Data Assimilation Of Tides In The Bohai Sea By Using The Adjoint Method

By using the variational method, the adjoint equations are derived from the 2-D tidal equations. And based on the Arakawa C grid, the finite deference schemes of the tidal and adjoint model are built. On the basis of the tidal and adjoint model, the adjoint numerical simulation of tidal components M2, S2, K1 and O1 in the Bohai Sea are achieved by using the harmonic constants at 19 tide gauge stations. The mean absolute differences, the root mean square deviations and the fitting degree between the simulated and the observed are computed. For M2, the mean absolute difference of the amplitude is 2.04cm, the mean absolute difference of the phase-lag is 1.81°, the root mean square deviation is 4.42cm, and the fitting degree is 99.70%. For S2, they are 0.76cm, 1.29°, 1.41cm and 99.65%. For K1, they are 1.38cm, 2.48°, 2.81cm and 98.91%. For O1, they are 0.55cm, 1.73°, 1.23cm and 99.58%. The results are better than previous researches.Optimizing the horizontal eddy viscosity coefficients of the tidal model is studied by using the adjoint method. Three numerical experiments are designed to test the effect of the horizontal eddy viscosity coefficients to the tidal model. Experiment 1 only optimizes the bottom friction coefficients; Experiment 2 only optimizes the horizontal eddy viscosity coefficients; Experiment 3 optimizes the bottom friction coefficients and the horizontal eddy viscosity coefficients at the same time. The mean absolute differences between the simulated and the observed of the three experiments for M2 are as follows respectively. For Experiment 1, the mean absolute difference of the amplitude is 4.83cm, and the mean absolute difference of the phase-lag is 6.36°. For Experiment 2, they are 7.14cm and 7.80°. For Experiment 3, they are 2.04cm and 1.81°. The results show that it is better when optimizing the bottom friction coefficients and the horizontal eddy viscosity coefficients simultaneously than optimizing any one separately. For S2, K1 and O1, the similar results are also obtained.