Evaluation of classical spatial-analysis schemes of extreme rainfall

Extreme rainfall is classically estimated using raingauge data at raingauge locations. An important related issue is to assess return levels of extreme rainfall at ungauged sites. Classical methods consist in interpolating extreme-value models. In this paper, such methods are referred to as regionalization schemes. Our goal is to evaluate three classical regionalization schemes. Each scheme consists of an extreme-value model (block maxima, peaks over threshold) taken from extreme-value theory plus a method to interpolate the parameters of the statistical model throughout the Cévennes-Vivarais region. From the interpolated parameters, the 100-yr quantile level can be estimated over this whole region. A reference regionalization scheme is made of the couple block maxima/kriging, where kriging is an optimal interpolation method. The two other schemes differ from the reference by replacing either the extreme-value model block maxima by peaks over threshold or kriging by a neural network interpolation procedure. Hyper-parameters are selected by cross-validation and the three regionalization schemes are compared by double cross-validation. Our evaluation criteria are based on the ability to interpolate the 100-yr return level both in terms of precision and spatial distribution. It turns out that the best results are obtained by the regionalization scheme combining the peaks-over-threshold method with kriging.