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Coarse-grained stochastic models for tropical convection and climate
  • B Khouider
  • AJ Majda
  • MA Katsoulakis, University of Massachusetts - Amherst
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Prototype coarse-grained stochastic parametrizations for the interaction with unresolved features of tropical convection are developed here. These coarse-grained stochastic parametrizations involve systematically derived birth/death processes with low computational overhead that allow for direct interaction of the coarse-grained dynamical variables with the smaller-scale unresolved fluctuations. It is established here for an idealized prototype climate scenario that, in suitable regimes, these coarse-grained stochastic parametrizations can significantly impact the climatology as well as strongly increase the wave fluctuations about an idealized climatology. The current practical models for prediction of both weather and climate involve general circulation models (GCMs) where the physical equations for these extremely complex flows are discretized in space and time and the effects of unresolved processes are parametrized according to various recipes. With the current generation of supercomputers, the smallest possible mesh spacings are ≈50–100 km for short-term weather simulations and of order 200–300 km for short-term climate simulations. There are many important physical processes that are unresolved in such simulations such as the mesoscale sea-ice cover, the cloud cover in subtropical boundary layers, and deep convective clouds in the tropics. An appealing way to represent these unresolved features is through a suitable coarse-grained stochastic model that simultaneously retains crucial physical features of the interaction between the unresolved and resolved scales in a GCM. In recent work in two different contexts, the authors have developed both a systematic stochastic strategy (1) to parametrize key features of deep convection in the tropics involving suitable stochastic spin-flip models and also a systematic mathematical strategy to coarse-grain such microscopic stochastic models (2) to practical mesoscopic meshes in a computationally efficient manner while retaining crucial physical properties of the interaction. This last work (2) is general with potential applications in material sciences, sea-ice modeling, etc. Crucial new scientific issues involve the fashion in which a stochastic model effects the climate mean state and the strength and nature of fluctuations about the climate mean. The main topic of this article is to discuss development of a family of coarse-grained stochastic models for tropical deep convection by combining the systematic strategies from refs. 1 and 2 and to explore their effect on both the climate mean and fluctuations for an idealized prototype model parametrization in the simplest scenario for tropical climate involving the Walker circulation, the east–west climatological state that arises from local region of enhanced surface heat flux, mimicking the Indonesian marine continent.

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Citation Information
B Khouider, AJ Majda and MA Katsoulakis. "Coarse-grained stochastic models for tropical convection and climate" PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Vol. 100 Iss. 21 (2003)
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