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ABSTRACT
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 solutionsdiffer significantly. In particular, anelastic baroclinic eddies propagate fasterand developslower 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.
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1. Introduction
This is the third paper in a series of works devoted to investigating the relative merits of the anelastic and compressible moist dynamics across the range of scales, from small to meso to planetary. The first paper (Kurowski et al. 2013) introduced our notion of an allscale moist simulation and documented the consistent anelastic and compressible solutions for idealized shallow convective and orographic cloud formations. The second paper (Kurowski et al. 2014) analyzed moist deep convection and demonstrated that anelastic approximation accurately represents severe convective dynamics. The current paper extends the earlier studies to planetary scales. Normal-mode analysis (Davies et al. 2003) indicates that the anelastic approximation of Lipps and Hemler (1982) misrepresents large-scale atmospheric flows compared to predictions based on fully compressible Euler equations. On the other hand, multiple-scales asymptotic analyses (Dolaptchiev and Klein 2009, 2013) show that, at synoptic-planetary length and time scales, atmospheric motions are predominantly anelastic. Both results are correct, and they do not contradict each other. Depending on the focus of interests, perturbations about a predominantly anelastic state of the atmosphere can be...