Applications of flexible spatial and temporal discretization techniques to a numerical weather prediction model

Numerical weather prediction is carried out by solving a set of governing partial differential equations (PDEs) based on fluid dynamics and thermodynamics principles, together with parameterizations of unresolved important physical processes. The Model for Prediction Across Scales - Atmosphere (MPAS-A) uses Spherical Centroidal Voronoi Tessellations (SCVT) to discretize the atmosphere spatially and an horizontally explicit finite volume method to time-integrate the PDEs. The use of a variable-resolution SCVT mesh, such as the 60km-to-3km mesh with circular region of refinement, can achieve good results in numerical weather prediction. However, MPAS-A uses a globally uniform time-step that needs to satisfy the Courant-Friedrichs-Lewy condition for the smallest mesh cells, and the computational cost would be unpractically large if the finest resolution is pushed further down like 1km. We modified the MPAS-A source code to support the use of hierarchical time steps for regions with different grid spacing ranges. This enables small regions of very fine resolution to be incorporated in a global mesh while saving computational cost for the rest of the globe. Moreover, we implemented a software tool for the generation of SCVT meshes with arbitrarily-shaped, hierarchical refinement regions. Both features enable using a global atmospheric model for regional or local high-resolution weather forecasting with affordable computational resources.