The circulation of the stratosphere transports important trace gases, including ozone, and can be thought of as having a fast horizontal mixing component and a slow meridional overturning component. Measuring the strength of the circulation directly is not possible, and so it must be inferred from tracer measurements. Long-lived trace gases can be related to the idealized tracer age of air, which describes how long an air parcel has been in the stratosphere. In this paper, we derive a quantitative relationship between the vertical gradient of age and the horizontal mixing between the tropics and the extratropics using a “leaky pipe” framework in isentropic coordinates. Mixing rates of air into and out of the tropics are related to the vertical gradient of age in the tropics and in the extratropics, respectively. The derivation is repeated with the hemispheres separated so that the vertical structure of the mixing in the two hemispheres can be compared directly. These theories are applied to output from an idealized model of the stratosphere and from a realistic chemistry-climate model to test our assumptions and calculate the mixing rates in the models. We then perform a quantitative comparison of the mixing rates in the Northern and Southern hemisphere along with an examination of where such a separation is valid. Finally, we perform a very preliminary calculation of mixing efficiency with satellite data to demonstrate the use of the mixing metric to compare mixing models and data.

Wave-induced adiabatic mixing in the winter midlatitudes is one of the key processes impacting stratospheric transport. Understanding its strength and structure is vital to understanding the distribution of trace gases and their modulation under a changing climate. age-of-air is often used to understand stratospheric transport, and this study proposes refinements to the vertical age gradient theory of Linz et al. (2021). The theory assumes exchange of air between a well-mixed tropics and a well-mixed extratropics, separated by a transport barrier, quantifying the adiabatic mixing flux across the interface using age-based measures. These assumptions are re-evaluated and a refined framework that includes the effects of meridional tracer gradients is established to quantify the mixing flux. This is achieved, in part, by computing a circulation streamfunction in age-potential temperature coordinates to generate a complete distribution of parcel ages being mixed in the midlatitudes. The streamfunction quantifies the “true” age of parcels mixed between the tropics and the extratropics. Applying the revised theory to an idealized and a comprehensive climate model reveals that ignoring the meridional gradients in age leads to an underestimation of the wave-driven mixing flux. Stronger, and qualitatively similar fluxes are obtained in both models, especially in the lower-to-middle stratosphere. While the meridional span of adiabatic mixing in the two models exhibits some differences, they show that the deep tropical pipe, i.e. latitudes equatorward of 15$^{\circ}$ barely mix with older midlatitude air. The novel age-potential temperature circulation can be used to quantify additional aspects of stratospheric transport.