Depth and homogeneity in regional flood frequency analysis

Abstract

Regional frequency analysis (RFA) consists generally of two steps: (1) delineation of hydrological homogeneous regions and (2) regional estimation. Existing regionalization methods which adopt this two-step approach suffer from two principal drawbacks. First, the restriction of the regional estimation to a particular region by excluding some sites can correspond to a loss of some information. Second, the definition of a region generates a border effect problem. To overcome these problems, a new method is proposed in the present paper. The proposed method is based on three elements: (1) a weight function to treat the border effect problem, (b) a function to evaluate how "similar" each site is to the target one, and (c) an iterative procedure to improve estimation results. Element (b) is treated using the statistical notion of depth functions which is introduced to provide a ranking of stations in a multivariate context. Furthermore, the properties of depth functions meet the characteristics sought in RFA. It is shown that the proposed method is flexible and general and that traditional RFA methods represent special cases of the depth-based approach corresponding to particular weight functions. A comparison is carried out with the canonical correlation analysis (CCA) approach. Results indicate that the depth-based approach performs better than does CCA both in terms of relative bias and relative root mean squares error. Copyright 2008 by the American Geophysical Union.