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

Abstract

Modelling a multivariate distribution is a ciassicai issue in statistics. Copuia functions offer a usefui 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 hydrologie data.In this study we explore the applicability of the copula concept for stochastic streamflow simulation.Parametric and non-parametric functions are appiied 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.

A Cautionary Note on the Reproduction of Dependencies through Linear Stochastic Models with Non-Gaussian White Noise

“…In hydrology, copulas have been popularized by the studies of De Michele and Salvadori [55] and Favre et al [56], and since then have been widely applied for the description of correlated yet time-independent variables [55][56][57][58][59][60][61][62][63], while only lately they have been adapted and modified accordingly to account for time-dependence, which led to the development of copula-based schemes for the simulation of hydrometeorological processes [64][65][66][67][68][69][70].…”

Bivariate hydrologic risk analysis based on a coupled entropy-copula method for the Xiangxi River in the Three Gorges Reservoir area, China

“…In recent years, copulas have been widely used for multivariate hydrologic modeling, such as multivariate flood frequency analysis (Zhang and Singh 2006;Sraj et al 2014), drought assessment (Song and Singh 2010;Kao and Govindaraju 2010;Ma et al 2013), storm or rainfall dependence analysis (Zhang and Singh 2007;Vandenberghe et al 2010), and streamflow simulation (Lee and Salas 2011;Kong et al 2015;Fan et al 2015a). The main advantage of copula functions over classical multivariate hydrologic modeling is that the marginal distributions and multivariate dependence modeling can be determined in two separate processes, giving additional flexibility to the practitioner in choosing different marginal and joint probability functions (Zhang and Singh 2006;Genest and Favre 2007;Karmakar and Simonovic 2009;Sraj et al 2014).…”

Bivariate analysis of typical hydrological series of the yellow river

“…Guo et al 8 summarized the using of copulas in multivariate hydrological analysis and prospected the future applying of the method. Lee, T. and Salas, J. D. 9 introduced copula method to stochastic streamflow simulation. Chowdhary, H. et al 10 discussed selection procedure of copulas and demonstrated their application in the bivariate flood frequency analysis.…”