A Method to Determine Nonhydrostatic Effects within Subdomains in a Mesoscale Model

Abstract

The exact solution of the nonhydrostatic pressure residual (total pressure perturbation minus hydrostatic pressure perturbation) in Defant's linear model is derived. The quasi-nonhydrostatic residual, introduced by Pielke, and the pressure-correction term by Orlanski are compared with the exact residual for varying physical situations. It is found that, within the linear framework, nonhydrostatic effects generally become relatively more important when the environmental stability is near the neutral state and/or the associated horizontal length scale is several kilometers or smaller. The residual components associated with buoyancy and horizontal momentum are the two important physical mechanisms contributing to the generation of nonhydrostatic effects. In a near-neutral environment, a pressure residual must include the horizontal momentum nonhydrostatic residual in order to approximate more accurately the nonhydrostatic effects, while in a sufficiently stable environment the total pressure tends to behave hydrostatically, although the nonhydrostatic effect which does occur is associated with the nonhydrostatic buoyancy term. The residual approach has the advantage in a numerical model in that it need only be applied in a subdomain of a model where vertical accelerations are important, while the more economical hydrostatic equation for pressure can be used elsewhere.