Choice of distribution functions for hydrologic design

The problem of selecting a bivariate probability density function (pdf) for the simultaneous water stages at both ends of a confluence reach is considered. This pdf is used to compute the expected flood losses in the design of a levee with minimum expected yearly cost. A case study in Hungary illustrates the methodology throughout the paper. Two model selection procedures are compared: ranking the candidate pdf's by the likelihood of the X2 statistic and ranking them by their sample likelihoods. A composite model consisting of a linear combination of candidate pdfs weighted proportionally to their sample likelihoods is also considered. It is found that the two selection procedures lead to different choices, which in the example represent a significant cost variation. Although the ranking of the distributions reduces the uncertainty by imposing an ordering within the candidate set, a unique pdf does not fully account for the model uncertainty. In this sense the composite model seems a more reasonable choice, especially if the decisions are based on expected values.