In Table 9.1 the dimension with subscript i identifies a particular feature within a collection of features. It is called the instance dimension. One-dimensional variables in a Discrete Geometry CF file, which have only this dimension (such as x(i) y(i) and z(i) for a timeseries), are instance variables. Instance variables provide the metadata that differentiates individual features.
The subscripts o and p distinguish the data elements that compose a single feature. For example in a collection of timeSeries features, each time series instance, i, has data values at various times, o. In a collection of profile features, the subscript, o, provides the index position along the vertical axis of each profile instance. We refer to data values in a feature as its elements, and to the dimensions of o and p as element dimensions. Each feature can have its own set of element subscripts o and p. For instance, in a collection of timeSeries features, each individual timeSeries can have its own set of times. The notation t(i,o) means there is a set of times with subscripts o for the elements of each feature i. Feature instances within a collection need not have the same numbers of elements. If the features do all have the same number of elements, and the sequence of element coordinates is identical for all features, savings in simplicity and space are achievable by storing only one copy of these coordinates. This is the essence of the orthogonal multidimensional representation (see section 9.3.1).
If there is only a single feature to be stored in a data variable, there is no need for an instance dimension and it is permitted to omit it. The data will then be one-dimensional, which is a special (degenerate) case of the multidimensional array representation. The instance variables will be scalar coordinate variables; the data variable and other auxiliary coordinate variables will have only an element dimension and not have an instance dimension, e.g. data(o) and t(o) for a single timeSeries.