Probabilistic structure of storm surface runoff considering the dependence between average intensity and storm duration of rainfall events

The probabilistic nature of rainfall and surface runoff events forms the basis of hydrologic design. Two defining characteristics of rainfall events, average intensity and duration, are selected to construct the probabilistic structure of storms using Gumbel's bivariate exponential distribution. This bivariate stochastic rainfall model is then utilized to derive the probabilistic structure of surface runoff using the Soil Conservation Service rainfall runoff model. The zero‐runoff probability, mean, and standard deviation of rainfall excess are evaluated. Copulas serve as an alternative way to derive zero‐runoff probability. The results indicate that the dependence between average intensity and duration has a significant effect on statistical properties of rainfall excess. The advantage of using copulas for complicated multivariate stochastic models is demonstrated. The proposed model is associated with land use and soil type information from the geographic information system to produce maps of statistical properties of rainfall excess. A case study of model application is performed for the state of Indiana, United States. Results show that while the mean and standard deviation of rainfall excess increase with curve number, these quantities are very sensitive to the dependence between average intensity and duration of storm events.