At-site flood frequency analyses are usually based on annual flood series. Assuming independence and stationarity, a statistical distribution is fitted to the data using a given estimation method, and a flood with prespecified exceedance probability can then be inferred from this distribution. Much of the recent research on at-site flood frequency procedures has focussed on the adequate choice of distributions (D) and estimation methods (E), in Cunnane's [1987] terminology a D/E-procedure. Two components have to be considered when evaluating a particular D/E procedure: the descriptive and predictive ability [ Cunnane, 1987]. The former relates to the ability of a distribution to reproduce selected statistical charactistics of the data, in particular the density shape typically expressed by skewness and kurtosis measures. The predictive ability, on the other hand, refers to the accuracy, usually measured in terms of bias and mean square error, with which flood quantiles can be estimated.
Among the statistical characteristics used to assess the descriptiveness of D/E-procedures, the separation of skewness has played a key role in the eighties. The phenomenon emerged from the regional studies of Matalas et al. [1975], and although the conclusions drawn from this and other similar studies were of strict regional character, they have led to the recommandation of at-site D/E-procedures which in a satisfactory way can reproduce the separation of skewness. However, as pointed out by Ashkar et al. [1992], the separation of skewness can be explained entirely by the regional variation of parent (population) skewness coefficients. It is therefore an artifact and should be abandoned as a selection criterion.
Other avenues for assessing the descriptive ability of D/E-procedures comprise goodness-of-fit tests and moment ratio diagrams. Vogel [1986], and Vogel and McMartin [1991] developed goodness-of-fit tests based on probability plot correlation coefficients for several common distributions in hydrology. Moment ratio diagrams are used mostly in a regional context. In the classical moment ratio diagram, functions of sample skewness and kurtosis are plotted together with curves for potential distribution populations. Recently, L-moment ratio diagrams have become popular alternatives [ Vogel and Fennessey, 1993] to the classical diagrams, and they are discussed in more detail later. Bobée et al. [1993b] presented a moment ratio diagram based on functions of the harmonic, geometric, and arithmetic means. The inherent uncertainty of statistics calculated from small samples makes goodness-of-fit tests and moment ratio diagrams little useful for discriminating between various 3-parameter distributions, and for that reason several researchers have suggested the identification of parent distributions at a regional scale. Vogel et al. [1993b] found that for a 10-state region in the southwestern United States, the log-Pearson type 3, lognormal, 3-parameter lognormal, and generalized extreme value distributions were all equally acceptable from a descriptive point of view. For Australian data, Vogel et al. [1993a] found that the generalized extreme value and Wakeby distributions outperformed other candidates. In some regions, however, the generalized Pareto distribution was found superiour. This distribution has been little used for modeling annual floods, but probably deserves more attention in the future. Other studies with relevance to the descriptive ability of D/E-procedures include Gunasekara and Cunnane [1991, 1992], Cong et al. [1993], and Naghavi et al. [1993].
The predictive ability of a D/E-procedure is a relative measure, because it necessitates an assumption on the true distribution of floods, which in practice is always unknown. Commonly, it is assumed that the fitted and the parent distributions belong to the same family, and under this assumption, the bias, the root mean square error, or some other figure of performance can be computed either analytically or by simulation. Some of the studies on sampling properties of D/E-procedures published during the last four years are listed in Table 1.
Evidently, the choice of D/E-procedure should embed considerations of descriptive as well as of predictive ability of the various candidates. However, not much has been done to formally combine these two aspects of flood frequency analysis. Chow and Watt [1990] developed a decision support system which emulates the experience of experts in frequency modeling. Further research in that direction should be given high priority in the future.