Use of the Kalman Filter for the Interpretation of Aquifer Tests Including Model and Measurement Errors

Abstract

The hydraulic parameters representative of actual aquifer conditions can be obtained through aquifer tests formerly known as pumping tests. Diverse methodologies based on analytical or numerical solutions have been proposed for the interpretation of aquifer tests; however, measurement and model errors are often neglected, which could lead to hydraulic parameter values that do not reflect the aquifer conditions. In this paper, a new alternative is presented for the interpretation of aquifer tests in confined aquifers based on the Cooper–Jacob solution by means of the dynamic Kalman filter and a nonlinear optimization method. This proposal was tested in two previously published case studies; the measured drawdowns were filtered by considering measurement and model errors to match the Cooper–Jacob solution. For the case studies, the results show that filtering the measured drawdowns leads to variations of up to 49.97% in the values for T and 150% for S when compared to the values determined by methodologies that neglect measurement and model errors. A poor match between filtered and measured data reflects large measurement errors and considerable deviations of the aquifer conditions with respect to the proposed model.