A feature point scheme for improving estimation of the temporally varying bottom friction coefficient in tidal models using adjoint method

Refined estimation of bottom friction coefficient (BFC) is significantly important for coastal engineers to determine precisely the hydrodynamic conditions and sediment transport rates, which can be realized by assimilating observations of sea surface elevation using the adjoint method. In this study, a new method, named as feature point scheme (FPS), is developed to further improve the estimation of temporally varying BFC. In FPS, BFCs at some feature points are assumed to be independent and BFCs at other temporal points are obtained by interpolating BFCs at feature points. By assimilating artificial observations in twin experiments, it is demonstrated that FPS can improve the estimated temporally varying BFC, especially with the nonuniformly distributed feature points and nonuniform spline interpolation (nonuniform FPS). The M₂ tide and four principal tidal constituents in the Bohai Sea are then simulated by assimilating real satellite-retrieved observations with FPS. In all the experiments, the performance of the tidal model with nonuniform FPS outperforms those using other schemes. The experimental results indicate that the temporally varying BFC is related to the tidal constituents. Moreover, the temporal variation of estimated BFC has a significantly negative correlation with the current speed, which is possibly related with the sediment transport.