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<p>Drought is a complex, slow-developing phenomenon that impacts agriculture, water resources, and ecosystems. Traditional drought indices capture different aspects of drought but cannot fully represent the entire situation on their own. The Recent Merged Drought Index (MDI), based on Triple Collocation (TC) and its extensions (MTC, STC), has limitations due to statistical assumptions and complexity, making it less practical, especially in data-sparse regions. The current study introduces an innovative approach called Kappa Merged Collocation (KMC), which uses agreement-based weights to combine individual drought indices by employing quadratic-weighted Cohen's Kappa. KMC emphasizes mutual consistency among indices, improving interpretability without relying on reference variables or covariance models. KMC was compared with TC, MTC, and STC using data from six northern Pakistani weather stations (1971–2017) and assessed using various performance metrics: Agreement Measure, Trend analysis, Machine learning validation, spatiotemporal structure, risk analysis, and visual comparison to test its reliability. KMC consistently demonstrated strong and stable results, achieving high agreement values for SPI and SPTI (0.970–0.996 at Chilas, Gupis, and Gilgit), CCC above 0.97, and Md over 0.90 at most sites. Without requiring copula-based modeling, it effectively smoothed severe anomalies (e.g., Bunji: SPTI = ∞, KMC = 3.76) and nearly matched joint drought estimates (e.g., Gilgit: KMC = 5.035, JRP = 32.57). Its simplicity (e.g., AIC = -38795.10 at Chilas) and low RMSE (7.32e-16 at Astore) further confirmed its accuracy. Even in topographically complex areas like Astore and Skardu, KMC showed notable classification accuracy (up to 99.82%) with kappa values over 0.994 and structural consistency (ARI up to 0.4915). These findings establish KMC as a statistically robust, scalable, and interpretable alternative for multi-index drought monitoring and climate risk assessment.</p>

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Improving drought index integration through kappa merged collocation relative to conventional methods

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Zanib Badar,
  • Ishfaq Ahmad,
  • Ibrahim M. Almanjahie,
  • Fatimah Alshahrani

摘要

Drought is a complex, slow-developing phenomenon that impacts agriculture, water resources, and ecosystems. Traditional drought indices capture different aspects of drought but cannot fully represent the entire situation on their own. The Recent Merged Drought Index (MDI), based on Triple Collocation (TC) and its extensions (MTC, STC), has limitations due to statistical assumptions and complexity, making it less practical, especially in data-sparse regions. The current study introduces an innovative approach called Kappa Merged Collocation (KMC), which uses agreement-based weights to combine individual drought indices by employing quadratic-weighted Cohen's Kappa. KMC emphasizes mutual consistency among indices, improving interpretability without relying on reference variables or covariance models. KMC was compared with TC, MTC, and STC using data from six northern Pakistani weather stations (1971–2017) and assessed using various performance metrics: Agreement Measure, Trend analysis, Machine learning validation, spatiotemporal structure, risk analysis, and visual comparison to test its reliability. KMC consistently demonstrated strong and stable results, achieving high agreement values for SPI and SPTI (0.970–0.996 at Chilas, Gupis, and Gilgit), CCC above 0.97, and Md over 0.90 at most sites. Without requiring copula-based modeling, it effectively smoothed severe anomalies (e.g., Bunji: SPTI = ∞, KMC = 3.76) and nearly matched joint drought estimates (e.g., Gilgit: KMC = 5.035, JRP = 32.57). Its simplicity (e.g., AIC = -38795.10 at Chilas) and low RMSE (7.32e-16 at Astore) further confirmed its accuracy. Even in topographically complex areas like Astore and Skardu, KMC showed notable classification accuracy (up to 99.82%) with kappa values over 0.994 and structural consistency (ARI up to 0.4915). These findings establish KMC as a statistically robust, scalable, and interpretable alternative for multi-index drought monitoring and climate risk assessment.