Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases

Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternat...
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Autor*in:	R. A. Khan [verfasserIn] N. K.-R. Kevlahan [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling

Übergeordnetes Werk:	In: Tellus: Series A, Dynamic Meteorology and Oceanography - Stockholm University Press, 2012, 73(2021), 1, Seite 25
Übergeordnetes Werk:	volume:73 ; year:2021 ; number:1 ; pages:25

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1080/16000870.2021.1976907

Katalog-ID:	DOAJ040399273

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allfields	10.1080/16000870.2021.1976907 doi (DE-627)DOAJ040399273 (DE-599)DOAJ2397821e664f41c6a303e106e503b495 DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 R. A. Khan verfasserin aut Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries. bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling Oceanography Meteorology. Climatology N. K.-R. Kevlahan verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 73(2021), 1, Seite 25 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:73 year:2021 number:1 pages:25 https://doi.org/10.1080/16000870.2021.1976907 kostenfrei https://doaj.org/article/2397821e664f41c6a303e106e503b495 kostenfrei http://dx.doi.org/10.1080/16000870.2021.1976907 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_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 73 2021 1 25
spelling	10.1080/16000870.2021.1976907 doi (DE-627)DOAJ040399273 (DE-599)DOAJ2397821e664f41c6a303e106e503b495 DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 R. A. Khan verfasserin aut Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries. bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling Oceanography Meteorology. Climatology N. K.-R. Kevlahan verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 73(2021), 1, Seite 25 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:73 year:2021 number:1 pages:25 https://doi.org/10.1080/16000870.2021.1976907 kostenfrei https://doaj.org/article/2397821e664f41c6a303e106e503b495 kostenfrei http://dx.doi.org/10.1080/16000870.2021.1976907 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_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 73 2021 1 25
allfields_unstemmed	10.1080/16000870.2021.1976907 doi (DE-627)DOAJ040399273 (DE-599)DOAJ2397821e664f41c6a303e106e503b495 DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 R. A. Khan verfasserin aut Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries. bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling Oceanography Meteorology. Climatology N. K.-R. Kevlahan verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 73(2021), 1, Seite 25 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:73 year:2021 number:1 pages:25 https://doi.org/10.1080/16000870.2021.1976907 kostenfrei https://doaj.org/article/2397821e664f41c6a303e106e503b495 kostenfrei http://dx.doi.org/10.1080/16000870.2021.1976907 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_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 73 2021 1 25
allfieldsGer	10.1080/16000870.2021.1976907 doi (DE-627)DOAJ040399273 (DE-599)DOAJ2397821e664f41c6a303e106e503b495 DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 R. A. Khan verfasserin aut Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries. bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling Oceanography Meteorology. Climatology N. K.-R. Kevlahan verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 73(2021), 1, Seite 25 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:73 year:2021 number:1 pages:25 https://doi.org/10.1080/16000870.2021.1976907 kostenfrei https://doaj.org/article/2397821e664f41c6a303e106e503b495 kostenfrei http://dx.doi.org/10.1080/16000870.2021.1976907 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_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 73 2021 1 25
allfieldsSound	10.1080/16000870.2021.1976907 doi (DE-627)DOAJ040399273 (DE-599)DOAJ2397821e664f41c6a303e106e503b495 DE-627 ger DE-627 rakwb eng GC1-1581 QC851-999 R. A. Khan verfasserin aut Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries. bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling Oceanography Meteorology. Climatology N. K.-R. Kevlahan verfasserin aut In Tellus: Series A, Dynamic Meteorology and Oceanography Stockholm University Press, 2012 73(2021), 1, Seite 25 (DE-627)324455895 (DE-600)2026987-0 16000870 nnns volume:73 year:2021 number:1 pages:25 https://doi.org/10.1080/16000870.2021.1976907 kostenfrei https://doaj.org/article/2397821e664f41c6a303e106e503b495 kostenfrei http://dx.doi.org/10.1080/16000870.2021.1976907 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_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 73 2021 1 25
language	English
source	In Tellus: Series A, Dynamic Meteorology and Oceanography 73(2021), 1, Seite 25 volume:73 year:2021 number:1 pages:25
sourceStr	In Tellus: Series A, Dynamic Meteorology and Oceanography 73(2021), 1, Seite 25 volume:73 year:2021 number:1 pages:25
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling Oceanography Meteorology. Climatology
isfreeaccess_bool	true
container_title	Tellus: Series A, Dynamic Meteorology and Oceanography
authorswithroles_txt_mv	R. A. Khan @@aut@@ N. K.-R. Kevlahan @@aut@@
publishDateDaySort_date	2021-01-01T00:00:00Z
hierarchy_top_id	324455895
id	DOAJ040399273
language_de	englisch
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callnumber-first	G - Geography, Anthropology, Recreation
author	R. A. Khan
spellingShingle	R. A. Khan misc GC1-1581 misc QC851-999 misc bathymetry estimation misc density-based sensitivity analysis (dbsa) misc global sensitivity analysis (gsa) misc shallow water equations misc tsunami modelling misc Oceanography misc Meteorology. Climatology Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases
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topic_title	GC1-1581 QC851-999 Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases bathymetry estimation density-based sensitivity analysis (dbsa) global sensitivity analysis (gsa) shallow water equations tsunami modelling
topic	misc GC1-1581 misc QC851-999 misc bathymetry estimation misc density-based sensitivity analysis (dbsa) misc global sensitivity analysis (gsa) misc shallow water equations misc tsunami modelling misc Oceanography misc Meteorology. Climatology
topic_unstemmed	misc GC1-1581 misc QC851-999 misc bathymetry estimation misc density-based sensitivity analysis (dbsa) misc global sensitivity analysis (gsa) misc shallow water equations misc tsunami modelling misc Oceanography misc Meteorology. Climatology
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title	Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases
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title_full	Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases
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title_sort	variational assimilation of surface wave data for bathymetry reconstruction. part i: algorithm and test cases
callnumber	GC1-1581
title_auth	Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases
abstract	Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries.
abstractGer	Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries.
abstract_unstemmed	Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries.
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title_short	Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases
url	https://doi.org/10.1080/16000870.2021.1976907 https://doaj.org/article/2397821e664f41c6a303e106e503b495 http://dx.doi.org/10.1080/16000870.2021.1976907 https://doaj.org/toc/1600-0870
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Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases

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