Compound hydrological and thermal extremes: A nonstationary risk modeling approach for riverine ecosystems

The increasing frequency and severity of compound hydro-climatic extremes pose a growing threat to cold-water aquatic ecosystems. This study develops a nonstationary multivariate risk modeling framework to assess the joint behavior of extreme summer river water temperature (Tw) and concurrent low flow (Q) in six unregulated Atlantic salmon rivers in eastern Canada. A dynamic additive copula approach is employed to model both the structure dependence and nonstationarity, with time-varying effects modeled via large-scale climate oscillation indices (teleconnections) and a temporal trend representing climate change. The proposed joint nonstationary model (J_NS) is benchmarked against a joint stationary model (J_S) and a univariate nonstationary model (U_NS). Results show that J_NS systematically outperforms both alternatives across all study sites. Temporal trends significantly increased Tw extremes at most rivers, while teleconnections emerged as dominant drivers of variability. Negative phases of the Southern Oscillation Index (SOI, El Niño conditions) and the North Atlantic Oscillation Index (NAO) increase the variability of Tw and low-flow events, respectively, while positive phases of the SOI (La Niña conditions) and NAO are associated with elevated joint and conditional exceedance probabilities, rising by up to 66 % in the Restigouche River and 45 % in the Highland River. By linking joint extremes to both long-term warming and oscillatory climate patterns, the study provides a predictive framework for anticipating compound risks and protecting thermally sensitive aquatic habitats under ongoing climate change and variability.