Institute for Landscape Ecology and Resources Management (ILR), Research Centre for Biosystems, Land Use and Nutrition (iFZ), Justus Liebig University Giessen, Heinrich-Buff-Ring 26, 35392, Giessen, Germany.
Centre for International Development and Environmental Research (ZEU), Justus Liebig University Giessen, Senckenbergstrasse 3, 35390, Giessen, Germany.
Environ Sci Pollut Res Int. 2023 Jan;30(4):9445-9455. doi: 10.1007/s11356-022-22670-0. Epub 2022 Sep 3.
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 NO/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 NO/l and the number of measurement sites above 50 mg NO/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 NO/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 NO/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.
针对欧盟硝酸盐指令下硝酸盐脆弱区的划定，一些德国联邦州使用反距离权重插值法（IDW）。本研究使用巴伐利亚州的 5790 个地下水监测点数据集，量化了 IDW 在指定地下水硝酸盐浓度超过 50mg/L 阈值的区域方面的准确性。结果表明，监测点之间硝酸盐浓度的绝对差异在不超过 0.4km 的范围内相关性较弱。IDW 交叉验证的测量点硝酸盐浓度的平均绝对误差为 7.0mg/L，对于所有测量点的整体插值，测量点中硝酸盐浓度超过 50mg/L 的数量低了 44%。对于巴伐利亚州的 18 个水文地质区域分别插值的相应值分别为 7.1mg/L 和 38%。通过使用随机森林模型地图作为参考空间分布的蒙特卡罗 IDW 插值分析，研究了由于 IDW 参数和采样点位置的变化导致的硝酸盐浓度图的灵敏度和准确性。与该参考地图相比，对于最佳 IDW 参数化，IDW 估计的地下水中浓度超过 50mg/L 的区域低了 46%。总体而言，IDW 插值系统低估了较高硝酸盐浓度范围的出现频率。鉴于这些低估，IDW 似乎都不适合作为划定硝酸盐脆弱区的区域化方法，无论是在整个联邦州应用还是在针对水文地质区域进行插值时都不适用。
