Geostatistics for spatial uncertainty characterization

Abstract

Most geospatial phenomena can be interpreted probabilistically because we are ignorant of the biophysical processes and mechanisms that have jointly created and observed events. This philosophy is important because we are certain about the phenomenon under study at sampled locations, except for measurement errors, but, in between the sampled, we become uncertain about how the phenomenon behaves. Geostatistical uncertainty characterization is to generate random numbers in such a way that they simulate the outcomes of the random processes that created the existing sample data. This set of existing sample is viewed as a partially sampled realization of that random function model. The random function’s spatial variability is described by a variogram or covariance model. The realized surfaces need to honour sample data at their locations, and reflect the spatial structure quantified by the variogram models. They should each reproduce the sample histogram representative of the whole sampling area. This paper will review the fundamentals in stochastic simulation by covering univariate and indicator techniques in the hope that their applications in geospatial information science will be wide-spread and fruitful.