Spatial dependences among precipitation maxima over Belgium

For a wide range of applications in hydrology, the probability distribution of precipitation maxima represents a fundamental quantity to build dykes, propose flood planning policies, or more generally, to mitigate the impact of precipitation extremes. Classical Extreme Value Theory (EVT) has been applied in this context by usually assuming that precipitation maxima can be considered as Independent and Identically Distributed (IID) events, which approximately follow a Generalized Extreme Value distribution (GEV) at each recording site. In practice, weather stations records can not be considered as independent in space. Assessing the spatial dependences among precipitation maxima provided by two Belgium measurement networks is the main goal of this work. The pairwise dependences are estimated by a variogram of order one, also called madogram, that is specially tailored to be in compliance with spatial EVT and to capture EVT bivariate structures. Our analysis of Belgium precipitation maxima indicates that the degree of dependence varies greatly according to three factors: the distance between two stations, the season (summer or winter) and the precipitation accumulation duration (hourly, daily, monthly, etc.). Increasing the duration (from one hour to 20 days) strengthens the spatial dependence. The full independence is reached after about 50 km (100 km) for summer (winter) for a duration of one hour, while for long durations only after a few hundred kilometers. In addition this dependence is always larger in winter than in summer whatever is the duration. An explanation of these properties in terms of the dynamical processes dominating during the two seasons is advanced.