A Practical Guide to Geostatistical Mapping by Tomislav Hengl

By Tomislav Hengl

The aim of this consultant is to help you in generating caliber maps by utilizing totally operational open resource software program applications.

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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).

2, spatial prediction can even be fully automated so that a user needs only to provide quality inputs and the system will select the most suitable technique. ✹✶ 12 ✶ ✷ Geostatistical mapping Trans-Gaussian (variable transformed using some link function); Localization of analysis — whether the model uses all sampling locations or only locations in local proximity: ✸ Local or moving window analysis (a local sub-sample; local models applicable); ✹ Global (all samples; the same model for the whole area); ✺ Convexity effect — whether the model makes predictions outside the range of the data: ✻ Convex (all predictions are within the range); ✼ Non-convex (some predictions might be outside the range); ✽ ✾ ✶✵ ✶✶ Support size — whether the model predicts at points or for blocks of land: Point-based or punctual prediction models; Area-based or block prediction models; Regularity of support — whether the output data structure is a grid or a polygon map: ✶✷ Regular (gridded outputs); ✶✸ Irregular (polygon maps); ✶✹ Quantity of target variables — whether there is one or multiple variables of interest: ✶✺ Univariate (model is estimated for one target variable at a time); ✶✻ Multivariate (model is estimated for multiple variables at the same time); ✶✼ ✶✽ ✶✾ ✷✵ ✷✶ ✷✷ ✷✸ ✷✹ ✷✺ ✷✻ ✷✼ ✷✽ ✷✾ ✸✵ ✸✶ ✸✷ ✸✸ ✸✹ Another way to look at spatial prediction models is to consider their ability to represent models of spatial variation.

13: Comparison of spatial prediction techniques for mapping ❩✐♥❝ (sampling locations are shown in Fig. 9). Note that inverse distance interpolation (✳✐❞) and kriging (✳♦❦) are often quite similar; the moving trend surface (✳tr; 2nd order polynomial) can lead to artifacts (negative values) — locally where the density of points is poor. The regression-based (✳❧♠) predictions were produced using distance from the river as explanatory variable (see further §5). , 2004). 2)), this time by averaging the predictors: zˆ❖▲❙ (s0 ) = ˆb0 + ˆb1 · q1 (s0 ) + .

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