Studies On Adjoint Method For Ocean Numerical Modeling

Application of Data Assimilation in Physical Oceanography was studied in this report. Much attention was paid to the adjoint method. The main results are summarized as follows: 1. The elementary problem of adjoint method is how to obtain the gradient of cost function with respect to the control variables. Some new points were proposed in applying adjoint to problems in physical oceanography: (1) The method to obtain the gradient of cost function with respect to the control variables can't be limited to the adjoint of model. (2) The time to integrate adjoint equations can be shortened. According to our study, it is not reasonable that one can only use the adjoint of the finite difference equation in data assimilation. The simulated numerical experiments show that the adjoint of the differential equation should attract much attention. 2. A variational optimal control technique is used to assimilate both meteorological and oceanographic (sea surface current and subsurface current) observations into an oceanic Ekman layer model. An identical twin experiment is discussed. By fitting the model results to the data, the unknown boundary condition (the wind stress drag coefficient) and the unknown vertical eddy viscosity distribution are deduced simultaneously from the data. 3. To simulate m1 and M 2 tides in the Bohai Sea, adjoint method was used to deduce the open boundary conditions and the bottom friction coefficients of the Bohai Sea by using the harmonic constants at 19 tide stations in the interior of the region. The results in the numerical simulation coincide with m1 and M 2 tides observed in the Bohai Sea. 4. Adjoint method was used to deduce M 2 tidal harmonic constants on the open boundary of the Bohai Sea by using M 2 tidal harmonic constants in the interior region: harmonic constants at 19 tidal stations and at some points on the T/P Satellite Tracks, Both of them or one of them. To improve the results of numerical simulation, both the prescribed bottom friction coefficients and the water depths were also adjusted by adjoint assimilation. The results in the experiments coincide with the observed M 2 tide in the Bohai Sea fairly well.