A bivariate copula-wavelet analysis approach for quantifying compound runoff-sediment risks under cascade reservoirs

Understanding compound dynamics of runoff and sediment is essential for managing river basins affected by cascade reservoirs. This study proposes a bivariate copula-wavelet risk analysis (BCWRA) approach to assess synchronous and asynchronous runoff-sediment risks. This approach integrates trend detection, periodicity analysis, copula-based joint probability modeling, and joint return period estimation. BCWRA is then applied to four hydrological stations in the Upper Yellow River Basin (UYRB) to demonstrate its advantages. The results show that cascade reservoir operations reduce synchronous runoff-sediment events by an average of 17.74%, while increasing asynchronous combinations by 18.25%. Particularly, midstream stations exhibit increased risks of sediment retention and channel erosion. The BCWRA approach reveals that reservoir regulation reduces runoff variability and significantly decreases sediment transport, resulting in shorter return periods under the OR condition, in which at least one of the two variables exceeds the defined threshold. We propose adaptive management strategies, including real-time monitoring and coordinated sediment flushing, to mitigate these risks. This study focuses on the two principal regulating reservoirs, Longyangxia and Liujiaxia, and therefore primarily captures their dominant regulation signals. Consequently, the presented dependence and risk changes may underestimate additional interactions arising from the broader cascade system in the upper Yellow River. This study advances risk analysis methodologies for regulated rivers, offering generalizable tools for managing compound hydrological hazards.