Dimensionality reduction for regional flood frequency analysis: Linear versus nonlinear methods

Abstract

AbstractRegional flood frequency analysis is still an important area of hydrology research as there are many ungauged catchments. The majority of hydrological methods in regional flood frequency analysis involve complex non‐linear relationships between predictor variables and flood characteristics. In the past, dimensionality reduction techniques based on linear methods such as canonical correlation analysis (CCA) were used in regional flood frequency analysis to delineate hydrological clusters. Non‐linear dimensionality reduction techniques, such as KCCA and multidimensional scaling (MDS), have been used in several fields of science, but not explicitly in regional flood frequency analysis. To determine hydrologically similar clusters, the approaches considered in this article use CCA, KCCA, and MDS as dimensionality reduction techniques in conjunction with Gaussian mixture models (GMM). Log‐linear regression and generalized additive models are then applied to the hydrological clusters to evaluate regional flood frequency analysis. A comparison of linear and non‐linear (NL) methods is performed using data from Victoria, Australia, to demonstrate the benefit of these methods. It has been found that the non‐linear frameworks of multi‐dimensional scaling with Gaussian mixture model‐non‐linear (MDSGMM‐NL) and KCCA with Gaussian mixture model‐non‐linear (KCCAGMM‐NL), as well as the mixed frameworks (i.e. KCCA and Gaussian mixture model‐non‐linear [CCAGMM‐NL]), can be used to represent the non‐linear complexities of hydrological processes in regional flood frequency analysis.