Development of a new dynamical core on the latitude-longitude grid targeting high resolution simulations

The issue of poles has been impeding the increase of horizontal resolution of global atmospheric models on the latitude-longitude grid. This is due to the strict limitation on the time step size. Although implicit or semi-implicit methods have been designed to enhance the numerical stability, their algorithms for solving the large matrix systems are very complex and not suitable for massive parallel computers. This study aims to address this problem by developing an effective Gaussian filter. The 1D filter is applied in the zonal direction, with its kernel width decreasing smoothly according to the zonal Courant-Friedrichs-Lewy (CFL) condition from the pole to the equator. By filtering the dynamic tendencies, the zonal spatial scale is enlarged to boost the numerical stability in the polar region. Parallelization is optimized through setting different zonal halo widths in different processes and using asynchronized MPI communication. The new dynamical core solves the nonhydrostatic equations under the terrain following mass coordinate, with the horizontal momentum equations in vector-invariant form. The variables are staggered on the C-grid for discretization. Compared with other dynamical cores, the implementation here is simpler and more user-friendly, which includes the shallow water and baroclinic versions in one code base. Several standard test cases are employed to verify the efficacy of this new dynamical core, including shallow water cases, hydrostatic/nonhydrostatic baroclinic cases. The results demonstrate that this method can effectively mitigate the pole problem, allowing for a larger explicit time step size comparable with quasi-uniform cores while preserving numerical accuracy as much as possible.