Damping of Gravity Waves by Radiation to the Stratosphere

The equilibrium state of weak horizontal temperature gradients in the tropics is maintained by the fast horizontal propagation of latent heating via the emission of gravity waves (e.g. Bretherton and Smolarkiewicz, 1989), which distribute the heating as ‘compensating subsidence' spreading radially away from the latent heat source. However, this picture of purely horizontal wave radiation is incomplete– the tropical troposphere is not capped by a rigid lid. In this study, we elucidate two important features of a simplified tropical atmosphere, composed of a heated region with uniform stratification capped by a semi-infinite layer of fluid with increased stratification. First, even a modest jump in stratification at the tropopause causes the heating to project strongly onto the wavelengths twice the depth of the heating, which partially justifies the use of simple models with truncated vertical spectra. Second, gravity waves in this system also possess a vertical group velocity, and we show that gravity waves radiate vertically on timescales relevant to tropospheric dynamics– a process not captured in models with truncated vertical structure. Shorter horizontal wavelengths radiate away first, which causes an initially-localized pulse of buoyancy to spread out rapidly. In fact, an initially localized first-baroclinic pulse of buoyancy spreads throughout the whole tropics in approximately 10 days. This provides a theoretical underpinning and possible alternate explanation for the 1-10-day damping timescale ubiquitous in studies of large-scale tropical dynamics, typically attributed to convective momentum transport. We also show that upward radiation of gravity waves may contribute to the dominance of low-frequency variability in the tropics, absent any scale-dependence of the forcing.