Regionalization of extreme precipitation distribution using the principal components of the topographical environment

This paper deals with the regionalization of the extreme rainfall intensities in the volcanic island of Tahiti (French Polynesia), and focuses how the method automatically takes into account the topographical relief features. Principal component analysis of a digital elevation model supplies a limited set of variables describing the topographical environment. These synthetic descriptors are linked to the parameters of the rainfall intensity Gumbel distribution by using a stepwise regression adjusted on 20 point-rainfall records. The model is then applied on a regular 300-points grid node, and interpolated using a spline function to provide an approximation of the pluviometric risk all over the island. In the case of the island of Tahiti, the relationship between the rainfall parameter distributions and the topographical descriptors is very strong, and the method supplies a direct estimation, in space, of the rainfall statistics through the regression model. Validation of the results and comparison with simple kriging interpolation show the relevance of the approach. However, more data are needed for a better confidence in the parameter estimation in some areas of the island. This automatic and objective method could be applied in any mountainous area, where topography has a major influence on the precipitation features, to characterize the non-stationarity of point-rainfall statistics in space.