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Nanjing Center for Ocean-Atmosphere Dynamical Studies

Predictability theory

The Liang-Kleeman Information Flow

    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, 2013Entropy 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.

Click to download related articles

Liang and Kleeman, 2005: Information Transfer between Dynamical System Components. Phys. Rev. Lett. 95, 244101.

X. San Liang, 2013: The Liang-Kleeman Information Flow: Theory and Applications. Entropy 15, 327-360.

X. San Liang, 2014: Unraveling the cause-effect relation between time series. Phys. Rev. E 90, 052150 (1-11)

X. San Liang, 2016: Information flow and causality as rigorous notions ab inito. Phys. Rev. E, 94, 052201-1-28