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Ensemble Kalman filtering (EnKF) is an efficient approach to addressing
uncertainties in subsurface groundwater models. The EnKF sequentially
integrates field data into simulation models to obtain a better
characterization of the model's state and parameters. These are generally
estimated following joint and dual filtering strategies, in which, at each
assimilation cycle, a forecast step by the model is followed by an update
step with incoming observations. The joint EnKF directly updates the
augmented state-parameter vector, whereas the dual EnKF empirically employs
two separate filters, 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-parameter estimates and their consistency, we
propose in this paper a one-step-ahead (OSA) smoothing formulation of the
state-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, which is 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 (2-D) synthetic groundwater aquifer model to investigate the
performance and robustness of the 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, providing further reliable estimates of their
uncertainties. Furthermore, it is found to be more robust to different
assimilation settings, such as the spatial and temporal distribution of the
observations, and the level of noise in the data. Based on our experimental
setups, it yields up to 25 % more accurate state and parameter estimations
than the joint and dual approaches
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