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

Mark Holzer Columbia University, New York, New York

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Abstract

A new path-density diagnostic for atmospheric surface-to-surface transport is formulated. The path density η gives the joint probability that air whose last surface contact occurred on patch Ωi at time ti will make its next surface contact with patch Ωf after a residence time τ ∈ (τ, τ + ) and that it can be found in d3r during its surface-to-surface journey. The dependence on τ allows the average surface-to-surface flow rate carried by the paths to be computed. A simple algorithm for using passive tracers to determine η 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.

Corresponding author address: Mark Holzer, Department of Applied Physics and Applied Mathematics, Columbia University, c/o NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025. Email: hm2220@columbia.edu

Abstract

A new path-density diagnostic for atmospheric surface-to-surface transport is formulated. The path density η gives the joint probability that air whose last surface contact occurred on patch Ωi at time ti will make its next surface contact with patch Ωf after a residence time τ ∈ (τ, τ + ) and that it can be found in d3r during its surface-to-surface journey. The dependence on τ allows the average surface-to-surface flow rate carried by the paths to be computed. A simple algorithm for using passive tracers to determine η 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.

Corresponding author address: Mark Holzer, Department of Applied Physics and Applied Mathematics, Columbia University, c/o NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025. Email: hm2220@columbia.edu

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