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Using ArcGIS Spatial Analyst, users can build and analyze complex surfaces to identify patterns or features within the data. Many patterns that are not readily apparent in the original data can be derived from the existing surface. These include shaded relief, contours, angle of slope, aspect, hillshade, viewshed, curvature, and cut/fill.

These topographic derivatives give you the power to effectively relate your data to real-world terrain and analyze how variations in the topography will affect the problem in question.

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

ArcGIS Spatial Analyst provides inverse distance weighted (IDW), kriging, and spline interpolation, as well as polynomial trend and natural neighbour methods, which can be used to estimate elevation, rainfall, temperature, chemical dispersion, or other spatially continuous phenomena.

ArcGIS Spatial Analyst can also create non-traditional surfaces using various other functions. These include the ability to derive a density surface showing the density of objects, such as number of people per square kilometre; distance-based surfaces showing distance to various features, such as retail stores; and other surfaces. Using the derived surfaces, users can then directly display this new data, such as elevation from a terrain surface, or color-coded density areas for crime analysis.

The inverse distance weighted and spline methods are referred to as deterministic interpolation methods because they assign values to locations based on the surrounding measured values. A second family of interpolation methods consists of geostatistical methods such as kriging, which are based on statistical models that include autocorrelation, the statistical relationship among the measured points. These geostatistical techniques not only have the capability to produce a prediction surface but also provide some measure of the certainty or accuracy of the predictions.