Efficient Time Integration Schemes for Atmosphere and Ocean Models

TLDR: In this paper, it was observed that the high-frequency gravity modes, which propagate faster than the Rossby modes, are quasilinear and carry only a small portion of the total energy.

Abstract: As atmospheric numerical models increased in complexity, the need for computationally efficient time integration schemes became apparent. Early efforts along this line began with Marchuk (1974) and Robert et al. (1972). They noted that atmospheric motions can be separated into two classes; the Rossby modes, where nonlinearity and quasigeostrophic balance (i.e., balance between Coriolis and pressure gradient forces) play an important role, and gravity modes, for which the pressure gradient terms are balanced by the inertial terms. It was also observed that the high-frequency gravity modes, which propagate faster than the Rossby modes, are quasilinear and carry only a small portion of the total energy.