USING LINEAR-APPROXIMATIONS TO RANK REALIZATIONS IN GROUNDWATER MODELING - APPLICATION TO WORST-CASE SELECTION

Cumulative distribution functions (cdf) of groundwater model responses are generally determined using Monte Carlo analysis. The procedure co nsists of (1) generating a number of realizations of the parameters co ntrolling groundwater flow, (2) solving the groundwater flow equation in each of the realizations to obtain the model responses, (3) ranking the model responses, and (4) assigning a probability to each model re sponse as a function of its rank and the total number of realizations. When one is only interested in determining one of the tails of the cd f, e.g., to determine model responses with a small probability of bein g exceeded, it would be more appropriate to try to reverse steps 2 and 3 above, so that the realizations are ranked first and then the groun dwater flow equation is solved only for those realizations leading to responses in the tail of the cdf. Because the ranking of the realizati ons must be done in terms of their model responses, which calls for th e solution of the groundwater flow equation, we propose to use a linea r approximation of the flow equation to approximate the ranks. The pro posal is based on the conjecture that first-order approximations are m ore robust for computing the ranks of the piezometric heads than for c omputing the heads themselves. The conjecture is demonstrated in two t wo-dimensional confined flow problems comparing the results of the app roximation to the results of full Monte Carlo analyses on several sets of 200 realizations with varying standard deviations of log10 T.