Analytical confidence intervals for index flow flow duration curves

Abstract

This study illustrates how analytical period‐of‐record flow duration curves (FDCs) and annual FDCs (AFDCs) of daily streamflow series developed in an index flow framework can be complemented by theoretical confidence intervals (CIs) deduced from the theory of nonparametric CIs for quantiles and fractional order statistics. By focusing on AFDCs, the proposed approach yields results very close to CIs for order statistics which are commonly used to construct AFDCs and CIs for AFDCs. When the method is applied to index flow FDCs, the comparison with Monte Carlo techniques allows the elucidation of some properties of FDCs which have not been previously explored in depth. The approach helps to overcome the problem of lack of CIs for index flow FDCs by introducing approximate analytical CIs based on an effective sample size. Thus, the underlying idea is emphasized that CIs of index flow FDCs and AFDCs can be coherently obtained by reasoning in terms of distribution of quantiles rather than distribution of order statistics. Moreover, a few results taken from nonparametric statistics allow the introduction of semiparametric index flow FDCs and AFDCs which are potentially useful for parsimonious regionalization procedures.