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.
Url:
DOI: 10.1002/fld.2523
Links to Exploration step
ISTEX:A9170F582575C99D23E5ABA2EB9A2645984DB171Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title><author><name sortKey="Chen, X" sort="Chen, X" uniqKey="Chen X" first="X." last="Chen">X. Chen</name><affiliation><mods:affiliation>Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Akella, S" sort="Akella, S" uniqKey="Akella S" first="S." last="Akella">S. Akella</name><affiliation><mods:affiliation>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Navon, I M" sort="Navon, I M" uniqKey="Navon I" first="I. M." last="Navon">I. M. Navon</name><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.</mods:affiliation></affiliation><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.===</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:A9170F582575C99D23E5ABA2EB9A2645984DB171</idno><date when="2012" year="2012">2012</date><idno type="doi">10.1002/fld.2523</idno><idno type="url">https://api.istex.fr/document/A9170F582575C99D23E5ABA2EB9A2645984DB171/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001879</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001879</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title><author><name sortKey="Chen, X" sort="Chen, X" uniqKey="Chen X" first="X." last="Chen">X. Chen</name><affiliation><mods:affiliation>Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Akella, S" sort="Akella, S" uniqKey="Akella S" first="S." last="Akella">S. Akella</name><affiliation><mods:affiliation>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Navon, I M" sort="Navon, I M" uniqKey="Navon I" first="I. M." last="Navon">I. M. Navon</name><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.</mods:affiliation></affiliation><affiliation><mods:affiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.===</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">International Journal for Numerical Methods in Fluids</title><title level="j" type="abbrev">Int. J. Numer. Meth. Fluids</title><idno type="ISSN">0271-2091</idno><idno type="eISSN">1097-0363</idno><imprint><publisher>John Wiley & Sons, Ltd.</publisher><pubPlace>Chichester, UK</pubPlace><date type="published" when="2012-01-30">2012-01-30</date><biblScope unit="volume">68</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="377">377</biblScope><biblScope unit="page" to="402">402</biblScope></imprint><idno type="ISSN">0271-2091</idno></series><idno type="istex">A9170F582575C99D23E5ABA2EB9A2645984DB171</idno><idno type="DOI">10.1002/fld.2523</idno><idno type="ArticleID">FLD2523</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0271-2091</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>4‐D Var</term><term>finite volume</term><term>inverse problem</term><term>proper orthogonal decomposition</term><term>shallow water equations</term><term>trust‐region method</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><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></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>X. Chen</name><affiliations><json:string>Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.</json:string></affiliations></json:item><json:item><name>S. Akella</name><affiliations><json:string>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, U.S.A.</json:string></affiliations></json:item><json:item><name>I. M. Navon</name><affiliations><json:string>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.</json:string><json:string>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.===</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>proper orthogonal decomposition</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>4‐D Var</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>finite volume</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>shallow water equations</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>trust‐region method</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>inverse problem</value></json:item></subject><articleId><json:string>FLD2523</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>article</json:string></originalGenre><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.</abstract><qualityIndicators><score>7.772</score><pdfVersion>1.3</pdfVersion><pdfPageSize>593.887 x 782.362 pts</pdfPageSize><refBibsNative>true</refBibsNative><abstractCharCount>1538</abstractCharCount><pdfWordCount>11996</pdfWordCount><pdfCharCount>64468</pdfCharCount><pdfPageCount>26</pdfPageCount><abstractWordCount>231</abstractWordCount></qualityIndicators><title>A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title><refBibs><json:item><host><author></author><title>Tan WY. Shallow‐water Hydrodynamics: Mathematical Theory and Numerical Solution for a Two‐dimensional System of Shallow‐water Equations. Elsevier Oceanography Series: Beijing, 1992.</title></host></json:item><json:item><host><author></author><title>Vreugdenhil CB. Numerical Methods for Shallow‐Water Flow. Kluwer Academic Publishers: Boston, 1994.</title></host></json:item><json:item><author><json:item><name>J Galewsky</name></json:item><json:item><name>RK Cott</name></json:item><json:item><name>LM Polvani</name></json:item></author><host><volume>56</volume><pages><last>440</last><first>429</first></pages><issue>5</issue><author></author><title>Tellus</title></host><title>An initial‐value problem for testing numerical models of the global shallow‐water equations</title></json:item><json:item><author><json:item><name>SJ Lin</name></json:item><json:item><name>WC Chao</name></json:item><json:item><name>YC Sud</name></json:item><json:item><name>GK Walker</name></json:item></author><host><volume>122</volume><pages><last>1593</last><first>1575</first></pages><author></author><title>Monthly Weather Review</title></host><title>A class of the van Leer transport schemes and its applications to the moisture transport in a general circulation model</title></json:item><json:item><author><json:item><name>SJ Lin</name></json:item><json:item><name>RB Rood</name></json:item></author><host><volume>124</volume><pages><last>2070</last><first>2046</first></pages><author></author><title>Monthly Weather Review</title></host><title>Multidimensional flux‐form semi‐Lagrangian transport schemes</title></json:item><json:item><author><json:item><name>SJ Lin</name></json:item><json:item><name>RB Rood</name></json:item></author><host><volume>123</volume><pages><last>2498</last><first>2477</first></pages><author></author><title>Quarterly Journal of the Royal Meteorological Society</title></host><title>An explicit flux‐form semi‐Lagrangian shallow‐water model on the sphere</title></json:item><json:item><author><json:item><name>SJ Lin</name></json:item><json:item><name>RB Rood</name></json:item></author><host><volume>123</volume><pages><last>1762</last><first>1749</first></pages><author></author><title>Quarterly Journal of the Royal Meteorological Society</title></host><title>A finite‐volume integration method for computing pressure gradient force in general vertical coordinates</title></json:item><json:item><author><json:item><name>SJ Lin</name></json:item></author><host><volume>132</volume><pages><last>2307</last><first>2293</first></pages><author></author><title>Monthly Weather Review</title></host><title>A ‘vertically Lagrangian’ finite‐volume dynamical core for global models</title></json:item><json:item><author><json:item><name>X Chen</name></json:item><json:item><name>IM Navon</name></json:item></author><host><volume>18</volume><pages><last>62</last><first>41</first></pages><issue>1</issue><author></author><title>Studies in Informatics and Control</title></host><title>Optimal control of a finite‐element limited‐area shallow‐water equations model</title></json:item><json:item><author><json:item><name>X Chen</name></json:item><json:item><name>IM Navon</name></json:item><json:item><name>F Fang</name></json:item></author><host><author></author><title>International Journal for Numerical Methods in Fluids</title></host><title>A dual‐weighted trust‐region adaptive POD 4D‐Var applied to a finite‐element shallow‐water equations model</title></json:item><json:item><host><author></author><title>Holmes P, Lumley JL, Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge Monographs on Mechanics: London, 1996.</title></host></json:item><json:item><author><json:item><name>L Sirovich</name></json:item><json:item><name>JL Lumley</name></json:item><json:item><name>G Berkooz</name></json:item></author><host><volume>45</volume><pages><last>590</last><first>583</first></pages><issue>3</issue><author></author><title>Quarterly of Applied Mathematics</title></host><title>Turbulence and the dynamics of coherent structures, part III: dynamics and scaling</title></json:item><json:item><host><author></author><title>Karhunen K. Zur Spektral Theorie Stochastischer Prozesse. Annals of the New York Academy of Sciences: Fenicae, 1946.</title></host></json:item><json:item><host><author></author><title>Loeve M. Fonctions Aleatoires De Second Ordre. Comptes rendus de l'Acadmie des sciences: Paris, 1945.</title></host></json:item><json:item><author><json:item><name>K Pearson</name></json:item></author><host><volume>2</volume><pages><last>572</last><first>559</first></pages><issue>1</issue><author></author><title>Philosophical Magazine</title></host><title>On lines and planes of closest fit to systems of points in space</title></json:item><json:item><author><json:item><name>K Levenberg</name></json:item></author><host><volume>2</volume><pages><last>168</last><first>164</first></pages><author></author><title>Quarterly Journal on Applied Mathematics</title></host><title>A method for the solution of certain problems in least squares</title></json:item><json:item><host><author></author><title>Morrison DD. Proceedings of the Seminar on Tracking Programs and Orbit Determination. Jet Propulsion Laboratory, U.S.A., 1960.</title></host></json:item><json:item><author><json:item><name>D Marquardt</name></json:item></author><host><volume>11</volume><pages><last>441</last><first>431</first></pages><author></author><title>SIAM Journal on Applied Mathematics</title></host><title>An Algorithm for least‐squares estimation of nonlinear parameters</title></json:item><json:item><host><author></author><title>Winfield D. Function and Functional Optimization by Interpolation in Data Tables. Cambridge, U.S.A., 1969.</title></host></json:item><json:item><host><author></author><title>A fortran subroutine for solving systems of nonlinear algebraic equations</title></host></json:item><json:item><host><author></author><title>A fortran subroutine for unconstrained minimization requiring first derivatives of the objective function</title></host></json:item><json:item><author><json:item><name>JE Dennis Jr</name></json:item></author><host><volume>22</volume><author></author><title>Numerical Analysis</title></host><title>A brief introduction to quasi‐Newton methods</title></json:item><json:item><author><json:item><name>JJ More</name></json:item><json:item><name>DC Sorensen</name></json:item></author><host><volume>4</volume><pages><last>572</last><first>553</first></pages><issue>3</issue><author></author><title>SISSC</title></host><title>Computing a trust region step</title></json:item><json:item><host><author></author><title>Trust‐region methods for flow control based on reduced order modeling</title></host></json:item><json:item><host><author></author><title>Trust‐region proper orthogonal decomposition for flow control. Institute for Computer Applications in Science and Engineering</title></host></json:item><json:item><host><author></author><title>Control of the cylinder wake in the laminar regime by trust‐region methods and POD reduced order models</title></host></json:item><json:item><author><json:item><name>M Bergmann</name></json:item><json:item><name>L Cordier</name></json:item><json:item><name>JP Brancher</name></json:item></author><host><volume>95</volume><pages><last>324</last><first>309</first></pages><author></author><title>Notes on Numerical Fluid Mechanics and Multidisciplinary Design</title></host><title>Drag minimization of the cylinder wake by trust‐region proper orthogonal decomposition</title></json:item><json:item><author><json:item><name>M Bergmann</name></json:item><json:item><name>L Cordier</name></json:item></author><host><volume>227</volume><pages><last>7840</last><first>7813</first></pages><issue>16</issue><author></author><title>Journal of Computational Physics</title></host><title>Optimal control of the cylinder wake in the laminar regime by trust‐region methods and pod reduced‐order models</title></json:item><json:item><host><author></author><title>Conn AR, Gould NIM, Toint PL. Trust‐region Methods. SIAM: Philadelphia, 2000.</title></host></json:item><json:item><author><json:item><name>PL Toint</name></json:item></author><host><volume>8</volume><pages><last>252</last><first>231</first></pages><issue>2</issue><author></author><title>IMA Journal of Numerical Analysis</title></host><title>Global convergence of a class of trust‐region methods for nonconvex minimization in Hilbert space</title></json:item><json:item><author><json:item><name>S Gratton</name></json:item><json:item><name> Sarttenaer</name></json:item><json:item><name>PL Toint</name></json:item></author><host><volume>19</volume><pages><last>444</last><first>414</first></pages><issue>1</issue><author></author><title>SIAM Journal on Optimization</title></host><title>Recursive trust‐region methods for multiscale nonlinear optimization</title></json:item><json:item><host><author></author><title>Nocedal J, Wright SJ. Numerical Optimization (2nd edn). Springer Series in Operations Research and Financial Engineering, 2006.</title></host></json:item><json:item><author><json:item><name>T Bui‐Thanh</name></json:item><json:item><name>K Willcox</name></json:item><json:item><name>O Ghattas</name></json:item><json:item><name>B Van Bloemen Waander</name></json:item></author><host><volume>224</volume><pages><last>896</last><first>880</first></pages><issue>2</issue><author></author><title>Journal of Computational Physics</title></host><title>Goal‐oriented model constrained for reduction of large‐scale systems</title></json:item><json:item><author><json:item><name>DN Daescu</name></json:item><json:item><name>IM Navon</name></json:item></author><host><volume>53</volume><pages><last>1004</last><first>985</first></pages><issue>10</issue><author></author><title>International Journal for Numerical Methods in Fluids</title></host><title>Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation</title></json:item><json:item><author><json:item><name>DN Daescu</name></json:item><json:item><name>IM Navon</name></json:item></author><host><volume>136</volume><pages><last>1041</last><first>1026</first></pages><issue>3</issue><author></author><title>Monthly Weather Review</title></host><title>A dual‐weighted approach to order reduction in 4DVAR data assimilation</title></json:item><json:item><host><author></author><title>Adaptive control of a wake flow using proper orthogonal decomposition</title></host></json:item><json:item><author><json:item><name>M Hinze</name></json:item><json:item><name>K Kunish</name></json:item></author><host><volume>65</volume><pages><last>298</last><first>273</first></pages><author></author><title>Flow, Turbulence and Combustion</title></host><title>Three control methods for time‐dependent fluid flow</title></json:item><json:item><author><json:item><name>K Kunisch</name></json:item><json:item><name>S Volkwein</name></json:item></author><host><volume>90</volume><pages><last>148</last><first>117</first></pages><issue>1</issue><author></author><title>Numerische Mathematik</title></host><title>Galerkin proper orthogonal decomposition methods for parabolic problems</title></json:item><json:item><author><json:item><name>K Kunisch</name></json:item><json:item><name>S Volkwein</name></json:item></author><host><volume>40</volume><pages><last>515</last><first>492</first></pages><issue>2</issue><author></author><title>SIAM Journal on Numerical Analysis</title></host><title>Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics</title></json:item><json:item><author><json:item><name>K Kunish</name></json:item><json:item><name>S Volkwein</name></json:item></author><host><volume>42</volume><pages><last>23</last><first>1</first></pages><issue>1</issue><author></author><title>Mathematical Modelling and Numerical Analysis</title></host><title>Proper orthogonal decomposition for optimality systems</title></json:item><json:item><author><json:item><name>Y Cao</name></json:item><json:item><name>J Zhu</name></json:item><json:item><name>IM Navon</name></json:item><json:item><name>Z Luo</name></json:item></author><host><volume>53</volume><pages><last>1583</last><first>1571</first></pages><issue>10</issue><author></author><title>International Journal for Numerical Methods in Fluids</title></host><title>A reduced‐order approach to four‐dimensional variational data assimilation using proper orthogonal decomposition</title></json:item><json:item><author><json:item><name>F Fang</name></json:item><json:item><name>CC Pain</name></json:item><json:item><name>IM Navon</name></json:item><json:item><name>MD Piggott</name></json:item><json:item><name>GJ Gorman</name></json:item><json:item><name>P Allison</name></json:item><json:item><name>AJH Goddard</name></json:item></author><host><volume>59</volume><pages><last>851</last><first>827</first></pages><issue>8</issue><author></author><title>International Journal for Numerical Methods in Fluids</title></host><title>Reduced order modelling of an adaptive mesh ocean model</title></json:item><json:item><author><json:item><name>F Fang</name></json:item><json:item><name>CC Pain</name></json:item><json:item><name>IM Navon</name></json:item><json:item><name>MD Piggott</name></json:item><json:item><name>GJ Gorman</name></json:item><json:item><name>P Allison</name></json:item><json:item><name>AJH Goddard</name></json:item></author><host><volume>60</volume><pages><last>732</last><first>709</first></pages><issue>7</issue><author></author><title>International Journal for Numerical Methods in Fluids</title></host><title>A POD reduced order 4D‐Var adaptive mesh ocean modelling approach</title></json:item><json:item><author><json:item><name>PTM Vermeulen</name></json:item><json:item><name>AW Heemink</name></json:item></author><host><volume>134</volume><pages><last>2899</last><first>2888</first></pages><issue>10</issue><author></author><title>Monthly Weather Review</title></host><title>Model‐reduced variational data assimilation</title></json:item><json:item><author><json:item><name>Z Luo</name></json:item><json:item><name>Y Zhou</name></json:item><json:item><name>XZ Yang</name></json:item></author><host><volume>59</volume><pages><last>1946</last><first>1933</first></pages><issue>8</issue><author></author><title>Applied Numerical Mathematics</title></host><title>A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation</title></json:item><json:item><host><author></author><title>Reduced order models(POD) for calibration problems in finance</title></host></json:item><json:item><author><json:item><name>MU Altaf</name></json:item><json:item><name>AW Heemink</name></json:item><json:item><name>M Verlaan</name></json:item></author><host><author></author><title>International Journal for Multiscale Computational Engineering</title></host><title>Inverse shallow water flow modeling using model reduction</title></json:item><json:item><author><json:item><name>MF Barone</name></json:item><json:item><name>I Kalashnikova</name></json:item><json:item><name>DJ Segalman</name></json:item><json:item><name>HK Thornquist</name></json:item></author><host><volume>228</volume><pages><last>1946</last><first>1932</first></pages><issue>6</issue><author></author><title>Journal of Computational Physics</title></host><title>Stable Galerkin reduced order models for linearized compressible flow</title></json:item><json:item><author><json:item><name>CW Rowley</name></json:item><json:item><name>T Colonius</name></json:item><json:item><name>RM Murray</name></json:item></author><host><volume>189</volume><pages><last>129</last><first>115</first></pages><issue>1–2</issue><author></author><title>Physica D</title></host><title>Model reduction for compressible flows using POD and Galerkin projection</title></json:item><json:item><author><json:item><name>BR Noack</name></json:item><json:item><name>S Michael</name></json:item><json:item><name>M Morzynski</name></json:item><json:item><name>G Tadmor</name></json:item></author><host><volume>63</volume><pages><last>248</last><first>231</first></pages><issue>2</issue><author></author><title>International Journal for Numerical Methods in Engineering</title></host><title>System reduction strategy for Galerkin models of fluid flows</title></json:item><json:item><author><json:item><name>G Tadmor</name></json:item><json:item><name>O Lehmann</name></json:item><json:item><name>BR Noack</name></json:item><json:item><name>M Morzynski</name></json:item></author><host><volume>22</volume><issue>3</issue><author></author><title>Physics of Fluids</title></host><title>System reduction mean field Galerkin models for the natural and actuated cylinder wake flow</title></json:item><json:item><author><json:item><name>B Van Leer</name></json:item></author><host><volume>18</volume><pages><last>198</last><first>163</first></pages><author></author><title>Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics</title></host><title>Towards the ultimate conservative difference scheme I. The quest for monotonicity</title></json:item><json:item><author><json:item><name>B Van Leer</name></json:item></author><host><volume>23</volume><pages><last>299</last><first>276</first></pages><author></author><title>Journal of Computational Physics</title></host><title>Towards the ultimate conservative difference scheme: a new approach to numerical convection</title></json:item><json:item><author><json:item><name>B Van Leer</name></json:item></author><host><volume>32</volume><pages><last>136</last><first>101</first></pages><author></author><title>Journal of Computational Physics</title></host><title>Towards the ultimate conservative difference scheme: a second order sequel to Godunov's method</title></json:item><json:item><author><json:item><name>M Celis</name></json:item><json:item><name>JE Dennis</name></json:item><json:item><name>RA Tapia</name></json:item></author><host><pages><last>82</last><first>71</first></pages><author></author><title>Numerical Optimization 1984</title></host><title>A trust region strategy for nonlinear equality constrained optimization</title></json:item><json:item><host><author></author><title>Akella S. Deterministic and stochastic aspects of data assimilation. Ph.D. Thesis, 2006. Available from: http://etd.lib.fsu.edu/theses/available/etd‐04052006–192927/.</title></host></json:item><json:item><author><json:item><name>M Bergmann</name></json:item><json:item><name>C Bruneau</name></json:item><json:item><name>A Iollo</name></json:item></author><host><volume>228</volume><pages><last>538</last><first>516</first></pages><issue>2</issue><author></author><title>Journal of Computational Physics</title></host><title>Enablers for robust pod models</title></json:item><json:item><author><json:item><name>S Akella</name></json:item><json:item><name>IM Navon</name></json:item></author><host><volume>61</volume><pages><last>128</last><first>112</first></pages><issue>A</issue><author></author><title>Tellus</title></host><title>Different approaches to model error formulation in 4D‐Var: a study with high resolution advection schemes</title></json:item><json:item><author><json:item><name>DC Liu</name></json:item></author><host><volume>45</volume><pages><last>528</last><first>503</first></pages><author></author><title>Mathematical Programming</title></host><title>Nocedal, a limited memory algorithm for bound constrained optimization</title></json:item><json:item><author><json:item><name>RH Byrd</name></json:item><json:item><name>P Lu</name></json:item><json:item><name>J Nocedal</name></json:item></author><host><volume>16</volume><pages><last>1208</last><first>1190</first></pages><issue>5</issue><author></author><title>SIAM Journal on Scientific and Statistical Computing</title></host><title>On the limited memory BFGS method for large scale minimization</title></json:item><json:item><author><json:item><name>C Zhu</name></json:item><json:item><name>RH Byrd</name></json:item><json:item><name>J Nocedal</name></json:item></author><host><volume>23</volume><pages><last>560</last><first>550</first></pages><issue>4</issue><author></author><title>ACM Transactions on Mathematical Software</title></host><title>L‐BFGS‐B: Algorithm 778: L‐BFGS‐B, FORTRAN routines for large scale bound constrained optimization</title></json:item><json:item><author><json:item><name>RN Bannister</name></json:item></author><host><volume>134</volume><pages><last>1970</last><first>1951</first></pages><author></author><title>Quarterly Journal of the Royal Meteorological Society</title></host><title>A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances</title></json:item><json:item><host><author></author><title>Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods</title></host></json:item><json:item><author><json:item><name>S Chaturantabut</name></json:item><json:item><name>DC Sorensen</name></json:item><json:item><name>JC Steven</name></json:item></author><host><volume>32</volume><pages><last>2764</last><first>2737</first></pages><issue>5</issue><author></author><title>SIAM Journal on Scientific Computing</title></host><title>Nonlinear model reduction via discrete empirical interpolation</title></json:item><json:item><author><json:item><name>RK Anthony</name></json:item><json:item><name>S Chaturantabut</name></json:item><json:item><name>DC Sorensen</name></json:item></author><host><volume>28</volume><pages><last>494</last><first>477</first></pages><author></author><title>Journal of Computational Neuroscience</title></host><title>Morphologically accurate reduced order modeling of spiking neurons</title></json:item><json:item><author><json:item><name>X Zou</name></json:item><json:item><name>IM Navon</name></json:item><json:item><name>FX Le Dimet</name></json:item></author><host><volume>44</volume><pages><last>296</last><first>273</first></pages><issue>A</issue><author></author><title>Tellus</title></host><title>Incomplete observations and control of gravity waves in variational data assimilation</title></json:item><json:item><author><json:item><name>A Weaver</name></json:item><json:item><name>P Courtier</name></json:item></author><host><volume>121</volume><pages><last>1846</last><first>1815</first></pages><author></author><title>Quarterly Journal of the Royal Meteorological Society</title></host><title>Correlation modeling on the sphere using a generalized diffusion equation</title></json:item><json:item><author><json:item><name>JC Derber</name></json:item><json:item><name>F Bouttier</name></json:item></author><host><volume>51A</volume><pages><last>221</last><first>195</first></pages><author></author><title>Tellus</title></host><title>A reformulation of the background error covariance in the ECMWF global data assimilation</title></json:item></refBibs><genre><json:string>article</json:string></genre><host><volume>68</volume><publisherId><json:string>FLD</json:string></publisherId><pages><total>26</total><last>402</last><first>377</first></pages><issn><json:string>0271-2091</json:string></issn><issue>3</issue><subject><json:item><value>Research Article</value></json:item></subject><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1097-0363</json:string></eissn><title>International Journal for Numerical Methods in Fluids</title><doi><json:string>10.1002/(ISSN)1097-0363</json:string></doi></host><categories><wos><json:string>science</json:string><json:string>physics, fluids & plasmas</json:string><json:string>mechanics</json:string><json:string>mathematics, interdisciplinary applications</json:string><json:string>computer science, interdisciplinary applications</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>applied mathematics</json:string></scienceMetrix></categories><publicationDate>2012</publicationDate><copyrightDate>2012</copyrightDate><doi><json:string>10.1002/fld.2523</json:string></doi><id>A9170F582575C99D23E5ABA2EB9A2645984DB171</id><score>0.012684426</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/A9170F582575C99D23E5ABA2EB9A2645984DB171/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/A9170F582575C99D23E5ABA2EB9A2645984DB171/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/A9170F582575C99D23E5ABA2EB9A2645984DB171/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>John Wiley & Sons, Ltd.</publisher><pubPlace>Chichester, UK</pubPlace><availability><p>Copyright © 2011 John Wiley & Sons, Ltd.</p></availability><date>2012</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title><author xml:id="author-1"><persName><forename type="first">X.</forename><surname>Chen</surname></persName><affiliation>Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.</affiliation></author><author xml:id="author-2"><persName><forename type="first">S.</forename><surname>Akella</surname></persName><affiliation>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, U.S.A.</affiliation></author><author xml:id="author-3"><persName><forename type="first">I. M.</forename><surname>Navon</surname></persName><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></author></analytic><monogr><title level="j">International Journal for Numerical Methods in Fluids</title><title level="j" type="abbrev">Int. J. Numer. Meth. Fluids</title><idno type="pISSN">0271-2091</idno><idno type="eISSN">1097-0363</idno><idno type="DOI">10.1002/(ISSN)1097-0363</idno><imprint><publisher>John Wiley & Sons, Ltd.</publisher><pubPlace>Chichester, UK</pubPlace><date type="published" when="2012-01-30"></date><biblScope unit="volume">68</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="377">377</biblScope><biblScope unit="page" to="402">402</biblScope></imprint></monogr><idno type="istex">A9170F582575C99D23E5ABA2EB9A2645984DB171</idno><idno type="DOI">10.1002/fld.2523</idno><idno type="ArticleID">FLD2523</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2012</date></creation><langUsage><language ident="en">en</language></langUsage><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></abstract><textClass xml:lang="en"><keywords scheme="keyword"><list><head>keywords</head><item><term>proper orthogonal decomposition</term></item><item><term>4‐D Var</term></item><item><term>finite volume</term></item><item><term>shallow water equations</term></item><item><term>trust‐region method</term></item><item><term>inverse problem</term></item></list></keywords></textClass><textClass><keywords scheme="Journal Subject"><list><head>article-category</head><item><term>Research Article</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2010-08-04">Received</change><change when="2010-11-28">Registration</change><change when="2012-01-30">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/A9170F582575C99D23E5ABA2EB9A2645984DB171/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>John Wiley & Sons, Ltd.</publisherName><publisherLoc>Chichester, UK</publisherLoc></publisherInfo><doi registered="yes">10.1002/(ISSN)1097-0363</doi><issn type="print">0271-2091</issn><issn type="electronic">1097-0363</issn><idGroup><id type="product" value="FLD"></id></idGroup><titleGroup><title type="main" xml:lang="en" sort="INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS">International Journal for Numerical Methods in Fluids</title><title type="short">Int. J. Numer. Meth. Fluids</title></titleGroup></publicationMeta><publicationMeta level="part" position="30"><doi origin="wiley" registered="yes">10.1002/fld.v68.3</doi><numberingGroup><numbering type="journalVolume" number="68">68</numbering><numbering type="journalIssue">3</numbering></numberingGroup><coverDate startDate="2012-01-30">30 January 2012</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="70" status="forIssue"><doi origin="wiley" registered="yes">10.1002/fld.2523</doi><idGroup><id type="unit" value="FLD2523"></id></idGroup><countGroup><count type="pageTotal" number="26"></count></countGroup><titleGroup><title type="articleCategory">Research Article</title><title type="tocHeading1">Research Articles</title></titleGroup><copyright ownership="publisher">Copyright © 2011 John Wiley & Sons, Ltd.</copyright><eventGroup><event type="manuscriptReceived" date="2010-08-04"></event><event type="manuscriptRevised" date="2010-11-23"></event><event type="manuscriptAccepted" date="2010-11-28"></event><event type="xmlConverted" agent="Converter:JWSART34_TO_WML3G version:3.0.1 mode:FullText mathml2tex" date="2011-12-23"></event><event type="publishedOnlineEarlyUnpaginated" date="2011-01-31"></event><event type="firstOnline" date="2011-01-31"></event><event type="publishedOnlineFinalForm" date="2011-12-23"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:4.0.1" date="2014-03-12"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.3.4 mode:FullText" date="2015-02-24"></event></eventGroup><numberingGroup><numbering type="pageFirst">377</numbering><numbering type="pageLast">402</numbering></numberingGroup><correspondenceTo>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.===</correspondenceTo><objectNameGroup><objectName elementName="appendix">Appendix</objectName></objectNameGroup><linkGroup><link type="toTypesetVersion" href="file:FLD.FLD2523.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="figureTotal" number="15"></count><count type="tableTotal" number="1"></count><count type="referenceTotal" number="68"></count></countGroup><titleGroup><title type="main" xml:lang="en">A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere</title><title type="short" xml:lang="en">A DUAL‐WEIGHTED TRUST‐REGION ADAPTIVE POD 4‐D VAR</title></titleGroup><creators><creator xml:id="au1" creatorRole="author" affiliationRef="#af1"><personName><givenNames>X.</givenNames><familyName>Chen</familyName></personName></creator><creator xml:id="au2" creatorRole="author" affiliationRef="#af2"><personName><givenNames>S.</givenNames><familyName>Akella</familyName></personName></creator><creator xml:id="au3" creatorRole="author" affiliationRef="#af3" corresponding="yes"><personName><givenNames>I. M.</givenNames><familyName>Navon</familyName></personName><contactDetails><email>inavon@fsu.edu</email></contactDetails></creator></creators><affiliationGroup><affiliation xml:id="af1" countryCode="US" type="organization"><unparsedAffiliation>Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.</unparsedAffiliation></affiliation><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></affiliation><affiliation xml:id="af3" countryCode="US" type="organization"><unparsedAffiliation>Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, U.S.A.</unparsedAffiliation></affiliation></affiliationGroup><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></keywordGroup><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></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><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></titleInfo><titleInfo type="abbreviated" lang="en"><title>A DUAL‐WEIGHTED TRUST‐REGION ADAPTIVE POD 4‐D VAR</title></titleInfo><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></titleInfo><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></role></name><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><role><roleTerm type="text">author</roleTerm></role></name><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><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>John Wiley & Sons, Ltd.</publisher><place><placeTerm type="text">Chichester, UK</placeTerm></place><dateIssued encoding="w3cdtf">2012-01-30</dateIssued><dateCaptured encoding="w3cdtf">2010-08-04</dateCaptured><dateValid encoding="w3cdtf">2010-11-28</dateValid><copyrightDate encoding="w3cdtf">2012</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><extent unit="figures">15</extent><extent unit="tables">1</extent><extent unit="references">68</extent></physicalDescription><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></subject><relatedItem type="host"><titleInfo><title>International Journal for Numerical Methods in Fluids</title></titleInfo><titleInfo type="abbreviated"><title>Int. J. Numer. Meth. Fluids</title></titleInfo><genre type="journal">journal</genre><subject><genre>article-category</genre><topic>Research Article</topic></subject><identifier type="ISSN">0271-2091</identifier><identifier type="eISSN">1097-0363</identifier><identifier type="DOI">10.1002/(ISSN)1097-0363</identifier><identifier type="PublisherID">FLD</identifier><part><date>2012</date><detail type="volume"><caption>vol.</caption><number>68</number></detail><detail type="issue"><caption>no.</caption><number>3</number></detail><extent unit="pages"><start>377</start><end>402</end><total>26</total></extent></part></relatedItem><identifier type="istex">A9170F582575C99D23E5ABA2EB9A2645984DB171</identifier><identifier type="DOI">10.1002/fld.2523</identifier><identifier type="ArticleID">FLD2523</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 2011 John Wiley & Sons, Ltd.</accessCondition><recordInfo><recordContentSource>WILEY</recordContentSource><recordOrigin>John Wiley & Sons, Ltd.</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001879 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 001879 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Rhénanie
|area= UnivTrevesV1
|flux= Istex
|étape= Corpus
|type= RBID
|clé= ISTEX:A9170F582575C99D23E5ABA2EB9A2645984DB171
|texte= A dual‐weighted trust‐region adaptive POD 4‐D Var applied to a finite‐volume shallow water equations model on the sphere
}}
| This area was generated with Dilib version V0.6.31. |  |