Necessary conditions for the instability of quasigeostrophic waves induced by trace shortwave radiative absorbers

Abstract

Necessary conditions for radiative–dynamical instability of quasigeostrophic waves induced by trace shortwave radiative absorbers are derived. The analysis pivots on a pseudomomentum conservation equation that is obtained by combining conservation equations for quasigeostrophic potential vorticity, thermodynamic energy, and trace absorber mixing ratio. Under the assumptions that the absorber-induced diabatic heating rate is small and the zonal-mean basic state is hydrodynamically neutral, a perturbation analysis of the pseudomomentum equation yields the conditions for instability. The conditions, which only require knowledge of the zonally averaged background distributions of wind and absorber, expose the physical processes involved in destabilization—processes not exposed in previous analytical and modeling studies of trace absorber-induced instabilities. The simplicity of instability conditions underscores their utility as a tool that is both interpretive and predictive. The conditions for instability, which have broad application to synoptic-scale waves in Earth's and other planetary atmospheres, are discussed in light of previous instability studies involving stratospheric ozone and Saharan mineral dust aerosols.