##  [Interpolation (GIS)](/interpolation-gis-0) 

 Definition

A geospatial methods concept defining how Earth-related information is measured, represented, and analyzed in space. It governs coordinate reference, data quality, and analytical operations used to derive patterns, change, and connectivity. It does not guarantee validity without scale awareness, validation, and uncertainty handling for inputs and outputs. It supports decision-making by producing repeatable spatial indicators and maps suitable for review. The concept is generally stable, though sensors, standards, and computation evolve over time.



 

 

 

 

 

 





## Principle

Principle

Assume spatial autocorrelation (nearby points are more similar) and apply rules or models—nearest neighbor, inverse distance weighting, spline, or variogram‑based models—to predict values while optionally quantifying uncertainty.

 

 

 

 

 





## Demonstration

Demonstration

Interpolate rainfall depths across a watershed from scattered gauge readings using inverse distance weighting to create a continuous raster of precipitation intensity for hydrologic modeling.

 

 

 

 

## Misapplication

Misapplication

Extrapolating far beyond the convex hull of samples or using an interpolation method without assessing sample density and spatial structure, producing misleading surfaces with inflated confidence.

 

 

 

 

 





## Consequence

Consequence

Generates continuous surfaces (rasters) that enable contouring, spatial modeling, and input to process models; when method and assumptions match the phenomenon, interpolations improve spatial inference and support decision making with known limitations.

 

 

 

 

## Reversal

Reversal

Aggregating interpolated surfaces back into discrete zonal summaries or using sample‑based point statistics replaces continuous estimation with coarse categorical summaries, reversing the goal of filling gaps between samples.

 

 

 

 

 





## Boundary

Boundary

Validity depends on sampling design, density, spatial structure, anisotropy, and the chosen algorithm; interpolation does not create new information beyond trends supported by data and model assumptions and is weak in regions of sparse sampling.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Often contrasted with kriging: deterministic methods (IDW, spline) produce smooth estimates without explicit error modeling, whereas kriging is geostatistical and provides formal estimates and prediction variances under stationarity assumptions.

 

 

 

 

 





## Synthesis

Synthesis

Interpolation transforms point measurements into continuous surfaces by exploiting spatial dependence; appropriate use requires matching method to data structure, avoiding over‑extrapolation, and communicating uncertainty in sparsely sampled areas.