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 α 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, β>1, which is typical for rainfall time series data but which cannot be produced by a standard α model. A procedure is proposed for estimating the cascade parameters of this new bounded α model from observed data. Parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents. The bounded α model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts.