The Path Density of Interhemispheric Surface-to-Surface Transport. Part I: Development of the Diagnostic and Illustration with an Analytic Model

A new path-density diagnostic for atmospheric surface-to-surface transport is formulated. The path density h gives the joint probability that air whose last surface contact occurred on patch Vi at time ti will make its next surface contact with patch Vf after a residence time t 2 (t, t 1 dt) and that it can be found in dr during its surface-to-surface journey. The dependence on t allows the average surface-to-surface flow rate carried by the paths to be computed. A simple algorithm for using passive tracers to determine h is developed. A key advantage of the diagnostic is that it can be computed efficiently without an adjoint model and using only a moderately large number of tracers. The nature of the path density is illustrated with a one-dimensional advection–diffusion model. In Part II of this study, the path density diagnostic is applied to quantify interhemispheric transport through the troposphere and stratosphere.