Fractal Nature of TOGA Surface Pressure Time Series

The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with increase in time(or space) resolution and for uncorrelated fluctuations dealt with in traditional statistics, is given as a linear function of Relative Dispersion at the smallest resolution and the ratio of the time resolutions.However, it is now established that temporal (or spatial) fluctuations of dynamical systems exhibit selfsimilarity or long-range correlations and traditional statistical concepts are not valid. In this paper, it is shown that resolution dependent variance is described by the fractal dimension .