Abstract
River water quality is fundamentally influenced by hydrological factors such as discharge and water
temperature, both of which are increasingly affected by climate variability and human-induced
pressures. These variables, when considered independently, can provide a limited view of water quality
risks. However, compound events, where low discharge coincides with high water temperatures, can
pose significant ecological threats, particularly to sensitive aquatic species and overall river health.
Existing studies often rely on univariate or deterministic models, which fail to capture the joint
behaviour of these interconnected variables. There is also a noticeable gap in translating advanced
statistical models into practical tools for river water quality risk management, especially in computing
compound event probabilities and supporting basin-specific decision-making.
This study addresses these gaps by developing a copula-based joint modelling framework to quantify
compound low-flow and high-temperature risks across six diverse Indian rivers: Yamuna, Bhadra,
Kaveri, Mahi, Sabarmati, and Vardha. The study begins by fitting appropriate univariate probability
distributions to river discharge and water temperatures using diagnostic tools such as skewness,
kurtosis, Q-Q plots, and information criteria to ensure statistically sound marginal modelling.
Dependence structures between the variables are assessed using rank correlation metrics to identify
rivers where joint modelling is both appropriate and necessary. An extensive set of 18 copula families,
including symmetric, asymmetric, and tail-dependent models, is evaluated to capture complex
interdependencies across river basins.
The selected copulas are then applied to estimate joint probabilities, conditional probabilities, and return
periods of compound events of discharge and water temperatures of various river gauging stations of
India. The findings reveal clear differences in compound event frequencies and intensities across the
studied rivers, underscoring the need for localized and river-specific water quality management
strategies.
The key objectives of this study include identifying the best-fit univariate distributions, selecting the
most appropriate copula families for joint modelling, and constructing a flexible, transferable statistical
framework that can support future applications, including multivariable risk assessments, climate
change impact studies, and adaptive water resource management. By addressing the underutilization of
joint probabilistic frameworks for Indian river systems and demonstrating their practical application,
this study contributes to a more holistic understanding of compound water quality risks and provides
valuable guidance for sustainable river management and policy development