A Bayesian Consistent Dual Ensemble Kalman Filter for State-Parameter Estimation in Subsurface Hydrology

摘要

Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties insubsurface groundwater models. The EnKF sequentially integrates field data into simulation modelsto obtain a better characterization of the model's state and parameters. These are generally estimatedfollowing joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step bythe model is followed by an update step with incoming observations. The Joint-EnKF directly up-dates the augmented state-parameter vector while the Dual-EnKF empirically employs two separatefilters, first estimating the parameters and then estimating the state based on the updated parameters.To develop a Bayesian consistent dual approach and improve the state-parameters estimates andtheir consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of thestate-parameter Bayesian filtering problem from which we derive a new dual-type EnKF; the Dual-EnKFOSA. Compared with the standard Dual-EnKF, it imposes a new update step to the state, whichis shown to enhance the performance of the dual approach with almost no increase in the computational cost.Numerical experiments are conducted with a two-dimensional synthetic groundwateraquifer model. Assimilation experiments are performed to assess the performance and robustness ofthe proposed Dual-EnKFOSA, and to evaluate its results against those of the Joint- and Dual-EnKFs.The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, further providing reliable estimates of their uncertainties. It is further found more robust todifferent assimilation settings, such as the spatial and temporal distribution of the observations, andthe level of noise in the data. Based on our experimental setups, it yields up to 25 % more accuratestate and parameters estimates than the joint and dual approaches.