Considerations on open boundary conditions for regional and coastal ocean models

This paper reviews the usual open boundary conditions (OBCs) for coastal ocean models and proposes a complete set of open boundaries based on stability criteria, on mass and energy conservation arguments, and on the ability to enforce external information. This set includes a radiation condition for barotropic variables, an equation of wave propagation for baroclinic velocities, and an advection equation for tracers. Considerations on mass and energy conservation properties suggest a suitable numerical treatment of the barotropic scheme, which is different from what is commonly used. Restoring terms, when classically added in the Sommerfeld OBCs, are not consistent with external fields. It is shown that this can be avoided if proper numerical schemes are used or if OBCs are applied on differences between the model and forcing rather than on absolute variables. Finally, this paper shows that simplistic advection-type methods for temperature and salinity should not be used in sigma coordinate models because this introduces errors in the computation of the horizontal pressure gradient.