Need for Meridional Resolution in Linear Steady State Models Using Different Methods of Treating the Critical Latitude

Abstract

The need for meridional resolution in steady state linear models depends on the damping near the critical latitude (CL). In barotropic models considered previously, a strong damping can be used, since the damping must include the effect of the surface friction. In the two-layer model considered here (as in all multimodels) the physically-justifable friction at the upper level is small and thus a very fine grid must be used. When no artificial extra friction near the CL was used, a meridional grid size of some tens of kilometers was needed to obtain a solution that is free from numerical error. A moderate bell-shaped extra CL friction was found to give almost the same response, with a grid one order of a magnitude coarser. On the other hand, when using a CL friction inversely proportional to the square of the basic-state zonal wind, the response was extremely sensitive to the exact location of the grid points near the CL, and the solution did not converge as the number of grid points was increased. When too coarse a grid was used, the amplitude of the response oscillated regularly as a function of the number of the grid points. This fluctuation was shown to be due to alteration in the CL reflectivity. Several previous studies appear to have used either insufficient meridional resolution or unsatisfactory methods of enhancing damping near the CL.