Time-dependent Relationship between Age of Air and Diabatic Circulation in the Stratosphere

We present a time-dependent theory to directly relate the age of air in the stratosphere to the diabatic circulation. The steady state theory predicts that the difference between the age of upwelling air and downwelling air on an isentrope is a measure of the diabatic circulation, neglecting diffusion. We explore the modified theory in an idealized atmospheric model with a seasonal cycle in the stratosphere in order to a) determine the time-dependent validity of the age difference metric, b) test sensitivity to temporal and spatial sampling biases, and c) determine whether the precision available using the age difference metric is sufficient to resolve recent trends in circulation. We find that the transient terms are small upon annual averaging, so the steady state theory holds approximately true at the yearly timescale.