Time Correlation Laws Inferred from Climatic Records: Long-Range Persistence and Alternative Paradigms

Abstract

Observational time series of climatic variables exhibit substantial changeability on spatial and temporal scales over many orders of magnitude. In statistical terms, this implies a continuous variance distribution involving all resolvable time scales (frequencies), starting from those comparable with the age of the Earth. A correct causal interpretation of such a variability is very difficult even in the context of a cognitive approach (e.g., von Storch, 2001) to the problem. Cognitive models are minimum complexity models aiming at the scientific understanding of the most relevant processes occurring at any given temporal and spatial scale. Although generally they cannot be useful for management decisions straightforwardly, their role is fundamental especially for understanding the internal climatic variability that cannot be passively related to external forcing factors. The concept of stochastic process is essential in this framework, since it synthesizes collective behaviours which contribute as a whole to the overall dynamics. As stochastic processes are the macroscopic result of many degrees of freedom, the characterization of their correlation properties across different scales through the analysis of observational data is a problem of statistical inference and their modelling is usually a mechanical-statistical problem. Maybe, the most famous early effort aiming to summarize the climate variance distribution among different frequencies, which is commonly referred as climate spectrum, is the ideal sketch proposed by Mitchell (1976) (see Fig. 1). All the features of this spectrum that deviate from the flat behaviour typical of white noise (pure random process) deserve dynamical interpretation in order to understand climate. Within the traditional picture of the climate dynamics, the variance distribution among different temporal scales is seen as the superposition of oscillations generated by astronomical cycles (spectral spikes), quasi-periodic or aperiodic fluctuations with a preferred scale (broad spectral peaks), and internal stochastic processes whose temporal correlation decays according to characteristic time scales. These last are responsible for all the continuous broad-band deviations of the spectrum from flatness. Within this picture, the variance accumulations that do not appear in the form of peaks and spikes, such as that we