A spatial cross-validation strategy for interpreting predicted groundwater vulnerability to nitrate concentration in the Province of Milan

Natural and anthropogenic factors are identified as critical in characterizing aquifer vulnerability in the Milan Province study area, in which the impact of elevated concentrations of NO3 is being assessed. In this contribution, map versions of such continuous and categorical data layers are used to establish relationships between their map units and the location of over 300 water wells with nitrate levels either clearly above a threshold of 20 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) relative ease with which nitrate may migrate in groundwater, are: population density, nitrogen fertilizer loading, precipitation and irrigation, protective capacity of soils, land use, vadose zone permeability, groundwater depth, and groundwater velocity. Two versions of the data layers database are used in the study: one in which the data layers maintain their original value ranges and one in which they are reclassified into simplified classes. The water wells are separated first into the two groups to locate and recognize sites to be used to map high and low vulnerabilities using an empirical likelihood ratio prediction model, ELR. Further partition 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 curves and tables are obtained and visualized as cumulative proportions of study area in decreasing order of predicted vulnerability class versus the corresponding relative proportion of impacted validation wells (i.e., not used to predict). A similar procedure is followed with the non-impacted well locations. Predictions are thus compared and interpreted and repeated predictions are obtained using randomized sub-sets of prediction and validation wells. Target of the strategy used is not only to assess the goodness of predictions but also to estimate their reliability levels.