  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.
