7.3. Cell Methods

To describe the characteristic of a field that is represented by cell values we define the cell_methods attribute of the variable. This is a string attribute comprising a list of blank-separated words of the form "name: method". Each "name: method" pair indicates that for the axis identified by name, the cell values representing the field have been determined or derived by the specified method. The token name can be a dimension of the variable, a scalar coordinate variable, or a valid standard name. 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, and this also is specified by Appendix D, Dimensionless Vertical Coordinates. It must be remembered that the method applies only to the axis indicated, and different methods may apply to other axes. If a precipitation value in a longitude-latitude cell is given the method maximum for these axes, for instance, it means that it is the maximum within these spatial cells, and does not imply that it is also the maximum in time.

The default interpretation for variables that have cells associated with their grid points, but 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 doesn't). So, for example, suppose the quantities "accumulated precipitation" and "precipitation rate" each have a time axis and that time intervals are associated with each point on the time axis via a boundary variable. A variable representing accumulated precipitation is extensive in time and requires a time interval to be completely specified. Hence its default interpretation should be that the cell associated with the grid point represents the time interval over which the precipitation was accumulated. This is 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 an instantaneous value or a mean value over the time interval specified by the cell. However, if the mean method is not specified then the default interpretation for the quantity would be instantaneous. The default method is indicated explicity by setting the cell method to point.

Example 7.4.  Methods applied to a timeseries

Consider 12-hourly 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:

  time = UNLIMITED; // (5 currently)
  station = 10;
  nv = 2;
  float pressure(station,time);
    pressure:long_name = "pressure";
    pressure:units = "kPa";
  float maxtemp(station,time);
    maxtemp:long_name = "temperature";
    maxtemp:units = "K";
    maxtemp:cell_methods = "time: maximum";
  float ppn(station,time);
    ppn:long_name = "depth of water-equivalent precipitation";
    ppn:units = "mm";
  double time(time);
    time:long_name = "time";
    time:units = "h since 1998-4-19 6:0:0";
    time:bounds = "time_bnds";
  double time_bnds(time,nv);
  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 left-most operation is assumed to have been applied first. Suppose a quantity varies in both longitude and time (dimensions lon and time) within each gridbox. Values that represent the time-average of the zonal maximum are labelled 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 time-averages are labelled 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, whose order is immaterial. Dimensions should be grouped in this way only if there is an essential difference from treating them individually. For instance, the standard deviation of topographic height within a longitude-latitude gridbox would have cell_methods="lat: lon: 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 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 non-standarized parts. Currently the only stardardized 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 does not have to be dimensionally equivalent to the unit of the corresponding dimension name, although it often will be. 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 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 non-standardized information, the non-standardized follows the standardized information and the keyword comment:. For instance, an area-weighted mean over latitude could be indicated as lat: mean (area-weighted) or lat: mean (interval: 1 degree_north comment: area-weighted).

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 and used to document the method and its domain.

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 measurments. The time dimension of size one has been retained.

  float TS_var(time,lat,lon);
    TS_var:long_name="surface air temperature variance"
    TS_var:cell_methods="time: variance (of hourly instantaneous)";
  float time(time);
    time:units="days since 1990-01-01 00:00:00";
  float time_bnds(time,nv);

Notice that a parenthesized comment in the cell_methods attribute provides the nature of the samples used to calculate the variance.

The convention of specifying a cell method for a standard_name rather than for a dimension with a coordinate variable is to allow one 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. There are two reasons for doing this.

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.