The Probabilistic Analysis of Drought Severity- Duration in North Khorasan Province using Copula Functions

Droughts have a set of negative environmental, social and economic effects in a region or country. Using a monthly index and its analysis that, in addition to precipitation values, takes into account the effect of evaporation on the numerical value of the index, is very useful in determining drought parameters. Different indices are also a combination of variables with different marginal distributions, and for this purpose, their statistical analysis is difficult. Therefore, in order to determine the structure of dependence between two or more random variables, copula functions can be used, the distribution of margins is separated from the modeling of the structure of dependence between variables.

In this study, RDI index was used to determine the severity and duration of drought in 6 stations of North Khorasan province between 1988-2018 and Copula functions were used to analyze the severiy and duration. 26 different Copula functions were investigated using different statistical values. Also, two methods of local optimization and Monte Carlo Markov chain simulation with Bayesian estimator were used to numerically estimate the posterior distribution of selected Copula parameters. In order to evaluate the fit of different copulas, the common criteria were used for measuring the fit of different copulas including mean squared error, Bayesian information criterion, Akaike information and Nash-Sutcliffe efficiency criterion.

In all stations, the values of correlation coefficient with Pearson and Kendall tests were positive and had the same trend. The results of the Kolmogorov-Smirnov test at a significance level of five percent for choosing the optimal distribution showed that the generalized Pareto distribution was selected for the intensity and duration of Bojnord station and the exponential distribution for other stations was selected as the appropriate fitted distribution. The optimal function for Bojnord, Maneh and Semelghan stations was Burr function, Jajarm and Shirvan stations, Joe function, Farouj station, Galambos function and Esfarayen station, BB1 function. The results of the local optimization method are highly consistent with the Markov chain Monte-Carlo method. For the 100-year return period, the drought severity at bojnord station is 6.8, at esfarayen station, drought severity is 7.8, at faruj station, drought severity is 7.5, at jajarm station, drought severity is 7.8, at the station in manesemelghan, the drought severity was 8 and in shirvan station, the drought intensity was 2.8.

Conclusion and Suggestions :

The current study shows the high capability of copula functions in solving two-variable problems and recommends the use of all possible functions in choosing marginal distributions and copula in solving problems. Also, the high correspondence between the two methods of local optimization and Markov chain Monte Carlo for estimating the parameters of the functions is probably due to the short statistical period used. Investigating the capabilities of these functions in solving multivariate problems, implementing other Monte Carlo Markov chain estimators, and using longer data to compare different optimization algorithms are suggested in future researches.