Assessment of environmental risk using trivariate joint distribution of river water temperature, river flow and dissolved oxygen with semiparametric D-vine copula framework

Quantifying trivariate joint and conditional exceedance probabilities of River Water Temperature (RWT), River Flow (RF), and Dissolved Oxygen (DO) provides critical insights into compound water-quality stress and its implications for aquatic life and ecosystem health. However, the concurrent occurrence of critical RWT, DO, and RF thresholds, and the associated potential implications for aquatic species that motivate our focus on joint risk, has yet to be fully explored. To address the simultaneous joint action of RWT, RF and DO events, this study incorporates a D-vine copula with nonparametric Gaussian Kernel density estimation (GKDE) for modelling trivariate joint and conditional hazard risks. Using this proposed framework, the study analyzed monthly triplet datasets from the Musi River basin (Dhamaracharla gauge, 1991-2005) in India. RWT-RF and RWT-DO exhibit a strong negative correlation, while RF-DO shows a positive correlation. The GKDE method outperformed the parametric models in estimating marginal densities for all selected variables. A DO-centered semiparametric D-vine (order RWT-DO-RF) outperforms alternative vine orders and fully parametric models, showing higher likelihood, lower information-criterion scores, and a good calibration under the Rosenblatt transform. It shows no detectable tail clustering and aligns with standard tail diagnostics and joint-exceedance curves, providing a reliable basis for joint-risk estimation within the observed ranges. The rotated Joe copula (270 degrees), BB8 copula, and Clayton copula (90 degrees) are selected with GKDE in establishing trivariate joint and conditional return periods (RPs). The estimated RWT, RF and DO quantiles indicate dangerous levels with potential significant threats to aquatic life. Trivariate AND-joint RPs are generally higher than their bivariate counterparts. Furthermore, lower trivariate AND-joint RPs are associated with higher RWT and low RF and DO quantiles, reflecting elevated concurrence risk. Conditional joint RPs are lowest when RWT is high and both RF and DO are low, indicating elevated compound risk for water quality and possibly for biota. These joint and conditional estimates quantify concurrent hazard within the observed range and inform ecological risk assessment.