Dual states estimation of a subsurface flow-transport coupled model using ensemble Kalman filtering

Handle URI:
http://hdl.handle.net/10754/563016
Title:
Dual states estimation of a subsurface flow-transport coupled model using ensemble Kalman filtering
Authors:
El Gharamti, Mohamad ( 0000-0002-7229-8366 ) ; Hoteit, Ibrahim ( 0000-0002-3751-4393 ) ; Valstar, Johan R.
Abstract:
Modeling the spread of subsurface contaminants requires coupling a groundwater flow model with a contaminant transport model. Such coupling may provide accurate estimates of future subsurface hydrologic states if essential flow and contaminant data are assimilated in the model. Assuming perfect flow, an ensemble Kalman filter (EnKF) can be used for direct data assimilation into the transport model. This is, however, a crude assumption as flow models can be subject to many sources of uncertainty. If the flow is not accurately simulated, contaminant predictions will likely be inaccurate even after successive Kalman updates of the contaminant model with the data. The problem is better handled when both flow and contaminant states are concurrently estimated using the traditional joint state augmentation approach. In this paper, we introduce a dual estimation strategy for data assimilation into a one-way coupled system by treating the flow and the contaminant models separately while intertwining a pair of distinct EnKFs, one for each model. The presented strategy only deals with the estimation of state variables but it can also be used for state and parameter estimation problems. This EnKF-based dual state-state estimation procedure presents a number of novel features: (i) it allows for simultaneous estimation of both flow and contaminant states in parallel; (ii) it provides a time consistent sequential updating scheme between the two models (first flow, then transport); (iii) it simplifies the implementation of the filtering system; and (iv) it yields more stable and accurate solutions than does the standard joint approach. We conducted synthetic numerical experiments based on various time stepping and observation strategies to evaluate the dual EnKF approach and compare its performance with the joint state augmentation approach. Experimental results show that on average, the dual strategy could reduce the estimation error of the coupled states by 15% compared with the joint approach. Furthermore, the dual estimation is proven to be very effective computationally, recovering accurate estimates at a reasonable cost. © 2013 Elsevier Ltd.
KAUST Department:
Earth Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Earth Fluid Modeling and Prediction Group; Earth Sciences and Engineering Program
Publisher:
Elsevier BV
Journal:
Advances in Water Resources
Issue Date:
Oct-2013
DOI:
10.1016/j.advwatres.2013.07.011
Type:
Article
ISSN:
03091708
Sponsors:
This paper is based on work supported in part by funds from the KAUST GCR Collaborative Fellow program.
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorEl Gharamti, Mohamaden
dc.contributor.authorHoteit, Ibrahimen
dc.contributor.authorValstar, Johan R.en
dc.date.accessioned2015-08-03T11:33:45Zen
dc.date.available2015-08-03T11:33:45Zen
dc.date.issued2013-10en
dc.identifier.issn03091708en
dc.identifier.doi10.1016/j.advwatres.2013.07.011en
dc.identifier.urihttp://hdl.handle.net/10754/563016en
dc.description.abstractModeling the spread of subsurface contaminants requires coupling a groundwater flow model with a contaminant transport model. Such coupling may provide accurate estimates of future subsurface hydrologic states if essential flow and contaminant data are assimilated in the model. Assuming perfect flow, an ensemble Kalman filter (EnKF) can be used for direct data assimilation into the transport model. This is, however, a crude assumption as flow models can be subject to many sources of uncertainty. If the flow is not accurately simulated, contaminant predictions will likely be inaccurate even after successive Kalman updates of the contaminant model with the data. The problem is better handled when both flow and contaminant states are concurrently estimated using the traditional joint state augmentation approach. In this paper, we introduce a dual estimation strategy for data assimilation into a one-way coupled system by treating the flow and the contaminant models separately while intertwining a pair of distinct EnKFs, one for each model. The presented strategy only deals with the estimation of state variables but it can also be used for state and parameter estimation problems. This EnKF-based dual state-state estimation procedure presents a number of novel features: (i) it allows for simultaneous estimation of both flow and contaminant states in parallel; (ii) it provides a time consistent sequential updating scheme between the two models (first flow, then transport); (iii) it simplifies the implementation of the filtering system; and (iv) it yields more stable and accurate solutions than does the standard joint approach. We conducted synthetic numerical experiments based on various time stepping and observation strategies to evaluate the dual EnKF approach and compare its performance with the joint state augmentation approach. Experimental results show that on average, the dual strategy could reduce the estimation error of the coupled states by 15% compared with the joint approach. Furthermore, the dual estimation is proven to be very effective computationally, recovering accurate estimates at a reasonable cost. © 2013 Elsevier Ltd.en
dc.description.sponsorshipThis paper is based on work supported in part by funds from the KAUST GCR Collaborative Fellow program.en
dc.publisherElsevier BVen
dc.subjectDual states estimationen
dc.subjectEnsemble Kalman filteren
dc.subjectFlow and transport coupled modelsen
dc.subjectJoint states estimationen
dc.titleDual states estimation of a subsurface flow-transport coupled model using ensemble Kalman filteringen
dc.typeArticleen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentEarth Fluid Modeling and Prediction Groupen
dc.contributor.departmentEarth Sciences and Engineering Programen
dc.identifier.journalAdvances in Water Resourcesen
dc.contributor.institutionSubsurface and Groundwater Systems, Deltares, Princetonlaan 6, Utrecht, 3584 CB, Netherlandsen
kaust.authorEl Gharamti, Mohamaden
kaust.authorHoteit, Ibrahimen
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