horizontal compression of a threedimensional array
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
.
Example 8.2. Compression of a threedimensional field
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)
.
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, C for variables containing coordinate data, and D for variables containing noncoordinate data. "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).
Table A.1. Attributes
Attribute  Type  Use  Links  Description 

add_offset

N  D  NUG (8.1) NUG (8.1) , 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
scale_factor
and
add_offset
attributes are present, the data are first scaled before the offset is added.

ancillary_variables

S  D  Section 3.4, “Ancillary Data”  Identifies a variable that contains closely associated data, e.g., the measurement uncertainties of instrument data. 
axis

S  C  Chapter 4, Coordinate Types  Identifies latitude, longitude, vertical, or time axes. 
bounds

S  C  Section 7.1, “Cell Boundaries”  Identifies a boundary variable. 
calendar

S  C  Section 4.4.1, “Calendar”  Calendar used for encoding time axes. 
cell_measures

S  D  Section 7.2, “Cell Measures”  Identifies variables that contain cell areas or volumes. 
cell_methods

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

S  C  Section 7.4, “Climatological Statistics”  Identifies a climatology variable. 
comment

S  G, D  Section 2.6.2, “Description of file contents”  Miscellaneous information about the data or methods used to produce it. 
compress

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

S  G  NUG (8.1) NUG (8.1)  Name of the conventions followed by the dataset. 
coordinates

S  D  Chapter 5, Coordinate Systems , Section 6.1, “Labels” , Section 6.2, “Alternative Coordinates”  Identifies auxiliary coordinate variables, label variables, and alternate coordinate variables. 
_FillValue

D  D  NUG (8.1) NUG (8.1)  A value used to represent missing or undefined data. 
flag_masks

D  D  Section 3.5, “Flags”  Provides a list of bit fields expressing Boolean or enumerated flags. 
flag_meanings

S  D  Section 3.5, “Flags” 
Use in conjunction with
flag_values
to provide descriptive words or phrases for each flag value. If multiword phrases are used to describe the flag values, then the words within a phrase should be connected with underscores.

flag_values

D  D  Section 3.5, “Flags” 
Provides a list of the flag values. Use in conjunction with
flag_meanings
.

formula_terms

S  C  Section 4.3.2, “Dimensionless Vertical Coordinate”  Identifies variables that correspond to the terms in a formula. 
grid_mapping

S  D  Section 5.6, “ Grid Mappings and Projections Horizontal Coordinate Reference Systems, Grid Mappings, and Projections ”  Identifies a variable that defines a grid mapping. 
history

S  G  NUG (8.1) NUG (8.1)  List of the applications that have modified the original data. 
institution

S  G, D  Section 2.6.2, “Description of file contents”  Where the original data was produced. 
leap_month

N  C  Section 4.4.1, “Calendar”  Specifies which month is lengthened by a day in leap years for a user defined calendar. 
leap_year

N  C  Section 4.4.1, “Calendar”  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. 
long_name

S  C, D  NUG (8.1) NUG (8.1) , Section 3.2, “Long Name”  A descriptive name that indicates a variable"s content. This name is not standardized. 
missing_value

D  D  Section 2.5.1, “Missing Data”  A value used to represent missing or undefined data (deprecated by the NUG). 
month_lengths

N  C  Section 4.4.1, “Calendar”  Specifies the length of each month in a nonleap year for a user defined calendar. 
positive

S  C  [ COARDS ]  Direction of increasing vertical coordinate value. 
references

S  G, D  Section 2.6.2, “Description of file contents”  References that describe the data or methods used to produce it. 
scale_factor

N  D  NUG (8.1) NUG (8.1) , 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
add_offset
attribute.

source

S  G, D  Section 2.6.2, “Description of file contents”  Method of production of the original data. 
standard_error_multiplier

N  D  Appendix C, Standard Name Modifiers  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. 
standard_name

S  C, D  Section 3.3, “Standard Name”  A standard name that references a description of a variable"s content in the standard name table. 
title

S  G  NUG (8.1) NUG (8.1)  Short description of the file contents. 
units

S  C, D  NUG (8.1) NUG (8.1) , Section 3.1, “Units”  Units of a variable"s content. 
valid_max

N  C, D  NUG (8.1) NUG (8.1)  Largest valid value of a variable. 
valid_min

N  C, D  NUG (8.1) NUG (8.1)  Smallest valid value of a variable. 
valid_range

N  C, D  NUG (8.1) NUG (8.1)  Smallest and largest valid values of a variable. 
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
and
<standard_name_table>
.
</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>
Example B.1. A name table containing three entries
<?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.
In the
Units
column,
u
indicates units dimensionally equivalent to those for the unmodified standard name.
Table C.1. Standard Name Modifiers
Modifier  Units  Description 

detection_minimum

u

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

1  The number of discrete observations or measurements from which a data value has been derived. 
standard_error

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
standard_error
ancillary variable should have an attribute
standard_error_multiplier
stating the multiplication factor.

status_flag

Flag values indicating the quality or other status of the data values. The variable
should have
flag_values
or
flag_masks
(or both)
and
flag_meanings
attributes to show how it should be interpreted (
Section 3.5, “Flags”
).

The definitions given here allow an application to compute
dimensional coordinate values from the dimensionless
ones 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 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.
standard_name
= "atmosphere_ln_pressure_coordinate"
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"
standard_name
= "atmosphere_sigma_coordinate"
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"
standard_name
= "atmosphere_hybrid_sigma_pressure_coordinate"
p(n,k,j,i) = a(k)*p0 + b(k)*ps(n,j,i)
or
p(n,k,j,i) = ap(k) + b(k)*ps(n,j,i)
where
p(n,k,j,i)
is the pressure at gridpoint
(n,k,j,i)
,
a(k)
or
ap(k)
and
b(k)
are components of the hybrid coordinate at
level
k
,
p0
is a reference
pressure, and
ps(n,j,i)
is the surface pressure at horizontal gridpoint
(j,i)
and time
(n)
.
The choice of whether
a(k)
or
ap(k)
is used depends on
model formulation; the former is a dimensionless fraction,
the latter a pressure value. In both formulations,
b(k)
is a dimensionless
fraction.
The format for the
formula_terms
attribute is
formula_terms
= "a: var1 b: var2 ps: var3 p0: var4"
where
a
is replaced by
ap
if appropriate.
The hybrid sigmapressure coordinate for level
k
is defined as
a(k)+b(k)
or
ap(k)/p0+b(k)
,
as appropriate.
standard_name
= "atmosphere_hybrid_height_coordinate"
z(n,k,j,i) = a(k) + b(k)*orog(n,j,i)
where
z(n,k,j,i)
is the height above the geoid (approximately mean sea level) at gridpoint
(k,j,i)
and
time (n)
,
orog(n,j,i)
is the height of the surface above
the geoid 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"
There is no dimensionless hybrid height coordinate. The hybrid
height is best approximated as
a(k)
if a leveldependent constant is needed.
standard_name
= "atmosphere_sleve_coordinate"
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 geoid (approximately mean sea level) at gridpoint
(k,j,i)
and time
(n)
,
ztop
is the height of the top of the model, 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 large and small parts of the topography. 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 hybrid height coordinate for level
k
is defined as
a(k)*ztop
.
standard_name
= "ocean_sigma_coordinate"
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
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)
,
sigma(k)
is the
dimensionless coordinate at vertical gridpoint
(k)
,
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
= "sigma: var1 eta: var2 depth: var3"
standard_name
= "ocean_s_coordinate"
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 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)
, and
depth(j,i)
is the distance
from ocean datum to sea floor (positive value) 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"
standard_name
= "ocean_sigma_z_coordinate"
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 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)
,
sigma(k)
is the dimensionless
coordinate at vertical gridpoint
(k)
for
k <= nsigma
,
and
depth(j,i)
is the distance from ocean datum to
sea floor (positive value) at horizontal gridpoint
(j,i)
.
Above depth
depth_c
there are
nsigma
layers.
The format for the
formula_terms
attribute is
formula_terms
= "sigma: var1 eta: var2 depth: var3 depth_c: var4 nsigma: var5
zlev: var6"
standard_name
= "ocean_double_sigma_coordinate"
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 ocean
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
from ocean datum to sea floor (positive value) 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"
In the
Units
column,
u
indicates the units of the physical quantity before the method is applied.
Table E.1. Cell Methods
cell_method
cell_methods

Units  Description 

point

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. 
sum

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. 
maximum

u

Maximum 
median

u

Median 
mid_range

u

Average of maximum and minimum 
minimum

u

Minimum 
mean

u

Mean (average value) 
mode

u

Mode (most common value) 
standard_deviation

u

Standard deviation 
variance

u
^{
2
}

Variance 
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.
grid_mapping_name
= albers_conical_equal_area
standard_parallel
 There may be 1 or 2 values.
longitude_of_central_meridian
latitude_of_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute values
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the
PROJ.4
software package for computing the mapping may be found at
http://www.remotesensing.org/geotiff/proj_list/albers_equal_area_conic.html
.
grid_mapping_name
= azimuthal_equidistant
longitude_of_projection_origin
latitude_of_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute values
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the
PROJ.4
software package for computing the mapping may be found at
http://www.remotesensing.org/geotiff/proj_list/azimuthal_equidistant.html
.
grid_mapping_name
= lambert_azimuthal_equal_area
longitude_of_projection_origin
latitude_of_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute values
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the
PROJ.4
software package for computing the mapping may be found at
http://www.remotesensing.org/geotiff/proj_list/lambert_azimuthal_equal_area.html
.
grid_mapping_name
= lambert_conformal_conic
standard_parallel
 There may be 1 or 2 values.
longitude_of_central_meridian
latitude_of_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute values
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the
PROJ.4
software package for computing the mapping may be found at
http://www.remotesensing.org/geotiff/proj_list/lambert_conic_conformal_2sp.html
.
grid_mapping_name
= lambert_cylindrical_equal_area
longitude_of_central_meridian
standard_parallel
or
scale_factor_at_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute value
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the PROJ.4 software packages for computing the mapping may be found at http://www.remotesensing.org/geotiff/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.
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.
None.
The rectangular coordinates are longitude and latitude identified by the usual conventions ( Section 4.1, “Latitude Coordinate” and Section 4.2, “Longitude Coordinate” ).
grid_mapping_name
= mercator
longitude_of_projection_origin
standard_parallel
(EPSG 9805) or
scale_factor_at_projection_origin
(EPSG 9804)
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute value
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the PROJ.4 software packages for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/mercator_1sp.html ("Mercator (1SP)" or EPSG 9804) or http://www.remotesensing.org/geotiff/proj_list/mercator_2sp.html ("Mercator (2SP)" or EPSG 9805).
More information on formulas available in [ OGP/EPSG_GN7_2 ].
grid_mapping_name
= orthographic
longitude_of_projection_origin
latitude_of_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates are identified by the
standard_name
attribute value
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the PROJ.4 software packages for computing the mapping may be found at http://www.remotesensing.org/geotiff/proj_list/orthographic.html ("Orthographic" or EPSG 9840).
More information on formulas available in [ OGP/EPSG_GN7_2 ].
grid_mapping_name
= polar_stereographic
straight_vertical_longitude_from_pole
latitude_of_projection_origin
 Either +90. or 90.
Either
standard_parallel
or
scale_factor_at_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute values
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the
PROJ.4
software package for computing the mapping may be found at
http://www.remotesensing.org/geotiff/proj_list/polar_stereographic.html
.
grid_mapping_name
= rotated_latitude_longitude
grid_north_pole_latitude
grid_north_pole_longitude
north_pole_grid_longitude
 This parameter is option (default is 0).
The rotated latitude and longitude coordinates
are identified by the
standard_name
attribute values
grid_latitude
and
grid_longitude
respectively.
grid_mapping_name
= stereographic
longitude_of_projection_origin
latitude_of_projection_origin
scale_factor_at_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute values
projection_x_coordinate
and
projection_y_coordinate
respectively.
Formulas for the mapping and its inverse along with notes on using the
PROJ.4
software package for doing the calcuations may be found at
http://www.remotesensing.org/geotiff/proj_list/stereographic.html
. See the section "Polar stereographic" for the special case when the projection origin is one of the poles.
grid_mapping_name
= transverse_mercator
scale_factor_at_central_meridian
longitude_of_central_meridian
latitude_of_projection_origin
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute values
projection_x_coordinate
and
projection_y_coordinate
respectively.
Formulas for the mapping and its inverse along with notes on using the
PROJ.4
software package for doing the calcuations may be found at
http://www.remotesensing.org/geotiff/proj_list/transverse_mercator.html
.
grid_mapping_name
= vertical_perspective
latitude_of_projection_origin
longitude_of_projection_origin
perspective_point_height
false_easting
false_northing
The x (abscissa) and y (ordinate) rectangular coordinates
are identified by the
standard_name
attribute
value
projection_x_coordinate
and
projection_y_coordinate
respectively.
Notes on using the
PROJ.4
software packages
for computing the mapping may be found at
http://www.remotesensing.org/geotiff/proj_list/geos.html
. These notes assume the point of perspective
is directly over the equator. A more general description
of vertical perspective projection is given in
[
Snyder
], pages 169181.
In the following table the "Type" values are S for string and N for numeric.
Table F.1. Grid Mapping Attributes
Attribute  Type  Description 

earth_radius

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. 
false_easting

N 
The value added to all abscissa values in the rectangular
coordinates for a map projection. This value frequently
is assigned to eliminate negative numbers. Expressed in
the unit of the coordinate variable identified by the
standard name
projection_x_coordinate
.

false_northing

N 
The value added to all ordinate values in the rectangular
coordinates for a map projection. This value frequently
is assigned to eliminate negative numbers. Expressed in
the unit of the coordinate variable identified by the
standard name
projection_y_coordinate
.

grid_mapping_name

N  The name used to identify the grid mapping. 
grid_north_pole_latitude

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

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

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.) 
latitude_of_projection_origin

N 
The latitude chosen as the origin of rectangular coordinates for a map projection.
Domain:
90.0 <= latitude_of_projection_origin <= 90.0

longitude_of_central_meridian

N 
The line of longitude at the center of a map projection generally used as the basis for constructing the projection.
Domain:
180.0 <= longitude_of_central_meridian < 180.0

longitude_of_prime_meridian

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.
longitude_of_projection_origin
, a.k.a. central
meridian) which defines the longitude of the map projection origin.
Domain:
180.0 <= longitude_of_prime_meridian < 180.0
decimal degrees.
Default =
0.0

longitude_of_projection_origin

N 
The longitude chosen as the origin of rectangular coordinates for a map projection.
Domain:
180.0 <= longitude_of_projection_origin < 180.0

north_pole_grid_longitude

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

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. 
scale_factor_at_central_meridian

N 
A multiplier for reducing a distance obtained from a map by
computation or scaling to the actual distance along the
central meridian.
Domain:
scale_factor_at_central_meridian > 0.0

scale_factor_at_projection_origin

N 
A multiplier for reducing a distance obtained from
a map by computation or scaling to the actual distance
at the projection origin.
Domain:
scale_factor_at_projection_origin > 0.0

semi_major_axis

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
inverse_flattening
attribute.

semi_minor_axis

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. 
standard_parallel

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.
Line of constant latitude at which the surface of the
Earth and plane or developable surface intersect.
This attribute may be vector valued if two standard
parallels are specified.
Domain:
90.0 <= standard_parallel <= 90.0

straight_vertical_longitude_from_pole

N 
The longitude to be oriented straight up from the North or South Pole.
Domain:
180.0 <= straight_vertical_longitude_from_pole < 180.0

Revision History  

14 June 2004  


1 July 2004  


20 September 2004  


22 October 2004  


25 November 2005  


21 March 2006  


17 January 2008  


4 May 2008  


15 July 2008  


9 October 2008  


7 November 2008  


10 December 2008  


11 December 2008  


12 December 2008  


27 February 2009  


25 October 2010  
Several closed tickets, mostly about minor issues. Tickets 33 and 49 were closed after discussions; the rest had elicited no objections.

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[ OGP/EPSG_GN7_2 ] OGP Surveying and Positioning Guidance Note 7, part 2: Coordinate Conversions and Transformations including Formulas .
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