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Discharge and water quality are two important attributes of rivers, although the joint response relationship between discharge and multiple water quality indicators is not clear. In this paper, the joint probability distributions are established by copula functions to reveal the statistical characteristics and occurrence probability of different combinations of discharge and multiple water quality indicators. Based on the data of discharge, ammonia nitrogen content index (NH4+) and permanganate index (CODMn) in the Xiaoqing River in Jinan, we first tested the joint change-point with the data from 1980–2016, before we focused on analyzing the data after the change-point and established the multivariate joint probability distributions. The results show that the Gaussian copula is more suitable for describing the joint distribution of discharge and water quality, while the year of 2005 is a joint change-point of water quantity and quality. Furthermore, it is more reasonable to use the trivariate joint probability distribution as compared to the bivariate distributions to reflect the exceedance probability of water quality combination events under different discharge conditions. The research results can provide technical support for the water quality management of urban rivers.

Combined Exceedance Probability Assessment of Water Quality Indicators Based on Multivariate Joint Probability Distribution in Urban Rivers