Methods

18 canonical methods · 28 accepted method keys.
Every method shares .fit(gdf) → .predict(bbox, resolution) → xr.DataArray.
Swap method= to compare — everything else stays the same.

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Distance-based

Fast and assumption-free. Good as a baseline or when data is dense and evenly distributed.

IDW

Nearest Neighbor

Linear (Delaunay)

Cubic (Clough-Tocher)

Key	Description	Key params
idw	Inverse Distance Weighting — KD-tree vectorized (v0.2, 50–200× faster)	power, n_neighbors
nearest	Nearest-neighbour via scipy griddata	—
linear	Delaunay triangulation, linear barycentric	—
cubic	Clough-Tocher C¹ cubic	—

Tip

Higher power in IDW makes the surface more local — distant stations contribute less. Use n_neighbors=10 to restrict each prediction to the 10 nearest stations.

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Spline & Trend

Fit smooth continuous surfaces. Splines minimise curvature; RBF offers 8 kernel choices; Trend fits a global polynomial for large-scale patterns.

Spline (Regularized)

Spline Tension

RBF

Trend Surface

Key	Description	Key params
spline	Minimum curvature regularized spline	smoothing
spline_tension	Tension spline — flatter between points	smoothing
rbf	Radial Basis Functions	kernel, smoothing
trend	Global polynomial trend surface	order (1–12)

RBF kernels: thin_plate_spline · multiquadric · inverse_multiquadric · inverse_quadratic · gaussian · linear · cubic · quintic

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Geostatistical

Account for spatial autocorrelation via a variogram model. Produce statistically optimal, unbiased estimates. Natural Neighbor uses Voronoi area-stealing weights — smooth and exact at data locations.

Ordinary Kriging

Universal Kriging

Natural Neighbor

Key	Aliases	Description	Key params
kriging	ok, ordinary_kriging	Ordinary Kriging — returns variance surface	variogram_model, nlags, anisotropy_scaling, anisotropy_angle
uk	universal_kriging	Universal Kriging — detrended residuals	variogram_model
natural_neighbor	nn	Voronoi/Sibson area-stealing weights	—
cokriging	ked	Kriging with External Drift — uses a secondary correlated variable	secondary_col, secondary_fn, variogram_model
sgs	simulation	Sequential Gaussian Simulation — stochastic realizations	n_realizations, variogram_model

Variogram models: linear · power · gaussian · spherical · exponential · hole-effect

Requires kriging extra

pip install "geointerpo[kriging]"

Cokriging and SGS require gstools

pip install "geointerpo[geostat]"
# or: pip install gstools

Kriging variance surface (new in v0.2)

from geointerpo.interpolators import KrigingInterpolator

model = KrigingInterpolator(
    variogram_model="spherical",
    anisotropy_scaling=0.5,  # 2:1 anisotropy ratio
    anisotropy_angle=45.0,   # major axis direction (degrees, clockwise from North)
).fit(gdf)

mean_da, var_da = model.predict_with_variance(bbox, resolution=0.1)
# mean_da: best estimate
# var_da:  prediction variance (highest where far from stations)

Sequential Gaussian Simulation

from geointerpo.interpolators import SGSInterpolator

model = SGSInterpolator(n_realizations=100).fit(gdf)
mean_da, std_da = model.predict_with_std(bbox)   # ensemble statistics
realizations = model.realize(bbox)               # (100, lat, lon) DataArray

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Machine Learning

Capture non-linear spatial patterns without variogram assumptions. GP also returns a per-pixel uncertainty surface alongside the mean prediction. Regression Kriging combines an ML trend with Kriging of the residuals.

Gaussian Process

Random Forest

Gradient Boosting

Regression Kriging

Key	Aliases	Description	Key params
gp	gaussian_process	Gaussian Process — mean + σ output	length_scale, alpha
rf	random_forest	Random Forest — bootstrap uncertainty	n_estimators, max_depth
gbm	gradient_boosting	Gradient Boosting — MAPIE conformal UQ	n_estimators, learning_rate
rk	regression_kriging	ML trend + Kriging of residuals	ml_method

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Uncertainty quantification

Every major method now supports prediction uncertainty (new in v0.2):

from geointerpo.interpolators import MLInterpolator, KrigingInterpolator

# --- GP: native posterior standard deviation ---
gp = MLInterpolator(method="gp").fit(gdf)
mean, lower, upper = gp.predict_with_uncertainty(bbox, alpha=0.1)  # 90% interval

# --- RF: bootstrap intervals from tree ensemble ---
rf = MLInterpolator(method="rf").fit(gdf)
mean, lower, upper = rf.predict_with_uncertainty(bbox, alpha=0.1)

# --- Kriging: prediction variance surface ---
kr = KrigingInterpolator().fit(gdf)
mean_da, var_da = kr.predict_with_variance(bbox)

For GBM, install MAPIE for conformal prediction:

pip install "geointerpo[uncertainty]"
# or: pip install mapie

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Spatial cross-validation

from geointerpo.validation.metrics import spatial_cv

# Blocked k-fold (default — fast, good for most cases)
result = spatial_cv(model, gdf, strategy="block", k=5)

# LOO with 50 km buffer — removes autocorrelation leakage
result = spatial_cv(model, gdf, strategy="loo", buffer_km=50)

print(result["rmse"], result["r"], result["per_fold"])

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Direct usage

from geointerpo.interpolators import KrigingInterpolator

model = KrigingInterpolator(variogram_model="spherical")
model.fit(gdf)                                   # GeoDataFrame with Point geometry + 'value'
grid  = model.predict(bbox, resolution=0.25)     # xr.DataArray (WGS-84)
cv    = model.cross_validate(gdf, k=5)           # blocked spatial k-fold CV

→ Full parameter reference in API: Interpolators