Estimation of New Points in the Sampling Area-Kriging

The semivariogram as a variance function can also be used to estimate the value and the variance for new points not sampled in the investigated area. The method applied for this purpose is termed kriging. Kriging is a special regression method for interpolation of spatially or temporally correlated data with minimization of variance. The normal distribution of the data is an important condition. If the original data are not normally distributed, which is often the case for trace components in environmental compartments, the logarithm of the data or otherwise transformed data have to be applied to obtain a normal distribution of the data (see also Section 9.4). 

The technique of kriging uses a weighted moving average interpolation method [BUSCHE and BURDEN, 1991] in the sense of a straightforward linear regression [JOURNEL, 1988]. The weights, w, are determined on the basis of the experimental 

The empirical weights have to be normalized with the following condition to obtain a distortion-free estimate  

The advantage of kriging is that it furnishes not only an estimate of the unsampled point, but also an estimate of the variance at this location. For a sampling location the exact value is estimated with the variance being zero. If the kriging method is applied, an exact and undistorted interpolation is possible. 

GILBERT and SIMPSON [1985] describe the estimation of the spatial pattern of radionuclides in soils. They demonstrate the advantage of the kriging method applied to logarithmically transformed data. But they refer to the fact that the validity of kriging 

---