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The Relationship between the Transilient Matrix and the Green’s Function for the Advection-Diffusion Equation

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  • 1 Program in Atmospheres, Oceans, and Climate, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

The Green’s function (or propagator) of the advection-diffusion equation is used to link the transilient matrix to the advection-diffusion equation. The Green’s function framework allows one to construct more rigorous and general derivations of various mixing properties of the transilient matrix. Unlike the transilient matrix or one-dimensional convective parameterizations, the Green’s function satisfies a composition property that allows a long-time propagator to be constructed from a series of short-time propagators.

Corresponding author address: Vincent E. Larson, Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, CO, 80523-1375.

Email: larson@cira.colostate.edu

Abstract

The Green’s function (or propagator) of the advection-diffusion equation is used to link the transilient matrix to the advection-diffusion equation. The Green’s function framework allows one to construct more rigorous and general derivations of various mixing properties of the transilient matrix. Unlike the transilient matrix or one-dimensional convective parameterizations, the Green’s function satisfies a composition property that allows a long-time propagator to be constructed from a series of short-time propagators.

Corresponding author address: Vincent E. Larson, Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, CO, 80523-1375.

Email: larson@cira.colostate.edu

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