Kopula Fonksiyonları Kullanılarak Meteorolojik Kuraklık ile Göl Su Yüzü Kotları Arasındaki İlişkinin Modellenmesi

Öz

Bu çalışma, kopula tabanlı istatistiksel bir yaklaşım kullanarak meteorolojik kuraklık ile Eğirdir Gölü’nün hidrolojik tepkisi arasındaki ilişkiyi incelemektedir. Analizde, Eğirdir, Isparta, Uluborlu, Senirkent ve Yalvaç meteoroloji istasyonlarından elde edilen 12 aylık Standartlaştırılmış Yağış İndeksi (SPI) verileri ile 1975–2019 dönemine ait su yüzü kotları (SYK) birlikte kullanılmıştır. Göl seviye serileri standartlaştırılmış ve kuraklık sinyalleri ile göl tepkileri arasındaki gecikme sürelerini belirlemek amacıyla run teorisi uygulanmıştır. SPI ve SYK seviyeleri için marjinal dağılımlar uyarlanmış, bu değişkenlerin ortak davranışı farklı kopula fonksiyonları ile modellenmiştir. Sonuçlar, Eğirdir, Isparta ve Senirkent istasyonlarında SPI ile SYK arasında istatistiksel olarak anlamlı ancak zayıf bir bağımlılık bulunduğunu göstermektedir. Meteorolojik kuraklıkların göl seviyesine etkisi yaklaşık 4–11,5 yıl arasında değişen gecikmelerle ortaya çıkmakta ve depolama kontrollü hidrolojik tepkiye işaret etmektedir. Kopula temelli dönüş periyodu analizine göre yaklaşık beş yıl süren negatif veya sıfıra yakın SPI-12 koşulları SYK’nın uzun dönem ortalama değerinin (917,3 m)altına düşmesiyle sonuçlanmaktadır. Ayrıca, aşırı kuraklık koşullarında (SPI ≈ -2,55) beş yıllık süreçte ek seviye düşüşü olasılığı yaklaşık %65’tir. Bu bulgular, kopula modellerinin kuraklık–göl etkileşimlerini başarılı bir şekilde temsil edebildiğini ve meteorolojik kuraklığın hidrolojik kuraklığa aktarımını ortaya koymakta ve göl havzalarında erken uyarı ile su yönetimi planlaması için sayısal eşikler sunmaktadır. 

Anahtar Kelimeler

• Meteorolojik kuraklık
• hidrolojik kuraklık
• run teorisi
• kopula fonksiyonları

Modeling of Relationship Between Meteorological Drought and Water Surface Elevation Using Copula Functions

Öz

This research analyzes the dependence structure between meteorological drought conditions and hydrological variations in Lake Eğirdir using a copula-based statistical framework. The study relies on 12-month Standardized Precipitation Index (SPI) records obtained from five meteorological stations (Eğirdir, Isparta, Uluborlu, Senirkent, and Yalvaç) and on water surface elevation (WSE) observations spanning 1975–2019. WSE were standardized and run theory was applied to identify potential time lags between atmospheric drought indicators and hydrological responses. Marginal probability distributions were estimated separately for SPI and WSE, after which their dependence structure was characterized using different copula functions. The analysis revealed weak yet statistically significant associations between WSE and SPI at the Eğirdir, Isparta, and Senirkent stations. The impact of meteorological droughts on WSE manifests with delays ranging from approximately 4 to 11.5 years, indicating a storage-controlled hydrological response. According to copula-based return period analysis, negative or near-zero SPI-12 conditions lasting approximately five years result in the WSE falling below its long-term mean elevation (917.3 m). Furthermore, under extreme drought conditions (SPI ≈ -2.55), the probability of further elevation decline over the five-year period is approximately 65%. These findings demonstrate that copula models can successfully represent drought-lake interactions, reveal the transfer of meteorological drought to hydrological drought, and provide numerical thresholds for early warning and water management planning in lake basins. 

Anahtar Kelimeler

• Meteorological drought
• hydrological drought
• run theory
• copula functions

Kaynakça

1. Aghakouchak, A. (2014). Entropy–copula in hydrology and climatology. Journal of Hydrometeorology, 15(6), 2176-2189. https://doi.org/10.1175/JHM-D-13-0207.1.
2. Aktaş, S., Kalyoncuoğlu, Ü.Y., & Kılıç, N.C.A. (2018). Drought Analysis Using De Martonne Method in The Eği̇rdi̇r Lake Basin. Journal of Engineering Sciences and Design, 6(2), 229-238. https://doi.org/10.21923/jesd.398521.
3. Barker, L.J., Hannaford, J., Chiverton, A., & Svensson, C. (2016). From meteorological to hydrological drought using standardised indicators. Hydrology and Earth System Sciences, 20(6), 2483-2505. https://doi.org/10.5194/hess-20-2483-2016.
4. Bazzaz, P.M.P., Sadeghfam, S., Khatibi, R., & Nourani, V. (2024). A drought study in the basin of Lake Urmia under climate change scenarios with higher spatial resolution to understand the resilience of the basin. Journal of Water and Climate Change, 15(2), 453-475. https://doi.org/10.2166/wcc.2024.407.
5. Bera, D., & Dutta, D. (2024). Analysing spatio-temporal drought characteristics and copula-based return period in Indian Gangetic Basin (1901–2021). Environmental Science and Pollution Research, 31(15), 22471-22493. https://doi.org/10.1007/s11356-024-32286-1.
6. Bhardwaj, K., Shah, D., Aadhar, S., & Mishra, V. (2020). Propagation of meteorological to hydrological droughts in India. Journal of Geophysical Research: Atmospheres, 125(22), e2020JD033455. https://doi.org/10.1029/2020JD033455.
7. Binoy, S., Jyoma, J.P., Adarsh, S., Siddik, A.M., Nourani, V., Alisha, A., & Sreeshma, T. (2023). Flood risk analysis and mapping under compound hazards: A copula approach for tropical coastal district of Alappuzha, India. Journal of Hydro-environment Research, 46, 60-71. https://doi.org/10.1016/j.jher.2022.11.004.
8. Cavus, Y., & Aksoy, H. (2019). Spatial drought characterization for Seyhan River basin in the Mediterranean region of Turkey. Water, 11(7), 1331. https://doi.org/10.3390/w11071331

9. Cavus, Y., & Aksoy, H. (2020). Critical drought severity/intensity-duration-frequency curves based on precipitation deficit. Journal of Hydrology, 584, 124312. https://doi.org/10.1016/j.jhydrol.2019.124312
10. Chen, L., & Guo, S. (2019). Copulas and its application in hydrology and water resources (pp. 13-38). Springer Water, Springer Singapore. https://doi.org/10.1007/978-981-13-0574-0.
11. Cheng, Y., Zhang, K., Chao, L., Shi, W., Feng, J., & Li, Y. (2023). A comprehensive drought index based on remote sensing data and nested copulas for monitoring meteorological and agroecological droughts: A case study on the Qinghai-Tibet Plateau. Environmental Modelling & Software, 161, 105629. https://doi.org/10.1016/j.envsoft.2023.105629.
12. Cui, A., Li, J., Zhou, Q., Zhu, H., Liu, H., Yang, C., Wu, G., & Li, Q. (2024). Propagation Dynamics from Meteorological Drought to GRACE-Based Hydrological Drought and Its Influencing Factors. Remote Sensing, 16(6), 976. https://doi.org/10.3390/rs16060976.
13. Dai, M., Huang, S., Huang, Q., Leng, G., Guo, Y., Wang, L., Fag, W., Li, P., & Zheng, X. (2020). Assessing agricultural drought risk and its dynamic evolution characteristics. Agricultural Water Management, 231, 106003. https://doi.org/10.1016/j.agwat.2020.106003
14. Davraz, A., Şener, E., Şener, Ş., & Varol, S. (2014). Water Balance of the Eğirdir Lake and the Influence of Budget Components, Isparta, Turkey. Suleyman Demirel University Journal of Natural and Applied Science, 18(2), 27-36. (In Turkish)
15. Dehghannik, M., Kavianpour, M.R., & Moazami, S. (2021). Spatial analysis of meteorological and hydrological drought characteristics using Copula model. Environmental Earth Sciences, 80(24), 802. https://doi.org/10.1007/s12665-021-09868-0.
16. Dixit, S., & Jayakumar, K.V. (2021). A study on copula-based bivariate and trivariate drought assessment in Godavari River basin and the teleconnection of drought with large-scale climate indices. Theoretical and Applied Climatology, 146(3), 1335-1353. https://doi.org/10.1007/s00704-021-03792-w.
17. Dupuis, D.J. (2007). Using copulas in hydrology: Benefits, cautions, and issues. Journal of Hydrologic Engineering, 12(4), 381-393. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(381).
18. Eşit, M., & Yüce, M.İ. (2021). Bivariate drought frequency analysis based on copula theory for Osmaniye Region. Academic Platform-Journal of Engineering and Science, 9(3), 388-396. https://doi.org/10.21541/apjes.728959. (In Turkish)
19. Eşit, M., & Yüce, M.İ. (2022). Multivariate drought frequency analysis and risk assessment: A case study for Kahramanmaras Province. Journal of Natural Hazards and Environment, 8(2), 368-382. https://doi.org/10.21324/dacd.1066958. (In Turkish)
20. Frees, E.W., & Valdez, E.A. (1998). Understanding relationships using copulas. North American Actuarial Journal, 2(1), 1-25. https://doi.org/10.1080/10920277.1998.10595667.
21. Ganguli, P., & Reddy, M.J. (2013). Probabilistic assessment of flood risks using trivariate copulas. Theoretical and Applied Climatology, 111, 341-360. https://doi.org/10.1007/s00704-012-0664-4.
22. Genest, C., & Favre, A.C. (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12(4), 347-368. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347).
23. González, J., & Valdés, J.B. (2003). Bivariate drought recurrence analysis using tree ring reconstructions. Journal of Hydrologic Engineering, 8(5), 247-258. https://doi.org/10.1061/(ASCE)1084-0699(2003)8:5(247).
24. Gu, S., Wei, Y., Chen, J., Zhao, Z., Gao, R., Chen, J., Gao, Z., He, M., Chen, G., & Li, J. (2023). Developing a vine copula model to simulate and predict long serial lake water levels. In E3S Web of Conferences (Vol. 393, p. 02003). EDP Sciences. https://doi.org/10.1051/e3sconf/202339302003.
25. Habibi, B., Meddi, M., Emre, T., Boucefiane, A., & Rahmouni, A. (2024). Drought assessment and characterization using SPI, EDI and DEPI indices in northern Algeria. Natural Hazards, 120(6), 5201-5231. https://doi.org/10.1007/s11069-024-06408-4.
26. Hansen, B.E. (1994). Autoregressive conditional density estimation. International Economic Review, 705-730. https://doi.org/10.2307/2527081.
27. Hao, Z., & Singh, V.P. (2016). Review of dependence modeling in hydrology and water resources. Progress in Physical Geography, 40(4), 549-578. https://doi.org/10.1177/03091333166324.
28. Hasan, I.F., & Abdullah, R. (2023). Multivariate index for monitoring drought (case study, Northeastern of Iraq). Natural Hazards, 116(3), 3817-3837. https://doi.org/10.1007/s11069-023-05837-x.
29. Hesami Afshar, M., Sorman, A. U., & Yilmaz, M.T. (2016). Conditional copula-based spatial–temporal drought characteristics analysis—a case study over Turkey. Water, 8(10), 426. https://doi.org/10.3390/w8100426.
30. Huang, S., Li, P., Huang, Q., Leng, G., Hou, B., & Ma, L. (2017). The propagation from meteorological to hydrological drought and its potential influence factors. Journal of Hydrology, 547, 184-195. https://doi.org/10.1016/j.jhydrol.2017.01.041.
31. Jehanzaib, M., Yoo, J., Kwon, H.H., & Kim, T.W. (2021). Reassessing the frequency and severity of meteorological drought considering non-stationarity and copula-based bivariate probability. Journal of Hydrology, 603, 126948. https://doi.org/10.1016/j.jhydrol.2021.126948.
32. Joe, H. (1997). Multivariate models and multivariate dependence concepts. (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9780367803896.
33. Kalisa, W., Zhang, J., Igbawua, T., Ujoh, F., Ebohon, O. J., Namugize, J. N., & Yao, F. (2020). Spatio-temporal analysis of drought and return periods over the East African region using Standardized Precipitation Index from 1920 to 2016. Agricultural Water Management, 237, 106195. https://doi.org/10.1016/j.agwat.2020.106195.
34. Kanthavel, P., Saxena, C.K., & Singh, R.K. (2022). Integrated drought index based on vine copula modelling. International Journal of Climatology, 42(16), 9510-9529. https://doi.org/10.1002/joc.7840.
35. Li, Y., Huang, Y., Li, Y., Zhang, H., Fan, J., Deng, Q., & Wang, X. (2024). Spatiotemporal heterogeneity in meteorological and hydrological drought patterns and propagations influenced by climatic variability, LULC change, and human regulations. Scientific Reports, 14(1), 5965. https://doi.org/10.1038/s41598-024-56526-z.
36. Liu, Z., Cheng, L., Lin, K., & Cai, H. (2021). A hybrid bayesian vine model for water level prediction. Environmental Modelling & Software, 142, 105075. https://doi.org/10.1016/j.envsoft.2021.105075.