A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere
Identifieur interne : 001879 ( Istex/Corpus ); précédent : 001878; suivant : 001880A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere
Auteurs : X. Chen ; S. Akella ; I. M. NavonSource :
- International Journal for Numerical Methods in Fluids [ 0271-2091 ] ; 2012-01-30.
English descriptors
- KwdEn :
Abstract
In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.
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DOI: 10.1002/fld.2523
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<front><div type="abstract" xml:lang="en">In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.</div>
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<abstract xml:lang="en"><p>In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.</p>
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<familyName>Navon</familyName>
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<contactDetails><email>inavon@fsu.edu</email>
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<affiliationGroup><affiliation xml:id="af1" countryCode="US" type="organization"><unparsedAffiliation>Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.</unparsedAffiliation>
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<affiliation xml:id="af2" countryCode="US" type="organization"><unparsedAffiliation>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, U.S.A.</unparsedAffiliation>
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<affiliation xml:id="af3" countryCode="US" type="organization"><unparsedAffiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.</unparsedAffiliation>
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<keywordGroup xml:lang="en" type="author"><keyword xml:id="kwd1">proper orthogonal decomposition</keyword>
<keyword xml:id="kwd2">4‐D Var</keyword>
<keyword xml:id="kwd3">finite volume</keyword>
<keyword xml:id="kwd4">shallow water equations</keyword>
<keyword xml:id="kwd5">trust‐region method</keyword>
<keyword xml:id="kwd6">inverse problem</keyword>
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<abstractGroup><abstract type="main" xml:lang="en"><title type="main">Abstract</title>
<p>In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen <i>et al.</i>
(<i>Int. J. Numer. Meth. Fluids</i>
2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.</p>
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<mods version="3.6"><titleInfo lang="en"><title>A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title>
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<titleInfo type="abbreviated" lang="en"><title>A DUAL‐WEIGHTED TRUST‐REGION ADAPTIVE POD 4‐D VAR</title>
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<titleInfo type="alternative" contentType="CDATA" lang="en"><title>A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title>
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<name type="personal"><namePart type="given">X.</namePart>
<namePart type="family">Chen</namePart>
<affiliation>Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.</affiliation>
<role><roleTerm type="text">author</roleTerm>
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<name type="personal"><namePart type="given">S.</namePart>
<namePart type="family">Akella</namePart>
<affiliation>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, U.S.A.</affiliation>
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<name type="personal"><namePart type="given">I. M.</namePart>
<namePart type="family">Navon</namePart>
<affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.</affiliation>
<affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.===</affiliation>
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<originInfo><publisher>John Wiley & Sons, Ltd.</publisher>
<place><placeTerm type="text">Chichester, UK</placeTerm>
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<dateIssued encoding="w3cdtf">2012-01-30</dateIssued>
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<abstract lang="en">In this paper we study solutions of an inverse problem for a global shallow water model controlling its initial conditions specified from the 40‐yr ECMWF Re‐analysis (ERA‐40) data sets, in the presence of full or incomplete observations being assimilated in a time interval (window of assimilation) with or without background error covariance terms. As an extension of the work by Chen et al. (Int. J. Numer. Meth. Fluids 2009), we attempt to obtain a reduced order model of the above inverse problem, based on proper orthogonal decomposition (POD), referred to as POD 4D‐Var for a finite volume global shallow water equation model based on the Lin–Rood flux‐form semi‐Lagrangian semi‐implicit time integration scheme. Different approaches of POD implementation for the reduced inverse problem are compared, including a dual‐weighted method for snapshot selection coupled with a trust‐region POD adaptivity approach. Numerical results with various observational densities and background error covariance operator are also presented. The POD 4‐D Var model results combined with the trust‐region adaptivity exhibit similarity in terms of various error metrics to the full 4D Var results, but are obtained using a significantly lesser number of minimization iterations and require lesser CPU time. Based on our previous and current work, we conclude that POD 4‐D Var certainly warrants further studies, with promising potential of its extension to operational 3‐D numerical weather prediction models. Copyright © 2011 John Wiley & Sons, Ltd.</abstract>
<subject lang="en"><genre>keywords</genre>
<topic>proper orthogonal decomposition</topic>
<topic>4‐D Var</topic>
<topic>finite volume</topic>
<topic>shallow water equations</topic>
<topic>trust‐region method</topic>
<topic>inverse problem</topic>
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<relatedItem type="host"><titleInfo><title>International Journal for Numerical Methods in Fluids</title>
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<titleInfo type="abbreviated"><title>Int. J. Numer. Meth. Fluids</title>
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<topic>Research Article</topic>
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<identifier type="ISSN">0271-2091</identifier>
<identifier type="eISSN">1097-0363</identifier>
<identifier type="DOI">10.1002/(ISSN)1097-0363</identifier>
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<part><date>2012</date>
<detail type="volume"><caption>vol.</caption>
<number>68</number>
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<number>3</number>
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<extent unit="pages"><start>377</start>
<end>402</end>
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