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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.

Precipitation and temperature are very important climatic parameters as their changes may affect life conditions. Therefore, predicting temporal trends of precipitation and temperature is very useful for societal and urban planning. In this research, in order to study the future trends in precipitation and temperature, we have applied scenarios of the fifth assessment report of IPCC. The results suggest that both parameters will be increasing in the studied area (Iran) in future. Since there is interdependence between these two climatic parameters, the independent analysis of the two fields will generate errors in the interpretation of model simulations. Therefore, in this study, copula theory was used for joint modeling of precipitation and temperature under climate change scenarios. By the joint distribution, we can find the structure of interdependence of precipitation and temperature in current and future under climate change conditions, which can assist in the risk assessment of extreme hydrological and meteorological events. Based on the results of goodness of fit test, the Frank copula function was selected for modeling of recorded and constructed data under RCP2.6 scenario and the Gaussian copula function was used for joint modeling of the constructed data under the RCP4.5 and RCP8.5 scenarios.

The study was carried out to assess meteorological drought on the basis of the standardized precipitation index (SPI) and standardized precipitation evapotranspiration index (SPEI) evaluated in future climate scenarios. Yazd province, located in an arid region in the centre of Iran, was chosen for analysis. The study area has just one synoptic station with a long‐term record (56 years). The impact of climate change on future drought was examined by using the CanESM2 of the CMIP5 model under three scenarios, that is, representative concentration pathways RCP2.6, RCP4.5 and RCP8.5. Given that a drought is defined by several dependent variables, the evaluation of this phenomenon should be based on a multivariate analysis. For this purpose, two main characteristics of drought (severity and duration) were extracted by run theory in a past (1961–2016) and future (2017–2100) period based on the SPI and SPEI, and studied using copula theory. Three functions, that is, Frank, Gaussian and Gumbel copula, were selected to fit with drought severity and duration. The results of the bivariate analysis using copula showed that, according to both indicators, the study area will experience droughts with greater severity and duration in future as compared with the historical period, and the drought represented by the SPEI is more severe than that associated with the SPI. Also, drought simulated using the RCP8.5 scenario was more severe than when using the other two scenarios. Finally, droughts with a longer return period will become more frequent in future.

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