The connection among different types of exponents characterizing multi
scaling properties of rainfall and a criterion for stationarity of ran
dom fields are discussed, and a new phenomenological model for rainfal
l 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 th
e cascade proceeds to smaller scales. This allows one to directly simu
late a multiscaling random field with an energy spectrum exponent, bet
a > 1, which is typical for rainfall time series data but which cannot
be produced by a standard alpha model. A procedure is proposed for es
timating the cascade parameters of this new bounded alpha model from o
bserved data. Parameters are estimated from two data sets with differe
nt degrees of intermittency and different spectral exponents. The boun
ded alpha model simulations using these parameters produced realistic
rainfall time series with spectral exponents similar to their observed
counterparts.