Linear, nonlinear, parametric and nonparametric regression models for nonstationary flood frequency analysis

In recent years, nonstationary flood frequency analysis (NFFA) has become an active area of research. It is crucial for water resources management and hydrologic engineering design to cope with the changing environment. Finding suitable and effective models could help perform better flood frequency analysis and make reliable estimates under the nonstationary environment. This study assesses different modelling techniques for nonstationary flood frequency analysis, including linear, nonlinear, parametric and nonparametric models using an extensive data set of 161 catchments across the UK. It identifies that rejection rates are generally higher for precipitation-informed NFFA models than time-varying NFFA models. For both time-varying and precipitation-informed NFFA, rejection rates for linear and cubic polynomial models are the highest. The models with the fewest rejections are fractional polynomial models followed by cubic spline models. Because of the flexibility, parsimony, and user-friendly features, fractional polynomial models could be a potential alternative for modelling the nonstationary behaviour of flood series. To investigate whether the seasonal flood variation and catchment characteristics influence the goodness-of-fit, a quantified seasonality index was calculated to illustrate the degree of seasonal variation of flooding for each catchment. It was found that the southeast of the UK has more significant seasonal flood variation than the northwest, and most of the catchments with high seasonality indexes are close to the Scotland and England border. Nevertheless, the correlation analysis shows insufficient evidence to conclude that catchment characteristics and seasonal flood variation impact the goodness-of-fit of the NFFA models.