Anelastic and compressible simulation of moist dynamics at planetary scales

Moist compressible and anelastic numerical solutions to the planetary baroclinic instability and climate benchmarks are documented and critically compared. The solutions are obtained applying a consistent numerical framework for discrete integrations of the mathematically distinct formulations of the nonhydrostatic fluid flow equations. Moist extension of the baroclinic instability benchmark is formulated as an analog of the dry case. Flow patterns, surface vertical vorticity and pressure, total kinetic energy, power spectra, and total amount of condensed water are analyzed. Short-term deterministic compressible and anelastic solutions differ significantly. In particular, anelastic baroclinic eddies propagate faster and develop slower owing to, respectively, modified dispersion relation and abbreviated baroclinic vorticity production. These eddies also carry less kinetic energy and the onset of their rapid growth occurs later than for the compressible solutions. However, the differences between the two solutions are sensitive to initial conditions as they diminish for large-amplitude initial perturbations. Regardless, the impact of dynamic pressure perturbations on moist thermodynamics is small for both anelastic and compressible solutions in linear and nonlinear flow regimes. The climate benchmark extends the baroclinic instability study by addressing long-term statistics of an idealized planetary equilibrium and associated meridional transports. On the climatic time scales the compressible and anelastic solutions agree more closely, evincing similar zonally averaged flow patterns with the matching meridional transports of entropy, momentum and moisture.