Predictability theory
Information flow, or information transfer as it may appear in the literature, is a fundamental notion in general physics and dynamical systems, which has wide applications in atmosphere-ocean science (particularly in the studies of atmosphere/ocean predictability), neuroscience, turbulence studies, financial economics, network dynamics, evolutionary biology, to name but a few. It has been of interest for decades, but prior to Liang and Kleeman (2005, PRL 95, 244101), only empirical/half-empirical formalisms existed. For details about this systematic work since 2005, refer to a recent review (Liang, 2013, Entropy 15, 327-360).
A direct application of the Liang-Kleeman information flow is that it can tell quantitatively the effect of one place or one mode to the predictability of another place/mode. Another important application is causality analysis. For example, it has long been observed that, in applying a baker transformation (see the figure below), information flows continually from the abscissa to the ordinate, but not vice versa. Information flow analysis thus quantitatively gives the cause-effect relation between the abscissa and ordinate. With this tool we are currently studying how the North Atlantic Oscillation (NAO) and El Nino are mutually affected.
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