Category: Computer Science

Geostatistical Analyst Prepared by Parikshit Ranade, Dr Ayse Irmak and David R. Maidment Spatial Interpolation Methods Figure 1 : The interpolated value at the unmeasured yellow point is a function of the neighboring red points (From ArcGIS Help Menu). A very basic problem in spatial analysis is interpolating a spatially continuous variable from point samples. Many spatially explicit hydrologic/watershed models require continuous surfaces of temperature. Three commonly used interpolation methods to model spatially distribution from point data are Inverse Distance Weighting (IDW), spline and ordinary kriging. The IDW is simple and intuitive deterministic interpolation method based on principle that sample values closer to the prediction location have more influence on prediction value than sample values farther apart. Using higher power assigns more weight to closer points resulting in less smoother surface. On the other hand, lower power assigns low weight to closer points resulting in smoother surface. We optimized power parameter using ArcGIS. Major disadvantage of IDW is “bull’s eye” effect (higher values near observed location) and edgy surface. Spline is deterministic interpolation method which fits mathematical function through input data to create smooth surface. Spline can generate sufficiently accurate surfaces from only a few sampled points and they retain small features (Anderson, 2008). Spline works best for gently varying surfaces like temperature. In ArcGIS Spline is Radial Basis Function. Unlike IDW and spline, kriging is method based on spatial autocorrelation. It uses semivariogram. . Basics of Kriging . Kriging was developed in the 1960s by the French mathematician Georges Matheron. The motivating application was to estimate gold deposited in a rock from a few random core samples. Kriging has since found its way into the earth sciences and other disciplines. It is an improvement over inverse distance weighting because prediction estimates tend to be less bias and because predictions are accompanied by prediction standard errors (quantification of the uncertainty in the predicted value). . The basic tool of geostatistics and kriging is the semivariogram. The semivariogram captures the spatial dependence between samples by plotting semivariance against separation distance (semivariance will be explained in the next paragraph). The premise of any spatial interpolation is that close samples tend to be more similar than distant samples (this is also called spatial autocorrelation). This property of spatial data is implicitly used in IDW. In kriging, one must model the spatial autocorrelation using a semivariogram instead of assuming a direct, linear relationship with...