A Non-Column Based, Fully Unstructured Implementation of Kessler's Microphysics With Warm Rain Using Continuous and Discontinuous Spectral Elements

Numerical weather prediction is pushing the envelope of grid resolution at local and global scales alike. Aiming to model topography with higher precision, a handful of articles introduced unstructured vertical grids and tested them for dry atmospheres. The next step toward effective high-resolution unstructured grids for atmospheric modeling requires that also microphysics is independent of any vertical columns, in contrast to what is ubiquitous across operational and research models. In this paper, we present a non-column based continuous and discontinuous spectral element implementation of Kessler's microphysics with warm rain. We test the proposed algorithm against standard three-dimensional benchmarks for precipitating clouds and show that the results are comparable with those presented in the literature across all of the tested effective resolutions. While presented for both continuous and discontinuous spectral elements in this paper, the method that we propose can be adapted to any numerical method used in other codes, as long as the code can already handle vertically unstructured grids.