Uncertainty analysis of the relationship between discharge and nitrate concentration in the Lower Illinois River using a copula model

The complex relationship between water quality and river discharge has long been an active area of research. This research applies bivariate statistics to river nitrate concentration and discharge, and develops a procedure for selecting the best bivariate distribution for the chosen models. Nitrate concentration (NO3) data from five stations on the Lower Illinois River, USA, collected from 1972 to 2012 were used for demonstration of this procedure. To explore the statistical relationship between discharge and nitrate concentration, three copula statistical models were applied to determine optimal bivariate distributions. The generalized Pareto (GPA), generalized extreme value (GEV), and lognormal two- (LN2) and three-parameter (LN3) distributions were used as marginal distributions, and were combined with the Clayton, Frank, and Gumbel copula models. The probability plot correlation coefficient (PPCC) test and the S-n statistic were used to select the most suitable copula models. As a result, the GPA distributions for streamfiow and nitrate concentration in the Frank copula model were more accurate for representing the data from the two mainstem stations, Havana (D-31) and Valley City (D-32), and those from the Oakford station along the Sangamon River (E-25). However, the Clayton copula model using NL3 for representing streamfiow and GPA for representing nitrate concentration was more accurate for stations along the Spoon (DJ-08) and La Moine Rivers (DG-01). This study enabled the development of a procedure for determining an optimal copula for application in the environmental sciences and also provided a case study for applying copula models using discharge and nutrient concentration as hydrologic and water quality variables, respectively. (C) 2019 Elsevier Ltd. All rights reserved.