A new nonparametric copula framework for the joint analysis of river water temperature and low flow characteristics for aquatic habitat risk assessment

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This study proposed a nonparametric copula hazard framework in the joint risk of river water temperature (RWT) and low flow (LF) events for aquatic ecosystems, specifically ectotherm fish. This nonparametric copula density can adapt to any mutual dependence structure, providing greater flexibility. This can reduce the risk of misspecification if the underlying assumption is violated compared to conventional parametric or semiparametric copula settings. The analysis uses nonparametric copulas densities like Beta kernel copula estimator (BKCE), Bernstein copula estimator (BCE), and Transformation kernel estimator (TKE), conjoined with Gaussian Kernel density estimations (GKDEs) and parametric marginals for joint annual maximum RWT (AMRWT) and LF. The study compares different models for analyzing five Swiss river basins: parametric copulas with best-fitted GKDE and parametric margins, versus nonparametric copula. Six bandwidth selectors are estimated to fit GKDE. BKCE with GKDE margins outperformed most stations, while TKE and BCE density with GKDE margins work best for only one station. However, at one station, BKCE with best-fitted parametric margins is outperformed. All stations except Station 2473 are characterized by temperature and low flows that may be conducive to stress of a number of aquatic species, causing high AMRWT (exceeding 19 °C) and minimum LF or specific discharge, SD) quantiles at low AND-joint return periods (RP). AND (i.e. low flow AND high temperature) hazard events are less likely to occur together than OR hazard events, while univariate RPs happen more often than OR-joint RPs. In addition, the joint RP of AMRWT, given LF at different percentiles, significantly affected AMRWT for various LF conditions. Higher AMRWT with low flow conditions results in lower joint RP (except station 2473), and this stress level would be reduced when conditioned with high LF events at the same AMRWT. Station 2473 has high LF even at low percentiles, and with low AMRWT makes it very less stressful than other station under different LF conditions. Summer river flow maintenance can improve aquatic environments with high RWT. Analyzing joint statistics is crucial to understanding mutual risk in freshwater ecosystems.