A practical scheme to introduce explicit tidal forcing into an OGCM
A practical scheme is proposed to explicitly introduce tides into ocean general circulation models (OGCM). In this scheme, barotropic linear response to the tidal forcing is calculated by the time differential equations modified for ocean tides, instead of the original barotropic equations of an OGCM. This allows for the usage of various parameterizations specified for tides, such as the self-attraction/loading (SAL) effect and energy dissipation due to internal tides, without unintentional violation of the original dynamical balances in an OGCM. Meanwhile, secondary nonlinear effects of tides, e.g., excitation of internal tides and advection by tidal currents, are fully represented within the framework of the original OGCM equations. That is, this scheme drives the OGCM by the barotropic linear tidal currents which are predicted progressively by a tuned tide model, instead of the equilibrium tide potential, without large additional numerical costs. We incorporated this scheme into Meteorological Research Institute Community Ocean Model and executed test experiments with a low-resolution global model. The results showed that the model can simulate both the non-tidal circulations and the tidal motion simultaneously. Owing to the usage of tidal parameterizations such as a SAL term, a root-mean-squared error in the tidal heights is found to be as small as 10.0 cm, which is comparable to that of elaborately tuned tide models. In addition, analysis of the speed and energy of the barotropic tidal currents is found to be consistent with that of past tide studies. The model also showed active excitement of internal tides and tidal mixing. In the future, the impacts of internal tides and tidal mixing should be examined using a model with a finer resolution, since explicit and precise introduction of tides into an OGCM is a significant step toward the improvement of ocean models.