Extreme Value Analysis of Meteorological Drought in Tlemcen, North-West Algeria: Evidence of a Heavy-Tailed Fréchet Distribution Using the SPI-3 Index

The Tlemcen region in North-West Algeria, characterized by a vulnerable Mediterranean climate, faces significant challenges from recurrent and intense climatic droughts. This study employs Extreme Value Theory (EVT), specifically the Generalized Extreme Value (GEV) distribution, to probabilistically quantify the risk of extreme meteorological drought events based on the annual minimum values of the Standardized Precipitation Index (SPI-3) over a 44-year period (1980–2024). The GEV model was found to provide an excellent fit to the observed data, confirming the suitability of the EVT approach. A critical finding is the positive shape parameter (ξ = 0.2843), which indicates a heavy-tailed Fréchet distribution. This result implies that the region is inherently more susceptible to severe and extreme droughts than conventional models suggest, with the probability of catastrophic events being significantly higher. The return level analysis provides concrete thresholds for risk management, revealing that the 50-year drought level (SPI-3 ≤ -2.001) formally crosses the threshold for an extreme event. Furthermore, the occurrence of an observed drought (SPI-3 ≤ -2.155) more severe than the calculated 100-year return level (SPI-3 ≤ -2.090) underscores the high vulnerability of the region. The study concludes with operational recommendations for water resource planning and proposes solutions, such as the integration of paleoclimatic data and Regional Frequency Analysis, to mitigate the limitations imposed by short instrumental records, thereby enhancing the robustness of the EVT-based risk assessment for climate resilience in North-West Algeria.