Necessary and Sufficient Conditions for the Destabilization of Quasigeostrophic Disturbances by Trace Shortwave Radiative Absorbers: Application to Saharan Mineral Dust Aersols

Necessary and sufficient conditions for the destabilization of quasigeostrophic (QG) disturbances by trace shortwave radiative absorbers are derived. The analysis pivots on a conservation equation for wave activity, which is obtained by combining equations for QG potential vorticity, thermodynamic energy, and trace absorber mixing ratio. Under the assumption that the diabatic heating rate due to the absorber is small, a perturbation analysis yields the conditions for instability; the conditions only require knowledge of the zonally-averaged background distributions of wind and absorber. Several limiting, but physically relevant, wind and absorber distributions are analyzed, which expose how radiative-dynamical feedbacks involving trace shortwave absorbers destabilize QG disturbances.

The conditions for instability have broad application, ranging from stratospheric ozone to dust storms on both Earth and Mars. As an example, we apply the conditions for instability to a recent study by Nathan et al. (2017; J. Atmos. Sci.), who showed that Saharan mineral dust (SMD) aerosols can produce African easterly wave-like disturbances in background flows that are subcritical with respect to barotropic and baroclinic instability. Nathan et al.’s analytical analysis required knowledge of the background flow, disturbance structure, and Doppler-shifted frequency. We show that their determination of SMD-instability can be predicted solely from knowledge of the background state. This underscores the utility of the necessary and sufficient conditions for instability as a predictive tool for a broad range of stability problems involving trace shortwave absorbers in QG flow.