Asymptotic methods have played a central role in the long history of equation hierarchies for geophysical fluid dynamics, especially for "balance dynamics." In contrast, probabilistic approaches to the hierarchy have received little attention. In this talk I will explore both approaches. Specifically, I will discuss "QG+1" asymptotic extensions to quasigeostrophy, which yield powerful surface models that have been applied to a wide range of problems including tropopause dynamics, oceanography, and paleoclimate. Motivated by the notion of "distinguished variables" in the asymptotic approach, a probabilistic framework to balance will be described. Although practical implementation of these models is, thus far, more limited, they provide in principle a path toward generalizing balance dynamics to include moist physics on the sphere. Moreover,this approach links naturally to information theory, which suggests a quantitative basis for comparing distinguished variables.
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