Study on Bottom friction parameterizations for two-dimensional tidal models using data assimilation

Adjoint method is applied to study the similarities and the differences of the Ekman (linear) and the Quadratic (nonlinear) bottom friction parameterizations for a two-dimensional regional tidal model. The adjoint expressions for the linear and the nonlinear parameterizations are derived based on the Largrangian multiplier method. By assimilating the model-generated observations, identical twin experiments are performed to test the inversion ability of the presented methodology. Four experiments which employ the linear parameterization, the nonlinear parameterizations, the constant bottom friction coefficient (BFC) and the spatially varying BFC are carried out to simulate the M ₂ tide in the Bohai and Yellow Seas by assimilating TOPEX/Poseidon altimetry and tidal gauge data. After the assimilation, the misfit between model-produced and observed data is significantly decreased. The simulation results indicate that the simulation results using the nonlinear Quadratic parameterization is more accurate than the linear Ekman parameterization if the traditional constant BFC is used. However, when the spatially varying BFCs are used, the difference between two approaches diminished. The reason is analyzed from the dissipation rate caused by bottom friction.