Copula-based stochastic simulation of hydrological data applied to Nile River flows

Abstract

Modelling a multivariate distribution is a classical issue in statistics. Copula functions offer a useful solution to this issue by modelling the multivariate distribution as a function of its marginal distributions. They have been used in various problems in hydrology and water management such as flood frequency analysis and drought or rainfall intensity-duration frequency analysis. However, to the knowledge of the author, they have 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 and non-parametric functions are applied for fitting the distribution of the original observed data and the serial dependence structure is then modelled with alternative copula functions. The pros and cons of different copula models are investigated by comparing the statistics of the generated data. Two major features of the copula models include: (1) portraying the heteroscedasticity embedded in the serial correlation of the observed data and (2) the flexibility of applicable marginal distributions. The suggested copula models are applied to simulate synthetic annual streamflow data of the Nile River. The results showed that the benefits of using these copula models are somewhat marginal with respect to the well-known modelling procedures.