Two-dimensional transport rates can be quantified using the "effective diffusivity" formalism of Nakamura; the technique has been applied in atmosphere and ocean data, and yields diffusivities K_eff that are spatially dependent, and which maximize in critical layers, consistent with dynamical expectations. Thus far, the theory has been based on an assumption that the whole process -- isentropic cascade of tracer variance to small scales by large-scale stirring, followed by isentropic dissipation of the small scale variance -- is two-dimensional. In reality, while the large-scale stirring may be isentropic, the ultimate small-scale dissipation is likely to be much more isotropic, meaning in practice that it is vertical diffusion that terminates the cascade. However, the theory can be modified to apply to this situation, and application of this modified theory to numerical simulations yields values of K_eff that are not too different from those derived in the 2D case, in line with theoretical expectation that it is the large-scale stirring that determines K_eff.

In the stratosphere, this stirring is mostly confined to the midlatitude regions. In Plumb & Ko (1992) we used a model in which stirring was assumed to be global in extent to describe the basis for, and properties of, compact relationships between mixing ratios of different long-lived tracers. One key result, that has subsequently been used to estimate tracer lifetimes from observations, is that ratio of the net global flux of two different tracers equals the slope of the tracer-tracer curve. When one of the tracers is age, whose flux is known, the tracer-age slope can be used to estimate the absolute lifetime of the second tracer. Recognition that rapid stirring does not extend globally affects these results: the tracer-tracer flux ratio result is unaffected for long-lived tracers, but the relationship with age becomes problematic.

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NOTE: Non-standard day.
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