Introducing uncertainty of aquifer parameters into an optimization model

A stochastic analysis is made for a previously described groundwater contaminant management model {Peralta and Ward, 1988). The stochastic model is based on incorporating uncertainty of the aquifer parameters transmissivity and effective porosity into the model. This is accomplished by finding the partial derivative of drawdown with respect to each of these parameters using a Taylor series expansion approximation of the Theis equation. Input that is required for the stochastic version is the mean of the transmissivity and effective porosity, the coefficient of variation of the transmissivity and effective porosity, and a reliability level (0%-100%) . The reliability is a measure of the user\u27s required confidence in the model solution. The user wants to be confident, at some probability, that the actual changes in head at pumping wells do not exceed the values calculated by the model, while 1 at the same time, he wants to be confident that actual changes in head at observation wells are at least as great as the calculated values. Thus, equations that are affected by heads at the observation wells are treated differently than equations that are affected by heads at the pumping wells. Optimal strategies are presented to demonstrate sensitivity to changes in standard deviation of aquifer parameters and to changes in reliability level. Tests show that uncertainty of transmissivity affects the optimal pumping more and the final gradient and objective function less than uncertainty of effective porosity. In general, as uncertainty of aquifer parameters increases, optimal pumping values decrease, resulting in a poorer final hydraulic gradient. As the reliability level is increased optimal pumping decreases, again resulting in a poorer final gradient