Regional flood frequency analysis in eastern Australia: Bayesian GLS regression-based methods within fixed region and ROI framework – Quantile Regression vs. Parameter Regression Technique

Abstract

Summary In this article, an approach using Bayesian Generalised Least Squares (BGLS) regression in a region-of-influence (ROI) framework is proposed for regional flood frequency analysis (RFFA) for ungauged catchments. Using the data from 399 catchments in eastern Australia, the BGLS-ROI is constructed to regionalise the flood quantiles (Quantile Regression Technique (QRT)) and the first three moments of the log-Pearson type 3 (LP3) distribution (Parameter Regression Technique (PRT)). This scheme firstly develops a fixed region model to select the best set of predictor variables for use in the subsequent regression analyses using an approach that minimises the model error variance while also satisfying a number of statistical selection criteria. The identified optimal regression equation is then used in the ROI experiment where the ROI is chosen for a site in question as the region that minimises the predictive uncertainty. To evaluate the overall performances of the quantiles estimated by the QRT and PRT, a one-at-a-time cross-validation procedure is applied. Results of the proposed method indicate that both the QRT and PRT in a BGLS-ROI framework lead to more accurate and reliable estimates of flood quantiles and moments of the LP3 distribution when compared to a fixed region approach. Also the BGLS-ROI can deal reasonably well with the heterogeneity in Australian catchments as evidenced by the regression diagnostics. Based on the evaluation statistics it was found that both BGLS-QRT and PRT-ROI perform similarly well, which suggests that the PRT is a viable alternative to QRT in RFFA. The RFFA methods developed in this paper is based on the database available in eastern Australia. It is expected that availability of a more comprehensive database (in terms of both quality and quantity) will further improve the predictive performance of both the fixed and ROI based RFFA methods presented in this study, which however needs to be investigated in future when such a database is available.