The equatorial counterpart of the quasi-geostrophic model

Abstract

A uniformly valid balanced model that represents the quasi-geostrophic model's counterpart in the equatorial region is derived. The quasi-geostrophic model itself fails in the equatorial region because it is only valid where the dominant balance is geostrophic, i.e. where the Rossby number is small. The smallness of the Rossby number is assumed in the quasi-geostrophic model's standard derivation and therefore this derivation cannot be repeated for the equatorial region. An alternative derivation of the quasi-geostrophic model that is independent of the Rossby number was presented by Leith in 1980, using the geometric framework of nonlinear normal mode initialization. Its independence of the Rossby number allows it to be repeated for the equatorial region, leading to an equatorial balanced model that thus represents the equatorial counterpart of the quasi-geostrophic model. As such it also coincides with the quasi-geostrophic model sufficiently far away from the equator. Its dispersion relation can be expressed in an explicit analytic form and, compared to that of other balanced models of similar simplicity, approximates that of the shallow water equations strikingly well.