A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments

4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect mode...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Javier Amezcua [verfasserIn] Michael Goodliff [verfasserIn] Peter Jan Van Leeuwen [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	hybrid data assimilation ensemble-variational methods model error

Übergeordnetes Werk:	In: Tellus: Series A, Dynamic Meteorology and Oceanography - Stockholm University Press, 2012, 69(2017), 1
Übergeordnetes Werk:	volume:69 ; year:2017 ; number:1

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1080/16000870.2016.1271564

Katalog-ID:	DOAJ040440028

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allfields	10.1080/16000870.2016.1271564 doi (DE-627)DOAJ040440028 (DE-599)DOAJ8298b4917b2d4e8e86fb848dc517e5fd DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 Javier Amezcua verfasserin aut A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection. hybrid data assimilation ensemble-variational methods model error Oceanography Meteorology. Climatology Michael Goodliff verfasserin aut Peter Jan Van Leeuwen verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 69(2017), 1 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:69 year:2017 number:1 https://doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/article/8298b4917b2d4e8e86fb848dc517e5fd kostenfrei http://dx.doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/toc/1600-0870 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 69 2017 1
spelling	10.1080/16000870.2016.1271564 doi (DE-627)DOAJ040440028 (DE-599)DOAJ8298b4917b2d4e8e86fb848dc517e5fd DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 Javier Amezcua verfasserin aut A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection. hybrid data assimilation ensemble-variational methods model error Oceanography Meteorology. Climatology Michael Goodliff verfasserin aut Peter Jan Van Leeuwen verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 69(2017), 1 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:69 year:2017 number:1 https://doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/article/8298b4917b2d4e8e86fb848dc517e5fd kostenfrei http://dx.doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/toc/1600-0870 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 69 2017 1
allfields_unstemmed	10.1080/16000870.2016.1271564 doi (DE-627)DOAJ040440028 (DE-599)DOAJ8298b4917b2d4e8e86fb848dc517e5fd DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 Javier Amezcua verfasserin aut A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection. hybrid data assimilation ensemble-variational methods model error Oceanography Meteorology. Climatology Michael Goodliff verfasserin aut Peter Jan Van Leeuwen verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 69(2017), 1 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:69 year:2017 number:1 https://doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/article/8298b4917b2d4e8e86fb848dc517e5fd kostenfrei http://dx.doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/toc/1600-0870 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 69 2017 1
allfieldsGer	10.1080/16000870.2016.1271564 doi (DE-627)DOAJ040440028 (DE-599)DOAJ8298b4917b2d4e8e86fb848dc517e5fd DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 Javier Amezcua verfasserin aut A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection. hybrid data assimilation ensemble-variational methods model error Oceanography Meteorology. Climatology Michael Goodliff verfasserin aut Peter Jan Van Leeuwen verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 69(2017), 1 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:69 year:2017 number:1 https://doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/article/8298b4917b2d4e8e86fb848dc517e5fd kostenfrei http://dx.doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/toc/1600-0870 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 69 2017 1
allfieldsSound	10.1080/16000870.2016.1271564 doi (DE-627)DOAJ040440028 (DE-599)DOAJ8298b4917b2d4e8e86fb848dc517e5fd DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 Javier Amezcua verfasserin aut A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection. hybrid data assimilation ensemble-variational methods model error Oceanography Meteorology. Climatology Michael Goodliff verfasserin aut Peter Jan Van Leeuwen verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 69(2017), 1 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:69 year:2017 number:1 https://doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/article/8298b4917b2d4e8e86fb848dc517e5fd kostenfrei http://dx.doi.org/10.1080/16000870.2016.1271564 kostenfrei https://doaj.org/toc/1600-0870 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 69 2017 1
language	English
source	In Tellus: Series A, Dynamic Meteorology and Oceanography 69(2017), 1 volume:69 year:2017 number:1
sourceStr	In Tellus: Series A, Dynamic Meteorology and Oceanography 69(2017), 1 volume:69 year:2017 number:1
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	hybrid data assimilation ensemble-variational methods model error Oceanography Meteorology. Climatology
isfreeaccess_bool	true
container_title	Tellus: Series A, Dynamic Meteorology and Oceanography
authorswithroles_txt_mv	Javier Amezcua @@aut@@ Michael Goodliff @@aut@@ Peter Jan Van Leeuwen @@aut@@
publishDateDaySort_date	2017-01-01T00:00:00Z
hierarchy_top_id	324455895
id	DOAJ040440028
language_de	englisch
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callnumber-first	G - Geography, Anthropology, Recreation
author	Javier Amezcua
spellingShingle	Javier Amezcua misc GC1-1581 misc QC851-999 misc hybrid data assimilation misc ensemble-variational methods misc model error misc Oceanography misc Meteorology. Climatology A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments
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topic_title	GC1-1581 QC851-999 A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments hybrid data assimilation ensemble-variational methods model error
topic	misc GC1-1581 misc QC851-999 misc hybrid data assimilation misc ensemble-variational methods misc model error misc Oceanography misc Meteorology. Climatology
topic_unstemmed	misc GC1-1581 misc QC851-999 misc hybrid data assimilation misc ensemble-variational methods misc model error misc Oceanography misc Meteorology. Climatology
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title	A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments
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title_full	A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments
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author_browse	Javier Amezcua Michael Goodliff Peter Jan Van Leeuwen
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title_sort	weak-constraint 4densemblevar. part i: formulation and simple model experiments
callnumber	GC1-1581
title_auth	A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments
abstract	4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection.
abstractGer	4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection.
abstract_unstemmed	4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection.
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title_short	A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments
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A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments

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