MultiGaussian Kriging: A Review

Abstract

The kriging estimate has an associated kriging variance which measures the variance of the error between the estimate and the true value. However, this measure of uncertainty does not depend on the actual value of the variable, but only on the spatial configuration of the sample data used in the estimation. Thus, it does not capture the “proportional effect”, that is, the fact that the variability depends on the local value of the variable. In this paper, we review the multiGaussian framework, which allows characterizing the uncertainty in a simple, yet effective manner. As most variables are not normally distributed, the approach requires a quantile transformation and a back transformation at the end of the analysis. We show that the simple kriging estimate and its corresponding variance identify the conditional expectation and variance in a multiGaussian framework. Thus, uncertainty quantification is simply achieved by transforming the data to a Gaussian distribution, performing simple kriging of the normally transformed values and back transforming the resulting distribution to original units.