Abstract
Abstract The accuracy of three anelastic systems (Ogura and Phillips; Wilhelmson and Ogura; Lipps and Hemler) and the pseudo-incompressible system is investigated for small-amplitude and finite-amplitude disturbances. Based on analytic solutions to the linearized, hydrostatic mountain wave problem, the accuracy of the Lipps and Hemler and pseudo-incompressible systems is distinctly superior to that of the other two systems. The linear dispersion relations indicate the accuracy of the pseudo-incompressible system should improve and the accuracy of the Lipps and Hemler system should decrease as the waves become more nonhydrostatic. Since analytic solutions are not available for finite-amplitude disturbances, five nonlinear, nonhydrostatic numerical models based on these four systems and the complete compressible equations are constructed to determine the ability of each “sound proof” system to describe finite-amplitude disturbances. A comparison between the analytic solutions and numerical simulations of th...
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