Tropospheric Thermal Forcing of the Stratosphere through Quasi-Balanced Dynamics

Abstract

Abstract The steady response of the stratosphere to tropospheric thermal forcing via an SST perturbation is considered in two separate theoretical models. It is first shown that an SST anomaly imposes a geopotential anomaly at the tropopause. Solutions to the linearized quasigeostrophic potential vorticity equations are then used to show that the vertical length scale of a tropopause geopotential anomaly is initially shallow, but significantly increased by diabatic heating from radiative relaxation. This process is a quasi-balanced response of the stratosphere to tropospheric forcing. A previously developed, coupled troposphere–stratosphere model is then introduced and modified. Solutions under steady, zonally symmetric SST forcing in the linear β-plane model show that the upward stratospheric penetration of the corresponding tropopause geopotential anomaly is controlled by two nondimensional parameters: 1) a dynamical aspect ratio and 2) a ratio between tropospheric and stratospheric drag. The meridional scale of the SST anomaly, radiative relaxation rate, and wave drag all significantly modulate these nondimensional parameters. Under Earthlike estimates of the nondimensional parameters, the theoretical model predicts stratospheric temperature anomalies 2–3 larger in magnitude than that in the boundary layer, approximately in line with observational data. Using reanalysis data, the spatial variability of temperature anomalies in the troposphere is shown to have remarkable coherence with that of the lower stratosphere, which further supports the existence of a quasi-balanced response of the stratosphere to SST forcing. These findings suggest that besides mechanical and radiative forcing, there is a third way the stratosphere can be forced—through the tropopause via tropospheric thermal forcing. Significance Statement Upward motion in the tropical stratosphere, the layer of atmosphere above where most weather occurs, is thought to be controlled by weather disturbances that propagate upward and dissipate in the stratosphere. The strength of this upward motion is important since it sets the global distribution of ozone. We formulate and use simple mathematical models to show the vertical motion in the stratosphere can also depend on the warming in the troposphere, the layer of atmosphere where humans live. We use the theory as an explanation for our observations of inverse correlations between the ocean temperature and the stratosphere temperature. These findings suggest that local stratospheric cooling may be coupled to local tropospheric warming.