M. Menabde et M. Sivapalan, Modeling of rainfall time series and extremes using bounded random cascades and Levy-stable distributions, WATER RES R, 36(11), 2000, pp. 3293-3300
A new model for simulation of rainfall time series is proposed. It is shown
that both the intensity and duration of individual rainfall events can be
best modeled by a "fat-tailed" Levy-stable distribution. The temporal downs
caling of individual events is produced by a new type of a bounded random c
ascade model. The proposed rainfall model is shown to successfully reproduc
e the statistical behavior of individual storms as well as, and in particul
ar, the statistical behavior of annual maxima. In contrast, a model based o
n a gamma distribution for rainfall intensity substantially underestimates
the absolute values of extreme events and does not correctly reproduce thei
r scaling behavior. Similarly, a model based on self-similar random cascade
(as opposed to the bounded cascade) substantially overestimates the extrem
e events.