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Abstract

A basic requirement of climate models is to account for the effects of processes that cannot be represented in spatial or temporal detail because of limitations imposed by resolution or other modeling considerations. Such parameterizations specify an average or expected effect of such processes on the resolved variables. This has traditionally been formulated in a deterministic way in terms of the resolved variables as the mean effect averaged across many realizations of the small scales with the same large-scale situation, implicitly or explicitly assuming the existence of some equilibrium state as a closure condition. More recently, the uncertainty of such closure assumptions has led to the use of stochastic forms of parameterization, where the required effects on the resolved scale are determined from a set of randomly chosen realizations of unresolved processes that have a known probability of occurrence given the resolved state. Theoretical and practical approaches to parameterization are discussed and illustrated with selected examples. New directions that employ hybrid modeling strategies and stochastic methods to overcome well-known parameterization difficulties are discussed. WIREs Clim Change 2011 2 482–497 DOI: 10.1002/wcc.122

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