Statistical analyses and stochastic modeling of the Cortaro aquifer in southern Arizona

Abstract

Transmissivity, specific capacity, and steady state hydraulic head data collected from the Cortaro aquifer in Southern Arizona are analyzed statistically by means of regression and Kriging techniques. The statistics obtained in this manner are used to develop a stochastic model of the aquifer based on the finite element and Monte Carlo simulation methods. Three stages of generated head uncertainties are considered; (1) non-conditional, (2) conditional on transmissivity data and (3) conditional on both transmissivity and initial hydraulic head data (or inverse method). We found that simulated head values in stage 1 and 2 are associated with high variance amounting to 144.0 ft². When the statistics obtained from regression and Kriging in stage 2 are processed by means of the statistical inverse method of Neuman (1980), the result is a drastic reduction in the input head variance amounting to 75 percent reduction in the input head variance (i.e., 144 ft²). From these results, one may conclude that in order to minimize the variance of outputs generated by stochastic aquifer models, the input into such models must be created with the aid of appropriate statistical inverse procedure.