Spatial interpolation

Spatial interpolation estimates values at locations where measurements are unavailable, using observations from nearby or otherwise related locations. Its methods encode different assumptions about spatial dependence, smoothness, and uncertainty.

Inverse distance weighting: A deterministic interpolation method that weights observed values by inverse powers of their distance from the prediction location. It estimates nearby values directly, with distance controlling each observation’s influence.
Spatial autocorrelation: The tendency for nearby or otherwise related locations to have correlated values. Interpolation depends on whether spatial proximity carries information about unmeasured values.
Digital elevation model: A digital representation of ground-surface elevation across a geographic area. Elevation surfaces are commonly built by estimating heights between surveyed or remotely sensed points.
Spatial extrapolation: The prediction of spatial values beyond the region or support represented by observed data. Interpolation estimates within the sampled spatial domain; extrapolation reaches beyond its observed support.
Kriging: A geostatistical estimator that predicts values using a modeled spatial covariance structure. It uses spatial dependence to choose weights and quantify prediction uncertainty.
Point pattern: A set of locations representing where events or observations occur in a spatial domain. The arrangement of sampled locations affects coverage, local neighborhoods, and prediction reliability.
Isopleth map: A map that uses lines or bands to connect locations with equal values of a continuous variable. Interpolated values provide the continuous field from which equal-value contours are drawn.
Spatial regression: Regression methods that model relationships while accounting for spatial structure or dependence. Regression explains values through predictors, whereas interpolation can rely chiefly on spatial arrangement.
Thin-plate spline: A smooth spline method that fits a surface by balancing data fit against bending energy. It produces a smooth surface by penalizing curvature rather than using distance weights alone.
Distance metric: A rule that assigns distances between points in a space. Interpolation weights and neighborhoods depend on how separation between locations is measured.

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