A regional GEV scale-invariant framework for Intensity-Duration-Frequency analysis

We propose in this paper a regional formulation of Intensity-Duration-Frequency curves of point-rainfall maxima in a scale-invariant Generalized Extreme Value (GEV) framework. The two assumptions we make is that extreme daily rainfall is GEV-distributed - which is justified by Extreme Value Theory (EVT) - and that extremes of aggregated daily rainfall follow simple-scaling relationships. Following these assumptions, we develop in a unified way a GEV simple-scaling model for extremes of aggregated daily rainfall over the range of durations where scaling applies. Then we propose a way of correcting this model for measurement frequency, giving a new GEV-scaling model for extremes of aggregated hourly rainfall. This model deviates from the simple-scaling assumption. This framework is applied to the Mediterranean region of Cévennes-Vivarais, France. A network of about 300 daily raingage stations covering the last 50 years and accumulated to span the range 1 day-1 week is used to fit the scale invariant GEV-model locally. By means of spatial interpolation of the model parameters, and correction for measurement frequency, we are able to build a regional model with good performances down to 1 h duration, even though only one hourly station is used to build the model. Finally we produce mean and return level maps within the region in the range 1 h-1 week and comment on the potential rain storms leading to these maps.