Estimation of Bottom Friction Coefficient in Multi-Constituent Tidal Models Using the Adjoint Method: Temporal Variations and Spatial Distributions

The bottom friction coefficient (BFC) is critical for precisely determining hydrodynamic conditions and sediment transport rates, which are important for scientific research and coastal ocean engineering. The BFC varies spatially and temporally, as indicated by in situ observations, but it is difficult to accurately set this parameter in tidal models. In this study, based on a two-dimensional multi-constituent tidal model and its adjoint model, the harmonic constants of four principal tidal constituents (M₂, S₂, K₁, and O₁) obtained from TOPEX/Poseidon altimeter data were assimilated to estimate spatially and temporally varying BFCs using the adjoint method in the Bohai, Yellow, and East China Seas. The model performance was significantly improved after data assimilation, which was independently tested by harmonic constants at coastal tidal gauge stations. Through several sensitivity experiments, the spatial distributions of the temporally averaged BFCs were verified to be robust and not affected by model settings, while the temporal variations of the spatially averaged BFCs were also robust but related to the tidal constituents. The variations in the estimated BFCs with the current speed and water depth were nearly consistent with those in the observations. Overall, the temporal and spatial variations in the estimated BFCs are significantly correlated with the current speed and water depth, which is attributed to the erosion-deposition of sediment on the seabed and the changes in seabed roughness under different current speeds. The results can be beneficial for determining reasonable parameters for the bottom stress and setting the BFC in multi-constituent tidal models.