Information flow between subspaces in ensemble prediction for complex dynamical systems

The quantification of information flow between subspaces in ensemble predictions for complex dynamical systems is an important practical topic, for example, in weather prediction and climate change projections. While information transfer between dynamical system components is an established concept for nonlinear multivariate time series, the specific nature of the nonlinear dynamics generating the observed flow of information is ignored in such statistical analysis.

In this lecture, I will present a general mathematical theory for information flow between subspaces in ensemble predictions of a dynamical system (Majda and Harlim, 2007), which accounts for the specific underlying dynamics. Specific elementary examples are developed here with both stable and unstable dynamics to both illustrate facets of the theory and to test Monte-Carlo solution strategies. The theory presented here builds on recent work of Liang and Kleeman (2005) on information transfer for two-dimensional systems. Particularly, we show that estimating the entropy transfer rate in higher dimensional system can be reduced to moment estimating problems. We also discuss a potential used of this measure for quantifying the information transfer from a high frequency-variability to a low-frequency variability, which can be applied to understand how much the weather-like pattern affect the large-scale teleconnection patterns such as the Arctic Oscillations or the North Atlantic Oscillations.