Semiparametric Trivariate D-Vine Copula Modelling of River Temperature, Dissolved Oxygen, and Flow for Compound Water-Quality Risk in the Yamuna and Tungabhadra Rivers, India

Latif, Shahid; Ouarda, Taha B. M. J.; Rehana, Shaik

doi:10.3390/w18172063

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Semiparametric Trivariate D-Vine Copula Modelling of River Temperature, Dissolved Oxygen, and Flow for Compound Water-Quality Risk in the Yamuna and Tungabhadra Rivers, India

by

Shahid Latif

^1,*

,

Taha B. M. J. Ouarda

¹

and

Shaik Rehana

²

¹

Canada Research Chair in Statistical Hydro-Climatology, Institut National de la Recherche Scientifique, Centre Eau Terre Environnement (INRS-ETE), 490 De la Couronne, Québec City, QC G1K 9A9, Canada

²

International Institute of Information Technology, Hyderabad 500032, India

^*

Author to whom correspondence should be addressed.

Water 2026, 18(17), 2063; https://doi.org/10.3390/w18172063

Submission received: 26 June 2026 / Revised: 6 August 2026 / Accepted: 18 August 2026 / Published: 22 August 2026

(This article belongs to the Special Issue Innovative Approaches in Hydrology Applied to the Study of River and Lakes Systems)

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Abstract

Concurrent high river water temperature (RWT), low dissolved oxygen (DO), and low river flow (RF) can degrade water quality and aquatic habitat, but their joint probability is rarely quantified in a fully trivariate framework. This study develops a semiparametric trivariate drawable-vine (D-vine) copula model that uses Gaussian kernel density estimation (GKDE) margins with parametric pair-copulas to estimate compound thermal–oxygen–low-flow hazards. The framework provides conditional exceedance probabilities and AND- and OR-joint return periods (RPs) for monthly synchronized RWT–RF–DO states. The analysis uses 117 synchronized monthly triplets from the Tungabhadra and 152 from the Yamuna. Kendall’s

Keywords: river water temperature; dissolved oxygen; river flow; compound water-quality risk; semiparametric D-vine copula; trivariate modelling; joint return periods

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MDPI and ACS Style

Latif, S.; Ouarda, T.B.M.J.; Rehana, S. Semiparametric Trivariate D-Vine Copula Modelling of River Temperature, Dissolved Oxygen, and Flow for Compound Water-Quality Risk in the Yamuna and Tungabhadra Rivers, India. Water 2026, 18, 2063. https://doi.org/10.3390/w18172063

AMA Style

Latif S, Ouarda TBMJ, Rehana S. Semiparametric Trivariate D-Vine Copula Modelling of River Temperature, Dissolved Oxygen, and Flow for Compound Water-Quality Risk in the Yamuna and Tungabhadra Rivers, India. Water. 2026; 18(17):2063. https://doi.org/10.3390/w18172063

Chicago/Turabian Style

Latif, Shahid, Taha B. M. J. Ouarda, and Shaik Rehana. 2026. "Semiparametric Trivariate D-Vine Copula Modelling of River Temperature, Dissolved Oxygen, and Flow for Compound Water-Quality Risk in the Yamuna and Tungabhadra Rivers, India" Water 18, no. 17: 2063. https://doi.org/10.3390/w18172063

APA Style

Latif, S., Ouarda, T. B. M. J., & Rehana, S. (2026). Semiparametric Trivariate D-Vine Copula Modelling of River Temperature, Dissolved Oxygen, and Flow for Compound Water-Quality Risk in the Yamuna and Tungabhadra Rivers, India. Water, 18(17), 2063. https://doi.org/10.3390/w18172063

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Semiparametric Trivariate D-Vine Copula Modelling of River Temperature, Dissolved Oxygen, and Flow for Compound Water-Quality Risk in the Yamuna and Tungabhadra Rivers, India

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