A general probabilistic framework for prediction of extreme flow events at river confluences

Abstract. River confluences are critical nodes within river systems and are often exposed to increased flood risk, as the co-occurrence of peak streamflows and thus the superposition of flood waves from two or more tributaries may amplify their magnitudes, leading to compound extreme flow events. However, a systematic and holistic framework to analyse and predict extreme streamflows downstream of river confluences remains largely absent from the literature. This study investigates the interaction between upstream and downstream streamflows during extreme events at river confluences and provides a computationally efficient probabilistic framework for estimating extreme downstream flows based on combinations of upstream conditions from individual tributaries. In this work, a confluence is defined as the junction of two upstream river branches that merge into a downstream channel. We introduce a novel probabilistic-based methodology to describe and predict concurrent streamflows, including uncertainty quantification across the three branches when an extreme event occurs in at least one of them. Building on this, a copula-based probabilistic model is developed with a twofold objective: (i) to predict downstream flow given different combinations of upstream conditions, and (ii) to determine combinations of upstream flows associated with downstream flows exceeding specified safety thresholds. The proposed framework is demonstrated and tested using three contrasting river confluences: two confluences in the Rhine river system in Germany i.e., Rhine–Nahe at Bingen and Rhine–Main at Mainz, and the Mississippi-Missouri confluence at St. Louis in the United States. The results demonstrate that confluences sharing the same main river can behave fundamentally differently under extreme conditions. In the Rhine-Nahe system the influence of Nahe to the downstream streamflow is limited due to its smaller size compared to the Rhine. On the other hand, for the Rhine-Main confluence which is characterized by an intermediate difference between the magnitudes of the two contributing river branches, the results show that the superimposition of the flood waves remains a major control of downstream extreme floods. In contrast, for the Mississippi–Missouri confluence, where upstream streamflows of the two contributing river branches are of comparable magnitude, the simultaneous occurrence of moderate peaks is a primary driver of downstream extreme streamflows. In other words, under such conditions, the superimposition of individual flood waves is not the only dominant control on downstream extreme floods, but has the potential to lead to extreme flow events that may have catastrophic consequences. The probabilistic model developed here demonstrates high predictive skill in reproducing downstream streamflows from upstream observations with Nash–Sutcliffe Efficiency, NSE > 0.97 in all cases, despite the contrasting mechanisms underlying the generation of flood waves at the three study confluences, indicating its generalizability and robustness for estimating and predicting upstream flow combinations that may lead to downstream streamflows beyond safety thresholds.