Two-Component Extreme Value Distribution

Abstract

It is well known that floods may be generated by different physical mechanisms. For instance, most of the annual flood maxima at a particular site might be the result of a primary mechanism, such as frontal storms. A smaller fraction of the events, however, might be associated with a secondary mechanism, such as rain on snow with frozen soils, that occasionally gives rise to floods larger than those associated with the primary mechanism. In this regard, Rossi et al. (1984) proposed a two-component extreme value distribution. This distribution belongs to the family of distributions of the annual maxima of a compound Poisson process, which forms a theoretical basis for annual flood series analysis. Single-component distribution methods of estimating return periods and probabilities of flood events do not work well when runoff originates from nonhomogeneous sources, i.e., when a mixture random variables is involved. The most important consideration in selecting a distribution for use in flood frequency analysis is the behavior of the right tail of the distribution. It is from the right tail that return periods and probabilities of rare events are determined. The two-component extreme value (TCEV) distribution permits a reasonable interpretation of the physical phenomenon which generates floods and is able to account for most of the characteristics of the real world flood data, important among them being the large variability of the sample skewness coefficient which mostly gives rise to the poor performance of many of the commonly used flood frequency distributions. The two component extreme value (TCEV) distribution has been shown to account for most of the characteristics of the real flood experience. The TCEV distribution also offers a practical approach to regional flood frequency estimation. Theoretical properties of the TCEV distribution have been widely investigated (Rossi, et al., 1984; Berm, et al., 1986; Rossi, et al., 1986; Fiorentino et al., 1987a, b). In his extensive review of a large number of commonly used distributions, Cunnane (1986) concluded that only the two-component extreme value distribution and the Wakeby distribution satisfied the important reproductive criterion--an ideal distribution must reproduce at least as much variability in flood characteristics as is observed in empirical data.