CMG COLLABORATIVE RESEARCH: Novel Mathematical Strategies for Superparameterization in Atmospheric and Oceanic Flows

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Improving our understanding of, and ability to model atmospheric and oceanic circulation impacts human society in a very direct way. Atmospheric and oceanic flows, however, encompass a wide range of scales, from the planetary scale, of order 10000km, to the microscale, on the order of a few millimeters. This raises a particular challenge for global climate simulations, which cannot directly resolve scales below a few kilometers at best, even with the most powerful computers. The proposed project will develop novel methods to represent the effects of unresolved scales on directly simulated scales in atmospheric and oceanic models through ʻsuperparameterizationʼ (SP), defined broadly as a general set of techniques by which small-scale dynamics can be represented mathematically and numerically as an embedded sub-grid model. Superparameterization is a relatively new approach that has had great success in the parameterization of clouds, but has yet to be applied to many other relevant problems in climate models. The present project will apply novel SPtechniques to accurately incorporate the effects of a wide variety of important unresolved processes in atmospheric and oceanic models.Our research will focus on the application of SP strategies to highly relevant and difficult geophysical problems, including moist convection in the atmosphere, mesoscale and submesoscale eddies in the oceans, and moist geostrophic turbulence associated with the midlatitude weather system, which combines elements of both moist convection and geostrophic turbulence. We approach these diverse problems with a systematic, three step SP process: (1) the development of multi-scale equations for the physical problem;(2) the use of a periodic approximation for the fluctuations; and (3) exploitation of intermittency to replace fluctuating dynamics with reduced models that may be solved by either inexpensive numerical methods or by analytic solutions. Our goals are to develop and test this SP approach in a set of idealized models, and ultimately to provide new parameterization algorithms that may be incorporated in operational global climatemodels.