A dynamic and thermodynamic foundation for modeling the moist atmosphere with parameterized microphysics

Moist convection is an exquisite yet powerful participant in the creation of weather on our planet. To facilitate numerical modeling of weather systems in a moist atmosphere, a direct and consistent application of dynamic and thermodynamic principles, in conjunction with parameterized microphysics, is proposed. An earlier formulation of reversible thermodynamics, in terms of the mass of air and water substance and the total entropy, is now extended to include the irreversible process of precipitation through parameterized microphysics. The dynamic equations are also formulated to account consistently for the mass and momentum of precipitation. The theoretical proposal is tested with a two-dimensional model that utilizes a versatile and accurate spectral method based on a cubic-spline representation of the spatial fields. In order to allow a wide range of scale interactions, the model is configured on multiply nested domains of outwardly decreasing resolution, with noise-free, two-way interfaces. The semi-implicit method provides efficient time integration for the nested spectral model. The tests performed are the simulation of the growth of single-cell clouds and also the generation of self-sustaining multicell squall lines, and the effects of various resolutions on the simulations are examined. The results favorably compare with similar results found in the literature, but also offer new insights into the interplay between dynamics and precipitation.