Improving the assessment of uncertainty and risk in the spatial prediction of environmental impacts: a new approach for fitting geostatistical model parameters based on dual Kriging in the presence of a trend

Abstract

Modern methods of geostatistics deliver an essential contribution to Environmental Impact Assessment (EIA). These methods allow for spatial interpolation, forecast and risk assessment of expected impact during and after mining projects by integrating different sources of data and information. Geostatistical estimation and simulation algorithms are designed to provide both, a most likely forecast as well as information about the accuracy of the prediction. The representativeness of these measures depends strongly on the quality of the inferred model parameters, which are mainly defined by the parameters of the variogram or the covariance function. Available data may be sparse, trend affected and of different data type making the inference of representative geostatistical model parameters difficult. This contribution introduces a new method for best fitting of the geostatistical model parameters in the presence of a trend, which utilizes the empirical and theoretical differences between Universal Kriging and trend-predictions. The method extends well known approaches of cross validation in two aspects. Firstly, the model evaluation is not only limited to sample data locations but is performed on any prediction locations of the attribute in the domain. Secondly, it extends the measure used in cross validation, based on a single point replacement by using error curves. These allow defining rings of influence representing errors resulting from separate variogram lags. By analyzing the different variogram lags the fit of the complete covariance can be assessed and the influence of the several model parameters separated. The use of the proposed method in an EIA context is illustrated in a case study related on the prediction of mining-induced ground movements.