Assessing tidal sensitivity to bottom friction: analytical insights for model optimization

Bottom friction coefficients (BFCs) are critical parameters in tidal modeling, with significant effects on hydrodynamic conditions and sediment transport. A comprehensive understanding of BFC variability and its influence on tidal models is essential for model optimization. In this study, we incorporate BFC perturbations through a Dirac delta function into a modified, depth-uniform idealized shallow-water model. By transforming the governing equations into polar coordinates, the non-homogeneous system is recast into a homogeneous form with dynamically consistent dipole sources. Analytical solutions constructed from Bessel function combinations, reveal a series of rotating Poincaré waves that propagate around the perturbation site at frequencies corresponding to odd multiples of the base tidal frequency. The weights of the Bessel functions, which depend non-linearly on local water depths, tidal current amplitudes, and phase lags, determine the rotational directions (clockwise, counterclockwise, or stationary) and provide a theoretical indicator of the tidal system’s sensitivity to BFC perturbations. The analytical solution captures the leading spatial pattern and relative response characteristics in the tested cases. The idealized M 2 experiment shows the best quantitative agreement with the analytical solution. Bohai Sea simulations retain qualitative consistency with the theory, although quantitative agreement decreases near the coast. Leveraging this framework, we theoretically assess BFC sensitivity across the Bohai Sea, the Yellow Sea, and the East China Sea. Our analysis indicates comparatively high sensitivity in shallow, strong-current regions, including some tidal-wave entrance and exit zones. This finding may provide a physically based prior for targeted model calibration.