Multivariate drought risk analysis based on copula functions: a case study

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Abstract
Drought is asserted as a natural disaster that encompasses vast territories for a long time and affects human life. Indicators are powerful tools for understanding this phenomenon. However, in order to get more information about the drought, multivariate indices were introduced for simultaneous evaluation of multiple variables. In this study, a combined drought index (CDI) based on three drought indices, the Standardized Precipitation Index (SPI), Streamflow Drought Index (SDI), and Standardized Water-level Index (SWI), is defined. Then, the Entropy method is used to determine the weight of each indicator. Among the calculated weights, SDI and SPI had the highest and lowest weight, respectively. The CDI is utilized to identify drought characteristics, such as duration and severity. In addition, the joint distribution function of drought characteristics is formed by copula functions and consequently the probability of different droughts is calculated. For the study area, data and information from eight regions located in Golestan province in the northern part of Iran are used to evaluate the performance of the proposed index. Four categories of drought were defined and their return period calculated. The shortest return period of severe drought was observed in the east and then in the west. In the south and center, the return period of severe drought was longer. Over the course of 30 years, all parts of the province experienced all drought categories.

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