A Bivariate Return Period Copula Application of Flood Peaks and Volumes for Climate Adaptation in Semi-Arid Regions

In semi-arid regions, flood events are often characterized by rapid runoff and high hydrological variability, posing significant challenges for infrastructure safety and flood risk assessment. Traditional flood frequency analysis methods, typically based on univariate models using annual flood peak, may fail to capture the full complexity of such events. This study investigates the limitations of the univariate approach through the analysis of the 2004 flood event in the Jaguaribe River basin (Brazil), which caused the Castanhão Reservoir to receive a discharge of more than 5 hm3 and fill from 4.5% to over 70% of its capacity in just 55 days. Although the peak discharge in 2004 was not an exceptional record, the combination of high flood volume and short duration revealed a much rarer event than suggested by peak flow alone. To improve compound flood risk assessment, a bivariate frequency analysis based on copula functions was applied to jointly model flood peak and average flood intensity. The latter is a variable newly proposed in this study to better capture the short-duration but high-volume flood until peak that can strongly influence dam safety. Specifically, for the 2004 event, the univariate return period of flood peak was only 35 years, whereas the joint return period incorporating both peak flow and average flood intensity reached 995 years—underscoring a potential underestimation of flood hazard when relying solely on peak flow metrics. Our bivariate return periods and the average flood intensity metric provide actionable information for climate adaptation, supporting adaptive rule curves and risk screening during initial impoundment and high-inflow events in semi-arid reservoirs. Collectively, the proposed methodology offers a more robust framework for assessing extreme floods in intermittent river systems and offers practical insights for dam safety planning in climatically variable regions such as the Brazilian Semi-Arid.