Multifractal characterisation of a simulated surface flow: A case study with Multi-Hydro in Jouy-en-Josas, France

In this paper we suggest to innovatively use scaling laws and more specifically Universal Multifractals (UM) to analyse simulated surface runoff and compare the retrieved scaling features with the rainfall ones. The methodology is tested on a 3 km² semi-urbanised with a steep slope study area located in the Paris area along the Bièvre River. First Multi-Hydro, a fully distributed model is validated on this catchment for four rainfall events measured with the help of a C-band radar. The uncertainty associated with small scale unmeasured rainfall, i.e. occurring below the 1 km × 1 km × 5 min observation scale, is quantified with the help of stochastic downscaled rainfall fields. It is rather significant for simulated flow and more limited on overland water depth for these rainfall events. Overland depth is found to exhibit a scaling behaviour over small scales (10 m–80 m) which can be related to fractal features of the sewer network. No direct and obvious dependency between the overland depth multifractal features (quality of the scaling and UM parameters) and the rainfall ones was found.