Using Cluster Analysis of Hydraulic Conductivity Realizations to Reduce Computational Time for Monte Carlo Simulations

Despite the conceptual simplicity of Monte Carlo-simulation methods in assessing uncertainty in hydrogeological systems, their use is limited by expensive computational requirements in terms of the large number of realizations that must be processed. Cluster analysis was applied in this paper to reduce the number of realizations to be processed by flow simulators while efficiently approximating flow-response statistics. Different clustering techniques were used to partition the ensemble of realizations into a few clusters that were significantly different from each other and had maximum intracluster similarity. The clustering step was achieved by using different similarity metrics. Then a subsample of the realizations was collected to represent the uncertainty in the whole ensemble. Two methods for collecting the subsample were investigated: the stratified sampling and centroid-based sampling. The performance of different clustering and sampling techniques was tested by evaluating the mismatch between the statistics of the ensemble response (the reference response) and the subsample response, which are estimated from the clusters. Results show that 25% of the realizations in the ensemble may be sufficient to estimate the uncertainty in the flow responses when a suitable clustering method and suitable similarity measures are used.