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<p>Classical drought indices like the Standardized Precipitation-Evapotranspiration Index (SPEI) assume short-range dependence through finite accumulation windows, limiting their ability to represent the long-term persistence characteristic of semi-arid regions like the Mediterranean Basin. Here, we introduce a fractionally integrated SPEI (FSPEI) that embeds scale-free memory into the climatic water balance. Using 85 years (1940–2024) of ERA5 monthly data, we first estimate spatially varying Hurst exponents (H) via Multifractal Detrended Fluctuation Analysis (MFDFA). These H values, which quantify long-term persistence, are then used to determine the order of a Grünwald-Letnikov fractional filter applied to the water-balance series prior to standardization. Results reveal a strong spatial persistence gradient, with H &gt; 0.6 across southeastern Europe, North Africa, and Anatolia. Incorporating these structures fundamentally alters drought diagnostics: compared to classical SPEI, FSPEI produces heavier dry tails, longer mean run lengths, and greater spatial coherence. These differences are most pronounced during the hydrologically sensitive transition months of April and October. The findings demonstrate that conventional indices underestimate drought clustering and severity in regions where evaporative demand and land–atmosphere feedback amplify deficits over multiple years. The fixed-order variant serves as a precautionary stress-testing scenario. The FSPEI framework offers a physically interpretable and mathematically rigorous approach for improving drought early warning and water resource planning under increasing climatic variability.</p>

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FSPEI: a novel fractionally integrated drought index with an application to the Mediterranean Basin

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Hasan Tatli

摘要

Classical drought indices like the Standardized Precipitation-Evapotranspiration Index (SPEI) assume short-range dependence through finite accumulation windows, limiting their ability to represent the long-term persistence characteristic of semi-arid regions like the Mediterranean Basin. Here, we introduce a fractionally integrated SPEI (FSPEI) that embeds scale-free memory into the climatic water balance. Using 85 years (1940–2024) of ERA5 monthly data, we first estimate spatially varying Hurst exponents (H) via Multifractal Detrended Fluctuation Analysis (MFDFA). These H values, which quantify long-term persistence, are then used to determine the order of a Grünwald-Letnikov fractional filter applied to the water-balance series prior to standardization. Results reveal a strong spatial persistence gradient, with H > 0.6 across southeastern Europe, North Africa, and Anatolia. Incorporating these structures fundamentally alters drought diagnostics: compared to classical SPEI, FSPEI produces heavier dry tails, longer mean run lengths, and greater spatial coherence. These differences are most pronounced during the hydrologically sensitive transition months of April and October. The findings demonstrate that conventional indices underestimate drought clustering and severity in regions where evaporative demand and land–atmosphere feedback amplify deficits over multiple years. The fixed-order variant serves as a precautionary stress-testing scenario. The FSPEI framework offers a physically interpretable and mathematically rigorous approach for improving drought early warning and water resource planning under increasing climatic variability.