ارزیابی انتخاب تابع توزیع احتمالاتی مناسب در استفاده از شاخص‌های خشکسالی SPI و RDI

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشیار، گروه مهندسی آب، دانشگاه ارومیه

2 دکتری مهندسی منابع آب، گروه مهندسی آب، دانشگاه ارومیه

چکیده

هدف این مقاله، انتخاب مناسب­ترین تابع توزیع احتمال برای محاسبه دو شاخص خشکسالی RDI و SPI و مقایسه این دو شاخص می­باشد. بر این اساس، با استفاده از آمار هواشناسی سی ایستگاه همدید در ایران، سری داده­های سالانه بارندگی و نسبت بارش به تبخیر- تعرق پتانسیل به­دست آمد. ابتدا تابع توزیع نرمال یا گاما برای تعیین مقادیر سالانه شاخص SPI و تابع توزیع لاگ­نرمال یا گاما برای تعیین مقادیر سالانه شاخص RDI مورد استفاده قرار گرفت. سپس با استفاده از آماره کلموگروف- اسمیرنف، برترین تابع توزیع جهت برازش سری داده­ها در ایستگاه­های مورد­مطالعه تعیین شد. بعد از تعیین مقادیر شاخص­ها بر اساس تابع توزیع مناسب و توابع توزیع اشاره شده، میزان جابجایی طبقات مختلف خشکسالی مورد ارزیابی قرار گرفت. نتایج نشان داد که در بیشتر ایستگاه­ها، توابع توزیع اشاره شده نمی­توانند به­عنوان مناسب­ترین تابع توزیع انتخاب شوند و کاربرد آنها در تعیین شاخص­ها، باعث تغییر طبقات خشکسالی خواهد شد. نتایج شاخص­های آماری (434/0 RMSE<و 819/0R2>) نشان داد که سری­های زمانی سالانه دو شاخص خشکسالی RDI و SPI (محاسبه شده بر اساس مناسب­ترین تابع توزیع احتمال) تقریبا مشابه می­باشد و اختلاف آنها در هیچ ایستگاهی معنی­دار نیست. همچنین نتایج نشان­دهنده حساسیت بیشتر شاخص RDI نسبت به شاخص SPI به انتخاب تابع توزیع می­باشد و انتخاب تابع توزیع برتر جهت تعیین این شاخص از اهمیت بیشتری برخوردار است.

کلیدواژه‌ها


عنوان مقاله [English]

Evaluating the Selection of the Most ‌Suitable Probability Distribution Function for Using the RDI and SPI Drought Indices

نویسندگان [English]

  • H Rezaie 1
  • N khanmohammadi 2
  • Majid montazeri 1
  • G Behmanesh 1
1 Assoc. Prof., Dept. of Water Engin., Univ. of Urmia., Urmia, Iran
2 Ph.D. of Water Resour. Engin., Dept. of Water Engin., Univ. of Urmia., Urmia, Iran
چکیده [English]

The purpose of this paper is the selection of the most suitable probability distribution function to calculate and compare the RDI and SPI drought indices. Accordingly, using the meteorological data of thirty synoptic stations in Iran, annual rainfall data series and the ratio of precipitation to potential evapotranspiration were obtained. At first, Normal or Gamma distributions and Log-normal or Gamma distributions were used to determine the SPI and RDI annual values, respectively. Then using Kolmogorov-Smirnov index, the best distribution function was obtained to fit with the data series in the studied stations. After determining the index values based on the superior distribution function and also the mentioned distribution functions, replacement of different drought classes was evaluated. The results showed that in the most stations, the mentioned distribution functions could not be selected as the most appropriate distribution function and using them in determination of the indices could change the drought classes. The results of the statistical indices (RMSER2>0.819) showed that the annual time series of the SPI and RDI indices (calculated on the basis of the most suitable probability distribution function) were approximately similar and their difference was not significant in none of the stations. Also the results showed that the RDI index was more sensitive than the SPI index to the selection of the distribution function, so the selection of the most suitable distribution function for determination of this index was more important.

کلیدواژه‌ها [English]

  • Drought
  • Iran
  • Probability distribution function
  • RDI index
  • SPI index
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