Idealized global nonhydrostatic atmospheric test cases on a reduced-radius sphere

Idealized simulations on a reduced-radius sphere can provide a useful vehicle for evaluating the behavior of nonhydrostatic processes in nonhydrostatic global atmospheric dynamical cores provided the simulated cases exhibit good agreement with corresponding flows in a Cartesian geometry, and for which there are known solutions. Idealized test cases on a reduced-radius sphere are presented here that focus on both dry and moist dynamics. The dry dynamics cases are variations of mountain-wave simulations designed for the Dynamical Core Model Intercomparison Project (DCMIP), and permit quantitative comparisons with linear analytic mountain-wave solutions in a Cartesian geometry. To evaluate moist dynamics, an idealized supercell thunderstorm is simulated that has strong correspondence to results obtained on a flat plane, and which can be numerically converged by specifying a constant physical diffusion. A simple Kessler-type routine for cloud microphysics is provided that can be readily implemented in atmospheric simulation models. Results for these test cases are evaluated for simulations with the Model for Prediction across scales (MPAS). They confirm close agreement with corresponding simulations in a Cartestian geometry; the mountain-wave results agree well with analytic mountain-wave solutions, and the simulated supercells are consistent with other idealized supercell simulation studies and exhibit convergent behavior.