Incorporation of Small- to Mid-Scale Turbulence and Diffusion into Large-Scale Atmospheric Models

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Abstract
Because of the large dynamic range of scales between 3-D turbulence and global circulation, the effects of small scale turbulence, and indeed turbulence at many scales, often need to be parameterized in some way for input into large global-scale computer models. Ideally, it would be good to have a computer program large enough, and powerful enough, to solve all motions at all scales simultaneously, but this objective is still far from possible. Yet if implemented poorly, parameterization can lead to errors which can propagate through the model. While turbulence is often considered as a “wastebasket” for larger scale motions, here we look in the other direction, and examine how these smaller scale motions work back to affect the larger-scale flows. The nature of background drag and diffusive forces is reviewed in the context of impact on larger scale motions, and the ways that these forces are implemented in models is discussed. The lack of use of measured (as distinct from hypothetical) small-scale turbulence data is noted. It is also noted that vertical diffusion is conceptually more important for atmospheric coupling than horizontal diffusion, and so-called “two-dimensional (2-D) turbulence”, sometimes discussed in regard to atmospheric mixing, is less capable of vertical mixing because associated organized vertical motions are generally weak. Very strong evidence from the Global Atmospheric Sampling Program (GASP) for a dominant gravity-wave spectral region at horizontal scales of 200-1000 km, as low in altitude as the tropopause, is presented. Errors in interpretation of earlier well-cited analyses of these data (often incorrectly cited as evidence for 2-D turbulence) are presented, which have profound impact on previous beliefs about the relative roles of gravity waves and nominally 2-D turbulence. Non- Kolmogorov diffusive processes which contribute to drag, diffusion and mixing, but that have rarely been practically employed, are considered, including the impact of intermittency, wave saturation, “whitecaps” and Stokes Diffusion. When these processes are included, typical realistic diffusion coefficients seem to be 2-3 × higher than those predicted by the Cospar International Reference Atmosphere. Finally a comparison between diffusivities using the Whole Atmosphere Community Climate Model (WACCM6) at the National Center for Atmospheric Research in the USA, and the Japanese Atmospheric GCM for Upper Atmosphere Research (JAGUAR), using very different strategies, is undertaken.
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