# Dimensions

HARP has strict rules regarding the dimensions of variables. Each dimension of a variable may be used to represent a physical dimension (such as time, latitude, longitude, height, etcetera), or it may be used as an independent dimension.

Only dimension types supported by HARP can be used. These types are:

time

Temporal dimension; this is also the only appendable dimension.

vertical

Vertical dimension, indicating height or depth.

spectral

Spectral dimension, associated with wavelength, wavenumber, or frequency.

latitude

Latitude dimension, only to be used for the latitude axis of a regular latitude x longitude grid.

longitude

Longitude dimension, only to be used for the longitude axis of a regular latitude x longitude grid.

independent

Independent dimension, used to index other quantities, such as the corner coordinates of ground pixel polygons.

Within a HARP product, all dimensions of the same type should have the same length, except independent dimensions. For example, it is an error to have two variables within the same product that both have a time dimension, yet of a different length.

A variable with more than one dimension has to use a fixed ordering of the dimensions. In the HARP documentation the ordering is always documented using the so-called ‘C convention’ for dimension ordering. Using the C convention, the last dimension (writing from left to right) is the fastest running dimension when enumerating all elements, compared to the Fortran convention, where the first dimension is the fastest running dimension. Note that different file access libraries may have different conventions with regard to how they deal with array ordering in their function interfaces.

The order in which dimensions need to be provided for a variable is defined by the following rules:

• If present, the time dimension is always the first (i.e. slowest running) dimension.

• Next are categorical dimensions used for grouping. For instance, this can be the spectral dimension when it is used to distinguish between retrievals performed using different choices of wavelength, or to distinguish data from different spectral bands.

• Next are the spatial dimensions, ordered as latitude, longitude, vertical.

• Next is the spectral dimension when it is used as an actual axis (e.g. for L1 spectral data for instruments that measure along a spectral axis).

• Any independent dimensions come last (i.e. they will always be the fastest running dimensions).

So, for a spectral axis used for grouping, the ordering should be:

time, spectral, latitude, longitude, vertical, independent

And, for a spectral axis used for L1 data from spectral instruments, the ordering should be:

time, latitude, longitude, vertical, spectral, independent

A variable should only use dimensions on which it is dependent. This means that the radiance variable for L1 data of a nadir looking spectral instrument on a satellite will generally only have the dimensions time and spectral (and not latitude, longitude, vertical, or independent).

Note that only a single grid can be used for each type of dimension per time value. This means that, for example, it is possible to change the vertical grid from sample to sample, but it is not possible to use different vertical grids for the same sample.

To allow a different vertical grid from sample to sample, the altitude variable should have dimensions {time,vertical} (instead of {vertical}). This way, the altitude values for the first sample, altitude[0,:], may differ from the altitude values for the second sample, altitude[1,:], and so on. However, for an averaging kernel, which has dimensions {time,vertical,vertical}, the altitude values for both vertical dimensions are necessarily the same for each single sample.

A grid that differs from sample to sample could have a different effective length per sample. This is implemented by taking the maximum length over all samples as the length of the dimension and padding the dimension for each sample at the end with ‘invalid’ values (e.g. NaN). For instance, you can have an altitude{time,vertical} variable where altitude[0,:] has 7 levels and equals [0, 5, 10, 15, 20, 25, 30] and altitude[1,:] has only 6 levels and equals [0, 6, 12, 18, 24, 30, NaN].

Operations performed by HARP will determine the effective length of a dimension for each sample by ignoring all trailing NaN values of the axis variable that is used for the operation (e.g. the altitude or pressure variable for a vertical dimension or the wavelength or wavenumber variable for a spectral dimension).