Spatial uncertainty of groundwater-vulnerability predictions assessed by a cross-validation strategy: an application to nitrate concentrations in the Province of Milan, northern Italy

Natural and anthropogenic factors are identified as critical in characterizing aquifer vulnerability in the Milan Province study area, where the impact of elevated concentrations of NO3 - is being assessed. In this contribution, map versions of continuous and categorical data layers are used to establish relationships between map units and the location of 305 water wells with nitrate levels either clearly above a threshold of 25 mg/l (impacted wells), or with wells clearly below that (non-impacted wells). The natural and anthropogenic data layers that are assumed to reflect (a) potential sources of nitrate, and (b) the relative ease with which nitrate may migrate in groundwater, are: population density, nitrogen fertilizer loading, precipitation and irrigation, the protective capacity of soils, land use, vadose zone permeability, groundwater depth, and groundwater velocity. The water wells are separated first into the two groups to locate and recognize sites to be used to map high vulnerabilities using a prediction model based on the empirical likelihood ratio, ELR. Further partitions of the two sub-groups into prediction and validation wells allows setting up blind tests to cross-validate the predictions of relative vulnerability classes (ranks). Prediction-rate tables are obtained and visualized either as histograms or as cumulative proportions of the study area in decreasing order of predicted vulnerability class versus the corresponding relative proportion of impacted validation wells, i.e., not used to predict. Predictions are thus compared and interpreted and repeated predictions are obtained using different sub-sets of prediction and validation wells in the two regions to obtain maps of uncertainty of the prediction classes. The target of the strategy used is not only to assess the goodness of predictions but also to estimate their reliability levels. In this application the uncertainty of the classes in the prediction map happens to be relatively high, which is due to the small number of water wells available in the spatial database.