Analysis of and Solution to the Polar Numerical Noise Within the Shallow‐Water Model on the Latitude‐Longitude Grid. (11th August 2020)

• Record Type: Journal Article
• Authors: Li, Jianghao; Wang, Bin; Dong, Li
• Is Part Of: Journal of advances in modeling earth systems. Volume 12:Number 8(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-08-11
• Subjects: Geological modeling -- Periodicals; Climatology -- Periodicals; Geochemical modeling -- Periodicals; 551.5011
• DOI: 10.1029/2020MS002047
• Languages: English
• ISSNs: 1942-2466

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. Plain Language Summary: The dynamical core describes the atmospheric motion and its thermodynamic state in a forecast model, acting like the engine of car. The dynamical core needs to numerically solve the governing equations, which involves considering various aspects, such as mathematical equations, numerical methods, a spherical grid, and so on. Designing a shallow‐water model is often the first step in designing a new generation of dynamical core. This paper describes a new shallow‐water model with vector‐invariant equations that differ from original model. The new model is designed to avoid the polar noise found in the original shallow‐water model. By comparing the two models, the source of polar noise on the latitude‐longitude grid is analyzed. Idealized experiments also demonstrate that the new shallow‐water model is able to overcome the problem of polar noise and maintains the computational performance of the original model. Key Points: The vector‐invariant form of the horizontal momentum equations is preferred due to the explicit calculation of potential vorticity The polar noise on the lat‐lon grid with zonal wind component staggered on the pole is eliminated by redefining the polar vorticity