## Parameter estimation for a three-dimensional numerical barotropic tidal model with adjoint method.(English)Zbl 1388.86013

Summary: The parameters of a three-dimensional (3-D) barotropic tidal model are estimated using the adjoint method. The mode splitting technique is employed in both forward and adjoint models. In the external mode, the alternating direction implicit method is used to discretize the two-dimensional depth-averaged equations and a semi-implicit scheme is used for the 3-D internal mode computations. In this model the bottom friction is expressed in terms of bottom velocity which is different from the previous works. Besides, the bottom friction coefficients (BFCs) are supposed to be spatially varying, i.e. the BFC at some grid points are selected as the independent BFC, while the BFC at the other grid points can be obtained through linear interpolation with these independent BFCs. On the basis of the simulation of $$M_{2}$$ tide in the Bohai and North Yellow Seas (BNYS), twin experiments are carried out to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of open boundary conditions (OBCs), the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The ‘observations’ are produced by the tidal model and recorded at the position of TOPEX/Poseidon altimeter data, tidal gauge data and current data. The experiments discuss the influence of initial guesses, model errors and data number. The inversion has obtained satisfactory results and the prescribed distributions have been successfully inverted. The results indicate that the inversion of BFC is more sensitive to data error than that of OBC and the vertical eddy viscosity profiles.

### MSC:

 86A05 Hydrology, hydrography, oceanography 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76U05 General theory of rotating fluids
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