Linear Stability of Free Planetary Waves in the Presence of Radiative–Photochemical Feedbacks

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Abstract
A simple β-plane model that couples radiative transfer, ozone advection, and ozone photochemistry with the quasi-geostrophic dynamical circulation is used to study the diabatic effects of Newtonian cooling and ozone–dynamics interaction on the linear stability of free planetary waves in the atmosphere. Under the assumption that the diabatic processes are sufficiently weak, an analytical expression is derived for the eigenfrequencies of these waves valid for arbitrary vertical distributions of background wind and ozone volume mixing ratio . This expression shows the following: 1) the influence of meridional ozone advection on wave growth or decay depends on the wave and basic state vertical structures; 2) vertical ozone advection is locally (de)stabilizing when , irrespective of the wave or basic state vertical structures; 3) photochemically accelerated cooling, which predominates in the upper stratosphere, augments the Newtonian cooling rate and is stabilizing. The one-dimensional linear stability problem also is solved numerically for a Charney basic state (constant vertical shear and constant stratification) and for zonal mean basic states constructed from observational data characteristic of each season. It is shown that ozone heating generated by ozone–dynamics interaction in the stratosphere can reduce (enhance) the damping rates due to Newtonian cooling by as much as 50% for planetary waves of large vertical scale and maximum amplitude in the lower (upper) stratosphere. For waves with relatively large density-weighted amplitude in the lower to midstratosphere and small Doppler-shifted frequency, ozone-dynamics interaction in the stratosphere can significantly influence the zonally rectified wave fluxes in the troposphere. For the summer basic state, adiabatic eastward- and westward-propagating neutral modes having the same zonal scale emerge; both are confined to the lower stratosphere and troposphere. For these modes ozone heating dominates over Newtonian cooling, and the modes amplify with growth rates comparable to those of baroclinically unstable waves of similar spatial scale. The effects of radiative–photochemical feedbacks on the transient time scales of observed waves in the atmosphere also are discussed.

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