کاربرد توابع مفصل ارشمیدسی در تحلیل فراوانی سیلاب (مطالعه موردی: حوضه آبریز دز)

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه شهید چمران

2 دانشگاه شهید چمران اهواز

3 دانشگاه شهرکرد

چکیده

یکی از پدیده­های هیدرولوژیکی که ماهیت بسیار پیچیده داشته و در صورت رخداد خسارات فراوانی را ایجاد می­کند، پدیده سیلاب می­باشد. در این مطالعه تحلیل فراوانی سیلاب حوضه آبریز دز در محل اتصال دو ایستگاه سپید دشت- سزار (س. د. س) و سپید دشت- زاز (س. د. ز) در دوره آماری 1391-1335 با استفاده از توابع مفصل مورد بررسی قرار گرفت. بدین منظور در ابتدا سری­های جزئی سیلاب در ایستگاه­های مورد مطالعه با استفاده از روش مالمود و توکارت استخراج گردید. در مرحله بعد 11 تابع توزیع مختلف به سری­های سیلاب استخراجی برازش داده شد و در نهایت توزیع‌های لجستیک تعمیم یافته (ایستگاه س. د. س) و تابع توزیع حدی تعمیم یافته (س. د. ز) به عنوان توزیع حاشیه‌ای مناسب انتخاب گردید. پس از انتخاب توزیع­ حاشیه­ای، از توابع مفصل خانواده ارشمیدسی (شامل مفصل­های علی- میخائیل- حق، فرانک و کلایتون) برای تحلیل فراوانی توام سیلاب حوضه آبریز دز استفاده شد. نتایج نشان داد که مفصل فرانک برای جفت داده­های ایستگاه­های سپید دشت- سزار و سپید دشت- زاز بیشترین تطابق را با تابع مفصل تجربی داشته است. برای بررسی دوره بازگشت وقایع در حالت توأم، از دوره بازگشت توأم در دو حالت «یا» و «و» و دوره بازگشت توأم شرطی استفاده شد. براساس نتایج به دست آمده از تحلیل توام سری­های سیلاب دو سرشاخه متصل به هم مشخص شد که دو رودخانه سپید دشت سزار و سپید دشت زاز هر 70 سال یک‌بار به صورت هم­زمان می­تواند در معرض سیلاب شدید قرار گیرند.

کلیدواژه‌ها

عنوان مقاله [English]

Application of Archimedean Copula Functions in Flood Frequency Analysis (Case Study: Dez Basin)

نویسندگان [English]

  • Farshad Ahmadi 1
  • Feridon Radmaneh 2
  • Gholamali Parham 2
  • Rasoul Mirabbasi najafabadi 3
1 Shahid Chamran University of Ahwaz
2
3 University of Shahrekord
چکیده [English]

Most of hydrological phenomena have a stochastic and probabilistic nature and the relationship governing on these phenomena are almost unknown and ambiguous. Therefore, the theories of statistic and probability apply for describing and forecasting of such phenomena. One of the hydrological phenomena which have a complicated nature and causes too much damage is the flood. In the present study, flood frequency analysis in the Dez basin at the junction of two hydrometric stations of Sepid Dasht Sezar (SDS) and Sepid Dasht Zaz (SDZ) was performed during the period of 1957-2012 using the copula functions. The copula is a function which joint the univariate marginal distribution to form a bivariate or multivariate distribution function. For this purpose, first the partial series of flood at studied stations were extracted using the Malmoud-Tookart method. In the next step, 11 different distribution functions were fitted on the extracted flood series and the Generalized Logistic (SDS station) and Generalized Extreme Value (SDZ station) distribution functions were selected as the best fitted ones. After selecting the suitable marginal distributions, some of Archimedean copula functions (Ali - Mikhail – Haq, Frank and Clayton) were used for joint flood frequency analysis in Dez basin. Results showed that the Frank copula had the highest match with empirical copula for paired flood data of SDS and SDZ stations. For investigating the return period of events the joint return periods in two states “AND” and “OR” and also the conditional return period were considered. Based on the results obtained from joint analysis of flood series in two river branches, it was found that the severe flood events may occur simultaneously at SDS and SDZ River branches every 70 years.

کلیدواژه‌ها [English]

  • Stationarity test
  • Copula function
  • Marginal distribution
  • Partial series
  • Power law

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تحقیقات آب و خاک ایران
دوره 48، شماره 3
مهر و آبان
مهر 1396
صفحه 477-489

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