Regional flood frequency analysis: evaluation of regions in cluster space using support vector regression

Regional flood frequency analysis (RFFA) remains an area of active research around the world. Obtaining reliable RFFA estimates is critical for many hydrological and environmental studies. To this end, RFFA models based on multidimensional scaling (MDS) are coupled with support vector regression (SVR) to obtain improved flood quantile estimates at ungauged sites. MDS is used to form regions in catchment data space using the site characteristics and geographical distance from gauged sites. Then SVR models are applied to identify the functional relationships between flood quantiles and the catchment characteristics variables in MDS space, in particular SVR is used to capture the complexity and nonlinearity in flood generation processes that may not be easily captured in loglinear models. Four SVR models: linear, polynomial, radial basis function (RBF) and the sigmoid kernel models, are developed. The proposed approaches are applied to 202 catchments in the States of New South Wales and Victoria, Australia. The leave-one-out validation procedure is used to evaluate the performance of the proposed models. Results of the proposed models are compared with Bayesian generalised least squares regression which is also developed in MDS space. The results indicate that the MDS-RBF-based SVR model provides more consistent flood quantile estimates than the competing SVR models. The RBF SVR approach also demonstrates better generalisation ability than the competing SVR models examined. The MDS-based SVR RBF kernel generally shows the best performance among all the models in terms of prediction accuracy. Overall, the main strengths of the SVR are that it captures efficiently the nonlinearity between the dependent and predictor variables and when coupled with MDS for delineation of regions, the prediction ability of the model increases along with a reduction in bias and relative error.