The barotropic, vortex-splitting sudden warming is analyzed in a simple global model, comprising the rotating shallow-water equations on the sphere with and without the effects of thermal forcing. A quasi-stationary approach is suggested as an effective means of exploring the two-dimensional parameter space of forcing amplitude and a suitable measure of vortex strength. We find that the main dynamical regimes obtained previously in a quasi-geostrophic f -plane model by Matthewman and Esler persist in the global model, with the exception of certain rotating vortex states that depend on the method of initialization. Short-lived regimes in which the vortex splits and reforms repeatedly are observed under certain parameters, although gradual dissipation of the vortex means that these cannot be classified as persistent vacillating states.

Water entering the stratosphere ([H2O]entry) is strongly constrained by temperatures in the tropical tropopause layer (TTL). Temperatures at tropical tropopause levels are 15–20 K below radiative equilibrium. A strengthening of the residual circulation as suggested by general circulation models in response to increasing greenhouse gases is, based on radiative transfer calculations, estimated to lead to a temperature decrease of about 2 K per 10% change in upwelling (with some sensitivity to vertical scale length). For a uniform temperature change in the inner tropics, [H2O]entry may be expected to change as predicted by the temperature dependence of the vapor pressure, referred here as “Clausius‐Clapeyron (CC) scaling.” Under CC scaling, this corresponds to ∼1 ppmv change in [H2O]entry per 10% change in upwelling. However, the change in upwelling also changes the residence time of air in the TTL. We show with trajectory calculations that this affects [H2O]entry, such that [H2O]entry changes ∼10 % less than expected from CC scaling. This residence time effect for water vapor is a consequence of the spatiotemporal variance in the temperature field. We show that for the present‐day TTL, a little more than half of the effect is due to the systematic relation between flow and temperature field. The remainder can be understood from the perspective of a random walk problem, with slower ascent (longer path) increasing each air parcel's probability to encounter anomalously low temperatures. Our results show that atmospheric water vapor may depart from CC scaling with mean temperatures even when all physical processes of dehydration remain unchanged.

The diagnostic relation between eddy potential vorticity flux and Eliassen–Palm flux convergence in the transformed Eulerian mean shallow‐water system is used to infer the flux convergence needed to establish a stratospheric surf zone comprising a single region of perfectly homogenized potential vorticity, or to maintain the surf zone in steady state against the restoring effect of radiative relaxation. In the transient case, and when wave breaking is assumed to mix potential vorticity on time‐scales shorter than the radiative time‐scale, the required flux convergence is an order of magnitude larger than that required to maintain the flow in steady state away from radiative equilibrium.