An efficient deterministic-probabilistic approach to modeling regional groundwater flow: 1. Theory
An efficient probabilistic model is developed and cascaded with a deterministic model for predicting water table elevations in regional aquifers. The objective is to quantify model uncertainty where precise estimates of water table elevations may be required. The probabilistic model is based on the two-point probability method which only requires prior knowledge of uncertain variables mean and coefficient of variation. The two-point estimate method is theoretically developed and compared with the Monte Carlo simulation method. The results of comparisons using hypothetical determinisitic problems indicate that the two-point estimate method is only generally valid for linear problems where the coefficients of variation of uncertain parameters (for example, storage coefficient and hydraulic conductivity) is small. The two-point estimate method may be applied to slightly nonlinear problems with good results, provided coefficients of variation are small. In such cases, the two-point estimate method is much more efficient than the Monte Carlo method provided the number of uncertain variables is less than eight.