Development And Application Of A Three-Dimensional Numerical Barotropic Adjoint Assimilation Tidal Model

The research on the tide and tidal current, which has close relation to those of the wind wave, ocean circulation, storm surge and other ocean phenomenon, is very important for the understanding of the dynamics of the ocean, especially in the continental marginal seas. Among all the data assimilation methods, four-dimensional variational (4DVAR) data assimilation is one of the most effective and powerful approaches. It is an advanced data assimilation method which involves the adjoint method and has the advantage of directly assimilating various observations distributed in time and space into numerical models while maintaining dynamical and physical consistency with the model. The major difficulties faced by numerical models of tidal flow concern the treatment of open boundary conditions (OBC) and bottom friction coefficients (BFC). By assimilating the data in the interior region, the adjoint method can optimize the OBC and BFC automatically and reach a global optimization of the model parameters. This paper researches the application of adjoint assimilation method in the numerical simulation of tides and tidal currents in-depth.This paper develops a two-dimensional (2-D) adjoint tidal model and studies the spatially varying BFC based on the numerical simulation of M2 tide in the Bohai, Yellow and East China Seas (BYECS). In the twin experiments the prescribed BFC distributions that the spatial structure is very complex are inverted successfully with the combination of spatially varying BFC and the adjoint method. Obviously the inversion would not succeed if the traditional ways about BFC were used. The bottom friction effect is decided by the ocean bottom topography. This study establishes a method of selecting the independent BFC according to the spatial characteristics of ocean topography. The numerical results show that the method can increase the simulation precision even if a small number of independent parameters are employed. The M2 tide in BYECS is simulated by assimilating the TOPEX/Poseidon (T/P) altimeter data. The results also prove that the spatially varying BFC is more powerful than the traditional ways in obtaining reasonable simulation results. The co-tidal charts obtained coincide with the observed M2 tide in BYECS fairly well.By assimilating the T/P data, the 2-D tidal model above is employed to optimize the OBC and BFC for the simulation of M2, S2, K1 and O1 constituents in BYECS, and the average absolute differences of amplitudes and phase-lags between simulation results and observations of 152 tidal gauge stations (independent data) are (5 .7cm ,5.2), (3 .2cm ,6.9), ( 2.6cm ,6.3) and ( 2.1cm ,8.5), respectively. The co-tidal charts obtained show that both the M2 and S2 constituents have three amphidromic points: one in the Bohai Sea and two in the Yellow Sea. Near the Yellow River mouth the amphidromes appear as degenerated systems. There are three amphidromic points for both the K1 and O1 constituents located in the Bohai Strait, in the Southern Yellow Sea and in the Tsushima Strait, respectively.In this study a numerical tidal model based on the discretization of three-dimensional (3-D) primitive equations is established to simulate the barotropic tides and tidal currents in the Bohai Sea and the North Yellow Sea (BNYS). The numerical schemes for solving the equations of motion and continuity use the internal-external mode splitting technique. The ADI method is employed for the external mode computations which give the surface elevations and depth-averaged currents. The time step of external mode is thus not restricted by the CFL condition. A semi-implicit scheme is used for the internal mode computations which give the vertical structure of the currents. The time step of internal mode can be significantly longer than that of the external mode. As a consequence, the overall computational speed can be several times faster than that of the general explicit models. For the bottom friction effect, turbulent boundary layer models of the near-bottom flow indicate that it is physically realistic to use a quadratic dependence of bottom friction on the bottom velocity. In our model the bottom friction is expressed in terms of bottom velocity, which is different from the previous works on 3-D adjoint tidal models. Based on the simulation of M2 tide and tidal current in BNYS, this study carries out twin experiments to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of OBC, the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The inversion has obtained satisfying results and the prescribed distributions have been successfully inverted, which demonstrates the strong ability of the adjoint model. In order to research the ill-posedness of parameter estimation inverse problems, the experiments also discuss the influences of parameter distributions, initial guesses, model errors and data number on the inversion. The results indicate the inversion of BFC is more sensitive to data error than that of OBC and vertical eddy viscosity profiles.