Theoretical aspects of upscale error growth on the mesoscales: Idealized numerical simulations

Abstract

The mechanism for the upscale growth of small errors through the atmospheric mesoscales has not been conclusively identified, but geostrophic adjustment in response to diabatically generated motions such as cumulus convection is a plausible candidate. In a companion paper, an analytic solution of the linearized, hydrostatic Boussinesq equations to an impulsive, localized heat source that mimics the effect of latent heating within a convective cloud on an unperturbed, rotating environment is found. Three characteristics of the solution are shown to be potentially useful for identifying the geostrophic adjustment process in numerical simulations. The predictions relate to the horizontal gravity wave speed, the Rossby number and the quantitative relationship between a precipitation anomaly and the balanced flow response (i.e. large‐scale vorticity).Here these predictions are tested in the framework of error growth experiments in idealized numerical simulations of a convective cloud field. Three different rotation rates are employed in order to identify the geostrophic adjustment mechanism and allow a quantitative comparison with the predictions of the analytic model. The gravity wave speed estimated from the simulations resembles the theoretical value and is independent of the Coriolis parameter, as predicted. The Rossby number resulting from the proposed scaling of temporal and spatial coordinates features a unique shape and the vorticity diagnostic agrees quantitatively with the analytical predictions. Based on these findings, it is proposed that upscale error growth through the atmospheric mesoscales is governed by the geostrophic adjustment process.