Modeling of rainfall time series and extremes using bounded random cascades and Levy-stable distributions

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.