Integrated Frequency Analysis of Extreme Flood Peaks and Flood Volumes Using the Regionalized Quantiles of Rainfall Depths as Auxiliary Variables

In its 1988 report, the U.S. National Research Council identified principles to be followed in order to improve estimation of extreme flood quantiles. In spite of the many advances attained by more recent research on extreme flood estimation, the NRC principles remain useful recommendations to be considered, which are used in the methodology to be described herein. According to the proposed method, flood peaks that have exceeded an arbitrary threshold and their associated flood volumes are modeled as a marked point process. The estimation method consists of separately estimating the marginal density function of flood volumes and the density function of flood peaks conditioned on volumes. The annual probability distribution of flood peaks can then be estimated by double integrating the product of both densities. Regionalized quantiles of rainfall depths have been used as auxiliary variables for guiding the estimation of the upper tail of the marginal density function of flood volumes by postulating simple assumptions regarding the rainfall-runoff transformation under extreme conditions. The inclusion of the regional frequency analysis of rainfall depths, for the same duration as that of flood volumes, is performed by fitting a regional two-component extreme value distribution to rainfall data observed at a number of gauging stations within a homogeneous region. This paper summarizes the basic ideas of the method and the details of its application to a 1,620km2 watershed in southeastern Brazil.