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

Abstract

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 V i at time t i will make its next surface contact with patch V f after a residence time t 2 (t, t 1 dt) and that it can be found in d 3 r 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.

Seasonal ventilation of the stratosphere: Robust diagnostics from one‐way flux distributions

“…The Ω i air mass leaving in the tropics does so via the near‐singular diffusive fluxes, which are purely numerical in our model and hence an aspect of the transport that we cannot reliably quantify. However, the qualitative aspects of these singular fluxes do match theoretical expectations (see Figure a), and they are consistent with modeling results in other contexts [ Primeau and Holzer , ; Holzer , , ; Orbe et al , ]. In contrast to the Ω i air mass regardless of residence time, the portion of this mass with residence times less than 6 months depends strongly on the time of year, , during which the air mass is partitioned. Specifically, during September 6 times more Ω i air with τ = 6 months will leave the NH stratosphere compared to during March.…”

“…For τ ≥ 2 years, away from the dominance of the nearly singular behavior, the pattern of is strikingly different at midlatitudes than in the tropics. The one‐way flux returning across the midlatitude tropopause is made up of air that, at different stages during upwelling in the tropics, crosses the tropical barrier isentropically and spends a broad range of times recirculating in the extratropical stratosphere before descending back into the troposphere [ Gettelman and Sobel , ; Seo and Bowman , ; Holzer , ; Orbe et al , ]. Note that large short‐ τ fluxes at midlatitudes are associated with rapid isentropic transport to midlatitudes, not with the rapid eddy‐diffusive near‐singularity, because the midlatitudes do not overlap with the tropical entry region.…”

“…The Ω i air mass leaving in the tropics does so via the near‐singular diffusive fluxes, which are purely numerical in our model and hence an aspect of the transport that we cannot reliably quantify. However, the qualitative aspects of these singular fluxes do match theoretical expectations (see Figure a), and they are consistent with modeling results in other contexts [ Primeau and Holzer , ; Holzer , , ; Orbe et al , ].…”

The Southern Ocean silicon trap: Data‐constrained estimates of regenerated silicic acid, trapping efficiencies, and global transport paths

“…Note that with this normalization the path density has dimensions of inverse volume (units of m −3 ). Further background and theory for the path‐density transport diagnostic may be found in [ Holzer and Primeau , ; Holzer , ].…”

Decoupling the Effects of Transport and Chemical Loss on Tropospheric Composition: A Model Study of Path‐Dependent Lifetimes

“…More detailed analysis of the differing sign of the Γ‐ τ c relationship among the different transport perturbations, and confirmation of the above speculations will require an explicit examination on the residence times in different regions, for example, analysis of path densities (Holzer, ; ), which is beyond the scope of this study.…”