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 Y-axis are identified, X-Y-up should define a right-handed 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 [coordinate-system]).
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 [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.
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.
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
upordown(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 includebar,millibar,decibar,atmosphere (atm),pascal (Pa), andhPa. -
units of length as listed in the file udunits.dat. For vertical axes the most commonly used of these include
meter (metre, m), andkilometer (km). -
other units listed in the file udunits.dat that may under certain circumstances reference vertical position such as units of density or temperature.
Plural forms are also acceptable.
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 [dimensionless-v-coord] . 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.
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 [dimensionless-v-coord] 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 1992-10-8 15:15:42.5 -6:00
indicates seconds since October 8th, 1992 at 3 hours, 15
minutes and 42.5 seconds in the afternoon in the time zone
which is six hours to the west of Coordinated Universal Time
(i.e. Mountain Daylight Time). The time zone specification
can also be written without a colon using one or two-digits
(indicating hours) or three or four digits (indicating hours
and minutes).
The acceptable units for time are 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 [climatological-statistics]).
Note: if the time zone is omitted the default is UTC, and if both time and time zone are omitted the default is 00:00:00 UTC.
We recommend that the unit year be used with caution. The Udunits package defines a year to be exactly 365.242198781 days (the interval between 2 successive passages of the sun through vernal equinox). It is not a calendar year. Udunits includes the following definitions for years: a common_year is 365 days, a leap_year is 366 days, a Julian_year is 365.25 days, and a Gregorian_year is 365.2425 days.
For similar reasons the unit month, which is defined in udunits.dat to be exactly year/12, should also be used with caution.
double time(time) ; time:long_name = "time" ; time:units = "days since 1990-1-1 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:
gregorianorstandard-
Mixed Gregorian/Julian calendar as defined by Udunits. This is the default.
proleptic_gregorian-
A Gregorian calendar extended to dates before 1582-10-15. 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.
noleapor365_day-
Gregorian calendar without leap years, i.e., all years are 365 days long.
all_leapor366_day-
Gregorian calendar with every year being a leap year, i.e., all years are 366 days long.
360_day-
All years are 360 days divided into 30 day months.
julian-
Julian calendar.
none-
No calendar.
The calendar attribute may be set to none in climate experiments that simulate a fixed time of year. The time of year is indicated by the date in the reference time of the units attribute. The time coordinate that might apply in a perpetual July experiment are given in the following example.
variables:
double time(time) ;
time:long_name = "time" ;
time:units = "days since 1-7-15 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 non-standard 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 non-leap 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 1-12, 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_yearis not specified.
The calendar attribute is not required when a non-standard 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 non-standard values and in that case defining the non-standard calendar using the appropriate attributes is required.
double time(time) ; time:long_name = "time" ; time:units = "days since 1-1-1 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 1582-10-15 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 1582-10-15 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 user-given time interval includes the changeover date. For example, utCalendar() and utInvCalendar() can be used to show that 1582-10-15 *preceded* 1582-10-14 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.
The spatiotemporal coordinates described in sections 4.1-4.4 are continuous variables, and other geophysical quantities may likewise serve as continuous coordinate variables, for instance density, temperature or radiation wavelength. By contrast, for some purposes there is a need for an axis of a data variable which indicates either an ordered list or an unordered collection, and does not correspond to any continuous coordinate variable. Consequently such an axis may be called “discrete”. A discrete axis has a dimension but might not have a coordinate variable. Instead, there might be one or more auxiliary coordinate variables with this dimension (see preamble to section 5). Following sections define various applications of discrete axes, for instance section 6.1.1 “Geographical regions”, section 7.3.3 “Statistics applying to portions of cells”, section 9.3 “Representation of collections of features in data variables”.