Parameter estimation for leaky aquifers using the extended Kalman filter, and considering model and data measurement uncertainties

Abstract

A method using the extended Kalman filter (EKF) is proposed to identify the hydraulic parameters in leaky aquifer systems both with and without considering the aquitard storage. In the case without considering the aquitard storage, Hantush and Jacob's model combined with EKF can optimally determine the parameters for the leaky aquifer when analyzing the drawdown data. Coupled with Neuman and Witherspoon's model, the EKF is also employed to estimate the four parameters of aquifers. The observed drawdown data may be either interpolated using the Lagrangian polynomial or recursively used while implementing the EKF. The proposed method can identify the parameters, using part of the interpolated drawdown data or recursively used data, and obtains results with good accuracy. In the field-pumping test, a long pumping time may not be necessary if the proposed method is implemented on a computer, which is connected to pressure transducers and a data logger. In the process of parameter estimation, the leakage coefficient changes marginally for the first few observations. This phenomenon reflects the fact that there is a time lag between the start of pumping and the leakage effect on the drawdown. The analyses of the data uncertainty demonstrate that the EKF approach is applicable for drawdown data even when it contains white noise or temporal correlated noise. Finally, the choice between Hantush and Jacob's model and Neuman and Witherspoon's model depends on the hydrogeological condition of the aquifer system indicated in the analyses of the model uncertainty. Hantush and Jacob's model is shown to be a good choice for representing the leaky aquifer system if the aquitard storage is comparatively small.