A general approach to deal with parameter uncertainty in natural systems is to use ensembles of many parameter realizations. However, this might result in extremely expensive computational time, especially when additional loops for transient simulation and for optimization are involved. One possibility to mitigate computing time is to use few but well-selected realizations that best represent the involved geological uncertainties, e.g., by clustering techniques.The goal of this paper is to address the search for representative realizations that best approximate the distribution and its tails of a model ensemble. In our test application, this ensemble is used to delineate wellhead protection areas (WHPAs) under transient flow conditions and subject to random heterogeneity of the aquifer. Our approach is based on clustering and proposes that the cluster medoids (representatives) should be optimized not for “statistical representation in the space of some selected proxy metrics”, but for “a minimum of decision-relevant errors”. And, if the underlying decision problem is multi-objective, then the clustering optimization can be made multi-objective, too. In this way, many subsequent analyses can be performed on the condensed set of representative scenarios that would be computationally too expensive otherwise, even if distribution tails and extreme realizations are relevant. We demonstrate the advantage of our clustering optimization methodology on a dynamic probabilistic WHPA delineation, and we compare its performance with a standard clustering analysis.Our results show that: (1) in probabilistic transient WHPA analysis, clustering is a suitable technique to account for geological uncertainty. (2) However, clustering analysis should be based on optimization concepts rather than on simple medoid concepts, and (3) of course, it should use problem-specific and decision-relevant metrics for cluster optimization. In our WHPA application, this leads to a more accurate representation of decision-relevant statistical extremes. (4) The additional extension to multi-objective cluster selection probes to be a valid approach in multi-objective WHPA delineation. (5) Using our framework, we reduce the computational cost of addressing highly expensive simulations.
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