Data collected during four heavy rainfall events that occurred in Ardeche (France) with the help of a 2D video disdrometer (2DVD) are used to investigate the structure of the raindrop distribution in both space and time. A first type of analysis is based on the reconstruction of 36-m-height vertical rainfall columns above the measuring device. This reconstruction is obtained with the help of a ballistic hypothesis applied to 1-ms time step series. The corresponding snapshots are analyzed with the help of universal multifractals. For comparison, a similar analysis is performed on the time series with 1-ms time steps, as well as on time series of accumulation maps of N consecutive recorded drops (therefore with variable time steps). It turns out that the drop distribution exhibits a good scaling behavior in the range 0.5-36 m during the heaviest portion of the events, confirming the lack of empirical evidence of the widely used homogenous assumption for drop distribution. For smaller scales, drop positions seem to be homogeneously distributed. The notion of multifractal singularity is well illustrated by the very high-resolution time series.