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. We develop the theory of cyclic Markov chains and apply it to the El Ni ?no-Southern Oscillation (ENSO) pre-dictability problem. At the core of Markov chain modelling is a partition of the state space such that the transition rates between different state space cells can be computed and used most efficiently. We apply a partition technique, which di-vides the state space into multidimensional cells containing an equal number of data points. This partition leads to mathe-matical properties of the transition matrices which can be ex-ploited further such as to establish connections with the dy-namical theory of unstable periodic orbits. We introduce the concept of most and least predictable states. The data basis of our analysis consists of a multicentury-long data set obtained from an intermediate coupled atmosphere-ocean model of the tropical Pacific. This cyclostationary Markov chain ap-proach captures the spring barrier in ENSO predictability and gives insight also into the dependence of ENSO predictabil-ity on the climatic state.

Cyclic Markov chains with an application to an intermediate ENSO model