Dynamical impacts associated with radiation boundary conditions

It is well known that the use of radiation conditions for the non-linear shallow water equations can lead to an incorrect model response in a variety of dynamical settings. In this study, we show that conditions aimed to handle the radiation of outgoing disturbances are not sufficient to ensure the correct mass and energy fluxes at the open boundaries in long-term wind-forced flows and short-term simulations dominated by wave radiation. Moreover, the mass and energy flux imbalance across the open boundaries introduces an accumulating error that deteriorates the interior solution. To ameliorate this problem, we tested damped schemes and integral constraints on surface elevation and mass flux. A comparison of the model results indicates that the proposed schemes improved the overall performance of the open boundary conditions in a series of experiments conducted in a rotating channel, although there are limitations when the oceanic response consists of dispersive wave packets. The practical experience gained from the idealised studies shows that a modified gravity wave is the only scheme that provides a reasonable response in all cases studied. It is also found that consistent with the ill-posedness of the analytical problem, the numerical behaviour of the corrected schemes depends on the nature of the problem to be investigated.