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

Handle URI:
http://hdl.handle.net/10754/622057
Title:
A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology
Authors:
Ait-El-Fquih, Boujemaa; El Gharamti, Mohamad ( 0000-0002-7229-8366 ) ; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Abstract:
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface ground-water 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 EnKF(OSA). 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.
KAUST Department:
Earth Science and Engineering Program
Citation:
Ait-El-Fquih B, El Gharamti M, Hoteit I (2016) A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology. Hydrology and Earth System Sciences 20: 3289–3307. Available: http://dx.doi.org/10.5194/hess-20-3289-2016.
Publisher:
Copernicus GmbH
Journal:
Hydrology and Earth System Sciences
Issue Date:
12-Aug-2016
DOI:
10.5194/hess-20-3289-2016
Type:
Article
ISSN:
1607-7938
Sponsors:
Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST).
Additional Links:
http://www.hydrol-earth-syst-sci.net/20/3289/2016/
Appears in Collections:
Articles; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorAit-El-Fquih, Boujemaaen
dc.contributor.authorEl Gharamti, Mohamaden
dc.contributor.authorHoteit, Ibrahimen
dc.date.accessioned2016-12-22T13:34:55Z-
dc.date.available2016-12-22T13:34:55Z-
dc.date.issued2016-08-12en
dc.identifier.citationAit-El-Fquih B, El Gharamti M, Hoteit I (2016) A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology. Hydrology and Earth System Sciences 20: 3289–3307. Available: http://dx.doi.org/10.5194/hess-20-3289-2016.en
dc.identifier.issn1607-7938en
dc.identifier.doi10.5194/hess-20-3289-2016en
dc.identifier.urihttp://hdl.handle.net/10754/622057-
dc.description.abstractEnsemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface ground-water 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 EnKF(OSA). 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.en
dc.description.sponsorshipResearch reported in this publication was supported by King Abdullah University of Science and Technology (KAUST).en
dc.publisherCopernicus GmbHen
dc.relation.urlhttp://www.hydrol-earth-syst-sci.net/20/3289/2016/en
dc.rightsThis work is distributed under the Creative Commons Attribution 3.0 License.en
dc.titleA Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrologyen
dc.typeArticleen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalHydrology and Earth System Sciencesen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionMohn-Sverdrup Center for Global Ocean Studies and Operational Oceanography, Nansen Environmental and Remote Sensing Center (NERSC), Bergen, Norwayen
kaust.authorAit-El-Fquih, Boujemaaen
kaust.authorEl Gharamti, Mohamaden
kaust.authorHoteit, Ibrahimen
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