In the present work, the joint response of key hydrologic variables, including total precipitation depths and the corresponding simulated peak discharges, are investigated for different antecedent soil moisture conditions using the copula method. The procedure started with the calibration and validation of the soil moisture accounting (SMA) loss rate algorithm incorporated in the Hydrologic Engineering Center – hydrologic modeling system (HEC–HMS) model for the study watershed. A 1000 year long time series of hourly rainfall was then generated by the Neyman–Scott rectangular pulses (NSRP) rainfall generator, which was then transformed into the runoff rate by the HEC–HMS model. This long-term continuous hydrological simulation resulted in characterizing the response of the watershed for various input conditions such as initial soil moisture content (AMC), total rainfall depth, and rainfall duration. For each initial soil moisture class, the copula method was employed to determine the joint probability distribution of rainfall depth and peak discharge. For instance, for dry AMC condition and 1 h rainfall duration, the Joe family fitted best to the data, compared with six other one-parameter families of copulas. Results showed that the bivariate analysis of rainfall–runoff using the copula method can well characterize the watershed hydrological behavior. The derived offline curves could provide a probabilistic real-time peak discharge forecast.
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