Bivariate Drought Frequency Analysis in Gharesoo-Gorganrud Basin by Using Copulas

The drought is considered to be one of the most important natural phenomenon affecting various aspects of human life. Therefore, understanding how this phenomenon behaves is an important part of the water resources management which is directly related to the concept of drought. Knowledge of frequency of drought events with specified magnitudes can be of great importance in water resources planning and management. This knowledge is provided by using the drought frequency analysis methods. However, because of the multivariable nature of the drought, studying its aspects or variables individually probably cannot result in an efficient and comprehensive knowledge about this phenomenon. Therefore, in the recent years, several multivariate methods and techniques have been developed for multivariate drought frequency analysis. Application of copulas in multivariate drought frequency analysis is one of the approaches that has shown a considerable efficiency in this field because of the multivariate nature of drought and the noticeable correlation between its variables. The objective of current research is to study the meteorological and hydrological drought events in Gharesoo-Gorganrud basin and perform bivariate drought frequency analysis in this basin by copulas based on the two variables drought severity and drought duration. In the current study, the copulas are utilized to perform bivariate drought frequency analysis in Gharesoo-Gorganrud basin. The two variables drought severity and drought duration are calculated based on the meteorological and hydrological drought indices for 23 watersheds in the study area and are used in the drought frequency analysis. In addition, the efficiency of different copulas are assessed in each watershed and the return periods corresponding to average values of drought severity and duration are calculated in each watershed. Finally, the maps of return periods of the meteorological and hydrological droughts are plotted for the study area. There are clear inverse correlations between the meteorological drought frequency and the variables severity and duration in the studied watersheds. In addition, a high correlation is seen between the mean statistics of the two meteorological drought variables severity and duration. Furthermore, there is a clear inverse correlation between the hydrological drought frequency and severity. However, it is observed that the correlation between the hydrological drought severity and duration is much lower than the corresponding value between the meteorological drought severity and duration. This issue can be caused by the effect of the magnitude of the recorded discharge in the watersheds on the value of hydrological drought severity variable. In general, Gumbel-Hougaard copula shows the highest efficiency for meteorological and hydrological drought frequency analysis in the study area. In addition, the highest values of the joint return period corresponding to the mean values of the drought severity and duration based on most of the assessed indices in this study are observed in the subbasins 18 and 22. According to the results, in the study area, the cumulative increase of meteorological drought severity is yielded by an increase in the duration of drought events. Also, in general, Gumbel-Hougaard copula can be considered as the most efficient option among the studied copulas for drought frequency analysis in the study area.