Comparison between quantile regression technique and generalised additive model for regional flood frequency analysis

Abstract

Design flood estimates are needed for the planning and design of hydraulic structures, and in many other water and environmental management tasks. Design flood estimation is a challenging task, in particular for poorly gauged and ungauged catchments. In Australia, there are numerous ungauged catchments; for these catchments Regional Flood Frequency Analysis (RFFA) techniques are generally adopted to estimate design floods. Most of the RFFA techniques previously adopted in Australia are based on rational method and/or linear modelling approaches. However, with the recent advancements in statistical computation methods, there are several other techniques becoming popular gradually in hydrological applications which can account for non-linearity in the rainfall-runoff processes. Generalized additive model (GAM) is one of the recently developed techniques which can deal with the non-linearity, which has not been widely explored in hydrological research, in particular for the RFFA problems. Therefore, this research is devoted to examining the applicability of GAM in RFFA and compare its performances with one of the most widely used linear RFFA technique (log-log linear model). This study is carried out using data from 114 small to medium sized gauged catchments of Victoria, Australia. This data has primarily been sourced from Australia Rainfall Runoff (ARR), Project 5 Regional Flood Methods. This study is based on a number of alternative groups, e.g. a combined group consisting of all the 114 catchments and sub-groups formed based on cluster analysis. Four regions are formed using hierarchical and k-means clustering techniques. All the five groups are used for developing log-log linear models and GAM based models. The predictor variables for each of these models are selected based on the statistical significance of the predictor variables, i.e. p-statistics. For validation of the developed prediction models, a 10-fold cross validation method is adopted. The performances of the prediction models for the alternative models are assessed using a number of statistical measures including coefficient of determination (R2), median relative error (RE) and median Qpred/Qobs ratio values. It is found that, none of the models from the combined group and clustering groups perform equally well for the six average recurrence intervals (ARIs) (2, 5, 10, 2, 50 and 100 years) with respect to the selected statistical measures. Overall, log-log linear model from clustering group A1 is found to be the best performing model. GAM based RFFA models perform better for smaller ARIs (i.e., 2, 5 and 10 years); which is as expected since the hydrological behaviour of catchments for smaller ARIs is generally more non-linear, e.g. higher loss and hence rainfall produces lower runoff for more frequent events. Some predictor variables (e.g., evap), which were not adopted in the previous RFFA models, in Australia are found to be significant in the GAM based RFFA models. Overall, it is found that consideration of non-linearity via GAM can add new dimensions in RFFA modelling for selecting appropriate predictor variables and to deal with non-linearity. Overall, the results of this study demonstrate that GAM has a strong potential to enhance the accuracy of RFFA models in Australia; however, additional predictor variables are needed (than what are included in this study) to capture the non-linearity more explicitly between runoff and flood producing variables.

Date of Award	2018
Original language	English