A Practical Guide to Geostatistical Mapping by Tomislav Hengl

By Tomislav Hengl

The aim of this advisor is to aid you in generating caliber maps by utilizing totally operational open resource software program programs.

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13). This is because both approaches deal with different aspects of spatial variation: regression deals with the deterministic and kriging with the spatially-correlated stochastic part of variation. The biggest criticism of the pure regression approach to spatial prediction is that the position of points in geographical space is completely ignored, both during model fitting and prediction. Imagine if we are dealing with two point data sets where one data set is heavily clustered, while the other is well-spread over the area of interest — a sophistication of simple non-spatial regression is needed to account for the clustering of the points so that the model derived using the clustered points takes this property into account.

2005). 4) where coordinates are used to explain the deterministic part of variation, and would yield very similar results. Splines have been widely regarded as highly suitable for interpolation of densely sampled heights and climatic variables (Hutchinson, 1995; Mitas and Mitasova, 1999). However, their biggest criticism is their inability to incorporate larger amounts of auxiliary maps to model the deterministic part of variation. In addition, the smoothing and tension parameters are commonly determined subjectively.

3 ✻ ✼ ✽ ✾ ✶✵ ✶✶ ✶✷ ✶✸ ✶✹ Splines A special group of interpolation techniques is based on splines. A spline is a type of piecewise polynomial, which is preferable to a simple polynomial interpolation because more parameters can be defined including the amount of smoothing. The smoothing spline function also assumes that there is a (measurement) error in the data that needs to be smoothed locally. There are many versions and modifications of spline interpolators. The most widely used techniques are thin-plate splines (Hutchinson, 1995) and regularized spline with tension and smoothing (Mitasova and Mitas, 1993).

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