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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 20, issue 8
Hydrol. Earth Syst. Sci., 20, 3289–3307, 2016
https://doi.org/10.5194/hess-20-3289-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 20, 3289–3307, 2016
https://doi.org/10.5194/hess-20-3289-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 12 Aug 2016

Research article | 12 Aug 2016

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

Boujemaa Ait-El-Fquih1, Mohamad El Gharamti1,2, and Ibrahim Hoteit1 Boujemaa Ait-El-Fquih et al.
  • 1Department of Earth Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), 23955-6900 Thuwal, Kingdom of Saudi Arabia
  • 2Mohn-Sverdrup Center for Global Ocean Studies and Operational Oceanography, Nansen Environmental and Remote Sensing Center (NERSC), 5006 Bergen, Norway

Abstract. 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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We derive a new dual ensemble Kalman filter (EnKF) for state-parameter estimation. The derivation is based on the one-step-ahead smoothing formulation, and unlike the standard dual EnKF, it is consistent with the Bayesian formulation of the state-parameter estimation problem and uses the observations in both state smoothing and forecast. This is shown to enhance the performance and robustness of the dual EnKF in experiments conducted with a two-dimensional synthetic groundwater aquifer model.
We derive a new dual ensemble Kalman filter (EnKF) for state-parameter estimation. The...
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