environmentaltools.spatiotemporal.covariance.compute_spatiotemporal_covariance

environmentaltools.spatiotemporal.covariance.compute_spatiotemporal_covariance(dfh, dfs, slag, tlag)

Compute empirical spatiotemporal covariance.

Calculates the covariance function for spatiotemporal data at specified spatial and temporal lag distances.

Parameters:

• dfh (pd.DataFrame) – Hard data with columns [‘x’, ‘y’, ‘t’, ‘h’].

• dfs (pd.DataFrame) – Soft data with columns [‘x’, ‘y’, ‘t’, ‘h’].

• slag (np.ndarray) – Vector of spatial lag distances at which to compute covariance.

• tlag (np.ndarray) – Vector of temporal lag distances at which to compute covariance.

Returns:

• empcovst (np.ndarray) – Matrix of empirical spatiotemporal covariance values, shape (n_spatial, n_temporal).

• pairsnost (np.ndarray) – Number of valid data pairs at each spatiotemporal lag, shape (n_spatial, n_temporal).

• covdists (np.ndarray) – Spatial distance grid for covariance values.

• covdistt (np.ndarray) – Temporal distance grid for covariance values.

Notes

The covariance at lag (0,0) is set to the variance of the data. Computes sample covariance: Cov(X,Y) = E[XY] - E[X]E[Y].