Investigation the Joint Probabilistic Behavior of River Flow Discharge-Suspended Sediment Load in Nazlochai Basin, Urmia

Accurately determining the relationship between river flow discharge and suspended sediment load in watersheds is challenging due to the influence of natural and human-induced variables on river estimations. Therefore, it is essential to employ modern methods to improve existing models. In this context, multivariate methods and copula-based modeling and simulation, given their ability to analyze data distributions, can be suitable options. In this study, joint frequency analysis of river flow discharge and suspended sediment load was conducted at the Abajalo and Tapik stations in the Nazlochai sub-basin, Lake Urmia, Iran using copula functions and marginal distributions. First, the correlation between variables was examined using Kendall’s tau coefficient, indicating a strong positive relationship between river flow discharge and suspended sediment load. For modeling marginal distributions, the Log-Normal and GEV distributions with NSE=0.99 at the Abajalo station were selected as the best distributions for flow discharge and suspended sediment load, respectively, while the GEV and Generalized Pareto distributions with NSE=0.99 at the Tapik station were chosen for river flow discharge and suspended sediment load, respectively. In the joint analysis, the Galambos and Gumbel-Hougaard copula functions demonstrated the best performance based on evaluation criteria. Bivariate analysis revealed that at the Abajalo station, with a 90% probability and river flow discharge exceeding 40 m³/s, the suspended sediment load reaches over 3,000 tons/day, while at the Tapik station, the same probability with a river flow discharge of 25 m³/s indicates a suspended sediment load exceeding 500 tons/day. Finally, based on the conditional density of copula functions and considering various probabilities, equations were proposed for simulating suspended sediment load conditioned on river flow discharge at both stations. The proposed equations were suggested for probability levels of 80–90%, 90–95%, and 95–99% and evaluated using various statistical metrics. The proposed equations for conditional estimation of suspended sediment load demonstrated high performance at the Abajalo station (NSE>0.95 and 386.20.84 and 26.8<RMSE<836.8 tons/day). This study emphasizes that multivariate methods based on copula functions are effective tools for modeling nonlinear hydrological relationships.