مدل‌سازی دما و بارش تبریز با بکارگیری توابع مفصل

نوع مقاله: مقاله پژوهشی

نویسندگان

1 عضو باشگاه پژوهشگران جوان دانشگاه آزاد اسلامی واحد تبریز

2 ستادیار گروه مهندسی آب، دانشکده کشاورزی، دانشگاه شهرکرد

3 دانشیار گروه مهندسی آب، دانشکده کشاورزی، دانشگاه تبریز

چکیده

به‌طور کلی توزیع احتمالاتی داده‌های تصادفی چند متغیره در مقایسه با حالت یک متغیره آن‌ها به دلیل وابستگی غیرخطی بین متغیرهای تصادفی، پیچیده‌تر است. یکی از روش‌های حل این مشکل استفاده از توابع مفصل می‌باشد که در سال‌های اخیر بیشتر مورد توجه محققین بوده است. در این مطالعه، وابستگی دما و بارش ایستگاه تبریز با استفاده از توابع مفصل مدل‌سازی شد. برای این منظور از داده‌های بارش و دمای ماهانه ایستگاه تبریز در دوره آماری 1387-1350 استفاده شد. ابتدا توزیع‌های تک متغیره مناسب برای بارش و دما بر مبنای تست کولموگروف-اسمیرنف به ترتیب نمایی و مقدار حدی تعمیم یافته (GEV) انتخاب شدند. سپس سه تابع مفصل کلایتون، گامبل و فرانک برای ایجاد توزیع دومتغیره بارش و دمای ایستگاه تبریز مورد بررسی قرار گرفت. نتایج نشان داد که عملکرد هر سه تابع مفصل نزدیک به هم بوده ولی با توجه به اینکه از بین سه تابع مفصل مورد بررسی، فقط مفصل فرانک قابلیت مدل کردن وابستگی‌های منفی را دارا می‌باشد، بنابراین به عنوان تابع مفصل مناسب جهت مدل کردن وابستگی بارش و دمای ایستگاه تبریز انتخاب گردید.

کلیدواژه‌ها


عنوان مقاله [English]

Modeling of Temperature and Rainfall of Tabriz Using Copulas

نویسندگان [English]

  • Hadi Sanikhani 1
  • Rasool Mirabbasi Najaf Abadi 2
  • Yaghoob Dinpashoh 3
1 Ph.D Student of Water Engineering, Young Researcher club, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2 Assistant Professor, Water Eng. Dep., Agriculture Faculty, Shahrekord University
3 Associate Professor, Water Eng. Dep., Agriculture Faculty, University of Tabriz
چکیده [English]

Because of nonlinear dependence between the random variables, probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts. One approach to solve this problem is the use of copulas, which have more considered by researchers over recent years. In this study, the dependence of rainfall and temperature in Tabriz station was modeled using copulas. In this regard, monthly data of rainfall and temperature of Tabriz for a period of 1971-2008 was used. At the first step, by application of Kolmogorov–Smirnov test, exponential and generalized extreme value (GEV) distributions are selected as appropriate univariate distributions for rainfall and temperature, respectively. Then three type of copulas functions namely, Clayton, Gumbel and Frank are used for creating bivariate distribution of rainfall and temperature in Tabriz. The results indicated that the performances of all types of copulas are close together. However, an only Frank copula has capability to modeling the negative dependence between variables. Therefore, Frank function is selected as appropriate copulas for modeling dependence between rainfall and temperature in Tabriz station.

کلیدواژه‌ها [English]

  • Rainfall
  • Tabriz
  • Bivariate analysis
  • Temperature
  • Copulas
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