Unsupervised learning for probabilistic wellhead protection area analysis: A novel approach to identify hydraulic conductivity fields that best approximate geological uncertainties

A general approach to deal with model uncertainty in natural systems is to use an ensemble of many realizations or other multiple representation approaches. The final output of such methods are usually highly aggregated maps or statistics of the involved uncertainty. The aggregation is meant to summarize the results to the decision maker in order to provide a simple communication of uncertainties. One example is Monte Carlo simulation of flow towards drinking water wells in the process of delineating wellhead protection areas. The final output of such simulations is a well capture probability map that, ranging on scale from zero to one, displays the pixel-wise probability map pixels to be inside the well's catchment or not. However, to reproduce this geological uncertainty by using the full set of conductivity field realizations, into further analysis (e.g., searching for robust Pareto fronts in multi-objective optimization) might result in prohibitive computational times. Alternatively, one possibility is to use a well-selected set of hydraulic conductivity realizations that best represent geological uncertainty. The goal of this study is to present a methodology to detect a limited subset of hydraulic conductivity fields that approximate geological uncertainty conditions of a model ensemble used to delineate wellhead protection areas. For this purpose, we propose a classification methodology that cluster the ensemble realizations according to some pixel-wise commonalities among all hydraulic conductivity fields. Thus, we can approximate the aggregated capture probability map of the ensemble but at a much lower cost. We achieve this reduction by means of unsupervised learning techniques. In this way, many subsequent analysis can be performed on the condensed set of representative scenarios that would be computationally too expensive otherwise. We implement and demonstrate our clustering analysis with a synthetic three-dimensional groundwater scenario used to delineate a wellhead protection area of a well gallery under the influence of geological uncertainty conditions.