Development and analysis of a simple model to represent the zero rainfall in a universal multifractal framework

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 enduring discussion on the source of this intermitt ncy, e.g. whether it requires 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 a wide range of scales with the help of a reduced number of parameters. However, this framework does not enable properly taking 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 cale invariant manner), it only has a predetermined probability to survive and is otherwise set to zero. A threshold can then be implemented at the maximum resolution to mimic the limit of detection of the rainfall measurement device. While also imperfect, this simple model enables explanation of most of the observed behaviour, e.g. the presence of scaling breaks, or the difference between statistics computed for single events or longer periods.