A finite-volume module for cloud-resolving simulations of global atmospheric flows

The paper extends to moist-precipitating dynamics a recently documented high-performance finite-volume module (FVM) for simulating global all-scale atmospheric flows (Smolarkiewicz et al., 2016) [62]. The thrust of the paper is a seamless coupling of the conservation laws for moist variables engendered by cloud physics with the semi-implicit, non-oscillatory forward-in-time integrators proven for dry dynamics of FVM. The representation of the water substance and the associated processes in weather and climate models can vary widely in formulation details and complexity levels. The representation adopted for this paper assumes a canonical “warm-rain” bulk microphysics parametrisation, recognised for its minimal physical intricacy while accounting for the essential mathematical complexity of cloud-resolving models. A key feature of the presented numerical approach is global conservation of the water substance to machine precision—implied by the local conservativeness and positivity preservation of the numerics—for all water species including water vapour, cloud water, and precipitation. The moist formulation assumes the compressible Euler equations as default, but includes reduced anelastic equations as an option. The theoretical considerations are illustrated with a benchmark simulation of a tornadic thunderstorm on a reduced size planet, supported with a series of numerical experiments addressing the accuracy of the associated water budget.