For flood risk analysis, precipitation modeling is of great interest. We propose modeling the distribution of rainfall measured at a high spatial and temporal resolution by the urban observatory of Montpellier since 2019. To our knowledge, there has been no such study in France concerning Mediterranean episodes at such a fine spatio-temporal scale in an urban environment. For our modeling approach, we consider moderate and intense rainfall. To avoid the explicit threshold selection that is often delicate in statistics of extremes, we use the Extended Generalized Pareto Distribution (EGPD) for our modeling. This family of distribution also allows us to limit the number of parameters to be estimated. Moreover, we conduct an analysis of the extremal dependence between the different rain gauges of the measurement network via indices of extremal autocorrelation to show its variability between the sites in relation to their spatial distances and to the temporality of the measurements. Finally, we estimate a parametric space-time extreme-value model for these rainfall data using weighted least squares between empirical and parametric versions of summary statistics of extremal dependence.