Thus, in ordinary kriging, the weight, λ i, depends on a fitted model to the measured points, the distance to the prediction location, and the spatial relationships among the measured values around the prediction location. To use the spatial arrangement in the weights, the spatial autocorrelation must be quantified. However, with the kriging method, the weights are based not only on the distance between the measured points and the prediction location but also on the overall spatial arrangement of the measured points. In IDW, the weight, λ i, depends solely on the distance to the prediction location. Λ i = an unknown weight for the measured value at the ith location Z(s i) = the measured value at the ith location The general formula for both interpolators is formed as a weighted sum of the data: Kriging is similar to IDW in that it weights the surrounding measured values to derive a prediction for an unmeasured location. It is often used in soil science and geology. Kriging is most appropriate when you know there is a spatially correlated distance or directional bias in the data. Kriging is a multistep process it includes exploratory statistical analysis of the data, variogram modeling, creating the surface, and (optionally) exploring a variance surface. The Kriging tool fits a mathematical function to a specified number of points, or all points within a specified radius, to determine the output value for each location. Kriging assumes that the distance or direction between sample points reflects a spatial correlation that can be used to explain variation in the surface. 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. A second family of interpolation methods consists of geostatistical methods, such as kriging, which are based on statistical models that include autocorrelation-that is, the statistical relationships among the measured points. The IDW (inverse distance weighted) and Spline interpolation tools are referred to as deterministic interpolation methods because they are directly based on the surrounding measured values or on specified mathematical formulas that determine the smoothness of the resulting surface. Unlike other interpolation methods in the Interpolation toolset, to use the Kriging tool effectively involves an interactive investigation of the spatial behavior of the phenomenon represented by the z-values before you select the best estimation method for generating the output surface. Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z-values. Understanding a semivariogram-Range, sill, and nugget.Fitting a model to the empirical semivariogram.Creating a prediction surface map with kriging.

Define raster kriged surface