Analysis of the Distance between the Measured and Assumed Location of a Point Source of Pollution in Groundwater as a Function of the Variance of the Estimation Error

Abstract

The localization of pollution sources is one of the main tasks in environmental engineering. For this paper, models of spatial distribution of nitrate concentration in groundwater were created, and the point of highest concentration was determined. This point represents the assumed location of the pollution source and differs from the actual location, so there is a certain distance between the measured and assumed location. This paper puts forward a new hypothesis that the distance between the measured and the assumed location is a function of the variance of the estimation error. The scientific contribution of this paper is based on the fact that the interaction of statistical and geostatistical methods can locate the dominant point source of pollution or narrow down the search area. The above hypothesis is confirmed by the example of the Varaždin wellfield, which was closed due to an excessively high groundwater nitrate concentration. Seven different interpolation methods were used to create spatial distribution models. Each method provides a different model, a different variance of the estimation error, and estimates of the location of the pollution source. The smallest value of variance of the estimation error of 1.65 was obtained for the minimum curvature interpolation method and the largest value of variance (24.49) was obtained for the kriging with logarithmic variogram. Our results show a nonlinear and monotonic relationship between the distance and the variance of the estimation error, so logarithmic and rational quadratic models were fitted to the scatter point data. The models were linearized, a t-test was performed, and the results show that the models can be considered reliable, which is confirmed by the values of the coefficients of determination of the linearized models, which are around 0.50. The obtained results can be used in planning additional research work to determine the measured location of the pollution source. The research methodology we used is universal and can be applied to other locations where high concentrations of certain contaminants have been detected in groundwater in alluvial aquifers.