Spatial Interpolation
Definition
Spatial interpolation estimates values at unsampled locations by leveraging nearby observations and the spatial structure of a variable. Common methods include inverse distance weighting (IDW), splines, trend surfaces, and geostatistical techniques such as ordinary kriging, universal kriging, and co-kriging. Kriging models spatial autocorrelation explicitly via variograms and provides prediction uncertainty; deterministic methods prioritize smoothness or simple distance decay. Interpolation quality depends on sampling density, anisotropy, nonstationarity, and measurement error. Preprocessing steps—transformations for skewed distributions, de-trending for broad gradients, and removal of outliers—often improve results. Outputs are continuous surfaces (rasters) with accompanying error or confidence layers that should always be communicated with the predictions.
Application
Environmental scientists interpolate air pollution, soil properties, groundwater levels, and precipitation. Public health agencies estimate exposure fields from monitors. Engineers fill gaps in elevation or bathymetry. Telecom planners interpolate signal strength across neighborhoods. Archaeologists interpolate artifact densities to guide excavation. Because decision makers frequently act on these surfaces, documenting assumptions and cross-validation performance is crucial.
FAQ
How do you choose between kriging and IDW for a project with sparse data?
If you can estimate a stable variogram and the phenomenon exhibits spatial autocorrelation, kriging provides unbiased estimates with quantified error. If data are very sparse or highly nonstationary, IDW or a trend model may be more robust. Cross-validate both and compare RMSE and bias before committing.
Why is anisotropy important and how do you model it?
Processes like wind-driven pollutants or valley-confined temperature show different correlation lengths by direction. Model anisotropy in the variogram and, when needed, rotate the coordinate system so kriging weights honor directional structure.
What steps keep interpolation from inventing impossible values?
Apply transforms that keep results within physical bounds (e.g., log for positive variables), clip to plausible ranges, and incorporate covariates via regression-kriging to anchor predictions.
How should uncertainty be conveyed to non-technical audiences?
Publish an error map and summarize ranges for key areas. Use plain-language annotations like ‘estimate has ±X units typical error’ and avoid implying false precision with overly smooth color ramps.