Probabilistic Event Based Rainfall-Runoff Modeling Using Copula Functions

Multivariate probability analysis of hydrological elements using copula functions can significantly improve the modeling of complex phenomena by considering several dependent variables simultaneously. The main objectives of this study were to: (i) develop a stand-alone and event-based rainfall-runoff (RR) model using the common bivariate copula functions (i.e. the BCRR model); (ii) improve the structure of the developed copula-based RR model by using a trivariate version of fully-nested Archimedean copulas (i.e. the FCRR model); and (iii) compare the performance of the developed copula-based RR models in an Iranian watershed. Results showed that both of the developed models had acceptable performance. However, the FCRR model outperformed the BCRR model and provided more reliable estimations, especially for lower joint probabilities. For example, when joint probabilities were increased from 0.5 to 0.8 for the peak discharge (qp) variable, the reliability criteria value increased from 0.0039 to 0.8000 in the FCRR model, but only from 0.0010 to 0.6400 in the BCRR model. This is likely because the FCRR considers more than one rainfall predictor, while the BCRR considers only one.