Using Copulas for Stochastic Streamflow Generation

A copula is a multivariate distribution function with standard uniform marginal. Copula has been a useful tool for various problems in hydrology and water resources such as flood frequency analysis, drought prediction, and rainfall intensity-duration frequency analysis. It allows modeling a multivariate distribution by separating it into its marginal distribution and Copula function. However, to the knowledge of the authors, it has not been applied for stochastic simulation of hydrologic data. In this study we explore the applicability of the Copula concept for stochastic streamflow simulation. Parametric (e.g. gamma) and non-parametric (e.g. Kernel density estimation) functions are utilized for fitting the distribution of the original observed data and the serial dependence structure is modeled with alternative Copula functions such as Clayton, Frank, Gumbel, and Gaussian Copulas. The pros and cons of different copula time series models are investigated by comparing the statistics of the generated data. Two salient features of the Copula time series models include: (1) portraying the heteroscedasticity (heterogeneity of variance) embedded in the serial correlation of the observed data (2) the flexibility of applicable marginal distributions. The suggested copula models are applied to simulate synthetic yearly streamflow data of the Nile River. We examined the applicability of the gamma and Kernel density estimate as marginal distributions of the trivariate normal copula and compared their results against the LTARMA(1,1) model. The results showed that the benefits of using the referred copula models are quite marginal respect to the well known modeling procedures (e.g. the LTARMA). Perhaps the only significant difference is in better reproducing short term droughts (e.g. one or two year droughts), but as far as longer term droughts and storage capacity statistics no significant difference have been found.