پديد آورندگان :
منتصري، مجيد دانشگاه اروميه - گروه مهندسي آب , اميرعطايي، بابك دانشگاه اروميه - گروه مهندسي آب , رضايي، حسين دانشگاه اروميه - گروه مهندسي آب
كليدواژه :
بزرگي خشكسالي , توزيع حاشيه اي , شاخص بارش استاندارد , مساحت تحت پوشش خشكسالي
چكيده فارسي :
خشكسالي ها رويدادهاي كرانه اي هستند كه بر اساس تداوم در زمان و تاثيرات مكاني آن مشخص مي شوند. بطوركلي خشكسالي هاي منطقه اي متاثر از گردش عمومي جو (در مقياس بزرگ) و عوامل طبيعي منطقه اي شامل شرايط توپوگرافي، درياچه هاي طبيعي، موقعيت نسبت به مركز و مسير جريان هاي آب و هوايي در جو (در مقياس ريز) بوده و اثرات كاملا همساني در يك منطقه وسيع را نشان نمي دهند. لذا در اين مطالعه توزيع احتمال توام بزرگي - مساحت تحت پوشش خشكسالي در حوضه آبريز درياچه اروميه با استفاده از تكنيك توابع مفصل انجام پذيرفته و منحني بزرگي - مساحت - فراواني/ احتمال خشكسالي (S-A-F) توسعه داده شده است. بدين منظور از سري داده هاي شاخص خشكسالي يكماهه SPI در 24 ايستگاه هواشناسي در محدوده مطالعاتي و 7 خانواده تابع مفصل شامل كلايتون، گامبل، فرانك، جو، گالامبوس، پلاكت و نرمال براي مدل سازي توزيع احتمال توام دو متغير همبسته بزرگي و مساحت تحت پوشش خشكسالي استفاده شده است. عملكرد توابع مفصل هفتگانه مذكور بر اساس معيارهاي آماري رايج مورد آزمون قرار گرفته و در نهايت بازاي مناسب ترين تابع مفصل (مفصل فرانك)، دوره هاي بازگشت شرطي تعيين و منحني S-A-F براي منطقه مطالعاتي استخراج شد. نتايج مطالعه نشان مي دهد كه رفتارهاي كرانه اي اقليمي (خشكسالي يا ترسالي) اكثريت محدوده مطالعاتي را تحت تاثير قرار مي دهند.درحاليكه رفتارهاي نيمه يا شبه خشك داراي پوشش مساحت متفاوت با پراكندگي قابل توجه در محدوده مطالعاتي بوده و با افزايش بزرگي خشكسالي مساحت بيشتري از حوضه آبريز را در بر مي گيرند. بطوريكه بعنوان مثال، بزرگي خشكسالي براي زمان برگشت 50 ساله با كمترين و بيشترين مقادير در منطقه يعني 0.42 و 1.0 بترتيب حدود 5 و 95 درصد مساحت محدوده مطالعاتي را پوشش مي دهد.
چكيده لاتين :
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-AF
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.
