geostatistics-interpolation

Geostatistics & Interpolation

Purpose: interpolation that reports what it doesn't know. The difference between a professional product and a pretty raster is the uncertainty surface and an honest cross-validation — both are non-optional here.

Method selection

Situation	Method
Dense, smooth phenomenon, quick look	IDW (report power parameter; test 1-3)
Physical phenomenon with spatial structure, need uncertainty	Ordinary kriging (default professional choice)
Clear trend (elevation gradient, coastal effect)	Universal kriging or regression kriging on covariates
Strong covariates available (DEM, land cover, distances)	Regression kriging / random-forest residual kriging
Categorical target	Indicator kriging
Honeycomb-free tessellation, no extrapolation wanted	Natural neighbor

IDW is a reasonable baseline but has no error model and bullseyes around extremes; say so when delivering IDW-only products.

Exploratory phase (before any interpolation)

• Map the points with values; look for duplicates at identical coordinates (average or offset them — kriging matrices go singular otherwise).
• Histogram + skew: strongly skewed variables (rainfall, concentrations) usually want a log/normal-score transform; back-transform predictions properly (bias correction for lognormal kriging).
• Trend check: regress value on x, y, and candidate covariates; visible trend → universal/regression kriging path.
• Declustering if sampling is preferential (dense where values are high).

Variogram discipline

The variogram is a MODELING decision, not an auto-fit output:

import gstools as gs

bin_center, gamma = gs.vario_estimate((x, y), values, max_dist=dmax)  # dmax ≈ half extent
model = gs.Exponential(dim=2)
model.fit_variogram(bin_center, gamma, nugget=True)
print(model)   # report: nugget, sill, range — plus the fitted plot

• Max lag ≈ half the domain diameter; ≥30 pairs per bin.
• Check anisotropy with directional variograms (0/45/90/135°); geological and meteorological fields are often anisotropic — fit an anisotropic model rather than ignoring it.
• Interpret and report the parameters in words: nugget (measurement error + micro-scale variance), range (correlation distance), sill. A nugget near the sill means the data barely support interpolation — say that honestly.
• Never interpolate meaningfully beyond the variogram range from the nearest sample; mask or flag those cells.