By Hengl, Tomislav
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Additional info for A Practical Guide to Geostatistical Mapping of Environmental Variables
18) where the identity qT · λKED = q0 has been used. Substituting φ back into Eq. 19) Let us now turn to RK. 19), which proves that KED will give the same predictions as RK if same inputs are used. A detailed comparison of RK and KED using a small dataset in MS Excel is also available as supplementary material. Although the KED seems, at first glance, to be computationally more straightforward than RK, the variogram parameters for KED must also be estimated from regression residuals, thus requiring a separate regression modelling step.
For example, if you study how model shape, nugget, sill and range affect the kriging results, you will notice that, assuming some standard variogram model (zero nugget, sill at global variance and practical range at 10% of the largest distance), the weights will decrease exponentially15 . This is an important characteristic of kriging because it allows us to limit the search window to speed up the calculation and put more emphasise on fitting the semivariances at shorter distances. Note also that, although it commonly leads to smoothing of the values, kriging is an exact and non-convex interpolator.
1 Kriging Kriging has for many decades been used as a synonym for geostatistical interpolation. It originated in the mining industry in the early 1950’s as a means of improving ore reserve estimation. The original idea came from the mining engineers D. G. Krige and the statistician H. S. Sichel. The technique was first published in Krige (1951), but it took almost a decade until a French mathematician G. , 2007). A standard version of kriging is called ordinary kriging (OK). 1) where µ is the constant stationary function (global mean) and ε (s) is the spatially correlated stochastic part of variation.
A Practical Guide to Geostatistical Mapping of Environmental Variables by Hengl, Tomislav