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Diffusion versus Nonlocal Models of Stratospheric Mixing, in Theory and Practice

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  • 1 University of Washington, Seattle, Washington
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Abstract

In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described and compared. The most general, including as special cases all of the other models considered, is the integral or “transilient matrix” model. Some known properties of transilient matrices are discussed in a more formal way than has been done previously, and some new results concerning these matrices and associated equations are derived. Simpler models include the familiar diffusion model, a simple model of nonlocal mixing in which tracer concentrations are everywhere relaxed toward the global average, and a “leaky barrier” model in which two regions of nonlocal mixing are separated by a weakly diffusive transport barrier. Solutions to the latter two models, with linear chemistry included to allow nontrivial steady states, are used to derive their “effective diffusivities.” These are then used to test how well a diffusion model can mimic the behavior of the nonlocal mixing models over finite regions of parameter space. The diffusion model proves fairly robust, yielding fairly accurate results in situations where no formal argument indicates that it should. These results provide qualified support, from a purely empirical perspective, for the practice of using the diffusion model to represent stratospheric mixing in zonally averaged models. Several important caveats suggest nonetheless that exploration of more theoretically satisfactory representations is warranted.

Corresponding author address: Dr. Adam H. Sobel, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640.

Email: sobel@atmos.washington.edu

Abstract

In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described and compared. The most general, including as special cases all of the other models considered, is the integral or “transilient matrix” model. Some known properties of transilient matrices are discussed in a more formal way than has been done previously, and some new results concerning these matrices and associated equations are derived. Simpler models include the familiar diffusion model, a simple model of nonlocal mixing in which tracer concentrations are everywhere relaxed toward the global average, and a “leaky barrier” model in which two regions of nonlocal mixing are separated by a weakly diffusive transport barrier. Solutions to the latter two models, with linear chemistry included to allow nontrivial steady states, are used to derive their “effective diffusivities.” These are then used to test how well a diffusion model can mimic the behavior of the nonlocal mixing models over finite regions of parameter space. The diffusion model proves fairly robust, yielding fairly accurate results in situations where no formal argument indicates that it should. These results provide qualified support, from a purely empirical perspective, for the practice of using the diffusion model to represent stratospheric mixing in zonally averaged models. Several important caveats suggest nonetheless that exploration of more theoretically satisfactory representations is warranted.

Corresponding author address: Dr. Adam H. Sobel, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640.

Email: sobel@atmos.washington.edu

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