Aquifer parameter identification using the extended Kalman filter

Abstract

An approach using the extended Kalman filter (EKF) and cubic spline is proposed to identify the aquifer parameters in both confined and unconfined aquifer systems. The cubic spline applied to the observation data can generate interpolated data with uniform time intervals and facilitates the implementation of EKF. The EKF combined with the Theis solution or Neuman's model, using the interpolated drawdown data produced by cubic spline, can optimally determine the parameters through the recursive process. The proposed approach can quickly identify the parameters, using only part of observed drawdown data, and the obtained parameters are shown to have good accuracy. Thus length of time of pumping tests may be shortened. Comparisons of results from nonlinear least squares combined with finite difference Newton's method (NLN) and EKF show that the EKF allows a wider range of initial guess values than NLN and have the accuracy of the results on the same order of magnitude as that of NLN. When determining the aquifer parameters, the identification process of specific yield reflects the effect of gravity drainage on the drawdown curve and conforms to the physical nature of an unconfined aquifer. Furthermore, this study shows that EKF can be successfully applied to analyze the drawdown data even with white noises or temporally correlated noises.