Anelastic and compressible simulation of moist dynamics at planetary scales

Moist anelastic and compressible numerical solutions to the planetary baroclinic instability and climate benchmarks are compared. The solutions are obtained by applying a consistent numerical framework for discrete integrations of the various nonhydrostatic 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. The climate benchmark extends the baroclinic instability study by addressing long-term statistics of an idealized planetary equilibrium and associated meridional transports. Short-term deterministic anelastic and compressible 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. The observed differences between the two solutions are sensitive to initial conditions as they diminish for large-amplitude excitations of the instability. In particular, on the climatic time scales, the anelastic and compressible solutions evince similar zonally averaged flow patterns with the matching meridional transports of entropy, momentum, and moisture.