Multivariate Analysis of Hydrological Droughts in Urmia Lake basin Using Artificial Data Generation Technique and Copula Functions

From a hydrological point of view, measuring the flow of rivers, lakes and groundwater is a measure of drought and there is a baseline time between the lack of rainfall and the decrease of running water of inlets and lakes and groundwater. More studies have been done on meteorological droughts compared to hydrological droughts. Therefore, the purpose of this study is multivariate analysis of hydrological droughts in Lake Urmia basin using artificial data generation models and Copula functions. Therefore, using a combination of the above methods for the analysis of hydrological droughts was used as a new method for the analysis of hydrological droughts.

In this study, in order to multivariate analysis of hydrological droughts in the Urmia Lake basin, the flow data of 28 hydrometric stations in which the flow regime is real were used during a statistical period of 40 years (1978-2017). Also, Ar (1) model was used to generate artificial data and SDImod index was used for drought analysis. For this purpose, artificial data were generated in 1000 sequence. Since univariate drought analysis and analysis based on historical data can not show the horizontal of future droughts alone, so using the Ar (1) model, annual data were generated and then using the model The Valencia and Schakke generated monthly artificial data. Then drought characteristics (intensity and duration) were extracted for both historical and generation data series and common distributions in hydrology were fitted to intensity, duration and flow data. Then the transfer probability matrix and their steady state condition matrix (SSC) were also calculated. Also, multivariate analysis of hydrological droughts was performed using ten Archimedean Copula functions. The above coding was done in MATLAB software environment.

The results of this study showed that after examining the homogeneity of data and their static test, most of the data had the necessary homogeneity and the results of data homogeneity showed that the coefficient of explanation was above 0.9 and the results of static test and Their trend showed that the data were within the allowable range of 1.2 ±2.1 and ±1.96. The results of fitting the data on the common statistical distributions showed that the Log Pearson Type3 (LP3) function was known as the superior distribution functions on the flow data and the gamma and exponential distribution functions on the severity and duration of the drought, respectively. The number of drought periods based on different scales of SDImod index showed that for different periods the number of drought periods for short-term scales was more than long-term scales. Also, the average intensity and duration of drought for generated and historical data indicate an increase in the intensity of drought for generated data compared to historical data. The results of classifying drought periods for historical and generated data showed that approximately 68% of the data were in the normal range during the statistical period and 32% were other classes. The result of the Copula functions showed that the Joe Copula function in the first order and Filip Gumble and Galambos functions in the next order were known as the superior Copula functions.

Finally, the results showed that the artificial data generation models for annual and monthly data for statistical years less than 30 years maintain the statistical characteristics of mean, standard deviation, skewness and correlation between two consecutive months, while increasing The number of statistical years of model performance becomes more favorable. The cumulative probability of non-annual drought and the probability of normal and wet season in hot months of the year is higher than other months of the year. Also, with increasing periods of drought, the cumulative probability of non-drought increases, so that with increasing periods, this probability decreases and becomes almost zero. The results of the joint and conditional return periods as well as the Kendall return period showed that the probability of drought occurring in future periods is expected to be at least similar to the historical data. The results also showed that the Joe Copula function was recognized as the superior Copula function for historical and generated data. Accordingly, the theoretical Copula function is close to the 45 degree angle bisector against the experimental Copula function.