Complex step-based low-rank extended Kalman filtering for state-parameter estimation in subsurface transport models

Handle URI:
http://hdl.handle.net/10754/563368
Title:
Complex step-based low-rank extended Kalman filtering for state-parameter estimation in subsurface transport models
Authors:
El Gharamti, Mohamad ( 0000-0002-7229-8366 ) ; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Abstract:
The accuracy of groundwater flow and transport model predictions highly depends on our knowledge of subsurface physical parameters. Assimilation of contaminant concentration data from shallow dug wells could help improving model behavior, eventually resulting in better forecasts. In this paper, we propose a joint state-parameter estimation scheme which efficiently integrates a low-rank extended Kalman filtering technique, namely the Singular Evolutive Extended Kalman (SEEK) filter, with the prominent complex-step method (CSM). The SEEK filter avoids the prohibitive computational burden of the Extended Kalman filter by updating the forecast along the directions of error growth only, called filter correction directions. CSM is used within the SEEK filter to efficiently compute model derivatives with respect to the state and parameters along the filter correction directions. CSM is derived using complex Taylor expansion and is second order accurate. It is proven to guarantee accurate gradient computations with zero numerical round-off errors, but requires complexifying the numerical code. We perform twin-experiments to test the performance of the CSM-based SEEK for estimating the state and parameters of a subsurface contaminant transport model. We compare the efficiency and the accuracy of the proposed scheme with two standard finite difference-based SEEK filters as well as with the ensemble Kalman filter (EnKF). Assimilation results suggest that the use of the CSM in the context of the SEEK filter may provide up to 80% more accurate solutions when compared to standard finite difference schemes and is competitive with the EnKF, even providing more accurate results in certain situations. We analyze the results based on two different observation strategies. We also discuss the complexification of the numerical code and show that this could be efficiently implemented in the context of subsurface flow models. © 2013 Elsevier B.V.
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:
Journal of Hydrology
Issue Date:
Feb-2014
DOI:
10.1016/j.jhydrol.2013.12.004
Type:
Article
ISSN:
00221694
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.date.accessioned2015-08-03T11:46:51Zen
dc.date.available2015-08-03T11:46:51Zen
dc.date.issued2014-02en
dc.identifier.issn00221694en
dc.identifier.doi10.1016/j.jhydrol.2013.12.004en
dc.identifier.urihttp://hdl.handle.net/10754/563368en
dc.description.abstractThe accuracy of groundwater flow and transport model predictions highly depends on our knowledge of subsurface physical parameters. Assimilation of contaminant concentration data from shallow dug wells could help improving model behavior, eventually resulting in better forecasts. In this paper, we propose a joint state-parameter estimation scheme which efficiently integrates a low-rank extended Kalman filtering technique, namely the Singular Evolutive Extended Kalman (SEEK) filter, with the prominent complex-step method (CSM). The SEEK filter avoids the prohibitive computational burden of the Extended Kalman filter by updating the forecast along the directions of error growth only, called filter correction directions. CSM is used within the SEEK filter to efficiently compute model derivatives with respect to the state and parameters along the filter correction directions. CSM is derived using complex Taylor expansion and is second order accurate. It is proven to guarantee accurate gradient computations with zero numerical round-off errors, but requires complexifying the numerical code. We perform twin-experiments to test the performance of the CSM-based SEEK for estimating the state and parameters of a subsurface contaminant transport model. We compare the efficiency and the accuracy of the proposed scheme with two standard finite difference-based SEEK filters as well as with the ensemble Kalman filter (EnKF). Assimilation results suggest that the use of the CSM in the context of the SEEK filter may provide up to 80% more accurate solutions when compared to standard finite difference schemes and is competitive with the EnKF, even providing more accurate results in certain situations. We analyze the results based on two different observation strategies. We also discuss the complexification of the numerical code and show that this could be efficiently implemented in the context of subsurface flow models. © 2013 Elsevier B.V.en
dc.publisherElsevier BVen
dc.subjectComplex step approximationen
dc.subjectJoint state-parameter estimationen
dc.subjectLow-rank extended Kalman filteringen
dc.subjectSubsurface contaminant transporten
dc.titleComplex step-based low-rank extended Kalman filtering for state-parameter estimation in subsurface transport modelsen
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.journalJournal of Hydrologyen
kaust.authorEl Gharamti, Mohamaden
kaust.authorHoteit, Ibrahimen
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