Stratospheric adiabatic mixing rates derived from the vertical gradient of age of air

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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.