Developing Combined Regional Drought Index and Presenting Return Period Curves Using Copula Function

Drought is an integral part of natural hazards. It usually occurs gradually and without any warning. Moreover, this phenomenon is usually created over time and does not disappear quickly Recently, some factors such as climate variability and the impact of climate change have influenced drought frequency and intensity in many parts of the world. Various definitions have been provided for drought but in general the lack of water resources in a specific period in a geographical area is considered as drought which implies this phenomenon as a regional hazard. IRAN is located in an arid and semi-arid region in which it experiences drought frequently. There are different types of drought such as meteorological, hydrological, agricultural and social-economic. These types are differentiated based on the factor which is rainfall, river flows, soil moisture, and social-economic consequences. There are many indices proposed for measuring drought severity; among them Standardized Precipitation Index (SPI), Palmer Drought Severity Index (PDSI) and Surface Water Supply Index (SWSI) could be mentioned. Each of these indices has its own pros and cons and is suitable for a particular type of drought. Therefore knowing the types of drought can provide a better understanding of shortages and their characteristics. Various factors are utilized for measuring these indices including precipitation, reservoir storage, discharge, temperature and potential evapotranspiration. In this study the three main aforementioned indices were first calculated for Aharchay watershed, located in East Azerbaijan province. Next based on combining these three indices with another two important parameters, groundwater level and solar radiation, a combined drought index is developed and calculated for the studied region. Considering the fact that the aforementioned parameters and indices have different level of importance in combined index, different weights based on expert opinions are assigned to the parameters considering how critical each parameter is in the overall drought analysis. This combined index demonstrated various climatic, hydrological and agricultural aspect of the region. In the next step, bivariate analysis of the two variables, intensity and duration, is carried out using copula. This is done by first checking the dependency between intensity and duration using Pearson, Spearman, and Kendall correlation coefficients. Second, various copula functions were fitted such as Gaussian, T, Clayton and Gumbel functions. Third, based on the Ordinary Least Square (OLS) and Kolmogorov–Smirnov (K-S) tests, the best copula functions were used. Lastly, based on the chosen copula the joint probability distributions were obtained. Two cases named “OR” and “AND” were defined for joint probability of the two variables and different return period curves is drawn. The results showed that the most severe drought in this watershed occurred in June 2004. Moreover, by assessing correlation coefficient between the considered indices it is shown that analysis of the drought in a region based solely on one index would neglect other imperative aspects in drought determination which necessitates a more integrated indicator. Furthermore, in bivariate analysis, return periods of “AND” cases were more than “OR” case. The results of this study could be utilized in preparedness and monitoring drought.