Numerical Tests of the Weak Pressure Gradient Approximation

Abstract

loud-resolving simulations of convection over a surface temperature hot spot are used to evaluate the weak pressure gradient (WPG) and weak temperature gradient (WTG) approximations. The premise of the relaxed form of WTG?that vertical velocity is equal to buoyancy times a positive time scale?is found to be violated by thick layers of negative buoyancy in steady-state ascent. The premise of WPG?that horizontal divergence and pressure anomalies are collocated?is validated by these simulations. When implemented in a cloud-resolving model, WPG replicates buoyancy transients exceptionally well, including the adiabatic lifting of air below buoyancy anomalies. WTG captures neither this effect nor the associated triggering of moist convection. For steady states, WTG produces vertical velocity profiles that are too top heavy. On the other hand, WPG generates velocity profiles that closely match fully resolved hot-spot simulations. Taken together, the evidence suggests that WPG is a relatively accurate method for parameterizing supradomain-scale (SDS) dynamics.