The Geomorphological Instantaneous Unit Hydrograph (GIUH) is widely used in rainfall-runoff modeling. We are proposing herein to apply the GIUH concept to characterize flash flood events. The width function-based GIUH has been adapted by means of inverse modeling to identify the Event-specific GIUH (hereafter denoted EGIUH), which takes into account the spatial variability of rainfall and channel topology. The EGIUH can be considered as a hydrological signature characterizing the catchment response to a rainfall event. The purpose of this manuscript is twofold. The first goal is to proceed with a rigorous evaluation of the EGIUH identification method, while the second is to study the variability of the EGIUHs that characterize flash floods, which tend to strike several catchments. Applications are run on 15 catchments of the French Mediterranean Region over the period 1997-2021, i.e. encompassing a total of 233 flash flood events over which the peak flow has a return period of at least two years. This study provides a unique set of EGIUHs derived from observed flash floods. An analysis of EGIUH variability and parameters is also performed. A study of the sensitivity to EGIUH parameters as well as to the initial hyetogram of effective rainfall, as defined by the user, serves to assess the benefit and limitations of this method. A hierarchical cluster analysis is used to combine the EGIUHs of each catchment into a limited number of GIUHs, which remain significantly different from one another and representative of the catchment flash floods. A comparison of GIUHs representative of each catchment is complemented by comparing the main hydrological signatures of catchment response, as derived from these GIUHs. The GIUHs representative of the flash-flood clusters pave the way to a typology of the flash floods affecting a catchment.