Development of a generalised least squares based quantile regression technique for design flood estimation in Victoria

Design flood estimation in small to medium sized ungauged catchments is frequently required in hydrologic analysis and design and is of notable economic significance. Australian Rainfall and Runoff (ARR) 1987 recommends the Probabilistic Rational Method for general use in south-east Australia. However, there have been recent developments that show significant potential to provide more meaningful and accurate design flood estimation in small to medium sized ungauged catchments. These include the L moments based index flood method and a range of quantile regression techniques. This paper focuses on quantile regression techniques and compares two methods: ordinary least squares (OLS) and generalised least squares (GLS) based regression techniques. The GLS based regression procedure accounts for the varying sampling error and model error in the regional model, thus one would expect more accurate flood quantile estimation by this method. This study uses data from 133 catchments in the state of Victoria to develop prediction equations involving readily obtainable catchment characteristics data. The GLS regression procedure is explored further by carrying out a 4-stage generalised least squares analysis where the development of the prediction equations is based on relating hydrological statistics such as mean flows, standard deviations, skewness and flow quantiles to catchment characteristics. The paper also presents the validation of the two techniques by carrying out a split sample validation on a set of independent test catchments. The results show that both the GLS and OLS methods can provide very reasonable quantile estimates for ungauged catchments in Victoria. However, based on the average variance of prediction and standard error of estimate, GLS method is preferable to OLS method.