Résumé
Rainfall-induced urban floods may trigger considerable damage. Free surface flow models incorporating the rainfall forcing are powerful tools for urban flood risk assessment. However, an accurate mapping of the flood risk requires space-time rainfall field resolutions that are not currently available from standard meteorological products (e.g. rainfall radar images). Relying on stochastic rainfall generators may provide promising surrogate rainfall fields. Key aspects that such a generator should reproduce are the alternance of rainy and dry time steps; within a rainy time step, spatial rainfall intermittency; the spatio-temporal dependence structure of rainfall fields and extreme events. The last aspect is especially relevant as far as rainfall-induced urban floods are concerned. However, existing stochastic generators are not designed explicitly to deal with extreme events. We present a review of spatial and spatio-temporal processes for extreme events arising from the extreme value theory framework. The main two classical types of processes are the max-stable and threshold exceedance processes which both assume that the process being modelled is asymptotically dependent. Flexible approaches have been proposed recently allowing also asymptotically independent framework.We discuss the inclusion of processes dedicated to extreme event modelling in a stochastic generator which raises a number of issues. In particular, transitions between regular and extreme events should be modelled, this being especially challenging for the dependence structure. Incorporating stochastic rainfall generators in operational systems flood risk assessment and/or warning systems requires fast running hydraulic simulation engines. Using stochastic generators in combination with upscaled hydraulic models appears as a promising research path.