A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model
As the sigma-p coordinate under hydrostatic approximation can be interpreted as the mass coordinate with out the hydro static approximation, we propose a method that up grades a hydro static model to a nonhydrostatic model with relatively less effort. The method adds to the primitive equations the e...
| Main Authors: | , , , , , , , , |
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| Format: | Article |
| Language: | English |
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Springer
2009-01-01
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| Series: | Terrestrial, Atmospheric and Oceanic Sciences |
| Subjects: | |
| Online Access: |
http://tao.cgu.org.tw/images/attachments/v205p727.pdf
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| _version_ | 1828364176426270720 |
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| author | Chi-Sann Liou Yang-Fan Sheng Tzay-Ming Leou Shwu-Ching Lin Tien-Chiang Yeh Chuen-Teyr Terng Der-Song Chen Kang-Ning Huang Mei-Yu Chang |
| author_facet | Chi-Sann Liou Yang-Fan Sheng Tzay-Ming Leou Shwu-Ching Lin Tien-Chiang Yeh Chuen-Teyr Terng Der-Song Chen Kang-Ning Huang Mei-Yu Chang |
| author_sort | Chi-Sann Liou |
| collection | DOAJ |
| description | As the sigma-p coordinate under hydrostatic approximation can be interpreted as the mass coordinate with out the hydro static approximation, we propose a method that up grades a hydro static model to a nonhydrostatic model with relatively less effort. The method adds to the primitive equations the extra terms omitted by the hydro static approximation and two prognostic equations for vertical speed w and nonhydrostatic part pres sure p'. With properly formulated governing equations, at each time step, the dynamic part of the model is first integrated as that for the original hydro static model and then nonhydrostatic contributions are added as corrections to the hydro static solutions. In applying physical parameterizations after the dynamic part integration, all physics pack ages of the original hydro static model can be directly used in the nonhydrostatic model, since the up graded nonhydrostatic model shares the same vertical coordinates with the original hydro static model. In this way, the majority codes of the nonhydrostatic model come from the original hydro static model. The extra codes are only needed for the calculation additional to the primitive equations. In order to handle sound waves, we use smaller time steps in the nonhydrostatic part dynamic time integration with a split-explicit scheme for horizontal momentum and temperature and a semi-implicit scheme for w and p'. Simulations of 2-dimensional mountain waves and density flows associated with a cold bubble have been used to test the method. The idealized case tests demonstrate that the pro posed method realistically simulates the nonhydrostatic effects on different atmospheric circulations that are revealed in the oretical solutions and simulations from other nonhydrostatic models. This method can be used in upgrading any global or mesoscale models from a hydrostatic to nonhydrostatic model. |
| first_indexed | 2024-04-14T05:12:16Z |
| format | Article |
| id | doaj.art-07d8fe980735495b9aa484308d6ac78f |
| institution | Directory Open Access Journal |
| issn | 1017-0839 2311-7680 |
| language | English |
| last_indexed | 2024-04-14T05:12:16Z |
| publishDate | 2009-01-01 |
| publisher | Springer |
| record_format | Article |
| series | Terrestrial, Atmospheric and Oceanic Sciences |
| spelling | doaj.art-07d8fe980735495b9aa484308d6ac78f2022-12-22T02:10:30ZengSpringerTerrestrial, Atmospheric and Oceanic Sciences1017-08392311-76802009-01-0120572710.3319/TAO.2008.09.24.01(A)871A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic ModelChi-Sann LiouYang-Fan ShengTzay-Ming LeouShwu-Ching LinTien-Chiang YehChuen-Teyr TerngDer-Song ChenKang-Ning HuangMei-Yu ChangAs the sigma-p coordinate under hydrostatic approximation can be interpreted as the mass coordinate with out the hydro static approximation, we propose a method that up grades a hydro static model to a nonhydrostatic model with relatively less effort. The method adds to the primitive equations the extra terms omitted by the hydro static approximation and two prognostic equations for vertical speed w and nonhydrostatic part pres sure p'. With properly formulated governing equations, at each time step, the dynamic part of the model is first integrated as that for the original hydro static model and then nonhydrostatic contributions are added as corrections to the hydro static solutions. In applying physical parameterizations after the dynamic part integration, all physics pack ages of the original hydro static model can be directly used in the nonhydrostatic model, since the up graded nonhydrostatic model shares the same vertical coordinates with the original hydro static model. In this way, the majority codes of the nonhydrostatic model come from the original hydro static model. The extra codes are only needed for the calculation additional to the primitive equations. In order to handle sound waves, we use smaller time steps in the nonhydrostatic part dynamic time integration with a split-explicit scheme for horizontal momentum and temperature and a semi-implicit scheme for w and p'. Simulations of 2-dimensional mountain waves and density flows associated with a cold bubble have been used to test the method. The idealized case tests demonstrate that the pro posed method realistically simulates the nonhydrostatic effects on different atmospheric circulations that are revealed in the oretical solutions and simulations from other nonhydrostatic models. This method can be used in upgrading any global or mesoscale models from a hydrostatic to nonhydrostatic model. http://tao.cgu.org.tw/images/attachments/v205p727.pdf Nonhydrostatic modelHydrostatic to nonhydrostatic |
| spellingShingle | Chi-Sann Liou Yang-Fan Sheng Tzay-Ming Leou Shwu-Ching Lin Tien-Chiang Yeh Chuen-Teyr Terng Der-Song Chen Kang-Ning Huang Mei-Yu Chang A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model Terrestrial, Atmospheric and Oceanic Sciences Nonhydrostatic model Hydrostatic to nonhydrostatic |
| title | A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model |
| title_full | A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model |
| title_fullStr | A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model |
| title_full_unstemmed | A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model |
| title_short | A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model |
| title_sort | method of upgrading a hydrostatic model to a nonhydrostatic model |
| topic | Nonhydrostatic model Hydrostatic to nonhydrostatic |
| url |
http://tao.cgu.org.tw/images/attachments/v205p727.pdf
|
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