Application of adjoint method to the evaluation of temporal and spatial variations of the eddy viscosity coefficient
This study investigated the temporal and spatial variations of the eddy viscosity coefficient (EVC) in an Ekman model using an adjoint method. The time- and depth-dependent EVC was represented as a Fourier series, which consisted of four summations. The effectiveness of the model was significantly i...
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| Vydáno v: | Frontiers in Marine Science Ročník 12 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Frontiers Media S.A
16.05.2025
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| ISSN: | 2296-7745, 2296-7745 |
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| Abstract | This study investigated the temporal and spatial variations of the eddy viscosity coefficient (EVC) in an Ekman model using an adjoint method. The time- and depth-dependent EVC was represented as a Fourier series, which consisted of four summations. The effectiveness of the model was significantly influenced by the number of terms included in each summation. In the first three groups of ideal experiments, a constant drag coefficient was used at low surface wind speeds. An analysis of the inversion results indicated that more terms should be added to each summation if the EVC varied over shorter periods, whether in time or depth. Additionally, the findings indicated that the model performed better when simulating the time- and depth-dependent EVC over longer periods. Two additional groups of ideal experiments were conducted to investigate the impact of near-surface wind speeds on the inversion of the K-Profile EVC. The drag coefficient associated with wind speeds over time was utilized in these experiments. An analysis of the inversion results indicated that the model effectively captured the temporal and spatial distribution of the EVC. Finally, the EVC was simulated during a super typhoon. The evaluation of the simulated EVC and ocean currents suggested that greater values of the simulated EVC appear at depths ranging from 50 to 65 m under strong wind conditions. Variations in wind directions could further enhance the inverted EVC within the Ekman layer. |
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| AbstractList | This study investigated the temporal and spatial variations of the eddy viscosity coefficient (EVC) in an Ekman model using an adjoint method. The time- and depth-dependent EVC was represented as a Fourier series, which consisted of four summations. The effectiveness of the model was significantly influenced by the number of terms included in each summation. In the first three groups of ideal experiments, a constant drag coefficient was used at low surface wind speeds. An analysis of the inversion results indicated that more terms should be added to each summation if the EVC varied over shorter periods, whether in time or depth. Additionally, the findings indicated that the model performed better when simulating the time- and depth-dependent EVC over longer periods. Two additional groups of ideal experiments were conducted to investigate the impact of near-surface wind speeds on the inversion of the K-Profile EVC. The drag coefficient associated with wind speeds over time was utilized in these experiments. An analysis of the inversion results indicated that the model effectively captured the temporal and spatial distribution of the EVC. Finally, the EVC was simulated during a super typhoon. The evaluation of the simulated EVC and ocean currents suggested that greater values of the simulated EVC appear at depths ranging from 50 to 65 m under strong wind conditions. Variations in wind directions could further enhance the inverted EVC within the Ekman layer. |
| Author | Zhang, Ting |
| Author_xml | – sequence: 1 givenname: Ting surname: Zhang fullname: Zhang, Ting |
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| Cites_doi | 10.3389/fmars.2023.1275565 10.1016/j.cpc.2009.10.024 10.1016/j.cma.2010.06.014 10.3390/jmse9111220 10.1029/2018JC01375 10.1017/S0022112075001814 10.1175/JPO-D-12-07.1 10.1002/2013JC009661 10.1088/0034-4885/59/10/001 10.1155/2015/309525 10.3390/jmse10081165 10.1016/j.dsr.2013.05.009 10.1175/1520-0485(1995)025<0019:SOTISC>2.0.CO;2 10.1007/BF01589116 10.1175/JPO-D-14-0115.1 10.1175/JTECH-D-14-00090.1 10.1155/2013/802136 10.3390/jmse11081487 10.1175/JTECH-D-17-0064.1 10.11759/hykx20180408002 10.1029/RG020i004p00851 10.1175/JTECH-D-18-0223.1 10.1016/j.nonrwa.2011.11.006 10.1002/pamm.200610269 10.1126/sciadv.abf4920 10.1175/1520-0485(1991)021,0709:VEOTWS.2.0.CO;2 10.1175/JTECH-D-18-0217.1 10.1145/355921.355933 10.1029/94RG01872 10.1007/s10546-010-9527-7 10.1029/2005JC002970 10.1175/1520-0493(1999)127,1497:IOPEOT.2.0.CO;2 10.1175/2008JPO3969.1 |
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| References | Wu (B24) 2021; 9 Large (B10) 1994; 32 Zhang (B30) 2015 Zhang (B32) 2010; 199 Launder (B11) 1975; 68 Luo (B14) 2023; 11 Rai (B19) 2021; 7 Wu (B25) 2022; 10 Lentz (B12) 1995; 25 Zhang (B29) 2023; 10 Yu (B28) 1991; 21 Yoshikawa (B27) 2015; 32 Zhang (B33) 2009 Guan (B5) 2014; 119 Zhang (B31) 2019; 36 Shanno (B21) 1980; 6 Anderson (B1) 1996; 59 Liu (B13) 1989; 45 Nie (B17) 2019; 36 Wirth (B23) 2010; 137 Kudryavtsev (B9) 2006; 111 Zhu (B34) 1999; 127 Kazantsev (B7) 2012; 13 Obermeier (B18) 2006; 6 Roach (B20) 2015; 45 Cao (B2) 2017; 34 Hülsmann (B6) 2010; 181 Kirincich (B8) 2009; 39 Cao (B3) 2018; 123 Mellor (B16) 1982; 20 Chen (B4) 2013 McWilliams (B15) 2012; 42 Song (B22) 2013; 80 Yi (B26) 2018; 42 |
| References_xml | – volume: 10 year: 2023 ident: B29 article-title: Features of upper ocean and surface waves during the passage of super typhoon Hinnamnor (2022) publication-title: Front. Marine Sci. doi: 10.3389/fmars.2023.1275565 – volume: 181 start-page: 499 year: 2010 ident: B6 article-title: GROW: A gradient-based optimization workflow forthe automated development of molecular models publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2009.10.024 – volume: 199 start-page: 3125 year: 2010 ident: B32 article-title: Inversion of three-dimensional tidal currents in marginal seas by assimilating satellite altimetry publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2010.06.014 – volume: 9 year: 2021 ident: B24 article-title: A scheme for estimating time-varying wind stress drag coefficient in the ekman model with adjoint assimilation publication-title: J. Mar. Sci. Eng. doi: 10.3390/jmse9111220 – volume: 123 start-page: 5026 year: 2018 ident: B3 article-title: Near-inertial waves and their underlying mechanisms based on the South China Sea Internal Wave Experiment, (2010-2011) publication-title: J. Geophysical Research: Oceans. doi: 10.1029/2018JC01375 – volume: 68 start-page: 537 year: 1975 ident: B11 article-title: Progress in the development of a Reynolds-stress turbulence closure publication-title: J. Fluid Mech. doi: 10.1017/S0022112075001814 – volume: 42 start-page: 1793 year: 2012 ident: B15 article-title: The wavy Ekman layer: Langmuir circulations, breaking waves, and Reynolds stress publication-title: J. Phys. Oceanogr. doi: 10.1175/JPO-D-12-07.1 – start-page: 9 year: 2009 ident: B33 article-title: Estimation of eddy viscosity on the South China Sea shelf with adjoint assimilation method publication-title: Acta Oceanologica Sinica. – volume: 119 start-page: 3134 year: 2014 ident: B5 article-title: Observed upper ocean response to typhoon Megi, (2010) in the northern south China sea publication-title: J. Geophys. Res. Oceans doi: 10.1002/2013JC009661 – volume: 59 start-page: 1209 year: 1996 ident: B1 article-title: Data assimilation in ocean models publication-title: Rep. Prog. Phys. doi: 10.1088/0034-4885/59/10/001 – start-page: 1-11, ID309525. year: 2015 ident: B30 article-title: Estimation of oceanic eddy viscosity profile and wind stress drag coefficient using adjoint method publication-title: Math. Probl. Eng. doi: 10.1155/2015/309525 – volume: 10 year: 2022 ident: B25 article-title: Application of the trigonometric polynomial interpolation for the estimation of the vertical eddy viscosity coefficient based on the ekman adjoint assimilation model publication-title: J. Mar. Sci. Eng. doi: 10.3390/jmse10081165 – volume: 80 start-page: 58 year: 2013 ident: B22 article-title: Wave-modified Ekman current solutions for the vertical eddy viscosity formulated by K-Profile Parameterization scheme publication-title: Deep Sea Res. Part I: Oceanographic Res. Papers doi: 10.1016/j.dsr.2013.05.009 – volume: 25 start-page: 19 year: 1995 ident: B12 article-title: Sensitivity of the inner-shelf circulation to the form of the eddy viscosity profile publication-title: J. Phys. Oceanography doi: 10.1175/1520-0485(1995)025<0019:SOTISC>2.0.CO;2 – volume: 45 start-page: 503 year: 1989 ident: B13 article-title: On the limited memory BFGS method for large scale optimization publication-title: Math. Program. doi: 10.1007/BF01589116 – volume: 45 start-page: 1205 year: 2015 ident: B20 article-title: Detecting and characterizing Ekman currents in the Southern Ocean publication-title: J. Phys. Oceanogr. doi: 10.1175/JPO-D-14-0115.1 – volume: 32 start-page: 793 year: 2015 ident: B27 article-title: Estimating the eddy viscosity profile from velocity spirals in the Ekman boundary layer publication-title: J. Atmos. Oceanic Technol. doi: 10.1175/JTECH-D-14-00090.1 – start-page: ID802136 year: 2013 ident: B4 article-title: Estimation of open boundary conditions for an internal tidal model with an adjoint method: A comparative study on optimization methods publication-title: Math. Probl. Eng. doi: 10.1155/2013/802136 – volume: 11 year: 2023 ident: B14 article-title: A study of wind stress effects on the vertical eddy viscosity coefficient using the ekman model with data assimilation publication-title: J. Marine Sci. Engineering. doi: 10.3390/jmse11081487 – volume: 34 start-page: 2163 year: 2017 ident: B2 article-title: Estimation of eddy viscosity profile in the bottom Ekman boundary layer publication-title: J. Atmospheric Oceanic Technology. doi: 10.1175/JTECH-D-17-0064.1 – volume: 42 start-page: 71 year: 2018 ident: B26 article-title: Estimation of the time-varying vertical eddy viscosity coefficient in an ekman layer model through the adjoint data assimilation approach publication-title: Mar. Sci. doi: 10.11759/hykx20180408002 – volume: 20 start-page: 851 year: 1982 ident: B16 article-title: Development of a turbulence closure model for geophysical fluid problems publication-title: Rev. Geophys. Space Phys. doi: 10.1029/RG020i004p00851 – volume: 36 start-page: 1789 year: 2019 ident: B31 article-title: A method on estimating time-varying vertical eddy viscosity for an Ekman layer model with data assimilation publication-title: J. Atmospheric Oceanic Technology. doi: 10.1175/JTECH-D-18-0223.1 – volume: 13 start-page: 1416 year: 2012 ident: B7 article-title: Sensitivity of a shallow-water model to parameters publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2011.11.006 – volume: 6 start-page: 577 year: 2006 ident: B18 article-title: Prandtl’s mixing length model-Revisited. Proc publication-title: Appl. Math. Mech. doi: 10.1002/pamm.200610269 – volume: 7 start-page: 1 year: 2021 ident: B19 article-title: Scale of oceanic eddy killing by wind from global satellite observations publication-title: Sci. Adv. doi: 10.1126/sciadv.abf4920 – volume: 21 start-page: 709 year: 1991 ident: B28 article-title: Variational estimation of the wind stress drag coefficient and the oceanic eddy viscosity profile publication-title: J. Phys. Oceanogr. doi: 10.1175/1520-0485(1991)021,0709:VEOTWS.2.0.CO;2 – volume: 36 start-page: 1957 year: 2019 ident: B17 article-title: Acquiring the arctic-scale spatial distribution of snow depth based on AMSR-E snow depth product publication-title: J. Atmos. Ocean. Technol. doi: 10.1175/JTECH-D-18-0217.1 – volume: 6 start-page: 618 year: 1980 ident: B21 article-title: Remark on “Algorithm 500: Minimization of Unconstrained Multivariate Functions [E4]” publication-title: ACM Trans. Math. Softw. doi: 10.1145/355921.355933 – volume: 32 start-page: 363 year: 1994 ident: B10 article-title: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization publication-title: Rev. Geophys. doi: 10.1029/94RG01872 – volume: 137 start-page: 327 year: 2010 ident: B23 article-title: On the Ekman spiral with an anisotropic eddy viscosity publication-title: Bound. Layer Meteor. doi: 10.1007/s10546-010-9527-7 – volume: 111 start-page: C070120 year: 2006 ident: B9 article-title: On the effect of sea droplets on the atmospheric boundary layer publication-title: J. Geophys. Res. doi: 10.1029/2005JC002970 – volume: 127 start-page: 1497 year: 1999 ident: B34 article-title: Impact of parameter estimation on the performance of the FSU global spectral model using its fullphysics adjoint publication-title: Mon. Wea. Rev. doi: 10.1175/1520-0493(1999)127,1497:IOPEOT.2.0.CO;2 – volume: 39 start-page: 602 year: 2009 ident: B8 article-title: Time-varying across-shelf ekman transport and vertical eddy viscosity on the inner shelf publication-title: J. Phys. Oceanogr. doi: 10.1175/2008JPO3969.1 |
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| Title | Application of adjoint method to the evaluation of temporal and spatial variations of the eddy viscosity coefficient |
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