Study on the adjoint method in data assimilation and the related problems
- 38 Downloads
It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observedM 2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulateM 2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. the satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.
Key wordsdata assimilation variational analysis adjoint method tide open boundary condition
Chinese Library ClassificationP731.2
2000 Mathematics Subject Classification65K10 85A05
Unable to display preview. Download preview PDF.
- Thacker W C, Long R B. Fitting dynamics to data[J].Journal of Geophysical Research, 1988,93 (2):1227–1240.Google Scholar
- LÜ Xian-qing, ZHANG Jie. How to deduce the open boundary conditions by using the height of the water level (1,2) [J].Journal of Hydrodynamics, Ser A, 1999,14(4B):92–109. (in China)Google Scholar
- Seiler U. Estimation of open boundary conditions with the adjoint method[J].Journal of Geophysical Research, 1993,98(12):22855–22870.Google Scholar
- LÜ Xian-qing, FANG Guo-hong. Numerical experiments of the adjoint model forM 2 tide in the Bohai Sea[J].Acta Oceanologica Sinica, 2002,24(1):17–24. (in Chinese)Google Scholar
- LÜ Xian-qing, FANG Guo-hong. Inversion of the tides on the open boundary of the Bohai Sea by adjoint method[J].Chinese Journal of Oceanography and Limnology, 2002,33(2):113–120. (in Chinese)Google Scholar
- LÜ Xian-qing, WU Zi-ku, YIN Zhong-bin,et al. Inversion of the tide on the open boundaries of the Bohai, the Yellow and the East China Sea[J].Journal of Ocean University of China, 2003,33 (2):155–172. (in Chinese)Google Scholar
- WANG Kai, FANG Guo-hong, FENG Shi-zuo. A 3-D numerical simulation ofM 2 tides and tidal currents in the Bohai Sea, the Yellow Sea and the East China Sea[J].Acta Oceanologica Sinica, 1999,21(4):1–13. (in Chinese)Google Scholar