Prediction uncertainty in a median‐based index flood method using L moments

Abstract

The standard for conducting flood frequency analysis in the UK, as set out in the Flood Estimation Handbook, is based on the index flood method, using the median of the annual maximum flood as the index flood. For a given target site, a region‐of‐influence approach is used, involving the creation of a collection of hydrologically similar catchments (pooling group). This paper examines the sampling uncertainty of quantile estimates on the basis of pooling groups and using the median as the index flood for both gauged and ungauged sites. Analytical approximations for the variance of the quantile estimates were derived, on the basis of asymptotic theory, and were used to calculate approximate confidence intervals for flood frequency curves obtained using both single‐site and pooled analysis at gauged and ungauged sites. A series of bootstrap experiments were conducted to quantify the intersite dependence and to develop generalized expressions to be included in the analysis. It is shown that the pooled analysis yields narrower confidence intervals than the single‐site analysis and that the presence of intersite correlations increases the sampling uncertainty. The method was extended to encompass estimation at ungauged sites in the UK on the basis of a regression model for the index flood, which significantly increases the prediction uncertainty compared with using an estimate of the index flood derived from observations at the target site.