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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 linearβ-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 StatementUpward 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. 

Abstract Recent observations have indicated significant modulation of the Madden–Julian oscillation (MJO) by the phase of the stratospheric quasi-biennial oscillation (QBO) during boreal winter. Composites of the MJO show that upper-tropospheric ice cloud fraction and water vapor anomalies are generally collocated, and that an eastward tilt with height in cloud fraction exists. Through radiative transfer calculations, it is shown that ice clouds have a stronger tropospheric radiative forcing than do water vapor anomalies, highlighting the importance of incorporating upper-tropospheric–lower-stratospheric processes into simple models of the MJO. The coupled troposphere–stratosphere linear model previously developed by the authors is extended by including a mean wind in the stratosphere and a prognostic equation for cirrus clouds, which are forced dynamically and allowed to modulate tropospheric radiative cooling, similar to the effect of tropospheric water vapor in previous formulations. Under these modifications, the model still produces a slow, eastward-propagating mode that resembles the MJO. The sign of zonal mean wind in the stratosphere is shown to control both the upward wave propagation and tropospheric vertical structure of the mode. Under varying stratospheric wind and interactive cirrus cloud radiation, the MJO-like mode has weaker growth rates under stratospheric westerlies than easterlies, consistent with the observed MJO–QBO relationship. These results are directly attributable to an enhanced barotropic mode under QBO easterlies. It is also shown that differential zonal advection of cirrus clouds leads to weaker growth rates under stratospheric westerlies than easterlies. Implications and limitations of the linear theory are discussed. Significance StatementRecent observations have shown that the strength of the Madden–Julian oscillation (MJO), a global-scale envelope of wind and rain that slowly moves eastward in the tropics and dominates global-weather variations on time scales of around a month, is strongly influenced by the direction of the winds in the lower stratosphere, the layer of the atmosphere that lies above where weather occurs. So far, modeling studies have been unable to reproduce this connection in global climate models. The purpose of this study is to investigate the mechanisms through which the stratosphere can modulate the MJO, by using simple theoretical models. In particular, we point to the role that ice clouds high in the atmosphere play in influencing the MJO. 

Observational data have long suggested that in the tropics, when the troposphere locally warms, the lower stratosphere locally cools. Here, the observed anti-correlation between tropospheric and lower stratospheric temperature is confirmed—the lower stratosphere cools by approximately 2 degrees per degree of warming in the mid-troposphere. This anti-correlation is explained through a recently proposed theory holding that there is a quasi-balanced response of the stratosphere to tropospheric heating [J. Lin, K. Emanuel, Tropospheric thermal forcing of the stratosphere through quasi-balanced dynamics.J. Atmos. Sci.(2024).]. The local-scale anti-correlation between tropospheric and lower stratospheric temperature also holds when considering climate change—where the troposphere has been anomalously warming relative to the zonal mean, the lower stratosphere has been anomalously cooling, and vice versa. This suggests that zonally asymmetries in tropospheric temperature trends will be reflected in that of the lower stratospheric temperature trends. The zonally asymmetric trends are also found to be comparable in magnitude to the mean temperature trends in the lower stratosphere, highlighting the importance of the pattern of warming. The results and proposed theory suggest that in addition to forcing via wave-dissipation, the lower stratosphere can also be subject to direct forcing by the troposphere, through quasi-steady, quasi-balanced dynamics. 

The impact of the quasi‐biennial oscillation (QBO) on tropical convection and precipitation is investigated through nudging experiments using the UK Met Office Hadley Center Unified Model. The model control simulations show robust links between the internally generated QBO and tropical precipitation and circulation. The model zonal wind in the tropical stratosphere was nudged above 90 hPa in atmosphere‐only and coupled ocean‐atmosphere configurations. The convection and precipitation in the atmosphere‐only simulations do not differ between the experiments with and without nudging, which may indicate that SST‐convection coupling is needed for any QBO influence on the tropical lower troposphere and surface. In the coupled experiments, the precipitation and sea‐surface temperature relationships with the QBO phase disappear when nudging is applied. Imposing a realistic QBO‐driven static stability anomaly in the upper‐troposphere lower‐stratosphere is not sufficient to simulate tropical surface impacts. The nudging reduced the influence of the lower troposphere on the upper branch of the Walker circulation, irrespective of the QBO, indicating that the upper tropospheric zonal circulation has been decoupled from the surface by the nudging. These results suggest that grid‐point nudging mutes relevant feedback processes occurring at the tropopause level, including high cloud radiative effects and wave mean flow interactions, which may play a key role in stratospheric‐tropospheric coupling.