Copula-based joint modelling of extreme river temperature and low flow characteristics in the risk assessment of aquatic life

Abstract

Compounding the joint impact of extreme river temperature and low flow characteristics can harm the aquatic habitat of certain organisms (e.g., ecototherm fish) and freshwater ecosystems. Considering only river temperature or low flow via univariate frequency distribution as a stress indicator would be incomplete. Maximum water temperature and low flow series are strongly negatively correlated; thus, their joint probability distribution can be helpful to assess better the risks associated with joint extreme events. This study incorporated the 2-D parametric copulas in the bivariate joint modelling of annual maximum river water temperature and corresponding low flow. This proposed bivariate framework is applied to 5 independent and identically distributed stations in Switzerland. Parametric 1-D probability density functions are employed in modelling the univariate marginal distribution of both variables separately. The efficacy of eighteen different parametric class negatively dependent 2-D copulas is tested. The best-fitted copulas and selected marginals are used to estimate joint return periods for quantiles corresponding to multiple return periods. The joint return periods of annual maximum temperatures conditional to low flows or vice versa are also estimated. Investigation reveals that the occurrence of bivariate events simultaneously is less frequent in the AND-joint case than in the OR-joint event case for all stations. Also, OR-return periods are less (nearly half) the value of univariate return periods. Secondly, higher conditional return periods are observed in annual maximum temperature (or low flow) when increasing the percentile value of the conditioning variable, i.e., low flow (or maximum temperature). Also, when the low flow (or water temperature) conditioning variable is fixed, higher bivariate event return periods are observed at a higher water temperature (or low flow) value. In conclusion, these estimated bivariate statistics can help provide a more complete picture for an adequate assessment of the risks associated with cold-water species.