environmentaltools.spatiotemporal.covariance.calculate_theoretical_covariance

environmentaltools.spatiotemporal.covariance.calculate_theoretical_covariance(name, D, param)[source]

Compute theoretical spatiotemporal covariance from parametric models.

Evaluates covariance functions from theoretical models at specified spatiotemporal separation distances.

Parameters:

  • name (str) – Covariance model family. Supported models: - ‘exponentialST’: Separable exponential model - ‘exponentialSTC’: Non-separable exponential model with interaction term

  • D (list of np.ndarray) – Separation distances [spatial_distances, temporal_distances].

  • param (array-like) – Model parameters. Length depends on model: - ‘exponentialST’: [sill, spatial_range, temporal_range, nugget] - ‘exponentialSTC’: [sill, spatial_range, temporal_range, interaction_range, nugget]

Returns:

res – Theoretical covariance values at the specified separations.

Return type:

np.ndarray

Raises:

Warning – If requested model is not implemented.

Notes

Exponential ST Model (separable):

C(d,t) = sill * exp(-d/range_s - t/range_t) - nugget

Exponential STC Model (non-separable with interaction):

C(d,t) = sill * exp(-√d/range_s - t/range_t - √d*t/range_st) - nugget

The nugget effect represents measurement error or micro-scale variability.