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| Some theoretical problems on variational data assimilation | |
| 作者姓名： | 腾加俊 张瑰 黄思训 |
| 作者单位： | Shanghai Institute of Applied Mathematics and Mechanics Shanghai University，Department of Mathematics and Physics，Institute of Science，Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai 200072，P. R. China Department of Mathematics and Physics，Institute of Science，PLAUST，Nanjing 211101，P. R. China，PLAUST，Nanjing 211101，P. R. China，Shanghai 200072，P. R. China Institute of Meteorology，PLAUST，Nanjing 211101，P. R. China |
| 摘 要： | Theoretical aspects of variational data assimilation (VDA) for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the validity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed. |
| 关 键 词： | 变异数据 数据同化 理论问题 收敛 气象观测数据 |
| 收稿时间： | 2007-03-05 |
Some theoretical problems on variational data assimilation |
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| Teng?Jia-jun,Zhang?Gui,Huang?Si-xun.Some theoretical problems on variational data assimilation[J].Applied Mathematics and Mechanics(English Edition),2007,28(5):651-663. | |
| Authors: | Teng Jia-jun Zhang Gui Huang Si-xun |
| Institution: | 1. Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072,P.R.China;Department of Mathematics and Physics,Institute of Science,PLAUST, Nanjing 211101,P.R.China 2. Department of Mathematics and Physics,Institute of Science,PLAUST, Nanjing 211101,P.R.China 3. Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072,P.R.China;Institute of Meteorology,PLAUST,Nanjing 211101,P.R.China |
| Abstract: | Theoretical aspects of variational data assimilation (VDA) for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the validity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed. |
| Keywords: | variational data assimilation (VDA) regularization method estimates of convergence rate |
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