Design flood estimation in ungauged catchments by quantile regression technique: Ordinary least squares and generalised least squares compared

Design flood estimation in small to medium sized catchments is frequently required in hydrologic analysis and design and is of notable economic significance. Australian Rainfall and Runoff 1987 recommends the Probabilistic Rational Method for general use in southeastern Australia. The central component of this method is a runoff coefficient which is assumed to vary smoothly over a geographical area and over a range of average recurrence intervals but there has been criticism of the runoff coefficients because it does not show meaningful links with catchment characteristics. More recent design flood estimation techniques have the potential to provide more meaningful and accurate design flood estimation in small-to-medium sized ungauged catchments; for instance, the L moments based index flood method and the quantile regression technique. This paper is concerned with the quantile regression technique and compares two methods: ordinary least squares and generalised least squares estimators. This study uses data from 98 catchments in southeastern Australia to develop prediction equations involving readily obtainable catchment characteristics data. Even though the differences in the model parameter estimates are modest, the generalised least squares technique is shown to be better than the ordinary least squares technique in terms of average variance of prediction.