Cyclic Markov chains with an application to an intermediate ENSO model

We develop the theory of cyclic Markov chains and apply it to the El Nino-Southern Oscillation (ENSO) predictability problem. At the core of the Markov-chain modelling is a partition of phase space such that the transition rate between different cells can be computed and used most efficiently. We apply a partition technique which divides the phase space into multidimensional cells containing an equal number of data points. This partition leads to mathematical properties of the transition matrices wich can be exploited further such as to establish a connection with the dynamical theory of unstable periodic orbits. We introduce the concepts of most and least predictable states. The data base of our analysis consists of a mutlticentury-long data set obtained from an intermediate coupled atmosphere-ocean model of the tropical Pacific. This cyclostationary Markov-chain approach captures the spring barrier in ENSO predictability and gives insight into the dependence of ENSO predictability on the climatic state.