Bivariate Drought Frequency Analysis based on Copula Theory for Osmaniye Region

Abstract

Keywords

• SPI
• Kopula
• Osmaniye
• Yağış

Kopula Yöntemi ile Osmaniye Bölgesinin İki Değişkenli Kuraklık Frekans Analizi

Abstract

Çok değişkenli frekans dağılımları, hidrolojik tasarım ve risk yönetimi için giderek daha fazla önem kazanmaktadır. Geleneksel çok değişkenli dağılımlar, tüm bileşen marjinallerinin aynı dağılım ailesinden olması gerektiği için ciddi şekilde sınırlamalara sahiptir. Kopula yöntemi, bu sınırlamanın üstesinden gelen çok değişkenli dağılımların türetilmesi için yeni ortaya çıkan bir yaklaşımdır. Bu çalışmada, Osmaniye ilinin yağış istasyonu uzun dönem veriler ile kuraklık analizi kopula fonksiyonu kullanılarak hesaplanmıştır. İlk olarak, kuraklık parametreleri olan kuraklık süresi ve şiddeti SPI metodu kullanılarak elde edilmiştir. Gözlemlenen kuraklık süresi için Lognormal, kuraklık şiddeti için ise Weibull en uygun marjinal dağılım olarak bulunmuştur. Her bir kuraklık parametresi için tek değişkenli dağılım fonksiyonu elde edildikten sonra, Gumbel kopulası belirlenen 10 kopula fonksiyonu arasında Akaike Bilgi Kriteri (AIC), Bayes Bilgi Kriteri (BIC), Maksimum olabilirlik (MLE) yöntemleri ve kuyruk bağımlılığı da dikkate alınarak seçilmiştir. En son olarak Osmaniye ili kuraklık ortak dönüş periyodu hesaplanmış olup, muhtemel yapılması düşünülen su temini sistemi, hidrolik tasarım ve su yönetimi gibi konularda yararlı bilgiler sağlamaktadır.

Keywords

• SPI
• Kopula
• Osmaniye
• Yağış

References

1. [1] Kao, S. C., & Govindaraju, R. S. A copula-based joint deficit index for droughts. Journal of Hydrology, 380(1-2), 121-134, 2010
2. [2] Heim Jr, R. R. A review of twentieth-century drought indices used in the United States. Bulletin of the American Meteorological Society, 83(8), 1149-1166, 2002
3. [3] Sheffield, J., Wood, E. F., & Roderick, M. L. Little change in global drought over the past 60 years. Nature, 491(7424), 435-438, 2012
4. [4] McKee, T. B., Doesken, N. J., & Kleist, J. The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology (Vol. 17, No. 22, pp. 179-183), January 1993
5. [5] Below, R., Grover-Kopec, E., & Dilley, M. Documenting drought-related disasters: A global reassessment. The Journal of Environment & Development, 16(3), 328-344, 2007
6. [6] Wilhite, D. A. Drought as a natural hazard: concepts and definitions, 2000
7. [7] Shiau, J. T., Feng, S., & Nadarajah, S. Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrological Processes: An International Journal, 21(16), 2157-2163, 2007
8. [8] Mishra, A. K., & Singh, V. P. A review of drought concepts. Journal of hydrology, 391(1-2), 202-216, 2010

9. [9] Kogan, F. N. Droughts of the late 1980s in the United States as derived from NOAA polar-orbiting satellite data. Bulletin of the American Meteorological Society, 76(5), 655-668, 1995
10. [10] Guttman, N. B. Accepting the standardized precipitation index: a calculation algorithm 1. JAWRA Journal of the American Water Resources Association, 35(2), 311-322, 1999
11. [11] Guttman, N. B. Comparing the palmer drought index and the standardized precipitation index 1. JAWRA Journal of the American Water Resources Association, 34(1), 113-121, 1998
12. [12] Ray, K. S., & Shewale, M. P. Probability of occurrence of drought in various sub-divisions of India. Mausam, 52(3), 541-546, 2001
13. [13] Efstathiou, M. N., & Varotsos, C. A. Intrinsic properties of Sahel precipitation anomalies and rainfall. Theoretical and applied climatology, 109(3-4), 627-633, 2012
14. [14] McKee, T. B. Drought monitoring with multiple time scales. In Proceedings of 9th Conference on Applied Climatology, Boston, 1995, 1995
15. [15] Eris, E., Aksoy, H., Onoz, B., Cetin, M., Yuce, M. I., Selek, B., ... & Karakus, E. U. Frequency analysis of low flows in intermittent and non-intermittent rivers from hydrological basins in Turkey. Water Supply, 19(1), 30-39, 2019
16. [16] Du, J., Fang, J., Xu, W., & Shi, P. Analysis of dry/wet conditions using the standardized precipitation index and its potential usefulness for drought/flood monitoring in Hunan Province, China. Stochastic environmental research and risk assessment, 27(2), 377-387, 2013
17. [17] Çetin, M., Aksoy, H., Önöz, B., Eriş, E., İshak, M., Yüce, B. S., ... & Orta, S. Deriving Accumulated Precipitation Deficits from Drought Severity-Duration-Frequency Curves: A Case Study in Adana Province, Turkey. SCIENTIFIC COMMITTEE-BİLİM KURULU, 39, 2018
18. [18] Aksoy, H., Onoz, B., Cetin, M., Yuce, M. I., Eris, E., Selek, B., ... & Cavus, Y. SPI-based drought severity-duration-frequency analysis. In Proceedings of the 13th International Congress on Advances in Civil Engineering, Izmır, Turkey (pp. 12-14), September 2018
19. [19] Tsakiris, G., Kordalis, N., Tigkas, D., Tsakiris, V., & Vangelis, H. Analysing drought severity and areal extent by 2D Archimedean copulas. Water Resources Management, 30(15), 5723-5735, 2016
20. [20] Shiau, J. T. Fitting drought duration and severity with two-dimensional copulas. Water resources management, 20(5), 795-815, 2006
21. [21] Cancelliere, A., & Salas, J. D. Drought length properties for periodic‐stochastic hydrologic data. Water resources research, 40(2), 2004
22. [22] Song, S., & Singh, V. P. Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm. Stochastic Environmental Research and Risk Assessment, 24(5), 783-805, 2010
23. [23] Salvadori, G., De Michele, C., Kottegoda, N. T., & Rosso, R. Extremes in nature: an approach using copulas (Vol. 56). Springer Science & Business Media, 2007
24. [24] Kuhn, G., Khan, S., Ganguly, A. R., & Branstetter, M. L. Geospatial–temporal dependence among weekly precipitation extremes with applications to observations and climate model simulations in South America. Advances in Water Resources, 30(12), 2401-2423, 2007
25. [25] Nelsen, R. B. An introduction to copulas. Springer Science & Business Media, 2007
26. [26] Mirakbari, M., Ganji, A., & Fallah, S. R. Regional bivariate frequency analysis of meteorological droughts. Journal of Hydrologic Engineering, 15(12), 985-1000, 2010
27. [27] Tosunoglu, F., & Can, I. Application of copulas for regional bivariate frequency analysis of meteorological droughts in Turkey. Natural Hazards, 82(3), 1457-1477, 2016
28. [28] Mirabbasi, R., Fakheri-Fard, A., & Dinpashoh, Y. Bivariate drought frequency analysis using the copula method. Theoretical and Applied Climatology, 108(1-2), 191-206, 2012
29. [29] Shiau, J. T., & Modarres, R. Copula‐based drought severity‐duration‐frequency analysis in Iran. Meteorological Applications: A journal of forecasting, practical applications, training techniques and modelling, 16(4), 481-489, 2009
30. [30] Lee, T., Modarres, R., & Ouarda, T. B. Data‐based analysis of bivariate copula tail dependence for drought duration and severity. Hydrological Processes, 27(10), 1454-1463, 2013
31. [31] Yusof, F., Hui-Mean, F., Suhaila, J., & Yusof, Z. Characterization of drought properties with bivariate copula analysis. Water resources management, 27(12), 4183-4207, 2013
32. [32] Sklar, A., SKLAR, A., & Sklar, C. A. Fonctions de reprtition an dimensions et leursmarges, 1959
33. [33] Salvadori, G., & De Michele, C. Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water resources research, 40(12), 2004
34. [34] Poulin, A., Huard, D., Favre, A. C., & Pugin, S. Importance of tail dependence in bivariate frequency analysis. Journal of Hydrologic Engineering, 12(4), 394-403, 2007