This tutorial lecture begins with a brief introduction to some elementary facets of information theory. This is followed by a discussion of how the various competing theories of equilibrium statistical mechanics for geophysical flows can be simplified, unified, and generalized by simple predictive principles based on information theory. An application of these ideas is given which involves the prediction of intense large scale vortices from statistical collections of “hetons,” small scale geophysical vortices, with angular momentum and energy constraints. This is a useful conceptual model for deep ocean convection, the oceanic analogue of hurricane formation. In a completely different direction, the lecturer will illustrate how ideas from information theory are useful in quantifying bimodality in ensemble predictions with small ensemble size in complex dynamical systems; an important practical contemporary topic. The material for this lecture can be found mostly in the new book by A. Majda and X. Wang, Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flow, Camb. Press, 2006, as well as in papers on Majda’s faculty website: http://www.math.nyu.edu/faculty/majda/ .
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