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

Abstract

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. 

Keywords

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

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

Abstract

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. 

Keywords

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

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