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In this study, Vector Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (VAR-GARCH), copula, and copula-GARCH models were used for joint frequency analysis of storms in the Aras river basin in northwestern Iran in period of 1998–2018. The heteroskedasticity in the series was considered using the vector autoregressive model. Two-dimensional copulas were also used for bivariate analysis. After confirming the correlation between the pair variables of storm with one event lag (S1) and storm with no lag (S0), bivariate frequency analysis was performed. In the simulation step, the residual series of the VAR model was extracted and fitted to the GARCH model. Then, the residual series of the GARCH model was modeled using the copula model. Finally, storm with no lag (S0) affected by storm with one event lag (S1) was simulated by VAR-GARCH, copula, and copula-GARCH models. According to the coefficient of determination (R2) and Nash–Sutcliffe Efficiency coefficient (NSE) and root mean square error (RMSE), the VAR-GARCH model had higher accuracy than copula and copula-GARCH models. The RMSE in the simulation of storm height using the VAR-GARCH model was estimated to be 18% and 11% less than copula and copula-GARCH models, respectively. The VAR-GARCH model provided higher accuracy in the simulations due to the consideration of different lags in the simulations and modeling the variance of the residual series. According to the Taylor diagram, the certainty of all three models in simulating storm height are acceptable. Finally, by two-dimensional analysis of pair variables of storm height and storm duration, typical curve was produced that can estimate the storm duration with different probabilities. In fact, having the storm information that has happened in the present can accurately predict the next storm information. It can be very useful in flood management and the generated curves can be used as a flood warning system in the basin. [ABSTRACT FROM AUTHOR]

In this study, the frequency analysis of river flow deficiency (FD) of the Siminehrood River in the south of Lake Urmia located in northwest Iran was investigated with regard to rainfall deficiency (RD) during the period of 1992–2013 using copula functions. The main purpose of this study is to provide a comprehensive method for bivariate simulation and forecasting based on marginal distribution and joint behavior of the studied series. For this purpose, the FD and RD values were extracted using the deficiency value method. By preparing deficiency values, 57 different distribution functions were fitted to the studied values, and the generalized extreme value (GEV) distribution was selected as the best marginal distribution function based on the evaluation criteria. Before fitting the copula function, the correlation between the RD and FD values was examined using Kendall's tau, and a correlation of 70% was obtained. After selecting the marginal distribution function and examining the correlation, the goodness of fit of seven different copula functions was examined for frequency analysis of RD and FD values in the Siminehrood River at the Dashband station. The results indicated that the Clayton copula had the best performance for creating a joint distribution of RD and FD values. It was also determined from the joint analysis of deficiency values that the FD values can be estimated with high accuracy for RD values of more than 0.68 mm. Also, the results indicated that if rainfall in the study area were less than long-term mean for 10-day and 60-day durations, with different return periods and probabilities, different conditions will occur for FD values, which can be used as typical curves for water resources management and allocation in the basin. Finally, the accuracy of the copula-based model and its conditional density in the two phases of simulation and forecasting were investigated. The accuracy of the copula-based model and its conditional density in the simulation phase was confirmed [ R2=0.87 , root mean square error (RMSE)=0.1 m3/s , and nash-sutcliffe efficiency (NSE)=0.86 ]. In the forecasting phase, the forecasting equation based on the proposed method had a RMSE of 0.14 m3/s and NSE of 0.89. By using the violin plot, the model certainty was also confirmed. According to the proposed equation, FD values can be forecasted affected by RD values for 10-day duration with high certainty and accuracy. In this paper, a method for forecasting and simulation of meteorological and hydrological parameters is presented that considers two parameters simultaneously. This study discusses meteorology and hydrology from a different perspective. Given the current climate change, this study uses deficiency values. The proposed forecasting method provides regional results that can be used in the water resources management in each basin specifically. By implementing this method, it is easy to forecast the desired values in the basin with different probabilities and return periods. In this study, river flow deficiency (FD) affected by rainfall deficiency (RD) can be forecasted. The difference between the proposed method and other methods and models of simulation and forecasting is in the connection of two variables with each other, which makes the results more certain and reliable. This method can be used in the field of basin management and water resources allocation and also water resources monitoring. [ABSTRACT FROM AUTHOR]

In this study, a new method was proposed to model the occurrence of related variables based on the conditional density of copula functions. The proposed method was adopted to investigate the dynamics of meteorological and hydrological droughts in the Zarinehroud basin, southeast of Lake Urmia, during the period 1994–2015. For this purpose, the modified precipitation anomaly percentage and streamflow drought indices were extracted. Finally, the joint frequency analysis of duration-duration and severity-severity characteristics of meteorological and hydrological droughts was analyzed. Analysis of 7 different copulas used to create the joint distribution in the Zarinehroud basin indicated that the Frank copula had the best performance in describing the relationship between the meteorological and hydrological drought severities and durations. By examining the results of the bivariate analysis of duration-duration of meteorological and hydrological droughts at different stations, the expected meteorological and hydrological drought durations were estimated in the years ahead. For example, at Chalkhmaz station, 4- to 7-month duration for the hydrological drought and 9- to 12-month duration for the meteorological drought is expected in the years ahead. The joint frequency analysis of drought characteristics allows to determine the meteorological and hydrological drought characteristics at a single station at the same time using joint probabilities. Also, the results indicated that by knowing the conditional density, the hydrological drought characteristics can be easily estimated for the given meteorological drought characteristics. This could provide users and researchers useful information about the probabilistic behavior of drought characteristics for optimal operation of surface water. [ABSTRACT FROM AUTHOR]