Joint frequency analysis and uncertainty estimation of coupled rainfall-runoff series relying on historical and simulated data

Joint frequency analysis and quantile estimation of extreme rainfall and runoff (ERR) are crucial for hydrological engineering designs. The joint quantile estimation of the historical ERR events is subject to uncertainty due to the errors that exist with flow height measurements. This study is motivated by the interest in introducing the advantages of using Hydrologic Simulation Program-Fortran (HSPF) simulations to reduce the uncertainties of the joint ERR quantile estimations in Taleghan watershed. Bivariate ERR quantile estimation was first applied on P-AMS-Q(SIM) pairs and the results were compared against the historical rainfall-runoff data (P-AMS-Q(obs)). Student's t and Frank copulas with respectively Gaussian-P3 and Gaussian-LN3 marginal distributions well suited to fit the P-AMS-Q(obs) and P-AMS-Q(SIM) pairs. Results revealed that confidence regions (CRs) around the p levels become wider for P-AMS-Q(obs) compared to P-AMS-Q(SIM), indicating the lower sampling uncertainties of HSPF simulations compared to the historical observations for bivariate ERR frequency analysis.