M. Montaseri; B. Amirataee; H. Rezaei
Abstract
Introduction: Drought is a natural phenomenon and was described when precipitation is less than expected. Since the precipitation amounts in terms of spatial and temporal characteristics are different from one region to another, so this phenomenon is known as a multivariate phenomenon. This phenomenon ...
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Introduction: Drought is a natural phenomenon and was described when precipitation is less than expected. Since the precipitation amounts in terms of spatial and temporal characteristics are different from one region to another, so this phenomenon is known as a multivariate phenomenon. This phenomenon often characterized by different variables such as drought duration, severity, intensity and spatial extent. Although site specific analysis can provide useful information on drought occurrences in a limited area, but these results have a fundamental uncertainty to drought risk assessment in a large region. Therefore regional drought analysis, provides a more comprehensive assessment in each region, and is essential for short and long term management of water resources. Meanwhile, the copula functions has been developed as a new advanced technique for modeling the two or multivariate joint probability distribution in different fields such as financial, hydrology, water resources and risk management. So, in this research, regional analysis of drought severity and percent of drought area were performed using the copula functions in Lake Urmia basin, as one of the Iran's drought-prone basin. Such study with emphasis on bivariate analysis of drought severity and drought areal extend were conducted for the first time in the study area. The main objectives of this study are: 1) Modeling drought characteristics in Lake Urmia basin, 2) Evaluation of copula functions in modeling the structure of the region's drought characteristics, and 3) Develop the Severity-Area-Frequency curve using the appropriate copula.
Materials and Methods: Copula is the stochastic model and based on probability. In other words, copulas are function for modeling the two or multivariate random variables. Copulas can be easily coupled the marginal distributions to multiple distributions. There are many parametric copula families available, that seven copula functions such as archimedean (Clayton, Frank, Gumbel and Joe), extreme value (Galambos), elliptical (Normal) and others (Plackett) were used. The SPI-1 was determined at each station and then, the whole area was divided into small grids with cell size of 2000×2000. Distances between the grid centers with all the selected stations were calculated with a programming code. Finally, the SPI values in each grid were calculated using IDW method. The severity and percentage of drought area variables were determined and used for regional drought modeling in the study area based on drought threshold equal to zero. After determining the best statistical distribution of two variables, the appropriate copula function was conducted based on different goodness of fit tests. Finally, the Severity-Area-Frequency curve for the study area was developed based on the appropriate copula function and conditional return periods.
Results and Discussion: The correlation between the two variables of percentage of drought area and severity was assessed using different graphical (Kendall plot and Chi plot) and statistical tests (Spearman rand order correlation and Kendal tau). The results showed a positive correlation between the drought severity and percentage of drought area variables. Based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) and graphical test, the Lognormal and Beta probability distributions were select as a best fit distribution of severity and percentage of area under drought, respectively. Finally, the Frank copula among other type of copulas was selected as an appropriate copula for modeling joint drought severity and percentage of area under drought for the study area based on Maximum log likelihood, AIC, BIC and RMSE criteria. The S-A-F curve was developed using conditional return periods based on Frank copula. According to S-A-F curve, it can be seen that increase in the percentage of area under drought in the study area led to increase in drought severity and vice versa. For example, drought severity with return period of 20 years and drought with 20 percent areal extend is obtained equal to 0.37.
Conclusions: Copula functions are of great importance in the analysis of drought, due to preserve correlation between variables and not have any limitation to have a same marginal distribution in long-term prediction of drought events. In this study, using best fit copula (Frank copula) and conditional return periods, the relationships between drought severity and percent of area under drought for the study area named S-A-F curve were developed. These curves can be useful for planning and management of drought in the region. Drought risk assessment based on the results of this study can be high priorities for drought monitoring in large areas.
Majid Montaseri; Babak Amirataee; Keyvan Khalili
Abstract
Introduction: Droughts are natural extreme phenomena, which frequently occur around the world. This phenomenon can occur in any region, but its effects will be more severe in arid and semi-arid regions. Several studies have highlighted the increasing of droughts trend around the world. The majority of ...
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Introduction: Droughts are natural extreme phenomena, which frequently occur around the world. This phenomenon can occur in any region, but its effects will be more severe in arid and semi-arid regions. Several studies have highlighted the increasing of droughts trend around the world. The majority of studies in assessing the trend of time series are based on basic Mann-Kendall or Spearman's methods and no serious attention has been paid to the impact of autocorrelation coefficient on time series. However, limited numbers of studies have included the lag-1 autocorrelation coefficient and its impacts on the time series trend. The aim of this study was to investigate the trend of dry and wet periods in northwest of Iran using Mann-Kendall trend test with removing all significant autocorrelations coefficients based on SPI and RAI drought indices.
Materials and Methods: Study area has a region of 334,000 square kilometers, with wet, arid and semiarid climate, located in the northwest of Iran. The rainfall data were collected from 39 synoptic stations with average rainfall of 146 mm as the minimum of Gom station, and the highest annual rainfall of 1687 mm, in the Bandaranzali station. In this study, Standardized Precipitation Index (SPI) and Rainfall Anomaly Index (RAI) were used for trend analysis of dry and wet periods. SPI was developed by McKee et al. in 1993 to determine and monitor droughts. This index is able to determine the wet and dry situations for a specific time scale for each location using rainfall data. RAI index was developed by Van Rooy in 1965 to calculate the deviation of rainfall from the normal amount of rainfall and it evaluates monthly or annual rainfall on a linear scale resulting from a data series. Then, correlation coefficients of time series of these drought indices with different lags were determined for check the dependence or independence of the SPI and RAI values. Finally, based on dependence or independence of the time series values, trend analysis of wet and dry periods was conducted in different stations using one of the basic or modified Mann-Kendall tests. Also, the magnitude of the trends was derived from the Theil- Sen’s slope estimator.
Results and Discussion: Time series of SPI and RAI drought indices for a given annual rainfall as an example for three stations of Marivan, Gom and Maku show that during 1991 to 1994 and from 2002 to 2007 are in wet period and during 1987 to 1990 and 1998 to 2001 are in the dry period. It is clearly show that, dry and wet periods in RAI index are more severe than SPI. Comparison the correlation between Lag-1 autocorrelation coefficients values of SPI and RAI time series and Lag-1 autocorrelation coefficients of annual rainfall data indicate that these correlations are high and about 0.97 and 0.99, respectively. This difference is due to the different classification of SPI and RAI drought indices. The results of trend analysis indicate a decreasing trend in most of stations. Also, Mann-Kendall statistic has been declining while eliminating the effect of all significant correlation coefficients of dry and wet periods. This result in both SPI and RAI indices are similar and have a high correlation with R = 0.99. According to results, west of the study area have a significant decreasing (negative) trend. The spatial distribution of dry and wet periods showed that the difference between Mann-Kendall statistics of SPI and RAI indices is minimal. Also, The results show that, the slope of the trend line based on the SPI and RAI drought indices is negative in most of stations and correlation between these two indices in determining the slope of the trend line is high. But, this correlation compared with the trend statistics of SPI and RAI time series is less.
Conclusions: In this study, first the time series of SPI and RAI time series based on annual precipitation and common quantitative classification of mentioned two drought indices were determined. Then, trends of dry and wet periods of selected stations in northwest of Iran were evaluated based on these indices using the Mann-Kendall trend test with removing all significant autocorrelation coefficients. The results from this study indicate that using Mann-Kendall test with removing all significant autocorrelation coefficients effects are essential in assessing trend in time series. Although, according to various studies available in the literature, SPI is known as more accurate than RAI in drought mitigation, but according the results of this study, can solely be used both RAI and SPI index for trend detection.
