HYDROLOGICAL PROCESSES (wileyonlinelibrary.com) DOI: 10.1002/hyp.8189 Regional flood frequency analysis using Bayesian generalized least squares: a comparison between quantile and parameter regression techniques Khaled Haddad, 1 Ataur Rahman 1 * and Jery R. Stedinger 2 1 School of Engineering, University of Western Sydney, Penrith, Sydney, Australia 2 School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14850, USA Abstract: Regression-based regional flood frequency analysis (RFFA) methods are widely adopted in hydrology. This paper compares two regression-based RFFA methods using a Bayesian generalized least squares (GLS) modelling framework; the two are quantile regression technique (QRT) and parameter regression technique (PRT). In this study, the QRT focuses on the development of prediction equations for a flood quantile in the range of 2 to 100 years average recurrence intervals (ARI), while the PRT develops prediction equations for the first three moments of the log Pearson Type 3 (LP3) distribution, which are the mean, standard deviation and skew of the logarithms of the annual maximum flows; these regional parameters are then used to fit the LP3 distribution to estimate the desired flood quantiles at a given site. It has been shown that using a method similar to stepwise regression and by employing a number of statistics such as the model error variance, average variance of prediction, Bayesian information criterion and Akaike information criterion, the best set of explanatory variables in the GLS regression can be identified. In this study, a range of statistics and diagnostic plots have been adopted to evaluate the regression models. The method has been applied to 53 catchments in Tasmania, Australia. It has been found that catchment area and design rainfall intensity are the most important explanatory variables in predicting flood quantiles using the QRT. For the PRT, a total of four explanatory variables were adopted for predicting the mean, standard deviation and skew. The developed regression models satisfy the underlying model assumptions quite well; of importance, no outlier sites are detected in the plots of the regression diagnostics of the adopted regression equations. Based on ‘one-at-a-time cross validation’ and a number of evaluation statistics, it has been found that for Tasmania the QRT provides more accurate flood quantile estimates for the higher ARIs while the PRT provides relatively better estimates for the smaller ARIs. The RFFA techniques presented here can easily be adapted to other Australian states and countries to derive more accurate regional flood predictions. Copyright  2011 John Wiley & Sons, Ltd. KEY WORDS regional flood frequency; Bayesian method; quantile regression; parameter regression; design floods Received 11 November 2010; Accepted 23 May 2011 INTRODUCTION Flood quantile estimation in ungauged catchments is a common problem in hydrology. Regional flood fre- quency analysis (RFFA) is often used for this purpose, which is to ‘trade space for time’ (Hosking and Wal- lis, 1997). Regression-based methods are widely used in RFFA which is based on the concept that spatial vari- ations in flood flow statistics are closely related with variations in regional catchment and climatic character- istics (Gupta et al., 2006; Pandey and Nguyen, 1999; Nezhad et al., 2010). The most common form of the regression approach is to develop a regression equation for a flood quantile of interest, known as the quantile regression technique (QRT) (Benson, 1962; Thomas and Benson, 1970). The United States Geological Survey has adopted the QRT as the standard RFFA method since the 1960s (Gupta et al., 1994). * Correspondence to: Ataur Rahman, School of Engineering, University of Western Sydney, Penrith, Sydney, Australia. E-mail: a.rahman@uws.edu.au Hydrologists commonly use ordinary least squares (OLS) estimators that are appropriate and statistically efficient if the flow records are of equal length and if concurrent flows between any pair of stations are uncor- related (Tasker et al., 1986). These are often violated with regional annual maximum flood series data. To over- come the problems with the OLS regression, Stedinger and Tasker (1985, 1986) developed a GLS model that accounts for the differences in at-site record lengths and inter-site correlation among at-site estimators. Stedinger and Tasker (1985, 1986) showed in a Monte Carlo simu- lation that the GLS estimators provide model regression parameters with smaller mean-squared errors than the competing OLS estimators, provide relatively unbiased estimates of the variance of the regression parameters and results in a more accurate estimate of the regression model error. GLS regression has been widely adopted in hydrology (Tasker and Stedinger, 1989; Madsen et al., 1995; Madsen and Rosbjerg, 1997; Kroll and Stedinger, 1999; Reis et al., 2005; Eng et al., 2005; Griffis and Ste- dinger, 2007; Gruber and Stedinger, 2008; Hackelbusch et al., 2009; Micevski and Kuczera, 2009). Copyright  2011 John Wiley & Sons, Ltd. Hydrol. Process. 26, 1008–1021 (2012) Published online 201 in Wiley Online Library 29 June 1