Obtaining Homogeneous Regions by Determining the Generalized Fractal Dimensions of Validated Daily Rainfall Data Sets

Abstract

Extreme rainfall data are widely used in several hydrological models and civil engineering design. Despite high temporal resolution rainfall data are not commonly available, daily rainfall data series are easily found. When these available data series are short in length the Regional Frequency Analysis (RFA) is a good tool to enlarge them by joining stations into homogeneous regions. This is by far, the most complicated step in RFA. This work presents a new method to form homogeneous regions of extreme annual daily rainfall data series. Daily rainfall data series from 53 weather stations in the Maule Region (Chile) have been used. Their fractal dimensions spectra have been obtained by applying the box counting method. Each station has been characterized by the fractal dimensions D1 and D2. A cluster analysis has been carried out based on these at-site characteristics and three regions have been obtained. After performing a RFA of extreme daily annual rainfall data series within each region they have shown as homogeneous. Only one of the available stations has not been possible to be included into any homogeneous regions, being the local frequency analysis the only suitable method to be applied at this location.