A cyclic Markov chain study of ENSO predictability

We use yearly-cyclic Markov chains in order to analyse the predictability characteristics of ENSO. These Markov chains are computed from multicentennial data sets generated by an intermediate coupled atmosphere-ocean model (Zebiak and Cane, 1987). We also introduce the ideas of most and least predictable states. We partition the multidimensional phase space into a number of cells, each cell containing an equal number of observations. This is not only efficient but also leads to a mathematical structure that connects smoothly with the unstable periodic orbits of dynamical system's theory.