A benchmark solution that facilitates testing the accuracy, efficiency, and efficacy of moist nonhydrostatic numerical model formulations and assumptions is presented. The solution is created from a special configuration of moist model processes and a specific set of initial conditions. The configuration and initial conditions are straightforward to construct and include: reversible phase changes, no hydrometeor fallout, a neutrally stable base state environment, and an initial buoyancy perturbation that is identical to the one used to test nonlinearly-evolving dry thermals. The results of the moist simulation exhibit many of the properties found in its dry counterpart. Given the similar results, and accurate conservation of mass and energy, it is argued that this new moist simulation design can be used as a benchmark to evaluate moist numerical model formulations.

The utility of the benchmark simulation is highlighted by comparing it to results obtained when using approximate forms of the governing equations found in the literature. The results of these tests have implications for the formulation of numerical models. For example, it is shown that both mass and energy conservation are crucial for obtaining the benchmark solution. Results suggest that the extra effort required to conserve mass in a numerical model may not lead to significant improvements in results unless energy is also conserved. The accuracy of ice-liquid water potential temperature, a thermodynamic variable that is approximately conserved during phase changes, is also evaluated with the benchmark simulation.