environmentaltools.spatiotemporal.covariance.fit_covariance_model

environmentaltools.spatiotemporal.covariance.fit_covariance_model(param, empcovst, dist, name)

Compute sum of squared errors between theoretical and empirical covariance.

Objective function for least squares fitting of covariance model parameters to empirical covariance estimates.

Parameters:

• param (array-like) – Covariance model parameters to optimize.

• empcovst (np.ndarray) – Empirical spatiotemporal covariance matrix.

• dist (list of np.ndarray) – Spatiotemporal separation distances [spatial, temporal].

• name (str) – Covariance model family name (e.g., ‘exponentialST’, ‘exponentialSTC’).

Returns:

Sum of squared errors between theoretical and empirical covariance.

Return type:

float

Notes

This function is typically used with scipy.optimize.minimize or similar optimization routines to find optimal model parameters.

The objective is: SSE = Σ(C_empirical - C_theoretical)²