mesmer.stats.find_localized_empirical_covariance_monthly

mesmer.stats.find_localized_empirical_covariance_monthly#

mesmer.stats.find_localized_empirical_covariance_monthly(data, weights, localizer, dim, k_folds, equal_dim_suffixes=('_i', '_j'))#

determine localized empirical covariance by cross validation for each month. data should be the residuals of the cyclo-stationary AR(1) process, see fit_auto_regression_monthly. Note that here, no additional adjustment is necessary.

Parameters:

  • data (xr.DataArray) – 2D DataArray with monthly data to calculate the covariance for (residuals of the AR(1) process).

  • weights (xr.DataArray) – Weights for the individual samples.

  • localizer (dict of DataArray) – Dictionary containing the localization radii as keys and the localization matrix as values. The localization must be 2D and of shape n_gridpoints x n_gridpoints. Currently only the Gaspari-Cohn localizer is implemented in MESMER.

  • dim (str) – Dimension along which to calculate the covariance.

  • k_folds (int) – Number of folds to use for cross validation.

  • equal_dim_suffixes (tuple of str, default: (“_i”, “_j”)) – Suffixes to add to the the name of dim for the covariance array (xr.DataArray cannot have two dimensions with the same name).

Returns:

  • localized_empirical_covariance (xr.Dataset) – Dataset containing three DataArrays:

  • localization_radius (float) – Selected localization radius.

  • covariance (xr.DataArray) – Empirical covariance matrix.

  • localized_covariance (xr.DataArray) – Localized empirical covariance matrix.

Notes

Runs a k-fold cross validation if k_folds is smaller than the number of samples and a leave-one-out cross validation otherwise.