## 2.4. Dimensions

A variable may have any number of dimensions, including zero, and the dimensions must all have different names. COARDS strongly recommends limiting the number of dimensions to four, but we wish to allow greater flexibility. The dimensions of the variable define the axes of the quantity it contains. Dimensions other than those of space and time may be included. Several examples can be found in this document. Under certain circumstances, one may need more than one dimension in a particular quantity. For instance, a variable containing a two-dimensional 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 one-element 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 single-valued quantity, including boundaries. For example, a variable containing data for temperature at 1.5 m above the ground has a single-valued coordinate supplying a height of 1.5 m, and a time-mean quantity has a single-valued time coordinate with an associated boundary variable to record the start and end of the averaging period.