Inferring Spatio-temporal Patterns in Extreme Snowfall in the French Alps Using Max-stable Processes

Abstract

Our objective is to study the dependence structure of extreme snowfall in the French Alps. Snowfall amount measurements (3 days accumulation period) from 90 monitoring stations providing data spanning from 1958 to 2013 were projected at the same altitude level (1800m). Annual maxima of projected snowfall were modeled with Generalized Extreme Value (GEV) distributions and transformed in unit Fréchet in order to focus on the dependence structure only. The final goal is to evaluate the spatio-temporal evolution of this dependence structure and to compare the ability of different max-stable models to capture it. In addition to the most classical max-stable models (Smith and Schlather), max-stable processes made available more recently (extremal-t, Geometric Gaussian and Brown-Resnick) were also considered, taking into account spatial anisotropy. These latter models are found to be the most suitable in our case according to CLIC. Further cross-validation on joint exceedance probabilities does not clearly discriminate these max-stable models. Results show that measurement stations in the Northern and Central Alps are strongly dependent whereas stations from the extreme Southern Alps, influenced by Mediterranean effects, are more isolated. Furthermore, extremal dependence appears controlled by the orientation of mountains and valleys. Finally, using an estimation window moving in time, we highlight a recent decrease in extremal dependence at large distances.