Multiscaling properties of rainfall and bounded random cascades

The connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed, and a new phenomenological model for rainfall time series simulation is proposed. The bounded random cascade model presented here is a generalization of the well-known alpha model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales. This allows one to directly simulate a multiscaling random field with an energy spectrum exponent, beta > 1, which is typical for rainfall time series data but which cannot be produced by a standard alpha model. A procedure is proposed for estimating the cascade parameters of this new bounded alpha model from observed data. Parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents. The bounded alpha model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts.