A Proper Time Integration with Split Stepping for the Explicit Free-Surface Modeling

Errors due to split time stepping are discussed for an explicit free-surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three-time-level structure because of leapfrog scheme. The barotropic one, however, has two-time-level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long-term integration for climate studies. It is applied to a free-surface model for the North Pacific Ocean.