A Practical Guide to Geostatistical Mapping of Environmental by Hengl, Tomislav

By Hengl, Tomislav

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G. radius=1000 or nmax=60. 2 Universal kriging, kriging with external drift The geostatistical literature uses many different terms for what are essentially the same or at least very similar techniques. This confuses the users and distracts them from using the right technique for their mapping projects. In this section, we will show that both universal kriging, kriging with external drift and regregression-kriging are basically the same technique. Matheron (1969) originally termed the technique Le krigeage universel, however, the technique was intended as a generalized case of kriging where the trend is modelled as a function of coordinates.

Start from KED where the predictions are T made as in ordinary kriging using zˆKED (s0 ) = λT KED · z. 15) where φ is a vector of Lagrange multipliers. 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.

195 (Fig. 4d). 164. ) Model the covariance structure of the OLS residuals. 5, R=5). The residual model is derived from the target variable model of the text by assuming that the residual variogram has approximately the same form and nugget but a somewhat smaller sill and range (Fig. , 2004a). ) Estimate the GLS coefficients using Eq. 3. 199. The GLS coefficients will not differ much from the OLS coefficients as long there is no significant clustering of the sampling locations (Fig. 4d) as in this case.

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