The strength of the Brewer-Dobson circulation is difficult to estimate using observations. Trends in the age of stratospheric air, deduced from observations of transient tracers, have been used to identify trends in the circulation, but there are ambiguities in the relationship between age and the strength of the circulation. This paper presents a steady-state theory and a time-dependent extension to relate age of air directly to the diabatic circulation of the stratosphere. In steady state, it is the difference between the age of upwelling and downwelling air through an isentrope and not the absolute value of age that is a measure of the strength of the diabatic circulation through that isentrope. For the time-varying case, expressions for other terms that contribute to the age budget are derived. An idealized atmospheric general circulation model with and without a seasonal cycle is used to test the time-dependent theory and to find that these additional terms are small upon annual averaging. The steady-state theory holds as well for annual averages of a seasonally varying model as for a perpetual-solstice model. These results are a step toward using data to quantify the strength of the diabatic circulation.

The distribution of gases such as ozone and water vapour in the stratosphere — which affect surface climate — is influenced by the meridional overturning of mass in the stratosphere, the Brewer–Dobson circulation. However, observation-based estimates of its global strength are difficult to obtain. Here we present two calculations of the mean strength of the meridional overturning of the stratosphere. We analyze satellite data that document the global diabatic circulation between 2007– 2011, and compare these to three re-analysis data sets and to simulations with a state-of-the-art chemistry-climate model. Using measurements of sulfur hexafluoride (SF6) and nitrous oxide, we calculate the global mean diabatic overturning mass flux throughout the stratosphere. In the lower stratosphere, these two estimates agree, and at a potential temperature level of 460 K (about 20 km or 60 hPa in tropics), the global circulation strength is 6.3–7.6 × 109 kg/s. Higher in the atmosphere, only the SF6-based estimate is available, and it diverges from the re-analysis data and simulations. Interpretation of the SF6 data-based estimate is limited because of a mesospheric sink of SF6; however, the reanalyses also differ substantially from each other. We conclude that the uncertainty in the mean meridional overturning circulation strength at upper levels of the stratosphere amounts to at least 100 %.