Variational Data Assimilation of Tides
This paper presents an incremental variational method to assimilate the observed tidal harmonic constants using a frequency domain linearized shallow water equation. A cost function was constructed with tidal boundary conditions and tidal forcing as its control (independent) variables. To minimize t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Journal of Marine Science and Engineering |
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| Online Access: | https://www.mdpi.com/2077-1312/8/1/54 |
| _version_ | 1818741012044972032 |
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| author | Lei Shi Liujuan Tang Edward Myers |
| author_facet | Lei Shi Liujuan Tang Edward Myers |
| author_sort | Lei Shi |
| collection | DOAJ |
| description | This paper presents an incremental variational method to assimilate the observed tidal harmonic constants using a frequency domain linearized shallow water equation. A cost function was constructed with tidal boundary conditions and tidal forcing as its control (independent) variables. To minimize the cost function, optimal boundary conditions and tidal forcing were derived using a conventional dual 4-Dimensional Variational (4D-Var) Physical-space Statistical Analysis System. The tangent linear and adjoint model were solved by using a finite element method. By adapting the incremental form, the variational method streamlines the workflow to provide the incremental correction to the boundary conditions and tidal forcing of a hydrodynamic forward model. The method was tested for semi-diurnal M<sub>2</sub> tides in a regional sea with a complex tidal system. The results demonstrate a 65−72% reduction of tidal harmonic constant vector error by assimilating the observed M<sub>2</sub> tidal harmonic constants. In addition to improving the tides of a hydrodynamic model by optimizing boundary conditions and tidal forcing, the method computes a spatially varying uncertainty of individual tidal constituents in the model. The method provides a versatile tool for mapping the spatially continuous tides and currents in coastal and estuarine waters by assimilating the harmonic constants of individual tidal constituents of observed tides and currents. |
| first_indexed | 2024-12-18T01:49:51Z |
| format | Article |
| id | doaj.art-ea24389b0a6f434090649778ac49fac7 |
| institution | Directory Open Access Journal |
| issn | 2077-1312 |
| language | English |
| last_indexed | 2024-12-18T01:49:51Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Marine Science and Engineering |
| spelling | doaj.art-ea24389b0a6f434090649778ac49fac72022-12-21T21:25:06ZengMDPI AGJournal of Marine Science and Engineering2077-13122020-01-01815410.3390/jmse8010054jmse8010054Variational Data Assimilation of TidesLei Shi0Liujuan Tang1Edward Myers2Coast Survey Development Laboratory, NOAA, Silver Spring, MD 20910, USAEarth Resources Technology, Laurel, MD 20707, USACoast Survey Development Laboratory, NOAA, Silver Spring, MD 20910, USAThis paper presents an incremental variational method to assimilate the observed tidal harmonic constants using a frequency domain linearized shallow water equation. A cost function was constructed with tidal boundary conditions and tidal forcing as its control (independent) variables. To minimize the cost function, optimal boundary conditions and tidal forcing were derived using a conventional dual 4-Dimensional Variational (4D-Var) Physical-space Statistical Analysis System. The tangent linear and adjoint model were solved by using a finite element method. By adapting the incremental form, the variational method streamlines the workflow to provide the incremental correction to the boundary conditions and tidal forcing of a hydrodynamic forward model. The method was tested for semi-diurnal M<sub>2</sub> tides in a regional sea with a complex tidal system. The results demonstrate a 65−72% reduction of tidal harmonic constant vector error by assimilating the observed M<sub>2</sub> tidal harmonic constants. In addition to improving the tides of a hydrodynamic model by optimizing boundary conditions and tidal forcing, the method computes a spatially varying uncertainty of individual tidal constituents in the model. The method provides a versatile tool for mapping the spatially continuous tides and currents in coastal and estuarine waters by assimilating the harmonic constants of individual tidal constituents of observed tides and currents.https://www.mdpi.com/2077-1312/8/1/54variational methodsweak constraintdata assimilationtidescurrentsharmonic constantstidal potentialbohai sea |
| spellingShingle | Lei Shi Liujuan Tang Edward Myers Variational Data Assimilation of Tides Journal of Marine Science and Engineering variational methods weak constraint data assimilation tides currents harmonic constants tidal potential bohai sea |
| title | Variational Data Assimilation of Tides |
| title_full | Variational Data Assimilation of Tides |
| title_fullStr | Variational Data Assimilation of Tides |
| title_full_unstemmed | Variational Data Assimilation of Tides |
| title_short | Variational Data Assimilation of Tides |
| title_sort | variational data assimilation of tides |
| topic | variational methods weak constraint data assimilation tides currents harmonic constants tidal potential bohai sea |
| url | https://www.mdpi.com/2077-1312/8/1/54 |
| work_keys_str_mv | AT leishi variationaldataassimilationoftides AT liujuantang variationaldataassimilationoftides AT edwardmyers variationaldataassimilationoftides |