Optimal estimation of unconfined aquifer parameters in uncertain environment based on fuzzy transformation method

In this paper, a fuzzy simulation–optimization model coupled with the genetic algorithm based on Boulton's equation is presented to estimate transmissibility (T), storage coefficient (S), specific yield (S_y) and leakage factor (D_t) of an unconfined aquifer. This model is capable of minimizing the deviation between observed and calculated drawdowns of pumping test data. To assess the applicability of the model, its results are compared with the graphically obtained solutions from Boulton's equation. To this end, real pumping test data obtained from an unconfined aquifer in Dayton, Ohio, are considered as the case problem to evaluate the efficacy of the model. In the fuzzy approach, pumping rate is considered as an uncertain variable. For evaluation of the model, several statistical error indices are utilized. Results show better matches for the model as evidenced by much smaller errors. As an example, mean absolute relative error for the proposed model and graphical Boulton's solution is 2.52% and 4.98%, respectively. It is concluded that the model is accurate and may replace the graphical Boulton's solution. T and S_y were found to be more sensitive to uncertainty in the pumping rate measurement, when compared with S and r/D_t.