Accuracy assessment of inverse distance weighting interpolation of groundwater nitrate concentrations in Bavaria (Germany)

Abstract

For the designation of nitrate vulnerable zones under the EU Nitrate Directive, some German federal states use inverse distance weighting (IDW) as interpolation method. Our study quantifies the accuracy of IDW with respect to the designation of areas with a groundwater nitrate concentration above the threshold of 50 mg NO3/l using a dataset of 5790 groundwater monitoring sites in Bavaria. The results show that the absolute differences of nitrate concentrations between the monitoring sites are only weakly correlated within a range of no more than 0.4 km. The IDW cross-validated nitrate concentration of measurement sites shows a mean absolute error of 7.0 mg NO3/l and the number of measurement sites above 50 mg NO3/l is 44% too low by interpolation for all sites as a whole. The corresponding values for interpolation separately for the 18 hydrogeological regions in Bavaria are 7.1 mg NO3/l and 38%. The sensitivity and the accuracy of nitrate concentration maps due to the variation of IDW parameters and the position of sampling points are analysed by Monte Carlo IDW interpolations using a Random Forest modelled map as reference spatial distribution. Compared to this reference map, the area with a concentration above 50 mg NO3/l in groundwater is estimated by IDW to be 46% too low for the best IDW parametrization. Overall, IDW interpolation systematically underrates the occurrence of higher range nitrate concentrations. In view of these underestimations, IDW does not appear to be a suitable regionalization method for the designation of nitrate vulnerable zones, neither when applied for a federal state as a whole nor when interpolated separately for hydrogeological regions.