Radar data are used to characterize the spatial variability of rainfall, in particular its scale invariant properties, which lead to nonlinear stochastic fractal models. The dataset was collected in summer 2006 by the RONSARD radar during the African Monsoon Multidisciplinary Analysis (AMMA) campaign and consists of reflectivity maps with a 400m pixel size. The statistics of the reflectivity field are shown to depend on the resolution in a multiscaling way that is adequately represented by the three-parameter Universal Multifractal (UM) model. The estimated parameters show that the process is greatly intermittent and may produce enough extreme values (singularities) so that the highorder statistical moments of the process diverge, resulting in heavy-tailed probability distributions. The physical meaning of the parameters may be easily illustrated by numerical simulations of UM fields. Moreover, it is demonstrated that the extreme values of the reflectivity maps follow a power-law of the resolution λ, as predicted by the UM model. The scaling exponent γ=0.75 is close to that expected from the equations of the UM theory and may be retrieved from the analysis of the simulated UM fields. Such a powerlaw has strong implications on the corrections to do when comparing measurements at different resolutions (e.g. radar pixel/ rain gauge size). To illustrate, some potential applications of the latter equation to spatial downscaling of meteorological and hydrological processes are exposed.