Stratospheric mean residence time and mean age on the tropopause: Connections and implications for observational constraints

Abstract

Stratospheric mean residence time and mean age on the tropopause Γ Ω are shown to measure physically distinct aspects of stratospheric transport. Both Γ Ω and τ̄ are mean transit times through the stratosphere of air that enters through tropopause region Ω i and exits through region Ω f, but they represent averages over different populations of fluid elements. The averaging for Γ Ω is based on the population of fluid elements exiting the stratosphere, while τ̄ is based on the population of Ω i → Ω f fluid elements residing in the stratosphere. Thus, Γ Ω is the mean age on exit, while τ̄ is the expected mean residence time in the interior of the stratosphere. The physical basis for defining and robustly computing both timescales is the one-way stratosphere-to-troposphere flux of air labeled with the boundary-propagator Green function, G. By re-expressing the boundary-value problem for G in terms of first-order loss in a tropopause layer with a timescale T c in the limit T c → 0, we show that both τ̄ and Γ Ω can be obtained as ratios of moments of G extrapolated to the tropopause. One obtains τ̄ = Γ Ω + 2Δ 2 /Γ Ω, where Δ quantifies the width of the transit-time distribution. Because the moments of G can be estimated from the mixing ratio of transient trace gases, it is in principle possible to estimate τ̄ from measurements of two independent transient tracers. The distinctness of τ̄ and Γ Ω is elucidated using idealized models. © 2012 American Geophysical Union. All Rights Reserved.