Rain gauge networks' limitations and the implications to hydrological modelling highlighted with a X-band radar

Precipitation risk and water management is a key challenge for densely populated urban areas. Applications derived from high spatio-temporal resolution observation of precipitations are to make our cities more weatherready. Finer resolution data available from dual polarised X-band radar measurements enhance engineering tools as used for urban planning policies as well as protection (mitigation/adaptation) strategies to tackle climate-change related weather events. For decades engineering tools have been developed to work conveniently either with very local rain gauge networks, or with mainly C-band radars that have gradually been set up for space-time remote sensing of precipitation. Most of the time, the C-band radars continue to be calibrated by the existing rain gauge networks. Inhomogeneous distributions of these networks lead to only a partial information on the rainfall fields. Here we show that the statistics of measured rainfall is strongly biased by the fractality of the measuring networks and that this fractality needs to be properly taken into account to retrieve the original properties of the rainfall fields, in spite of the radar data calibration. In this work, we use the semi-distributed hydrological modelling over the Bievre catchment to generate a virtual rain gauges' network. And, firstly, performing a fractal analysis of this network distribution, we demonstrate that the semi-distributed hydrological models statistically reduce the distributed (weather radar) rainfall fields into rainfall measured by a much scarcer network of virtual rain gauges. Then, with the help of the Intersection Theorem and multifractal theory, we statistically compare the virtual rain gauges' data with the rainfall data measured by the dual-polarimetric X-band radar operated at Ecole des Ponts with a spatial resolution of 250 m, providing pre-factors that indicate the need of a proper renormalisation of rain gauge rainfall data when comparing (or calibrating) with radar data and the possible counter productivity of this conditioning.