Universal Inverse Power law distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter - annual Variability of Indian and USA Region Rainfall

TL;DR

This paper presents a universal inverse power law distribution model for fractal fluctuations in dynamical systems, demonstrating its applicability to predict inter-annual rainfall variability in India and the USA, with implications for understanding extreme weather events.

Contribution

It introduces a general systems theory predicting a universal inverse power law distribution for fractal fluctuations, linking eddy continuum dynamics to rainfall variability analysis.

Findings

Rainfall data follow the predicted inverse power law distribution.

Power spectral analysis confirms the eddy continuum structure.

Model explains the occurrence of extreme rainfall events.

Abstract

Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and therefore the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory which predicts the following (i) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (ii) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. The predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900 to 2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. Global warming related atmospheric energy input will result in intensification of fluctuations of all scales and can be seen immediately in high frequency (short-term) fluctuations such as devastating floods/droughts resulting from excess/deficit annual, quasi-biennial and other shorter period (years) rainfall cycles.