Application of Gauss algorithm and Monte Carlo simulation to the identification of aquifer parameters

Abstract

The Gauss optimization technique can be used to identify the parameters of a model of a groundwater system for which the parameter identification problem is formulated as a least squares comparison between the response of the prototype and the response of the model. Unavoidable uncertainty in the true stress on the prototype and in the true response of the prototype to that stress will introduce errors into the parameter identification problem. A method for evaluating errors in the predictions of future water levels due to errors in recharge estimates was demonstrated. The method involves a Monte Carlo simulation of the parameter identification problem and of the prediction problem. The steps in the method are: (1) to prescribe the distribution of the recharge estimates; (2) to use this distribution to generate random sets of recharge estimates; (3) to use the Gauss optimization technique to identify the corresponding set of parameter estimates for each set of recharge estimates; (4) to make the corresponding set of hydraulic head predictions for each set of parameter estimates; and (5) to examine the distribution of hydraulic head predictions and to draw appropriate conclusions. Similarly, the method can be used independently or simultaneously to estimate the effect on hydraulic head predictions of errors in the measured water levels that are used in the parameter identification problem. The fit of the model to the data that are used to identify parameters is not a good indicator of these errors. A Monte Carlo simulation of the parameter identification problem can be used, however, to evaluate the effects on water level predictions of errors in the recharge (and pumpage) data used in the parameter identification problem. (Lantz-PTT)