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\begin{document}

\title{Analysis of and solution to the polar numerical noise within the
shallow-water model on the latitude-longitude grid}



\author[1]{Jianghao Li}%
\author[2]{Bin Wang}%
\author[1]{Li Dong}%
\affil[1]{Institute of Atmospheric Physics, Chinese Academy of Sciences}%
\affil[2]{LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\begin{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. 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.%
\end{abstract}%



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