Türkiye'deki Şehirlerin Yağışları için Robust Panel Kümeleme Analizi

Öz

Bu çalışma, Türkiye genelinde istasyon düzeyi yıllık yağış serilerini kullanarak homojen yağış rejimlerini nesnel biçimde ortaya koyar. Önce k-ortalamalar, PAM, ve hiyerarşik (agglomeratif) yöntemleri K=2"-" 10 aralığında uyguladık; çözümleri APN, AD, ADM, FOM, Connectivity, Dunn, ve Silhouette endeksleriyle doğruladık. Klasik algoritmalar K=2’yi işaret etse de, Rize’nin yüksek kaldıraçlı bir gözlem olarak centroid tahminini orantısız etkilemesi, geri kalan istasyonlarda mevcut anlamlı alt yapıyı maskeledi ve tekil bir küme ortaya çıkardı. Bu nedenle robust budanmış k-ortalamalar yaklaşımına geçtik. Çok ölçütlü değerlendirme, APN/ADM/FOM’da K=4’ün en uygun olduğunu gösterdi; Rize trimmed tekil olarak ayrılırken kalan ağ dört yapısal rejime ayrıldı (C1–C4). Elde edilen rejimler, Türkiye yağış klimatolojisindeki kıyısal/orografik güçlendirme ile kıtasal kuruma arasındaki bilinen dikotomiyi istasyon ölçeğinde nicel olarak doğrular; kümeler daha kompakt, daha az örtüşen ve klimatolojik olarak yorumlanabilir niteliktedir.

Anahtar Kelimeler

• Robust kümeleme
• Budanmış k-ortalamalar
• Küme geçerlilik endeksleri
• Yağış

Robust Panel Clustering of Station-Scale Precipitation in Türkiye

Öz

This study uses station-level annual precipitation series for Türkiye to objectively delineate homogeneous precipitation regimes. We first applied k-means, PAM, and hierarchical (agglomerative) clustering for K=2"–" 10 and evaluated the solutions using the APN, AD, ADM, FOM, Connectivity, Dunn, and Silhouette indices. Although classical algorithms favored K=2, Rize acted as a high-leverage observation, exerting a disproportionate influence on centroid estimation, producing a singleton cluster, and obscuring meaningful substructure among the remaining stations. We therefore adopted a robust trimmed k-means approach. A multi-index assessment identified K=4 as optimal for APN/ADM/FOM, yielding four structural regimes (C1–C4) while treating Rize as a trimmed singleton. The resulting partition quantifies—at the station scale—the well-known contrast between coastal/orographic enhancement and continental drying, producing clusters that are more compact, less overlapping, and climatologically interpretable.

Anahtar Kelimeler

• Robust clustering
• Trimmed k-means
• Cluster validation indices
• Precipitation

Kaynakça

1. Aggarwal, C. C. & Reddy, C. K. (Eds.). (2014). Data clustering: Algorithms and applications. Boca Raton, FL: CRC Press.
2. Brock, G., Pihur, V., Datta, S. & Datta, S. (2008). clValid: An R package for cluster validation. Journal of Statistical Software, 25(4), 1-22. https://doi.org/10.18637/jss.v025.i04
3. Bulut, H. (2023). Multivariate statistical methods with R applications [R uygulamaları ile çok değişkenli istatistiksel yöntemler] (2. bs.). Ankara: Nobel Akademik Yayıncılık.
4. Cuesta-Albertos, J. A., Gordaliza, A. & Matrán, C. (1997). Trimmed k-means: An attempt to robustify quantizers. The Annals of Statistics, 25(2), 553-576.
5. Demircan, M., Gürkan, H., Eskioğlu, O., Arabacı, H. & Coşkun, M. (2017). Climate change projections for Turkey: Three models and two scenarios. Turkish Journal of Water Science and Management, 1(1), 22-43. https://doi.org/10.31807/tjwsm.297183
6. Deniz, Z. A., Gönençgil, B., & Mestav, B. (2016). Türkiye ekstrem sıcaklıklarının kümeleme analizine göre değerlendirilmesi. TÜCAUM Uluslararası Coğrafya Sempozyumu Bildiriler Kitabı içinde (ss. 220-229). Ankara: TÜCAUM.
7. Dikbas, F., Firat, M., Koc, A. C., & Gungor, M. (2012). Classification of precipitation series using fuzzy cluster method. International Journal of Climatology, 32(10), 1596-1603. https://doi.org/10.1002/joc.2350
8. García-Escudero, L. A., Gordaliza, A., Matrán, C. & Mayo-Iscar, A. (2008). A general trimming approach to robust cluster analysis. The Annals of Statistics, 36(3), 1324-1345. https://doi.org/10.1214/07-AOS515

9. Hubert, L. & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2(1), 193-218. https://doi.org/10.1007/BF01908075
10. Intergovernmental Panel on Climate Change (IPCC). (2021).Climate change 2021: The physical science basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, ... & B. Zhou, Eds.). Cambridge University Press.
11. Iyigun, C., Türkeş, M., Batmaz, İ., Yozgatligil, C., Purutçuoğlu, V., Koç, E. K. & Öztürk, M. Z. (2013). Clustering current climate regions of Turkey by using a multivariate statistical method. Theoretical and Applied Climatology, 114(1), 95-106. https://doi.org/10.1007/s00704-012-0823-7
12. Jain, A. K., Murty, M. N. & Flynn, P. J. (1999). Data clustering: A review. ACM Computing Surveys (CSUR), 31(3), 264-323. https://doi.org/10.1145/331499.331504
13. Kartal, E., İyigün, C., Fahmi, F. M., Yozgatlıgil, C., Purutçuoğlu, V., Batmaz, İ., ... & Türkeş, M. (2011). Türkiye iklim bölgelerinin hiyerarşik kümeleme yöntemi ile belirlenmesi. İstatistik Araştırma Dergisi, 8(1), 13-25. https://izlik.org/JA75EU78ZY
14. Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data: An introduction to cluster analysis. New York, NY: John Wiley & Sons.
15. Kömüşcü, A. Ü., Turgu, E. & DeLiberty, T. (2022). Dynamics of precipitation regions of Turkey: A clustering approach by K-means methodology in respect of climate variability. Journal of Water and Climate Change, 13(10),3578-3606. https://doi.org/10.2166/wcc.2022.186
16. MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In L. M. Le Cam & J. Neyman (Eds.), Proceedings of the fifth Berkeley symposium on mathematical statistics and probability (Vol. 1, pp. 281–297). Berkeley, CA: University of California Press.
17. Maechler, M. (2018). cluster: Cluster analysis basics and extensions (R package version 2.0-7–1).
18. Mahmud, S., Sumana, F. M., Mohsin, M., & Khan, M. H. R. (2022). Redefining homogeneous climate regions in Bangladesh using multivariate clustering approaches. Natural Hazards, 111(2), 1863-1884. https://doi.org/10.21203/rs.3.rs-633865/v1
19. Rencher, A. C. (2002). Methods of multivariate analysis (2nd ed.). New York, NY: John Wiley & Sons.
20. Taşoğlu, E., Öztürk, M. Z. & Yazıcı, Ö. (2024). High resolution Köppen–Geiger climate zones of Türkiye. International Journal of Climatology, 44(14), 5248–5265. https://doi.org/10.1002/joc.8635
21. Team, R. C. (2023). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
22. Tekin, M. K., Tatli, H., & Koç, T. (2021). Climate classification in Turkey: A case study evaluating Holdridge life zones. Theoretical & Applied Climatology, 144. https://doi.org/10.1007/s00704-021-03565-5
23. Trenberth, K. E. (2011).Changes in precipitation with climate change. Climate Research, 47(1-2), 123-138. https://doi.org/10.3354/cr00953
24. Türkeş, M. (1996). Spatial and temporal analysis of annual rainfall variations in Turkey. International Journal of Climatology: A Journal of the Royal Meteorological Society, 16(9), 1057-1076. https://doi.org/10.1002/(SICI)1097-0088(199609)16:9 <1057::AID-JOC75>3.0.CO;2-D
25. Türkeş, M. & Tatlı, H. (2011). Use of the spectral clustering to determine coherent precipitation regions in Turkey for the period 1929–2007. International Journal of Climatology, 31(14), 2055-2067. https://doi.org/10.1002/joc.2212
26. Turkish State Meteorological Service (2023). Annual precipitation data for 81 provinces in Turkey (1965–2022) [Data set]. Ankara: Turkish State Meteorological Service.
27. Unal, Y., Kindap, T. & Karaca, M. (2003). Redefining the climate zones of Turkey using cluster analysis. International Journal of Climatology, 23(9), 1045-1055. https://doi.org/10.1002/joc.910
28. Wilks, D. S. (2011). Statistical methods in the atmospheric sciences. Oxford: Academic Press.
29. Zeybekoğlu, U. & Ülke Keskin, A. (2020). Defining rainfall intensity clusters in Turkey by using the fuzzy c-means algorithm. Geofizika, 37(2), 181–195. https://doi.org/10.15233/gfz.2020.37.8