Estimation of flood peak distributions considering reservoir effects on tail behavior

Hydrological extremes pose significant challenges to flood risk assessment and mitigation, particularly under non-stationary climatic and hydrological conditions. Hydraulic structures, such as large reservoirs, modify flood distributions by attenuating peak flows, with their effectiveness varying over return periods. This variability introduces non-stationarity in flood frequencies and has a significant impact on the tail of the distribution. As a result, data-driven approaches to flood frequency estimation can lead to under- or overestimation of flood quantiles, especially when limited observations are available. To address these challenges, we propose an analytical framework capable of defining the full probability distribution of floods at a control section. This method explicitly incorporates key physical processes, including the influence of reservoir volume, non-linear spillway behavior and threshold discharge on inflow hydrographs. The accuracy of the estimations is demonstrated by comparisons with numerical simulations of reservoir routing using the continuity equation in a real case study. Our results highlight the critical role of integrating physical processes into flood modelling to capture tail behavior, and show how statistical approaches applied to small samples of flood peak observations can instead lead to significant biases. The proposed analytical solution provides a robust and parsimonious tool for estimating the impact of reservoirs on floods, with applications in both risk assessment and infrastructure planning.