In large urban areas, storm water management is a challenge with enlarging impervious areas. Many cities have implemented real time control (RTC) of their urban drainage system to either reduce overflow or limit urban contamination. A basic component of RTC is hydraulic/hydrologic model. In this paper we use the multifractal framework to suggest an innovative way to test the sensitivity of such a model to the spatio-temporal variability of its rainfall input. Indeed the rainfall variability is often neglected in urban context, being considered as a non-relevant issue at the scales involve. Our results show that on the contrary the rainfall variability should be taken into account. Universal multifractals (UM) rely on the concept of multiplicative cascade and are a standard tool to analyze and simulate with a reduced number of parameters geophysical processes that are extremely variable over a wide range of scales. This study is conducted on a 3 400 ha urban area located in Seine-Saint-Denis, in the North of Paris (France). We use the operational semi-distributed model that was calibrated by the local authority (Direction Eau et Assainnissement du 93) that is in charge of urban drainage. The rainfall data comes from the C-Band radar of Trappes operated by Météo-France. The rainfall event of February 9th, 2009 was used. A stochastic ensemble approach was implemented to quantify the uncertainty on discharge associated to the rainfall variability occurring at scales smaller than 1 km x 1 km x 5 min that is usually available with C-band radar networks. An analysis of the quantiles of the simulated peak flow showed that the uncertainty exceeds 20 % for upstream links. To evaluate a potential gain from a direct use of the rainfall data available at the resolution of X-band radar, we performed similar analysis of the rainfall fields of the degraded resolution of 9 km x 9 km x 20 min. The results show a clear decrease in uncertainty when the original resolution of C-band radar data is used. This analysis highlights the interest of implementing X-band radars in urban areas. Indeed such radars provide the rainfall data at a hectometric resolution that would enable a better nowcasting and management of storm water. The multifractal properties of the simulated hydrographs were analysed with the help of simulated rainfall fields of resolution 111 m x 111 m x 1 min, lasting 4 hours, and corresponding to a 5 year return period event. On the whole, the discharge exhibits a good scaling behaviour over the range 4 h - 5 min. Both UM parameters tend to be greater for the discharge than for the rainfall. The notion of maximum probable singularity was used to clarify the consequences on the assessment of extremes. It appears that the urban drainage network basically reproduces the extremes, or only slightly damps them, at least in terms of multifractal statistics. The results were obtained with the financial support from the EU FP7 SMARTesT Project and the Chair "Hydrology for Resilient Cities" (sponsored by Veolia) of Ecole des Ponts ParisTech.