Regionalization of watersheds by fuzzy cluster analysis

Because of the paucity of flood data, it is not always possible to use at-site frequency analysis to arrive at estimates of flood quantiles. To contend with this problem, hydrologists use regionalization methods to classify catchments in a region into groups that are homogeneous in flood response. In traditional methods of regionalization, a catchment is classified as belonging to a group on the basis of its dissimilarity with other catchments in the region in a multi-dimensional space of attributes affecting their flood response. However, most catchments only partly resemble other catchments in a region. Therefore one cannot fully justify assigning a catchment to one group or another. The fuzzy clustering algorithm (FCA) allows a catchment to have partial or distributed memberships in all the regions (groups) identified. In this paper, a FCA is tested for regionalization of watersheds. The regions given by clustering algorithms are, in general, not statistically homogeneous. Consequently, they are adjusted to improve their homogeneity. The effort needed to adjust a region is considerable when hard clustering algorithms are used to form hydrologic regions. In fuzzy cluster analysis, the knowledge of distribution of membership of a catchment among the fuzzy regions is useful in adjusting the regions to improve their homogeneity. The effectiveness of the FCA in deriving homogeneous regions for flood frequency analysis is illustrated through its application to annual maximum flow data from the watersheds in Indiana, USA. The effectiveness of several fuzzy cluster validation measures in determining optimal partition provided by the FCA is also addressed.