Tropospheric thermal forcing of the stratosphere through quasi-balanced dynamics

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 quasi-geostrophic 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 upwards stratospheric penetration of the corresponding tropopause geopotential anomaly is controlled by two non-dimensional 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 non-dimensional parameters. Under Earth-like estimates of the non-dimensional 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.