Applied Mathematics and Mechanics

, Volume 25, Issue 6, pp 636–646 | Cite as

Study on the adjoint method in data assimilation and the related problems

  • Lü Xian-qing
  • Wu Zi-ku
  • Gu Yi
  • Tian Ji-wei


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 words

data assimilation variational analysis adjoint method tide open boundary condition 

Chinese Library Classification


2000 Mathematics Subject Classification

65K10 85A05 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2004

Authors and Affiliations

  • Lü Xian-qing
    • 1
    • 2
  • Wu Zi-ku
    • 1
    • 2
  • Gu Yi
    • 3
  • Tian Ji-wei
    • 1
    • 2
  1. 1.College of Physical and Environmental OceanographyOcean University of ChinaQingdaoP. R. China
  2. 2.Ministry of EducationKey Laboratory of Physical OceanographyQingdaoP.R. China
  3. 3.College of Information EngineeringQingdao UniversityQingdaoP.R. China

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