A Note on the Horizontal Boundary Condition in Quasi-Geostrophic Models

Abstract

Attention is given to the extra term appearing in the quasi-geostrophic horizontal boundary condition when it is required that the vertical velocity (?), rather than the material derivative of pressure (?), be zero on a constant pressure surface. This extra term (here called the stratification term) has been retained in recent baroclinic instability studies by Geisler and Dickinson (1975) and Geisler and Garcia (1977). Their linearized problems, which used log pressure as vertical coordinate, are shown to be isomorphic with problems formulated in the altitude coordinate set put forward by White (1977). Examination of the small-amplitude free modes on a uniform barotropic zonal flow shows that the effects of the stratification term are: 1) in the absence of an upper lid, to allow the existence of progressive modes if the flow is easterly, and to disallow the Rossby mode if the easterly flow exceeds a certain value depending on the wavelength; 2) in the presence of an upper lid, to allow the existence of progressive modes in easterly or westerly flow; and 3) whether or not an upper lid is present, to reduce significantly the retrogression phase speeds of the largest scale Rossby modes, at least for flows of an intensity comparable with observed average zonal flows in the earth's atmosphere.