High resolution rainfall fields contain numerous zeros (i.e pixels or time steps with no rain) which are either real or artificial that is to say associated with the limit of detection of the rainfall measurement device. In this paper we revisit the long lasting discussion on the source of this intermittency, e.g. whether it requires a specific modelling. We first review the framework of Universal multifractals (UM), which are commonly used to analyse and simulate geophysical fields exhibiting extreme variability over wide range of scales with the help of reduced number of parameters. However this framework does not enable to properly take into account these numerous zeros. For example it has been shown that performing a standard UM analysis directly on the field can lead to low observed quality of scaling and severe bias in the estimates of UM parameters. In this paper we propose a new simple model to deal with this issue. It is a UM discrete cascade process, where at each step if the simulated intensity is below a given level (defined in a scale invariant manner), it only has a predetermined probability to survive and is otherwise set to zero. This threshold can then be chosen at the maximum resolution to model the limit of detection of the rainfall measurement device. Also imperfect, this simple model enables to explain most of the observed behaviour e.g. the presence of scaling breaks, or the difference between statistics computed for single events or longer periods.