Spatial hydrological drought characteristics in Karkheh River basin, southwest Iran using copulas

Abstract

Investigation on drought characteristics such as severity, duration, and frequency is crucial for water resources planning and management in a river basin. While the methodology for multivariate drought frequency analysis is well established by applying the copulas, the estimation on the associated parameters by various parameter estimation methods and the effects on the obtained results have not yet been investigated. This research aims at conducting a comparative analysis between the maximum likelihood parametric and non-parametric method of the Kendall τ estimation method for copulas parameter estimation. The methods were employed to study joint severity-duration probability and recurrence intervals in Karkheh River basin (southwest Iran) which is facing severe water-deficit problems. Daily streamflow data at three hydrological gauging stations (Tang Sazbon, Huleilan and Polchehr) near the Karkheh dam were used to draw flow duration curves (FDC) of these three stations. The Q 75 index extracted from the FDC were set as threshold level to abstract drought characteristics such as drought duration and severity on the basis of the run theory. Drought duration and severity were separately modeled using the univariate probabilistic distributions and gamma-GEV, LN2-exponential, and LN2gamma were selected as the best paired drought severity-duration inputs for copulas according to the Akaike Information Criteria (AIC), Kolmogorov-Smirnov and chi-square tests. Archimedean Clayton, Frank, and extreme value Gumbel copulas were employed to construct joint cumulative distribution functions (JCDF) of droughts for each station. Frank copula at Tang Sazbon and Gumbel at Huleilan and Polchehr stations were identified as the best copulas based on the performance evaluation criteria including AIC, BIC, log-likelihood and root mean square error (RMSE) values. Based on the RMSE values, nonparametric Kendall-τ is preferred to the parametric maximum likelihood estimation method. The results showed greater drought return periods by the parametric ML method in comparison to the nonparametric Kendall τ estimation method. The results also showed that stations located in tributaries (Huleilan and Polchehr) have close return periods, while the station along the main river (Tang Sazbon) has the smaller return periods for the drought events with identical drought duration and severity.

Observed and projected trends of extreme precipitation and maximum temperature during 1992–2100 in Isfahan province, Iran using REMO model and copula theory

“…The parameter of the copulas was estimated by both parametric and nonparametric methods for extreme combinations and then the best fit copula was selected on the basis of the AIC, BIC, and OLS criteria. According to these criteria, the parametric method resulted in better estimation than the nonparametric method, consistent with previous work (Dodangeh et al, 2017;Mesbahzadeh et al, 2019;Mirakbari et al, 2010). Among the five fitted copula functions at the Daran station, the Gaussian copula was used to jointly model the combinations of (R10, SDII), (R10, PRCPTOT), (SDII, PRCPTOT), and the Frank, and Gumbel Copulas were used for the combinations of (R95p, SDII) and (R95, R10), respectively, in the historical period.…”

“…Zhang, Li, Singh, & Xu, 2013). In Iran, many studies have analyzed multivariate modeling of extreme events such as floods and droughts using copulas (Amirataee, Montaseri, & Rezaie, 2018;Azam, Maeng, Kim, & Murtazaev, 2018;Cheraghalizadeh, Ghameshlou, Bazrafshan, & Bazrafshan, 2018;Dodangeh et al, 2017;Mirakbari et al, 2010). However, few studies have been carried out on the joint frequency analysis of climate parameters and their extreme values under climate change conditions.…”

Meteorological drought analysis using copula theory and drought indicators under climate change scenarios (RCP)

“…Given that the drought characteristics may have different marginal distribution functions, the most suitable tool for achieving the joint behaviour of the drought characteristics is multivariate copula functions. Copula functions as a multivariate analysis method are widely used to analyse the functional structure of drought characteristics (Mirakbari et al, 2010;Chen et al, 2013;Dodangeh et al, 2017;Hao et al, 2017).…”

Simulation of extreme temperatures using a new method: TIN‐copula

“…Copulas are commonly used in the fields of finance, insurance, engineering and more recently, in hydrology (Cech, 2006;Kpanzou, 2007;Genest et al, 2013;Maity et al, 2013;Fermanian, 2017;Dodangeh et al, 2017;D'Amico and Petroni, 2018). Furthermore, copulas have been applied in the field of tourism (Zhu et al, 2016;Tansuchat and Maneejuk, 2018).…”