Topography based local spherical Voronoi grid refinement on classical and moist shallow-water finite volume models

Abstract

Abstract. Locally refined grids for global atmospheric models are attractive since they are expected to provide an alternative to solve local phenomena without the requirement of a global high-resolution uniform grid, whose computational cost may be prohibitive. The Spherical Centroidal Voronoi Tesselations (SCVT), as used in the atmospheric Model for Prediction Across Scales (MPAS), allows a flexible way to build and work with local refinement. Alongside, the Andes Range plays a key role in the South American weather, but it is hard to capture its fine structure dynamics in global models. This paper describes how to generate SCVT grids that are locally refined in South America and that also capture the sharp topography of the Andes Range by defining a density function based on topography and smoothing techniques. We investigate the use of the mimetic finite volume scheme employed in the MPAS dynamical core on this grid considering the non-linear classic and moist shallow-water equations on the sphere. We show that the local refinement, even with very smooth transitions from different resolutions, generates spurious numerical inertia-gravity waves that may even numerically de-stabilize the model. In the moist shallow-water model, where physical processes such as precipitation and cloud formation are included, our results show that the local refinement may generate spurious rain that is not observed in uniform resolution SCVT grids. Fortunately, the spurious waves originate from small-scale grid-related numerical errors and therefore can be mitigated using small amounts of numerical diffusion. We show that, in some cases, the clouds are better represented in a variable resolution grid when compared to a respective uniform resolution grid with the same number of cells, while in other cases, grid effects can deteriorate the cloud and rain representation.

Adaptive Wavelet Methods for Earth Systems Modelling

“…Variable resolution unstructured triangular meshes, or finite elements, are used extensively in ocean modelling to provide higher resolution near coastlines. Local static refinement has also been proposed to improve representation of orography (e.g., the Andes mountain range [35]). However, this approach can produce instabilities and does not always improve accuracy.…”