Physical basis of long-range persistence in the climate system

Accepted explanations for the Hurst effect in a time series are either non-stationarity, or a non-summable correlation function. Despite its practical and theoretical importance, a physical understanding of Hurst statistics from climate dynamics has remained a fundamental open problem in hydro-climatology. It is well known that, even for simple dynamical systems, the topological and geometric structure of the orbits can be extremely complicated. However it is possible to obtain important results by focusing on the statistical properties of these orbits rather than on their precise deterministic structure. In fact, the sensitive dependence on initial conditions, which was the basis for the widely known chaos theory, can give rise to mixing of the orbits in phase space, which produces a probabilistic structure, and a well-defined statistical coherence. We will illustrate that the dynamics of non-uniformly mixing systems, which arises when orbits spend long time near neutral fixed points in an overall mixing systems, result in a slowing down of the mixing. It gives rise to slower than exponential rates of decay of correlation, and furnishes a dynamical basis for a possible explanation of the Hurst effect. Our work offers a clue for developing a physical understanding of long range persistence in natural hydro-climatic time series.