A Theory for Stratospheric Transport from Age of Air

We derive theory that relates the idealized tracer age of air to both the diabatic circulation and to the adiabatic mixing of the stratosphere. The horizontal and vertical gradients of age in isentropic coordinates are directly related to the diabatic and adiabatic components of the circulation respectively, neglecting diabatic diffusion and in steady state. We validate this theory in an idealized atmospheric model and examine differences in circulation caused by changes to the idealized forcing. By calculating the difference in the average age of downwelling and upwelling air on each isentropic surface we can identify the local minimum in the velocity, which is the separation between the upper and lower branches of the Brewer-Dobson circulation. The vertical gradient of the tropical age of air enables a calculation of entrainment by mixing, thereby showing at what level the "leaky" tropical pipe becomes isolated from the extratropics. We explore assumptions required to apply the theory to the hemispheres separately, and show the hemispheric differences in mixing and circulation strength.