Kriging

Kriging module

This module provides kriging functions from variogram estimation to kriging interpolation.

empirical_variogram(arr_coords, arr_values, bin_size, max_dist=None, normalize=True)

Calculate an empirical variogram function of spatial data.

Parameters:

Name	Type	Description	Default
arr_coords	ndarray	2D array (m, 2) array with first column corresponding to 'Longitude' and the second one to 'Latitude' and with one location per row.	required
arr_values	ndarray	2D array (t, m) containing values with one row per timestep and one column per location.	required
bin_size	int	size of each bin in kilometers.	required
max_dist	int	maximum distance between two locations to consider this pair as valid.	None
normalize	bool	boolean indicating whether to normalize the variogram by global variability values.	True

Returns:

Name	Type	Description
emp_vario	Empirical_Variogram	empirical variogram with one value per bin. Array of size n_bins.
count	Empirical_Variogram	number of data points used to compute each bin. Array of size n_bins.

fit_variogram(emp_vario, fit_model, weight=True, kwargs_fit_model=None)

Fit an empirical variogram with a covariance model.

Parameters:

Name	Type	Description	Default
emp_vario	Empirical_Variogram	Empirical_Variogram object with one value of variability per bin.	required
fit_model	CovModel	covariance model used to fit the variogram (see gstools.covmodel.CovModel documentation).	required
weight	bool	if True, weights are applied to each point in the estimation. Weights are positively correlated to the count per bin and negatively correlated to the distance.	True
kwargs_fit_model	dict	kwargs to pass in other parameters to the gstools.covmodel.CovModel. For example '{nu: 0.3}' for a Matern kernel.	None

Returns:

Name	Type	Description
coef		fitted covariance model's main coefficients (full sill, range, nugget).
fit_model		covariance model fitted to the variogram (see gstools.covmodel.CovModel documentation).
r2_score		r2 score of the curve fitting results.

krige_field_timestep(vario_model, field, station_coords, lon_grid, lat_grid, sigma=None, kwargs_krige_class=None, kwargs_krige_call=None)

Compute the kriged field over space using the gstools.krig.Krige class.

Parameters:

Name	Type	Description	Default
vario_model	CovModel	variogram covariance kernel to be used in the kriging interpolation	required
field	DataFrame	field to interpolate as a pd.DataFrame with with dates as index and the different locations as columns	required
station_coords	DataFrame	pd.DataFrame object with location names as index, and columns 'Longitude' and 'Latitude'	required
lon_grid	ndarray	1D array of longitude coordinates of the interpolation grid	required
lat_grid	ndarray	1D array of latitude coordinates of the interpolation grid	required
sigma	int	standard deviation for Gaussian kernel filter used for the kriged field smoothing	None
kwargs_krige_class	dict	dict with arguments to pass in the gs.krige.Krige class creation	None
kwargs_krige_call	dict	dict with arguments to pass in the gs.krige.Krige() object call	None

Returns:

Name	Type	Description
kriged_field		field kriged by Gaussian process regression

variogram(df_coords, df_values, fit_model, bin_size, weight, max_dist=None, normalize=True, month_filter=None, kwargs_fit_model=None)

Calculate and fit the empirical variogram using gstools

Parameters:

Name	Type	Description	Default
df_coords	DataFrame	pd.DataFrame object with location names as index, and columns 'Longitude' and 'Latitude'	required
df_values	DataFrame	pd.DataFrame object containing values to study with dates as index and the different locations as columns	required
fit_model	CovModel	covariance model used to fit the variogram (see gstools.covmodel.CovModel documentation)	required
bin_size	int	size of bins grouping pairs of locations with similar distances from one another	required
weight	bool	if True, weights are applied to each point in the estimation	required
max_dist	int	maximum distance between points paired together (if None, maximum distance between all locations considered)	None
normalize	bool	boolean indicating whether to normalize the variogram by global variability values.	True
month_filter	int | list	month or list of months to filter the dataset on for variogram computation	None
kwargs_fit_model	dict	kwargs to pass in other parameters to the gstools.covmodel.CovModel. For example '{"nu": 0.3}' for a Matern kernel.	None

Returns:

Name	Type	Description
Variogram_Outputs	(coef, model, r2)	coef: model's main coefficients (full sill, range, nugget) model: gstools model object r2_score: r2 score of the curve fitting results emp_vario: empirical variogram with one value of variance per bin. Array of size n_bins. count: number of data points used to compute each bin. Array of size n_bins.