Physically informed non-stationary modelling of flood parameters in UK rivers using copulas

Traditional bivariate flood frequency analysis often assumes stationarity, but climate change, land-use alterations, and other anthropogenic factors increasingly violate this assumption. This study introduces a novel, physically informed non-stationary bivariate framework for UK rivers, integrating flood peak discharge (Q) and volume (V) using copula functions. Daily streamflow records from six gauging stations were analysed, revealing significant upward trends through Mann-Kendall tests. The study applies GAMLSS with physically-based covariates, linking distribution parameters to annual total rainfall and time, identifying lognormal and gamma distributions as optimal non-stationary marginals. Dependence between Q and V is captured via the Gumbel-Hougaard copula, enabling dynamic joint return period estimation. Non-stationary risk indices highlight pronounced flood risk increases, especially in upstream basins. By explicitly coupling physically informed non-stationary marginals with copula-based dependence modelling, this approach offers an innovative framework for capturing evolving flood dynamics, enhancing the reliability of flood risk assessment and management under a changing climate.