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 &agr; 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, &bgr;>1, which is typical for rainfall time series data but which cannot be produced by a standard &agr; model. A procedure is proposed for estimating the cascade parameters of this new bounded &agr; model from observed data. Parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents. The bounded &agr; model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts. ¿ 1997 American Geophysical Union