# Interpolation geoprocessing functions

The Interpolation geoprocessing functions create a continuous (or prediction) surface from sampled point values that represents some measure, such as the height, concentration, or magnitude (for example, elevation, acidity, or noise level). Surface interpolation geoprocessing functions make predictions from sample measurements for all locations in an output raster dataset, whether or not a measurement has been taken at the location.

Visiting every location in a study area to measure the height, concentration, or magnitude of a phenomenon is usually difficult or expensive. Instead, you can measure the phenomenon at strategically dispersed sample locations, and predicted values can be assigned to all other locations. Input points can be either randomly or regularly spaced or based on a sampling scheme.

There are a variety of ways to derive a prediction for each location; each method is referred to as a model. With each model, there are different assumptions made of the data, and certain models are more applicable for specific data—for example, one model may account for local variation better than another. Each model produces predictions using different calculations.

The interpolation geoprocessing functions are generally divided into deterministic and geostatistical methods.

• The deterministic interpolation methods assign values to locations based on the surrounding measured values and on specified mathematical formulas that determine the smoothness of the resulting surface.

The deterministic methods include IDW (inverse distance weighting), Natural Neighbor, Trend, and Spline.

• The geostatistical methods are based on statistical models that include autocorrelation (the statistical relationship among the measured points). Because of this, geostatistical techniques not only have the capability of producing a prediction surface but also provide some measure of the certainty or accuracy of the predictions.

Kriging is a geostatistical method of interpolation.

The remaining interpolation geoprocessing functions, Topo to Raster and Topo to Raster by File, use an interpolation method specifically designed for creating continuous surfaces from contour lines, and the methods also contain properties favorable for creating surfaces for hydrologic analysis.

The following table lists the available geoprocessing functions and provides a brief description of each.

Geoprocessing FunctionDescription

IDW

Interpolates a raster surface from points using an inverse distance weighted (IDW) technique.

Kriging

Interpolates a raster surface from points using kriging.

Natural Neighbor

Interpolates a raster surface from points using a natural neighbor technique.

Spline

Interpolates a raster surface from points using a two-dimensional minimum curvature spline technique.

The resulting smooth surface passes exactly through the input points.

Spline with Barriers

Interpolates a raster surface, using barriers, from points using a minimum curvature spline technique. The barriers are entered as either polygon or polyline features.

Topo to Raster

Interpolates a hydrologically correct raster surface from point, line, and polygon data.

Topo to Raster by File

Interpolates a hydrologically correct raster surface from point, line, and polygon data using parameters specified in a file.

Trend

Interpolates a raster surface from points using a trend technique.

Geoprocessing functions in the Interpolation category