Sequential Ensemble Based Optimal Design for Parameter Estimation in Unsaturated Water Flow Models.

The ensemble Kalman filter (EnKF) has been widely used in inverse parameter estimation for hydrological models. The focus of most previous studies was to develop more efficient analysis (estimation) algorithm using the measurements On the other hand, it is intuitively understandable that a well-designed sampling strategy should provide more informative measurements and subsequently improve the parameter estimation. Nevertheless efficient sampling design was overlooked in past decades in spite of the popularity of EnKF. In this paper, a sequential ensemble based sampling design method was proposed to improve the performance of EnKF in estimating unsaturated soil hydraulic properties from pressure head measurements. Different information metrics, including Shannon entropy difference (SD), degrees of freedom for signal (DFS) and relative entropy (RE), were used to design the optimal sampling strategy. The effectiveness of the proposed method was illustrated by synthetic one-dimensional unsaturated flow cases. Results showed that the new designed sampling strategies provided more accurate parameter estimation, comparing with those conventional sampling strategies. Optimal sampling designs based on various information metrics performed similarly well in our cases. The effect of ensemble size on the optimal design was also investigated. Overall, larger ensemble size improved the parameter estimation and convergence of optimal sampling strategy. Although the method was applied to unsaturated water flow problem in this study, the proposed method can be equally applied to any other hydrological problems.