Precipitation modeling is of great interest for flood risk analysis. We propose to model the distribution of urban precipitation measured at high spatial and temporal resolution by the Montpellier Urban Observatory rain gauge network over four years of measurements. We combine them with radar reanalysis data to extend our analysis to a longer period with less fine resolution. For our modeling approach, we simultaneously consider moderate and intense rainfall by using the Extended Generalised Pareto Distribution (EGPD) to avoid explicit threshold selection, often tricky in extreme statistics, and to reduce the complexity of parameter estimation. We also model the spatio-temporal dependence by incorporating advection through a spatio-temporal Brown-Resnick process. We use indices of extremal autocorrelation, to show its variability between locations in relation to their spatial distances and to the temporality of the measurements. We will highlight the importance of including advection by comparing it with a simpler separable model.