Integrating vector and copula-based models with conditional heteroskedasticity for enhanced suspended sediment load simulation

Abstract

Multivariate models are essential for simulating hydrological variables due to interdependencies between parameters and the stochastic nature of hydrological time series. This study evaluates and compares two hybrid methods—VAR-GARCH and Copula-GARCH—for simulating suspended sediment load (SSL) using discharge data from the Deh Molla station (Zohre River basin). The VAR-GARCH model demonstrated strong performance, achieving a Nash–Sutcliffe efficiency (NSE = 0.99) in SSL simulation, though some residuals fell outside the 95% confidence interval. Under flood discharge conditions, the VAR-GARCH model yielded an RMSE of 4295 tons/day. By contrast, the Copula-GARCH model, fitted to the residuals of VAR-GARCH, significantly improved accuracy, reducing RMSE to 1455 tons/day—a 66% reduction in error (improvement rate: 70%). Both models performed robustly given the data variability, as confirmed by RMSE and NSE metrics. Results highlight the Copula-GARCH model’s superior precision for SSL simulation, particularly in capturing non-linear dependencies.