Analysis of and Solution to the Polar Numerical Noise Within the Shallow‐Water Model on the Latitude‐Longitude Grid

Abstract

Abstract This study conducts an analysis of the polar numerical noise in the barotropic shallow‐water version of the Grid‐point Atmospheric Model of IAP LASG (GAMIL‐SW) and provides a good solution to the problem. GAMIL‐SW suffers from numerical noise in the polar region in some ideal test cases, which is likely to be detrimental to the full physical model. The noise is suspected to be related to the nonlinear advection term in the momentum equation. Thus, a new shallow‐water model with a vector‐invariant form of the momentum equation is developed on the latitude‐longitude grid to analyze the polar noise. It is found that the version with meridional wind component staggered on the pole is free from noise, while the version with zonal wind component staggered on the pole is still contaminated. By redefining the polar relative vorticity, the polar noise is eliminated in the latter version, and the global conservation properties are maintained. In addition, the test cases demonstrate that the new shallow‐water model maintains the properties of the original GAMIL‐SW with respect to numerical accuracy and computational stability. This study helps to identify appropriate governing equations to further develop the next generation of GAMIL dynamical core.