Observation error covariance with cross-variable (cross-channel) correlations

The observation error covariance can be set up to use cross-variable (cross-channel) correlations from a file. In this case correlations between variables (channels) are the same at all locations and are read from the file specified in the configuration. Observation error standard deviations are read from the ObsError group of the observation space, similar to the diagonal observation error covariances.

The full observation error covariance matrix is \(R = D^{1/2} * C * D^{1/2}\) where \(D^{1/2}\) is a diagonal matrix with the observation error standard deviations (ObsError group) on the diagonal, and \(C\) is the correlation matrix.

This type of observation error covariance is set up using the following options:

  • input file: filename for the input file containing cross-variable correlations or covariances (the file has to contain only one of those).

Important

Input files are always used to set up correlations, and not covariances. If the input file contains covariances, they would be converted to correlations.

obs error:
  covariance model: cross variable covariances
  input file: obserror_correlations.nc4

Observation error correlations file format

The input file for the observation error correlations must have the following dimensions and groups:

  • nvars or nchannels dimension – number of variables or channels

  • variables (string, size nvars) or channels (int, size nchannels) variable: variable names, or channels numbers.

  • obserror_correlations or obserror_covariances (float, size nvars, nvars, or nchannels, nchannels) variable: cross-variable or cross-channel correlations or covariances. The file has to contain only one of these variables. Covariances will be converted to correlations.

If a particular assimilated variable or channel is missing from the input correlations file, its correlation with other variables or channels will be set to zero.