An empirical formula of bottom friction coefficient with a dependence on the current speed for the tidal models

Tides are of great importance for ocean mixing and nearshore ocean engineering. Bottom friction is a major factor in tidal dissipation and is usually parameterized by the bottom friction coefficient (BFC). BFC is a critical parameter in numerical tidal models and is known to vary with time and space, as calculated with measured data. However, it is difficult to accurately adjust the spatially-temporally varying BFC in numerical tidal models. Based on the relationship between the spatially-temporally varying BFC estimated by adjoint data assimilation and the simultaneously simulated current speed, an empirical formula of BFC with a dependence on the current speed is proposed. This new empirical formula of BFC is compared with several traditional empirical formulas, including the constant BFC, the Chezy-Manning BFC, and two depth-dependent BFCs. When the four principal tidal constituents (M2, S2, K1, and O1) in the Bohai, Yellow and East China Seas (BYECS) are simulated, the mean vector error between the simulated results obtained using the current speed-dependent BFC and the TOPEX/Poseidon satellite altimetry data (the tidal gauge data) is 8.81 cm (10.62 cm), which is decreased by up to 8.1% (18.2%) compared with those using the several commonly used empirical formulas of BFC. Furthermore, in the sensitivity experiments where only the M2 tide in the BYECS, the M2, S2, K1, and O1 tides in the Bohai and Yellow Sea (BYS), and the M2, S2, K1, and O1 tides in the South China Sea (SCS) are simulated, the errors between the simulated results obtained by using current speed-dependent BFC and the tidal gauge data are less than those using the other empirical formulas of BFC, further demonstrating the superiority of the current speed-dependent BFC proposed in this study. From numerical model experiments, the current speed-dependent BFC can adequately reflect the spatial and temporal variations of BFC and improve the simulation accuracy of tides, thus having a broad application scope.