River water quality assessment has traditionally been conducted using univariate or threshold-based approaches; however, the exploration of extremes assessment under bivariate water quality variables has been limited by many studies. Understanding the compound extremes of low river discharge (Q) and elevated river water temperatures (RWTs) resulting from climatic variability is essential for effective water quality management and protection of the river. This study investigates the joint behaviour of RWTs and Q in six Indian rivers: Kaveri, Mahi, Sabarmati, Vardha, Bhadra, and Yamuna. The Weibull-3P and Generalised Extreme Value (GEV-3P) distributions best fit for Q and RWTs, respectively. The adequacy of eighteen different parametric copula classes was evaluated. The Gaussian copula provided the best fit for the Vardha River, the Frank copula for Bhadra, and the BB8 copula for the Yamuna River. The evaluation of joint return periods (RPs) and conditional distributions has identified notable spatial variability in compound hydrological and thermal extreme hazards. The semi-arid Vardha River showed the shortest RPs for simultaneous low Q and high RWTs, indicating a greater likelihood of combined extremes. Conversely, the monsoon-fed Bhadra River displayed moderate hazard levels, while the Himalayan-fed Yamuna River had the longest joint RPs and the lowest conditional probabilities. This suggests that simultaneous extreme drought and heat events are less likely in the Yamuna basin, although significant risks remain for less severe thresholds.
Buchupalle et al. (2026) studied this question.