The Study Of The Inversion Of The Bottom Friction Coefficient Of The Bohai Sea,the Huanghai Sea And The East China Sea

In the numerical models of tidal flows, how to deal with the bottom friction coefficient is a very important problem, which has not been solved by now. In the traditional numerical simulation, the bottom friction coefficient has been treated as a constant or different constant in different region. The calibration of the bottom friction coefficient depends on the experiences and subject estimation, too much work to be done for the satisfying results. Adjoint method could change the treatment of the bottom friction coefficients to a process of the numerical iteration which depending on the results of the observation. It realizes the automation of the treatment of the bottom friction coefficients.In this paper, under the condition that the M2 tidal harmonic constants at the open boundaries are fixed, adjoint method is used to inverse the prescribed bottom friction coefficient of the Bohai Sea, the Huanghai Sea and the East China Sea. The data used in the work is M2 tidal harmonic constants at 584 points under Topex/Poseidon tracks.In this paper, a series of twin experiments including 4 inversion strategies have been done, and the 4 strategies contain: 1. the bottom friction coefficient is supposed a constant, 2. the bottom friction coefficient is can be presented by 4 dependent variables, 3. one independent bottom friction coefficient from each 1°×1° area, and the bottom friction coefficient of other grids is obtained through linear interpolation with the independent bottom friction coefficient, 4. the bottom friction coefficients are supposed to be different in different points. In the above twin experiment, 4 kinds distribution of the bottom friction coefficient are given, including 1. constant, 2. curve surface which can be presented by 4 dependent variables, 3. conical surface, 4. revolution parabolic surface.Twin experiments show that while the inversion strategy close to the prescribed bottom friction coefficient, the inversion result is good. And while the inversion strategy is identity with the prescribed bottom friction coefficient, the inversion result is much better. Twin experiments show that the adjoint method can inverse the prescribed bottom friction coefficients perfectly.On the basis of the twin experiments, practical experiments including 4 strategies have been done and the results are analyzed and compared with each other. The results show that the more independent variables, the better results have been made. The strategy 4 in this paper efficiently increases the precision of the numerical simulation, and its results coincide with the observed M2 tide in the Bohai Sea, the Huanghai Sea and the East China Sea fairly well.From the bottom friction coefficient distribution obtained in PE4, it can be seen that in the area far from land and island, the deeper water corresponds to bigger bottom friction coefficient, and the shallower water corresponds to smaller BFC, which coincides to the traditional theory. But in the area near the land and island, the spatial variation of BFC is complicated, even shallow water corresponds to big bottom friction coefficient. This contradicts the traditional theory, but it may illuminate the matter of the bottom friction coefficient.