The high variability of rainfall fields comes from (1) the occurrence
of wet and dry events and (2) from the intermittency of precipitation
intensities. To model these two aspects for spatial variability, Over
and Gupta [1996] have proposed a lognormal cascade model with an atom
at zero, which corresponds to combine in one model two independent cas
cade models, the beta and the lognormal multifractal models. In the pr
esent work, we test this approach for time variability, using a high-r
esolution rainfall time series. We built a continuous version of the d
iscrete beta model and investigate some of its dynamical properties. W
e show that the beta model cannot fit the probability density for the
duration of the wet state. In order to model the succession of wet and
dry periods we therefore use a two-state (or alternate) renewal proce
ss based on appropriate fits of the empirical densities. The synthetic
series obtained this way reproduces the scaling of the original suppo
rt. The intensity of the rainfall events is then modeled using the uni
versal multifractal model, generalizing the lognormal model. We show t
hat the fractal support of the rainfall events must be taken into acco
unt to retrieve the parameters of this model. This combination of two
different models allows to closely reproduce the high variability at a
ll scales and long-range correlations of precipitation time series, as
well as the dynamical properties of the succession of wet and dry eve
nts. Simulations of the high-resolution rainfall field are then perfor
med displaying the salient features of the original time series.