Importance of the nugget effect in variography on modeling zinc leaching from a contaminated site using simulated annealing

Abstract

Summary The spatial heterogeneity of measured data from contaminated sites is a serious problem with regard to uncertainty and risk assessment. Stochastic simulation permits the generation of several realizations of the spatial data distribution without aiming to minimise local error variance (as in kriging, for example), but retaining important statistics such as the histogram, the semivariogram, and the measured data. The nugget-to-sill ratio will, however, influence spatial data interpolation based on geostatistical models. The nugget effect is generally unknown to the investigator and influenced by the sampling density and sampling grid, as well as by complex geological settings, analytical errors, or an unknown small-scale site-specific contaminant input. Using simulated annealing to generate 30 randomly combined input data realizations and a simple transport model, we can show that the modeled zinc discharge is up to 70% higher if the nugget-to-sill ratio is varied by a factor of two times. The variance of zinc discharge was influenced by the nugget-to-sill ratio by a factor of 10 times. By reducing the number of drill holes to one half from the data set at random we have shown that the variance of the reduced data set did not provide a reliable prediction of the data heterogeneity for the complete data set, and the mean zinc discharge was up to 170% higher when only half of the drill holes were considered. Uncertainty analysis based on equal-probability realizations should further be founded by additional variation of nugget-to-sill ratio within a reasonable spectrum.