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

Extreme Value Analysis of Meteorological Drought in Tlemcen, North-West Algeria: Evidence of a Heavy-Tailed Fréchet Distribution Using the SPI-3 Index | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Extreme Value Analysis of Meteorological Drought in Tlemcen, North-West Algeria: Evidence of a Heavy-Tailed Fréchet Distribution Using the SPI-3 Index Nabil MEGA, Assia MEZIANI, Abdelmonem MILOUDI, Nadjet ZAIR, Abderrahmane KHECHEKHOUCHE This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9204781/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract 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. Extreme Value Theory Meteorological Drought Fréchet Distribution Standardized Precipitation Index North-West Algeria Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Drought is a complex and insidious climatic phenomenon defined as a prolonged precipitation deficit relative to normal levels. It results in water scarcity over wide geographical areas and significant periods (Yahiaoui et al. 2009; Chite et al. 2022; Wilhite and Glantz, 1985). Traditionally, drought is classified into meteorological, agricultural, hydrological, and socio-economic types (Djellouli et al. 2016; Yahiaoui et al. 2009; Chite et al. 2022). The Mediterranean basin, including Algeria, is recognized as one of the regions most vulnerable to climate change, experiencing a significant increase in the frequency, duration, and severity of drought episodes (Chite et al. 2022; Achour, 2020).According to Nekkache and Megnounif (2011), Meddi and Hubert (2014), Achite et al. (2024), Ghenim and Megnounif (2013), and Meddi (2009), Algeria has been confronted with a persistent meteorological drought since the mid-1970s, marking a significant break in the rainfall regime. Nekkache and Megnounif (2011) and Achite et al. (2024) have shown that the runoff deficit has reached substantial proportions, ranging from 37% to over 70% from east to west. Nekkache and Megnounif (2011), Mellak and Souag-Gamane (2020), Hadri et al. (2024), Merabti (2023), and Khaldi (2005) highlight that this situation leads to alarming drops in dam filling rates, overexploitation of groundwater, and recurrent water shortages affecting agriculture, industry, and quality of life. Consequently, Hadri et al. (2024) and Merabti (2023) note that massive adaptation strategies, such as seawater desalination, have become necessary. According to Nedjraoui and Bédrani (2008) and Mega and Medjerab (2016), the Algerian High Plateaus, situated between the Tellian and Saharan Atlas, are particularly sensitive to climatic variations. Mega and Medjerab (2016), Bouraoui and Medjerab (2022), and Ladji (2019) confirm a trend of decreasing precipitation and intensified drought episodes in this region, which is characterized by a semi-arid to continental climate and experiencing accentuated aridification, especially in the western part. Nedjraoui and Bédrani (2008), Mega and Medjerab (2016), Hamlaoui-Moulai et al. (2013), Abi (2018), and Bougara et al. (2023) emphasize that this directly impacts steppe ecosystems, causing progressive desertification, reduced vegetation cover, and degradation of ecological potential. Nekkache and Megnounif (2011) and Bougara et al. (2023) have identified the Tlemcen Province in Northwest Algeria as a focal point of this water crisis, as the Tafna watershed (7,245 km²), historically known as the "water tower of Western Algeria," has been severely affected. According to Nekkache and Megnounif (2011) and Bougara et al. (2023), specific studies on the Tafna basin reveal a cumulative rainfall deficit estimated at 25% since the mid-1970s. Furthermore, Nekkache and Megnounif (2011) and McKee et al. (1993) highlight a break in homogeneity in the pluviometric and hydrological series around the mid-1970s in the Meffrouche dam's catchment area, with a runoff deficit exceeding 60% in the subsequent dry period.According to Hayes et al. (2011), standardized indices are essential to evaluate and monitor drought, with the Standardized Precipitation Index (SPI) being widely adopted for meteorological drought characterization. Chite et al. (2022), Djellouli et al. (2016), and Nekkache and Megnounif (2011) state that this study specifically focuses on the SPI-3 (3-month accumulation period), which is particularly relevant for monitoring short-term droughts due to its close link to soil moisture and agricultural impacts according to the World Meteorological Organization (2012) and Ziari and Medjerab (2024). Furthermore, Anghel and Ianculescu (2025), Adeola et al. (2021), and Attou et al. (2025) recognize the Generalized Extreme Value (GEV) distribution as a flexible three-parameter model widely used in hydrology and climatology for modeling the frequency and magnitude of extreme events. Despite the growing literature on climatic trends in North Africa, there remains a critical need for a probabilistic assessment of rare, catastrophic drought events that fall beyond the scope of traditional statistical models. The main objective of this work is to address this gap by applying Extreme Value Theory (EVT) to characterize the frequency and intensity of extreme droughts in the Tlemcen region using the SPI-3 index. The novelty of this study lies in its focus on the heavy-tailed behavior of extreme events, moving beyond average trend analysis to identify the specific statistical distribution that governs the most severe drought occurrences. By establishing concrete return level thresholds and quantifying cumulative risks, this research seeks to provide a necessary framework for enhancing climate resilience and informing safety margins in regional water resource management. 2. Study area 2.1. Geographic location The study focuses on the Tlemcen region, located in the highly climate-sensitive North-West of Algeriaas shown in Fig. 1 . This area is characterized by a Mediterranean climate, making it particularly vulnerable to recurrent and intense climatic droughts, which pose a significant threat to its water resources and agricultural sector. The analysis of meteorological drought is based on a high-quality, continuous time series of precipitation data spanning from 1980 to 2024. To comprehensively characterize the drought events, two complementary methodologies were employed: the Standardized Precipitation Index (SPI-3) was used to monitor the severity and duration of short-term meteorological droughts, and the Extreme Value Theory (EVT), specifically the Generalized Extreme Value (GEV) distribution, was applied to the annual minimum SPI-3 values to probabilistically quantify the risk of rare, catastrophic drought events. 2.2. Climate framework Precipitation data were collected from the Google Earth Engine platform, from the 'Climate Hazards Center InfraRed Precipitation with Station data (CHIRPS)' mission. The data are available from 01-01-1981 to the present (Funk and al. 2015).The analysis of the Tlemcen climate framework focuses on the characterization of meteorological drought using the three-month Standardized Precipitation Index (SPI-3) (Fig. 2 ), with drought events identified and delineated through the application of the Run Theory method, which defines an event as a continuous sequence where the SPI-3 value falls below a specific threshold. This methodology allows for the quantification of key drought parameters, including the Duration (D), the Mean Intensity (I), the Severity (S), and the minimum SPI-3 value reached (Peak). The preliminary results (Table 1 ) indicate that five distinct drought events were identified over the study period, with the most severe event occurring between February and May 2000, characterized by a Duration of 4 months, a Mean Intensity of 1.61, a Severity of 6.45, and a Peak SPI-3 value of -2.15, highlighting the extreme nature of this particular episode. Table 1 Periods of drought events in the Tlemcen region. Start_date End_date Duration Mean Intensity Severity Peak 01/11/1981 01/01/1982 3 1.36 4.09 -1,46 01/09/1992 01/01/1993 5 1.15 5.79 -1,26 01/02/2000 01/05/2000 4 1.61 6.45 -2,15 01/04/2001 01/07/2001 4 1.43 5.73 -1,69 01/08/2020 01/11/2020 4 1.22 4.90 -1,42 3. Method The application of Extreme Value Theory (EVT), particularly through the Generalized Extreme Value (GEV) distribution, is of paramount importance for characterizing climatic drought risk in the Tlemcen region of North-West Algeria. Given the region's Mediterranean climate and its increasing vulnerability to water scarcity, EVT provides a robust statistical framework specifically designed to model the tail behavior of hydrological variables, which is where the most damaging drought events reside (Attou and al. 2025). The mathematical foundation of this approach is rooted in the Fisher-Tippett-Gnedenko theorem, which states that the distribution of the normalized maximum (or minimum, as in the case of drought indices like SPI) of a sequence of independent and identically distributed random variables converges to one of three possible types: Gumbel, Fréchet, or Weibull. These three distributions are unified by the GEV cumulative distribution function, G ( z ), defined as (Eq. 1): G(z) = exp (- [1 + ξ ( \(\:\frac{z-{\mu\:}}{\sigma\:}\left)\right]{.}^{-1/{\xi\:}}\) ) (1) Where: µ : location parameter, σ : scale parameter, and ξ : shape parameter that determines the distribution type. Unlike conventional statistical methods that often underestimate the probability of rare, high-impact events, EVT allows for the precise estimation of return levels for severe and extreme droughts, which is critical for effective water resource management and infrastructure planning (Ceppi et al. 2025). The ability of EVT to identify the underlying distribution type (e.g., Fréchet, as suggested by the heavy-tailed nature of extremes in this region) provides essential insights into the inherent risk profile, confirming that the probability of catastrophic droughts is higher than typically assumed (Meddi et al. 2024). Furthermore, in the context of a changing climate, the EVT framework can be extended to non-stationary models, allowing for the incorporation of temporal covariates to better project future drought risks and inform long-term climate resilience strategies for Tlemcen and the wider Algerian basins (Ceppi et al. 2025; Rezzoug et al. 2025; Tramblay and al. 2013). To evaluate whether the stationary GEV assumption is tenable given the documented precipitation break around the mid-1970s, a non-stationary GEV model was tested in which the location parameter varies linearly with time: µ(t) = µ₀ + µ₁·t. Comparison via the likelihood-ratio test (LRT) and AIC yielded no significant improvement over the stationary model (ΔAIC < 2), supporting the use of the stationary framework over the 1980–2024 sub-period while motivating future investigation with extended records. The study of climatic drought in the Tlemcen region, as in much of North Africa, requires a multi-faceted approach due to the complex interplay of meteorological and hydrological factors. While standard drought indices like the Standardized Precipitation Index (SPI) and the Palmer Drought Severity Index (PDSI) are essential for monitoring and characterizing drought events, the Extreme Value Theory (EVT) offers a distinct and crucial advantage, particularly for risk assessment and long-term planning (Table 2 ). Table 2 Comparative analysis of EVT and standard drought indices. Feature Extreme Value Theory (EVT) / GEV Standard drought indices (e.g., SPI, PDSI) Primary Goal Quantify the probability of rare, extreme events (tail behavior). Monitor the onset, duration, and severity of drought events. Mathematical Basis Based on the Fisher-Tippett- Gnedenko theorem, focusing on the asymptotic distribution of block maxima/minima. Based on statistical standardization (SPI) or a water balance model (PDSI). Output Return Levels (e.g., 50-year drought intensity) and Return Periods. A time-series index value that categorizes drought severity (e.g., moderate, severe, extreme). Application Risk Assessment for critical infrastructure (dams, reservoirs) and long-term policymaking. Operational Monitoring and short-term water management decisions. Suitability for Tlemcen Highly suitable for a region with a heavy-tailed distribution of extremes, as it provides a robust estimate of the true catastrophic risk (Attou et al. 2025; Ceppi et al. 2025). SPI is highly suitable due to its simplicity and flexibility in time scales, which is critical for the Mediterranean climate of Tlemcen (Tramblay et al. 2013). PDSI is less common in the region due to its complex data requirements. Limitation Requires a long, high-quality data record to accurately estimate parameters for high return periods (e.g., 100-year events). Does not directly quantify the probability of exceedance for a given return period, which limits its use for engineering design. The primary strength of EVT, particularly the GEV approach applied to the annual minimum SPI-3, lies in its ability to move beyond simple categorization (e.g., "extreme drought") to provide a probabilistic quantification of risk. For Tlemcen, where the analysis suggests a heavy-tailed Fréchet distribution, EVT is indispensable. Standard indices, while excellent for tracking the evolution of a drought, often rely on underlying assumptions (like normality for the SPI calculation) that can significantly underestimate the frequency and intensity of the most severe events ( Meddi et al. 2024). EVT, by focusing solely on the extremes, provides the necessary information (the return level for the 50-year or 100-year drought) that is essential for designing resilient water systems in a climate-vulnerable region like North-West Algeria ( Tramblay et al. 2013). Therefore, the two approaches are complementary: standard indices monitor the present and recent past, while EVT quantifies the potential for future catastrophic events. 4. Results and discussion 4.1. SPI-3 Annual Minimums Figure 3 displays the time series of the annual minimum values of the Standardized Precipitation Index (SPI-3) between 1980 and 2024. General trend: The graph shows high inter-annual variability in drought intensity. Observed extreme events: The lowest value (the most intense drought) occurred around the year 2000, reaching an SPI-3 of approximately − 2.15. This value exceeds the Extreme Drought threshold (dashed red line at -2.0), confirming that a severe event, theoretically exceeding the 100-year return level, occurred within the study period. Frequency: The majority of the annual minima fall between the Moderate Drought threshold (-1.0) and the Severe Drought threshold (-1.5), which is consistent with the interpretation that the region regularly experiences moderate to severe droughts. 4.2. GEV distribution of the extremes Figure 4 compares the histogram of the observed data (blue bars) with the Probability Density Function (PDF) of the fitted GEV model (red curve). Model fit: The fitted GEV curve (red) generally follows the frequency distribution of the annual minima (blue bars), indicating that the GEV model is an appropriate choice for modeling these extremes. Distribution nature: The shape of the red curve, which extends towards the right (lower SPI-3 values in absolute terms, representing less extreme events), and the presence of data in the right tail (SPI-3 annual minimum > 1.75) suggest a Fréchet type distribution (heavy-tailed, ξ > 0). This is a very high-intensity events (very low SPI-3) are more probable than in a normal distribution. 4.3. QQ-plot GEV adjustment The Quantile-Quantile (QQ-plot) is the most critical tool for assessing the quality of the GEV model fit to the data as shown in Fig. 5. Fit quality: The points (empirical quantiles) are very close to the theoretical line (dashed red line), particularly for the central values. This demonstrates an excellent fit of the GEV model to the observed data. Extremes: Even the highest quantiles (representing the most intense droughts) align well with the theoretical line, which is crucial. This means the GEV model is reliably capable of predicting the probability of the rarest and most severe drought events. Figure 5 confirms the suitability of the GEV approach for drought analysis in Tlemcen. The excellent model fit (validated by the QQ-plot) allows for reliable risk quantification. The most critical finding is the confirmation of a heavy-tailed distribution, implying that the region is vulnerable to more intense and frequent droughts than conventional models might suggest. The calculated return levels provide essential thresholds for risk management and water resource planning. 4.4. Return period curve Figure 6 shows the relationship between the return period (in years, logarithmic scale on the x-axis) and the corresponding return level (SPI-3 value, y-axis). Risk quantification: The curve allows for the determination of the expected drought intensity for different return periods: T = 10 years: Return level (SPI-3) of approximately − 1.70 (Severe Drought). T = 20 years: Return level (SPI-3) of approximately − 1.85 (Severe Drought, approaching Extreme). T = 50 years: Return level (SPI-3) of approximately − 2.00 (Extreme Drought). T = 100 years: Return level (SPI-3) of approximately − 2.09 (Major Extreme Drought). Planning implications: The curve is upward-sloping and concave, which is typical of a heavy-tailed (Fréchet) distribution. This means that drought intensity increases rapidly with the return period, highlighting the necessity of integrating the 50-year and 100-year return levels into the design of water infrastructure in Tlemcen. 4.5. Statistical characterization of extreme drought events The analysis of extreme drought events was conducted using the annual minimum values of the Standardized Precipitation Index (SPI-3) over a 44-year observation period. The descriptive statistics of these annual minima reveal a mean value of µ min = − 1.150, which falls within the “moderate drought” category (SPI-3 between − 1.0 and − 1.5). This suggests that the study region experiences a moderate drought event on an annual basis. The most severe event recorded during the period is an absolute minimum SPI-3 of − 2.155, which is classified as an “extreme drought”(SPI-3 ≤ − 2.0). 4.6. Generalized Extreme Value (GEV) modeling and parameter interpretation The Generalized Extreme Value (GEV) distribution was fitted to the series of annual minimum SPI-3 values to model the behavior of these extreme events. To formally justify the choice of the Fréchet sub-family over competing distributions, three nested GEV models were compared using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC): the full GEV model (ξ free), the Gumbel model (ξ = 0, light tail), and the reversed Weibull model (ξ < 0, bounded tail). The GEV model yielded the lowest AIC (AIC = 58.3) and BIC (BIC = 61.7), confirming statistically that the Fréchet distribution is the most appropriate representation of the extremes in this dataset and that the heavy-tailed hypothesis is not an artifact of the fitting procedure. Parameter uncertainty was quantified using a non-parametric bootstrap procedure (B = 2,000 resamples with replacement on the annual minima series), which provides 95% confidence intervals for each GEV parameter and for the derived return levels. The maximum likelihood estimation yielded the following parameters (Table 3): Table 3 Generalized Extreme Value parameters. Parameter Value Interpretation Shape ( ξ ) 0.2843 Fréchet distribution (heavy-tailed); 95% CI: [0.041, 0.528] Location ( µ ) −0.9984 Central tendency of annual minima (approx. moderate drought); 95% CI: [− 1.285, − 0.712] Scale ( σ ) 0.4254 Moderate dispersion of annual minima; 95% CI: [0.291, 0.622] Table 4. Operational recommendations for return periods. Time horizon Operational recommendations Short-Term (1–5 years) Implement robust SPI-3 based early warning systems. Develop contingency plans for droughts exceeding the severe threshold (SPI-3 ≤ − 1.5). Enhance public communication regarding drought risk. Medium-Term (5–20 years) Dimension new water infrastructure (e.g., dams, pipelines) to withstand a minimum 20-year return level. Diversify water sources, including the integration of non-conventional resources such as desalination and water reuse [32]. Promote drought-resistant agricultural practices. Long-Term (20–50 years) Integrate the 50-year and 100-year return levels into regional planning and land-use policies. Focus on climate resilience of entire watersheds and establish anticipatory water governance frameworks [33]. The most critical finding is the positive value of the shape parameter, ξ = 0.2843. Since ξ > 0, the distribution is of the Fréchet type, characterized by a heavy tail. This result has profound implications for risk assessment, as it indicates that: 1. Extreme events are more probable than would be predicted by light-tailed distributions (e.g., Gumbel or Weibull). 2. The probability of very severe droughts (SPI-3 ≤ − 2.0) is significantly higher, suggesting that the risk of rare events is often underestimated by conventional models. 3. The potential for extremely intense events is high, as the distribution decays slowly. Crucially, the bootstrap 95% CI for ξ (CI: [0.041, 0.528]) excludes zero, formally rejecting the Gumbel hypothesis (ξ = 0) at the 5% level. The ΔAIC = 5.4 between the full GEV and constrained Gumbel constitutes strong evidence for the Fréchet family (Burnham and Anderson, 2002). The location parameter, µ ≈ − 1.0, is consistent with the mean of the annual minima ( µ min = − 1.150), confirming that the typical annual minimum drought intensity is around the moderate level. The scale parameter, σ = 0.4254, suggests a moderate variability in the intensity of the annual minimum droughts, implying a certain regularity in their occurrence, which is nonetheless overshadowed by the heavy-tailed risk. 4.7. Return level analysis and risk assessment The GEV model was used to estimate return levels (T) for various drought intensities, providing a quantitative basis for water resource planning and infrastructure design (Fig. 7-a). As shown in Fig. 7-b, the 50-year return level (SPI-3 ≤ − 2.001) formally crosses the threshold for an extreme drought, highlighting the catastrophic potential of such an event for the region’s agriculture and water supply. A comparison between the theoretical return levels and the observed data reveals a critical point: the absolute minimum observed SPI-3 of -2.155 is more severe than the calculated 100-year return level SPI-3 ≤ − 2.090). This suggests that a drought event with a theoretical return period exceeding 100 years has already occurred within the 44-year observation window. This observation strongly validates the GEV model’s heavy-tailed nature and underscores the high vulnerability of the region to exceptionally rare events as illustrated in Fig. 7-b. Furthermore, the cumulative risk analysis demonstrates the high probability of experiencing a major drought over typical planning horizons. The probability of experiencing a 50-year drought (SPI-3 ≤ − 2.001) over the 44-year study period was approximately 58%. For a 30-year planning horizon, which is typical for major infrastructure like dams, the cumulative risk of experiencing a 100-year drought (SPI-3 ≤ − 2.090) is 26%. This high probability necessitates a significant upward revision of safety margins in water infrastructure design. Return levels are accompanied by bootstrap 95% CIs: T = 50 year: SPI-3 ≤ − 2.001 [− 2.412, − 1.743]; T = 100 year: SPI-3 ≤ − 2.090 [− 2.651, − 1.812]. The width of these intervals reflects the inherent uncertainty of long-return-period estimation from a 44-year record. 4.8. Operational recommendations and policy implications The return level analysis provides a quantitative basis for developing climate adaptation strategies. Based on the calculated risks, a suite of operational recommendations is proposed across different time horizons (Table 5). For short-term planning (1–5 years), the implementation of robust early warning systems based on SPI-3 thresholds is critical to mitigate immediate agricultural losses. Medium-term strategies (5–20 years) should prioritize the dimensioning of new water infrastructure, such as dams and pipelines, to withstand at least a 20-year return level. This aligns with recent findings emphasizing the need for diversifying water sources through non-conventional resources like desalination (Rezzoug et al. 2025). For long-term resilience (20–50 years), the 50-year and 100-year return levels must be integrated into regional land-use policies to establish anticipatory governance frameworks (Tramblay et al. 2013). Table 5 Operational recommendations for different return periods and planning horizons. Time horizon Operational recommendations Short-Term (1–5 years) Implement robust SPI-3 based early warning systems. Develop contingency plans for droughts exceeding the severe threshold (SPI-3 ≤ − 1.5). Enhance public communication regarding drought risk. Medium-Term (5–20 years) Dimension new water infrastructure (e.g., dams, pipelines) to withstand a minimum 20-year return level. Diversify water sources, including the integration of non-conventional resources such as desalination and water reuse (Rezzoug et al. 2025). Promote drought-resistant agricultural practices. Long-Term (20–50 years) Integrate the 50-year and 100-year return levels into regional planning and land-use policies. Focus on climate resilience of entire watersheds and establish anticipatory water governance frameworks ( Tramblay et al. 2013). 5. Conclusion The application of the Generalized Extreme Value (GEV) distribution to the SPI-3 series has provided a robust framework for characterizing extreme drought risk in the study region. The findings lead to the following key conclusions: Distribution type: The extreme drought occurrences are governed by a heavy-tailed Fréchet distribution ( ξ = 0.2843). This indicates that the region is inherently more susceptible to severe and extreme droughts than previously estimated by lighter-tailed models. Model validation: The discovery of an observed drought event (SPI-3 = -2.155) that exceeds the theoretical 100-year return level (-2.090) within a 44-year record strongly validates the GEV model’s capacity to capture exceptionally rare climatic extremes. Infrastructure Standards: Based on the return level analysis, the 50-year drought level (SPI-3 ≤ − 2.001) is recommended as the minimum design standard for critical regional water infrastructure to mitigate catastrophic potential. Cumulative risk: Risk analysis reveals a high probability (58%) of experiencing a 50-year drought within a 44-year period, and a 26% cumulative risk of a 100-year event over a standard 30-year planning horizon, necessitating urgent updates to safety margins. Future research should implement non-stationary GEV models with climate covariates (e.g., NAO index, AMO) and Regional Frequency Analysis (Hosking and Wallis, 1997) across multiple CHIRPS grid pixels to reduce parametric uncertainty and provide spatially coherent drought return levels for the wider Tafna watershed. Declarations Declaration of competing interest The authors have no competing interests to declare that are relevant to the content of this article. Funding Information No funding was received for conducting this study. Author Contribution N.M. and A.M.: Conceptualization, methodology, investigation, software, supervision, formal analysis, data collection - curation, writing—original draft, writing—review & editing. N.Za. and A.M.: Formal analysis, methodology, writing - review & editing. K.A.: Methodology, supervision & software. References Abi K (2018) A review of the climate change funding under the UNFCCC: With reference to the case of Algeria. J Adv Economic Res 3:320–338. https://asjp.cerist.dz/en/article/66583 Achite M, Simsek O, Sankaran A, Katipoğlu OM, Caloiero T (2024) Analyzing the dynamical relationships between meteorological and hydrological drought of Wadi Mina basin, Algeria using a novel multiscale framework. Stoch Env Res Risk Assess 38:1935–1953. https://doi.org/10.1007/s00477-024-02663-w Achour K, Meddi M, Zeroual A, Bouabdelli S, Maccioni P, Moramarco T (2020) Spatio-temporal analysis and forecasting of drought in the plains of northwestern Algeria using the standardized precipitation index. J Earth Syst Sci 129:42. https://doi.org/10.1007/s12040-019-1306-3 Adeola OM, Masinde M, Botai JO, Adeola AM, Botai CM (2021) An analysis of precipitation extreme events based on the SPI and EDI values in the Free State Province, South Africa. Water 13:3058. https://doi.org/10.3390/w13213058 Anghel CG, Ianculescu D (2025) Application of the GEV distribution in flood frequency analysis in Romania: An in-depth analysis. Climate 13:152. https://doi.org/10.3390/cli13070152 Attou AK, Baba-Hamed K, Bouanani A (2025) Developing a method to model extreme rainfall events using drought indices in northern Algeria under climate change. H2Open J 8:313–335. https://doi.org/10.2166/h2oj.2025.003 Bougara H, Hamed KB, Borgemeister C, Tischbein B, Kumar N, Baba K (2023) A comparative assessment of meteorological drought in the Tafna basin, Northwestern Algeria. J Water Land Dev. https://doi.org/10.24425/jwld.2021.139018 Bouraoui S, Medjerab A (2022) A spatiotemporal approach in detecting and analyzing hydro-climatic change in Northwest Algeria. Eng Technol Appl Sci Res 12:9632–9639 Burnham KP, Anderson DR (2002) : Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). Springer . https://doi.org/10.1007/b97636 Ceppi A, Achite M, Toubal AK, Caloiero T (2025) Mapping drought characteristics in northern Algerian basins using the ERA5-Land dataset. Sci Rep 15:10720. https://doi.org/10.1038/s41598-025-95418-8 Chite M, Bazrafshan O, Wałęga A, Azhdari Z, Krakauer N, Caloiero T (2022) Meteorological and hydrological drought risk assessment using multi-dimensional copulas in the WadiOuahrane Basin in Algeria. Water 14:653. https://doi.org/10.3390/w14040653 Djellouli F, Bouanani A, Babahamemed K (2016) Climate change: Assessment and monitoring of meteorological and hydrological drought of Wadi El Hammam Basin (NW-Algeria). J Fundamental Appl Sci 8:1037–1053 Funk C, Peterson P, Landsfeld M, Pedreros D, Verdin J, Shukla S, Husak G, Rowland J, Harrison L, Hoell A, Michaelsen J (2015) The climate hazards infrared precipitation with stations—A new environmental record for monitoring extremes. Sci Data 2:150066. https://doi.org/10.1038/sdata.2015.66 Ghenim AN, Megnounif A (2013) Ampleur de la sécheresse dans le bassin d'alimentation du barrage Meffrouche (Nord-Ouest de l’Algérie). Physio-Géo 7:35–49 Hadri A, Ndiaye AS, Khadir L, Jaffar O, Zamzami HA, El Khalki EM, Amazirh A, Bouchaou L, Chehbouni A (2024) Spatio-temporal analysis of meteorological drought return periods in a Mediterranean arid region, the center of Morocco. J Water Clim Change 15:4573–4595. https://doi.org/10.2166/wcc.2024.192 Hamlaoui-Moulai L, Mesbah M, Souag-Gamane D, Medjerab A (2013) Detecting hydro-climatic change using spatiotemporal analysis of rainfall time series in Western Algeria. Nat Hazards 65:1293–1311. https://doi.org/10.1007/s11069-012-0411-2 Hayes M, Svoboda M, Wall N, Widhalm M (2011) : The Lincoln Declaration on Drought Indices: Universal meteorological drought index recommended. Drought Mitigation Cent Fac Publications, 14. http://digitalcommons.unl.edu/droughtfacpub/14 Hosking JRM, and James R. Wallis (1997) Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, Cambridge Khaldi A (2005) : Impacts of drought on the groundwater flow regime in the limestone massifs of Western Algeria: Tlemcen–Saida Mountains. Ph.D. thesis, University of Oran Ladji H, Benrachdi K, Djoumad S (2019) Analysis of climatic drought using drought indices in Algiers region. Algerian J Environ Sci Technol 5:1062–1071 McKee T, Doesken N, Kleist J (1993) : The relationship of drought frequency and duration to time scales. Proc. Eighth Conf. on Applied Climatology , Anaheim, CA Meddi M (2009) Annual variability of precipitation of the northwest of Algeria. Sécheresse 20:57–65 Meddi M, Hubert P (2014) : Impact de la modification du régime pluviométrique sur les ressources en eau du nord-ouest de l'Algérie. IAHS Publ, 229–235 Meddi M, Bouabdelli S, Hallouz F, Rahmouni A, Taibi S, Zeroual A (2024) Impacts of climate change on drought in northern Algeria. Hydroclimatic Extremes in the Middle East and North Africa. Elsevier, pp 101–128. https://doi.org/10.1016/B978-0-12-824130-1.00019-9 Mega N, Medjerab A (2016) Study of climatic drought in Algerian high plateaus using standardized precipitation index and MODIS observations. J Appl Remote Sens 10:046002. https://doi.org/10.1117/1.JRS.10.046002 Mellak S, Souag-Gamane D (2020) Spatio-temporal analysis of maximum drought severity using Copulas in Northern Algeria. J Water Clim Change 11:68–84. https://doi.org/10.2166/wcc.2020.070 Merabti A, Darouich H, Paredes P, Meddi M, Pereira LS (2023) Assessing spatial variability and trends of droughts in Eastern Algeria using SPI, RDI, PDSI, and MedPDSI. Water 15:626. https://doi.org/10.3390/w15040626 Nedjraoui D, Bédrani S (2008) : La désertification dans les steppes algériennes: Causes, impacts et actions de lutte. VertigO, 8. http://journals.openedition.org/vertigo/5375 NekkacheGhenim A, Megnounif A (2011) Caractérisation de la sécheresse par les indices SPI et SSFI (Nord-Ouest de l’Algérie). LJEE 18:59–67 Rezzoug C, Merzougui T, Bouchiba A (2025) Wastewater treatment technologies and challenges in Algeria and their future prospects. Discover Sustain 6:884. https://doi.org/10.1007/s43621-025-01731-7 Tramblay Y, Adlouni SE, Servat E (2013) Trends and variability in extreme precipitation indices over Maghreb countries. Nat Hazards Earth Syst Sci 13:3235–3248. https://doi.org/10.5194/nhess-13-3235-2013 Wilhite DA, Glantz MH (1985) Understanding the drought phenomenon: The role of definitions. Water Int 10:111–120 World Meteorological Organization (2012) : Standardized Precipitation Index User Guide . WMO-No. 1090 Yahiaoui A, Touaïbia B, Bouvier C (2009) Frequency analysis of the hydrological drought regime: Case of Oued Mina catchment in western Algeria. Revue Nat et Technologie 1:3–15. https://asjp.cerist.dz/en/article/41191 Ziari A, Medjerab A (2024) Impact of drought in Northeastern Algeria: Comparative study of the SPI and SPEI indices. Revista de Gestão – RGSA 18:e06591. https://doi.org/10.24857/rgsa.v18n9-078 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9204781","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":613719734,"identity":"7470338b-c92a-4182-8d75-c2a9181884d1","order_by":0,"name":"Nabil MEGA","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVRIiWNgGAWjYBCDBDZ25gMMDAZAJjuIz8bA2EBQCzNbAkQLM7FaGJh5DCBMQlp029svfmDcYZfHx8zzTbqg4DADPzPzMYkPZQyy83HoMTtzpliC8UxyMRsz7zbpGQaHGSSb2dIkZ5xjMG7EpeVGToL03zbmxDaQFh6DtPoNh3nMpHnbGBKbcTjM7P6b5B+MbfVALTzPQFoY7EFa/gK1tOHScoP9mARj22GQFjagFhsGA2agFkaglh5cWs7ksFkwth0H+oXN2BqkReIwW7JlzzkJ4xm4tBw//vgGY1t1nnx788PbPH8kGPjbmw/e+FFmgzPEGBhg0YEGJHCpBwL2B3gkR8EoGAWjYBQAAQAG9EyzUbe9hgAAAABJRU5ErkJggg==","orcid":"","institution":"University of El Oued","correspondingAuthor":true,"prefix":"","firstName":"Nabil","middleName":"","lastName":"MEGA","suffix":""},{"id":613719735,"identity":"51f3ec0f-8e99-4e04-9100-d1ab5066a1ec","order_by":1,"name":"Assia MEZIANI","email":"","orcid":"","institution":"University of El Oued","correspondingAuthor":false,"prefix":"","firstName":"Assia","middleName":"","lastName":"MEZIANI","suffix":""},{"id":613719736,"identity":"e285c561-1c36-4e59-9c04-5f8a3edd4a5f","order_by":2,"name":"Abdelmonem MILOUDI","email":"","orcid":"","institution":"University of El Oued","correspondingAuthor":false,"prefix":"","firstName":"Abdelmonem","middleName":"","lastName":"MILOUDI","suffix":""},{"id":613719737,"identity":"69c57a3f-56ef-444d-a4c2-8745af227554","order_by":3,"name":"Nadjet ZAIR","email":"","orcid":"","institution":"University of El Oued","correspondingAuthor":false,"prefix":"","firstName":"Nadjet","middleName":"","lastName":"ZAIR","suffix":""},{"id":613719738,"identity":"116cfc87-bc25-403e-8326-86f3968bd158","order_by":4,"name":"Abderrahmane KHECHEKHOUCHE","email":"","orcid":"","institution":"University of El Oued","correspondingAuthor":false,"prefix":"","firstName":"Abderrahmane","middleName":"","lastName":"KHECHEKHOUCHE","suffix":""}],"badges":[],"createdAt":"2026-03-23 22:23:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9204781/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9204781/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105850568,"identity":"e54dffe4-d191-4c60-8981-c0d03cda553a","added_by":"auto","created_at":"2026-03-31 19:26:29","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":51652,"visible":true,"origin":"","legend":"\u003cp\u003eStudy area location.\u003c/p\u003e","description":"","filename":"Fig.1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/6b491b8365f82df7d7c39c19.jpg"},{"id":106093437,"identity":"7f801afa-3acc-43a6-b4cf-6a8f1f5a5fc2","added_by":"auto","created_at":"2026-04-03 11:37:22","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":46419,"visible":true,"origin":"","legend":"\u003cp\u003eDrought periods distribution.\u003c/p\u003e","description":"","filename":"Fig.2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/135597387285c955501aad61.jpg"},{"id":105850573,"identity":"5053c24c-8744-4b26-b9a6-9d3597af2fb1","added_by":"auto","created_at":"2026-03-31 19:26:29","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":36094,"visible":true,"origin":"","legend":"\u003cp\u003eAnnual minimums\u003c/p\u003e","description":"","filename":"Fig.3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/09a289391876b7b464808eb7.jpg"},{"id":105850570,"identity":"a2cd5e93-0c79-4aa0-8c54-e37cfaf996f9","added_by":"auto","created_at":"2026-03-31 19:26:29","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":28585,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of the extremes\u003c/p\u003e","description":"","filename":"Fig.4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/c581e88a57cf88002ad5907c.jpg"},{"id":105850571,"identity":"f03cd611-54c9-4c06-859e-cbe6e9948aaf","added_by":"auto","created_at":"2026-03-31 19:26:29","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":22547,"visible":true,"origin":"","legend":"\u003cp\u003eQQ-plot - GEV adjustment\u003c/p\u003e","description":"","filename":"Fig.5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/70c7c7a8365322783a185046.jpg"},{"id":105905531,"identity":"e33103b9-d389-447b-9daf-8cc1f36d1eca","added_by":"auto","created_at":"2026-04-01 10:12:40","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":19384,"visible":true,"origin":"","legend":"\u003cp\u003eReturn period curve\u003c/p\u003e","description":"","filename":"Fig.6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/acdc63ea034bc4efc55ff06f.jpg"},{"id":105905337,"identity":"692b97ad-0a32-431c-b2fa-5c9c199c45f4","added_by":"auto","created_at":"2026-04-01 10:11:52","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":103927,"visible":true,"origin":"","legend":"\u003cp\u003eProbabilistic risk assessment of drought events based on GEV model return levels and severity categories. a) Drought intensity by classification, b) Drought return level analysis.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/401920407a0b911b747b45c0.jpg"},{"id":108140281,"identity":"e072b18a-dcf4-4bfd-954e-42446c298c6a","added_by":"auto","created_at":"2026-04-29 18:54:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":603374,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9204781/v1/af563acc-68c0-4097-a9f4-27b0129968e4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Extreme Value Analysis of Meteorological Drought in Tlemcen, North-West Algeria: Evidence of a Heavy-Tailed Fréchet Distribution Using the SPI-3 Index","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eDrought is a complex and insidious climatic phenomenon defined as a prolonged precipitation deficit relative to normal levels. It results in water scarcity over wide geographical areas and significant periods (Yahiaoui et al. 2009; Chite et al. 2022; Wilhite and Glantz, 1985). Traditionally, drought is classified into meteorological, agricultural, hydrological, and socio-economic types (Djellouli et al. 2016; Yahiaoui et al. 2009; Chite et al. 2022). The Mediterranean basin, including Algeria, is recognized as one of the regions most vulnerable to climate change, experiencing a significant increase in the frequency, duration, and severity of drought episodes (Chite et al. 2022; Achour, 2020).According to Nekkache and Megnounif (2011), Meddi and Hubert (2014), Achite et al. (2024), Ghenim and Megnounif (2013), and Meddi (2009), Algeria has been confronted with a persistent meteorological drought since the mid-1970s, marking a significant break in the rainfall regime. Nekkache and Megnounif (2011) and Achite et al. (2024) have shown that the runoff deficit has reached substantial proportions, ranging from 37% to over 70% from east to west. Nekkache and Megnounif (2011), Mellak and Souag-Gamane (2020), Hadri et al. (2024), Merabti (2023), and Khaldi (2005) highlight that this situation leads to alarming drops in dam filling rates, overexploitation of groundwater, and recurrent water shortages affecting agriculture, industry, and quality of life. Consequently, Hadri et al. (2024) and Merabti (2023) note that massive adaptation strategies, such as seawater desalination, have become necessary. According to Nedjraoui and B\u0026eacute;drani (2008) and Mega and Medjerab (2016), the Algerian High Plateaus, situated between the Tellian and Saharan Atlas, are particularly sensitive to climatic variations. Mega and Medjerab (2016), Bouraoui and Medjerab (2022), and Ladji (2019) confirm a trend of decreasing precipitation and intensified drought episodes in this region, which is characterized by a semi-arid to continental climate and experiencing accentuated aridification, especially in the western part. Nedjraoui and B\u0026eacute;drani (2008), Mega and Medjerab (2016), Hamlaoui-Moulai et al. (2013), Abi (2018), and Bougara et al. (2023) emphasize that this directly impacts steppe ecosystems, causing progressive desertification, reduced vegetation cover, and degradation of ecological potential. Nekkache and Megnounif (2011) and Bougara et al. (2023) have identified the Tlemcen Province in Northwest Algeria as a focal point of this water crisis, as the Tafna watershed (7,245 km\u0026sup2;), historically known as the \"water tower of Western Algeria,\" has been severely affected. According to Nekkache and Megnounif (2011) and Bougara et al. (2023), specific studies on the Tafna basin reveal a cumulative rainfall deficit estimated at 25% since the mid-1970s. Furthermore, Nekkache and Megnounif (2011) and McKee et al. (1993) highlight a break in homogeneity in the pluviometric and hydrological series around the mid-1970s in the Meffrouche dam's catchment area, with a runoff deficit exceeding 60% in the subsequent dry period.According to Hayes et al. (2011), standardized indices are essential to evaluate and monitor drought, with the Standardized Precipitation Index (SPI) being widely adopted for meteorological drought characterization. Chite et al. (2022), Djellouli et al. (2016), and Nekkache and Megnounif (2011) state that this study specifically focuses on the SPI-3 (3-month accumulation period), which is particularly relevant for monitoring short-term droughts due to its close link to soil moisture and agricultural impacts according to the World Meteorological Organization (2012) and Ziari and Medjerab (2024). Furthermore, Anghel and Ianculescu (2025), Adeola et al. (2021), and Attou et al. (2025) recognize the Generalized Extreme Value (GEV) distribution as a flexible three-parameter model widely used in hydrology and climatology for modeling the frequency and magnitude of extreme events.\u003c/p\u003e \u003cp\u003eDespite the growing literature on climatic trends in North Africa, there remains a critical need for a probabilistic assessment of rare, catastrophic drought events that fall beyond the scope of traditional statistical models. The main objective of this work is to address this gap by applying Extreme Value Theory (EVT) to characterize the frequency and intensity of extreme droughts in the Tlemcen region using the SPI-3 index. The novelty of this study lies in its focus on the heavy-tailed behavior of extreme events, moving beyond average trend analysis to identify the specific statistical distribution that governs the most severe drought occurrences. By establishing concrete return level thresholds and quantifying cumulative risks, this research seeks to provide a necessary framework for enhancing climate resilience and informing safety margins in regional water resource management.\u003c/p\u003e"},{"header":"2. Study area","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Geographic location\u003c/h2\u003e \u003cp\u003eThe study focuses on the Tlemcen region, located in the highly climate-sensitive North-West of Algeriaas shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. This area is characterized by a Mediterranean climate, making it particularly vulnerable to recurrent and intense climatic droughts, which pose a significant threat to its water resources and agricultural sector. The analysis of meteorological drought is based on a high-quality, continuous time series of precipitation data spanning from 1980 to 2024. To comprehensively characterize the drought events, two complementary methodologies were employed: the Standardized Precipitation Index (SPI-3) was used to monitor the severity and duration of short-term meteorological droughts, and the Extreme Value Theory (EVT), specifically the Generalized Extreme Value (GEV) distribution, was applied to the annual minimum SPI-3 values to probabilistically quantify the risk of rare, catastrophic drought events.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Climate framework\u003c/h2\u003e \u003cp\u003ePrecipitation data were collected from the Google Earth Engine platform, from the 'Climate Hazards Center InfraRed Precipitation with Station data (CHIRPS)' mission. The data are available from 01-01-1981 to the present (Funk and al. 2015).The analysis of the Tlemcen climate framework focuses on the characterization of meteorological drought using the three-month Standardized Precipitation Index (SPI-3) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), with drought events identified and delineated through the application of the Run Theory method, which defines an event as a continuous sequence where the SPI-3 value falls below a specific threshold. This methodology allows for the quantification of key drought parameters, including the Duration (D), the Mean Intensity (I), the Severity (S), and the minimum SPI-3 value reached (Peak). The preliminary results (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) indicate that five distinct drought events were identified over the study period, with the most severe event occurring between February and May 2000, characterized by a Duration of 4 months, a Mean Intensity of 1.61, a Severity of 6.45, and a Peak SPI-3 value of -2.15, highlighting the extreme nature of this particular episode.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePeriods of drought events in the Tlemcen region.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eStart_date\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eEnd_date\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eDuration\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eMean Intensity\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eSeverity\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003ePeak\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/11/1981\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e01/01/1982\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1,46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/09/1992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e01/01/1993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1,26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/02/2000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e01/05/2000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2,15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/04/2001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e01/07/2001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1,69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/08/2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e01/11/2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1,42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Method","content":"\u003cp\u003eThe application of Extreme Value Theory (EVT), particularly through the Generalized Extreme Value (GEV) distribution, is of paramount importance for characterizing climatic drought risk in the Tlemcen region of North-West Algeria. Given the region's Mediterranean climate and its increasing vulnerability to water scarcity, EVT provides a robust statistical framework specifically designed to model the tail behavior of hydrological variables, which is where the most damaging drought events reside (Attou and al. 2025). The mathematical foundation of this approach is rooted in the Fisher-Tippett-Gnedenko theorem, which states that the distribution of the normalized maximum (or minimum, as in the case of drought indices like SPI) of a sequence of independent and identically distributed random variables converges to one of three possible types: Gumbel, Fr\u0026eacute;chet, or Weibull. These three distributions are unified by the GEV cumulative distribution function, \u003cem\u003eG\u003c/em\u003e(\u003cem\u003ez\u003c/em\u003e), defined as (Eq.\u0026nbsp;1):\u003c/p\u003e \u003cp\u003eG(z)\u0026thinsp;=\u0026thinsp;exp (- [1\u0026thinsp;+\u0026thinsp;ξ (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{z-{\\mu\\:}}{\\sigma\\:}\\left)\\right]{.}^{-1/{\\xi\\:}}\\)\u003c/span\u003e\u003c/span\u003e) (1)\u003c/p\u003e \u003cp\u003eWhere: \u003cem\u003e\u0026micro;\u003c/em\u003e: location parameter, \u003cem\u003eσ\u003c/em\u003e: scale parameter, and \u003cem\u003eξ\u003c/em\u003e: shape parameter that determines the distribution type.\u003c/p\u003e \u003cp\u003eUnlike conventional statistical methods that often underestimate the probability of rare, high-impact events, EVT allows for the precise estimation of return levels for severe and extreme droughts, which is critical for effective water resource management and infrastructure planning (Ceppi et al. 2025). The ability of EVT to identify the underlying distribution type (e.g., Fr\u0026eacute;chet, as suggested by the heavy-tailed nature of extremes in this region) provides essential insights into the inherent risk profile, confirming that the probability of catastrophic droughts is higher than typically assumed (Meddi et al. 2024). Furthermore, in the context of a changing climate, the EVT framework can be extended to non-stationary models, allowing for the incorporation of temporal covariates to better project future drought risks and inform long-term climate resilience strategies for Tlemcen and the wider Algerian basins (Ceppi et al. 2025; Rezzoug et al. 2025; Tramblay and al. 2013). To evaluate whether the stationary GEV assumption is tenable given the documented precipitation break around the mid-1970s, a non-stationary GEV model was tested in which the location parameter varies linearly with time: \u0026micro;(t) = \u0026micro;₀ + \u0026micro;₁\u0026middot;t. Comparison via the likelihood-ratio test (LRT) and AIC yielded no significant improvement over the stationary model (ΔAIC\u0026thinsp;\u0026lt;\u0026thinsp;2), supporting the use of the stationary framework over the 1980\u0026ndash;2024 sub-period while motivating future investigation with extended records.\u003c/p\u003e \u003cp\u003eThe study of climatic drought in the Tlemcen region, as in much of North Africa, requires a multi-faceted approach due to the complex interplay of meteorological and hydrological factors. While standard drought indices like the Standardized Precipitation Index (SPI) and the Palmer Drought Severity Index (PDSI) are essential for monitoring and characterizing drought events, the Extreme Value Theory (EVT) offers a distinct and crucial advantage, particularly for risk assessment and long-term planning (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparative analysis of EVT and standard drought indices.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFeature\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eExtreme Value Theory (EVT) / GEV\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eStandard drought indices (e.g., SPI, PDSI)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePrimary Goal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQuantify the probability of rare, extreme events (tail behavior).\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMonitor the onset, duration, and severity of drought events.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMathematical Basis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBased on the Fisher-Tippett- Gnedenko theorem, focusing on the asymptotic distribution of block maxima/minima.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBased on statistical standardization (SPI) or a water balance model (PDSI).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOutput\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eReturn Levels (e.g., 50-year drought intensity) and Return Periods.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA time-series index value that categorizes drought severity (e.g., moderate, severe, extreme).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eApplication\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRisk Assessment for critical infrastructure (dams, reservoirs) and long-term policymaking.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOperational Monitoring and short-term water management decisions.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSuitability for Tlemcen\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHighly suitable for a region with a heavy-tailed distribution of extremes, as it provides a robust estimate of the true catastrophic risk (Attou et al. 2025; Ceppi et al. 2025).\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSPI is highly suitable due to its simplicity and flexibility in time scales, which is critical for the Mediterranean climate of Tlemcen (Tramblay et al. 2013). PDSI is less common in the region due to its complex data requirements.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLimitation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRequires a long, high-quality data record to accurately estimate parameters for high return periods (e.g., 100-year events).\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDoes not directly quantify the probability of exceedance for a given return period, which limits its use for engineering design.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe primary strength of EVT, particularly the GEV approach applied to the annual minimum SPI-3, lies in its ability to move beyond simple categorization (e.g., \"extreme drought\") to provide a probabilistic quantification of risk. For Tlemcen, where the analysis suggests a heavy-tailed Fr\u0026eacute;chet distribution, EVT is indispensable. Standard indices, while excellent for tracking the evolution of a drought, often rely on underlying assumptions (like normality for the SPI calculation) that can significantly underestimate the frequency and intensity of the most severe events\u003cb\u003e(\u003c/b\u003eMeddi et al. 2024). EVT, by focusing solely on the extremes, provides the necessary information (the return level for the 50-year or 100-year drought) that is essential for designing resilient water systems in a climate-vulnerable region like North-West Algeria \u003cb\u003e(\u003c/b\u003eTramblay et al. 2013). Therefore, the two approaches are complementary: standard indices monitor the present and recent past, while EVT quantifies the potential for future catastrophic events.\u003c/p\u003e"},{"header":"4. Results and discussion","content":"\u003cdiv id=\"Sec7\"\u003e\n \u003ch2\u003e4.1. SPI-3 Annual Minimums\u003c/h2\u003e\n \u003cp\u003eFigure\u0026nbsp;3 displays the time series of the annual minimum values of the Standardized Precipitation Index (SPI-3) between 1980 and 2024.\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eGeneral trend: The graph shows high inter-annual variability in drought intensity.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eObserved extreme events: The lowest value (the most intense drought) occurred around the year 2000, reaching an SPI-3 of approximately\u0026thinsp;\u0026minus;\u0026thinsp;2.15. This value exceeds the Extreme Drought threshold (dashed red line at -2.0), confirming that a severe event, theoretically exceeding the 100-year return level, occurred within the study period.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eFrequency: The majority of the annual minima fall between the Moderate Drought threshold (-1.0) and the Severe Drought threshold (-1.5), which is consistent with the interpretation that the region regularly experiences moderate to severe droughts.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\"\u003e\n \u003ch2\u003e4.2. GEV distribution of the extremes\u003c/h2\u003e\n \u003cp\u003eFigure\u0026nbsp;4 compares the histogram of the observed data (blue bars) with the Probability Density Function (PDF) of the fitted GEV model (red curve).\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eModel fit: The fitted GEV curve (red) generally follows the frequency distribution of the annual minima (blue bars), indicating that the GEV model is an appropriate choice for modeling these extremes.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eDistribution nature: The shape of the red curve, which extends towards the right (lower SPI-3 values in absolute terms, representing less extreme events), and the presence of data in the right tail (SPI-3 annual minimum\u0026thinsp;\u0026gt;\u0026thinsp;1.75) suggest a Fr\u0026eacute;chet type distribution (heavy-tailed, \u003cem\u003e\u0026xi;\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0). This is a very high-intensity events (very low SPI-3) are more probable than in a normal distribution.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\"\u003e\n \u003ch2\u003e4.3. QQ-plot GEV adjustment\u003c/h2\u003e\n \u003cp\u003eThe Quantile-Quantile (QQ-plot) is the most critical tool for assessing the quality of the GEV model fit to the data as shown in Fig.\u0026nbsp;5.\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eFit quality: The points (empirical quantiles) are very close to the theoretical line (dashed red line), particularly for the central values. This demonstrates an excellent fit of the GEV model to the observed data.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eExtremes: Even the highest quantiles (representing the most intense droughts) align well with the theoretical line, which is crucial. This means the GEV model is reliably capable of predicting the probability of the rarest and most severe drought events.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003cp\u003eFigure\u0026nbsp;5 confirms the suitability of the GEV approach for drought analysis in Tlemcen. The excellent model fit (validated by the QQ-plot) allows for reliable risk quantification. The most critical finding is the confirmation of a heavy-tailed distribution, implying that the region is vulnerable to more intense and frequent droughts than conventional models might suggest. The calculated return levels provide essential thresholds for risk management and water resource planning.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\"\u003e\n \u003ch2\u003e4.4. Return period curve\u003c/h2\u003e\n \u003cp\u003eFigure\u0026nbsp;6 shows the relationship between the return period (in years, logarithmic scale on the x-axis) and the corresponding return level (SPI-3 value, y-axis).\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eRisk quantification: The curve allows for the determination of the expected drought intensity for different return periods:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eT\u0026thinsp;=\u0026thinsp;10 years: Return level (SPI-3) of approximately\u0026thinsp;\u0026minus;\u0026thinsp;1.70 (Severe Drought).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eT\u0026thinsp;=\u0026thinsp;20 years: Return level (SPI-3) of approximately\u0026thinsp;\u0026minus;\u0026thinsp;1.85 (Severe Drought, approaching Extreme).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eT\u0026thinsp;=\u0026thinsp;50 years: Return level (SPI-3) of approximately\u0026thinsp;\u0026minus;\u0026thinsp;2.00 (Extreme Drought).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eT\u0026thinsp;=\u0026thinsp;100 years: Return level (SPI-3) of approximately\u0026thinsp;\u0026minus;\u0026thinsp;2.09 (Major Extreme Drought).\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003ePlanning implications: The curve is upward-sloping and concave, which is typical of a heavy-tailed (Fr\u0026eacute;chet) distribution. This means that drought intensity increases rapidly with the return period, highlighting the necessity of integrating the 50-year and 100-year return levels into the design of water infrastructure in Tlemcen.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\"\u003e\n \u003ch2\u003e4.5. Statistical characterization of extreme drought events\u003c/h2\u003e\n \u003cp\u003eThe analysis of extreme drought events was conducted using the annual minimum values of the Standardized Precipitation Index (SPI-3) over a 44-year observation period. The descriptive statistics of these annual minima reveal a mean value of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e\u003cstrong\u003e\u0026nbsp;=\u003c/strong\u003e \u0026minus; 1.150, which falls within the \u0026ldquo;moderate drought\u0026rdquo; category (SPI-3 between \u0026minus;\u0026thinsp;1.0 and \u0026minus;\u0026thinsp;1.5). This suggests that the study region experiences a moderate drought event on an annual basis. The most severe event recorded during the period is an absolute minimum SPI-3 of \u0026minus; 2.155, which is classified as an \u0026ldquo;extreme drought\u0026rdquo;(SPI-3\u003cstrong\u003e\u0026nbsp;\u0026le;\u003c/strong\u003e \u0026minus; 2.0).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\"\u003e\n \u003ch2\u003e4.6. Generalized Extreme Value (GEV) modeling and parameter interpretation\u003c/h2\u003e\n \u003cp\u003eThe Generalized Extreme Value (GEV) distribution was fitted to the series of annual minimum SPI-3 values to model the behavior of these extreme events. To formally justify the choice of the Fr\u0026eacute;chet sub-family over competing distributions, three nested GEV models were compared using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC): the full GEV model (\u0026xi; free), the Gumbel model (\u0026xi;\u0026thinsp;=\u0026thinsp;0, light tail), and the reversed Weibull model (\u0026xi;\u0026thinsp;\u0026lt;\u0026thinsp;0, bounded tail). The GEV model yielded the lowest AIC (AIC\u0026thinsp;=\u0026thinsp;58.3) and BIC (BIC\u0026thinsp;=\u0026thinsp;61.7), confirming statistically that the Fr\u0026eacute;chet distribution is the most appropriate representation of the extremes in this dataset and that the heavy-tailed hypothesis is not an artifact of the fitting procedure. Parameter uncertainty was quantified using a non-parametric bootstrap procedure (B\u0026thinsp;=\u0026thinsp;2,000 resamples with replacement on the annual minima series), which provides 95% confidence intervals for each GEV parameter and for the derived return levels. The maximum likelihood estimation yielded the following parameters (Table\u0026nbsp;3):\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eGeneralized Extreme Value parameters.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eParameter\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e\u003cem\u003eValue\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e\u003cem\u003eInterpretation\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eShape (\u003cem\u003e\u0026xi;\u003c/em\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.2843\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eFr\u0026eacute;chet distribution (heavy-tailed); 95% CI: [0.041, 0.528]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eLocation (\u003cem\u003e\u0026micro;\u003c/em\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e\u0026minus;0.9984\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eCentral tendency of annual minima (approx. moderate drought); 95% CI: [\u0026minus;\u0026thinsp;1.285, \u0026minus;\u0026thinsp;0.712]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eScale (\u003cem\u003e\u0026sigma;\u003c/em\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.4254\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eModerate dispersion of annual minima; 95% CI: [0.291, 0.622]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eTable 4. Operational recommendations\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003efor return periods.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eTime horizon\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e\u003cem\u003eOperational recommendations\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eShort-Term (1\u0026ndash;5 years)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eImplement robust SPI-3 based early warning systems. Develop contingency plans for droughts exceeding the severe threshold (SPI-3 \u0026le; \u0026minus; 1.5). Enhance public communication regarding drought risk.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eMedium-Term (5\u0026ndash;20 years)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eDimension new water infrastructure (e.g., dams, pipelines) to withstand a minimum 20-year return level. Diversify water sources, including the integration of non-conventional resources such as desalination and water reuse [32]. Promote drought-resistant agricultural practices.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eLong-Term (20\u0026ndash;50 years)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eIntegrate the 50-year and 100-year return levels into regional planning and land-use policies. Focus on climate resilience of entire watersheds and establish anticipatory water governance frameworks [33].\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe most critical finding is the positive value of the shape parameter, \u003cem\u003e\u0026xi;\u003c/em\u003e = 0.2843. Since \u003cem\u003e\u0026xi;\u003c/em\u003e \u0026gt; 0, the distribution is of the Fr\u0026eacute;chet type, characterized by a heavy tail. This result has profound implications for risk assessment, as it indicates that: 1. Extreme events are more probable than would be predicted by light-tailed distributions (e.g., Gumbel or Weibull). 2. The probability of very severe droughts (SPI-3 \u0026le; \u0026minus; 2.0) is significantly higher, suggesting that the risk of rare events is often underestimated by conventional models. 3. The potential for extremely intense events is high, as the distribution decays slowly. Crucially, the bootstrap 95% CI for \u0026xi; (CI: [0.041, 0.528]) excludes zero, formally rejecting the Gumbel hypothesis (\u0026xi;\u0026thinsp;=\u0026thinsp;0) at the 5% level. The \u0026Delta;AIC\u0026thinsp;=\u0026thinsp;5.4 between the full GEV and constrained Gumbel constitutes strong evidence for the Fr\u0026eacute;chet family (Burnham and Anderson, 2002).\u003c/p\u003e\n \u003cp\u003eThe location parameter, \u003cem\u003e\u0026micro;\u003c/em\u003e \u0026asymp; \u0026minus; 1.0, is consistent with the mean of the annual minima (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e = \u0026minus; 1.150), confirming that the typical annual minimum drought intensity is around the moderate level. The scale parameter, \u003cem\u003e\u0026sigma;\u003c/em\u003e = 0.4254, suggests a moderate variability in the intensity of the annual minimum droughts, implying a certain regularity in their occurrence, which is nonetheless overshadowed by the heavy-tailed risk.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\"\u003e\n \u003ch2\u003e4.7. Return level analysis and risk assessment\u003c/h2\u003e\n \u003cp\u003eThe GEV model was used to estimate return levels (T) for various drought intensities, providing a quantitative basis for water resource planning and infrastructure design (Fig.\u0026nbsp;7-a). As shown in Fig.\u0026nbsp;7-b, the 50-year return level (SPI-3 \u0026le; \u0026minus; 2.001) formally crosses the threshold for an extreme drought, highlighting the catastrophic potential of such an event for the region\u0026rsquo;s agriculture and water supply. A comparison between the theoretical return levels and the observed data reveals a critical point: the absolute minimum observed SPI-3 of -2.155 is more severe than the calculated 100-year return level SPI-3 \u0026le; \u0026minus; 2.090). This suggests that a drought event with a theoretical return period exceeding 100 years has already occurred within the 44-year observation window. This observation strongly validates the GEV model\u0026rsquo;s heavy-tailed nature and underscores the high vulnerability of the region to exceptionally rare events as illustrated in Fig.\u0026nbsp;7-b. Furthermore, the cumulative risk analysis demonstrates the high probability of experiencing a major drought over typical planning horizons. The probability of experiencing a 50-year drought (SPI-3 \u0026le; \u0026minus; 2.001) over the 44-year study period was approximately 58%. For a 30-year planning horizon, which is typical for major infrastructure like dams, the cumulative risk of experiencing a 100-year drought (SPI-3 \u0026le; \u0026minus; 2.090) is 26%. This high probability necessitates a significant upward revision of safety margins in water infrastructure design. Return levels are accompanied by bootstrap 95% CIs: T\u0026thinsp;=\u0026thinsp;50\u0026nbsp;year: SPI-3\u0026thinsp;\u0026le;\u0026thinsp;\u0026minus;\u0026thinsp;2.001 [\u0026minus;\u0026thinsp;2.412, \u0026minus;\u0026thinsp;1.743]; T\u0026thinsp;=\u0026thinsp;100\u0026nbsp;year: SPI-3\u0026thinsp;\u0026le;\u0026thinsp;\u0026minus;\u0026thinsp;2.090 [\u0026minus;\u0026thinsp;2.651, \u0026minus;\u0026thinsp;1.812]. The width of these intervals reflects the inherent uncertainty of long-return-period estimation from a 44-year record.\u003c/p\u003e\n \u003cdiv\u003e\u003cbr\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\"\u003e\n \u003ch2\u003e4.8. Operational recommendations and policy implications\u003c/h2\u003e\n \u003cp\u003eThe return level analysis provides a quantitative basis for developing climate adaptation strategies. Based on the calculated risks, a suite of operational recommendations is proposed across different time horizons (Table\u0026nbsp;5). For short-term planning (1\u0026ndash;5 years), the implementation of robust early warning systems based on SPI-3 thresholds is critical to mitigate immediate agricultural losses.\u003c/p\u003e\n \u003cp\u003eMedium-term strategies (5\u0026ndash;20 years) should prioritize the dimensioning of new water infrastructure, such as dams and pipelines, to withstand at least a 20-year return level. This aligns with recent findings emphasizing the need for diversifying water sources through non-conventional resources like desalination (Rezzoug et al. 2025). For long-term resilience (20\u0026ndash;50 years), the 50-year and 100-year return levels must be integrated into regional land-use policies to establish anticipatory governance frameworks (Tramblay et al. 2013).\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 5\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eOperational recommendations for different return periods and planning horizons.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eTime horizon\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e\u003cem\u003eOperational recommendations\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eShort-Term (1\u0026ndash;5 years)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eImplement robust SPI-3 based early warning systems. Develop contingency plans for droughts exceeding the severe threshold (SPI-3 \u0026le; \u0026minus; 1.5). Enhance public communication regarding drought risk.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eMedium-Term (5\u0026ndash;20 years)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eDimension new water infrastructure (e.g., dams, pipelines) to withstand a minimum 20-year return level. Diversify water sources, including the integration of non-conventional resources such as desalination and water reuse (Rezzoug et al. 2025). Promote drought-resistant agricultural practices.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eLong-Term (20\u0026ndash;50 years)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eIntegrate the 50-year and 100-year return levels into regional planning and land-use policies. Focus on climate resilience of entire watersheds and establish anticipatory water governance frameworks \u003cstrong\u003e(\u003c/strong\u003eTramblay et al. 2013).\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThe application of the Generalized Extreme Value (GEV) distribution to the SPI-3 series has provided a robust framework for characterizing extreme drought risk in the study region. The findings lead to the following key conclusions:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eDistribution type: The extreme drought occurrences are governed by a heavy-tailed Fr\u0026eacute;chet distribution (\u003cem\u003eξ\u003c/em\u003e = 0.2843). This indicates that the region is inherently more susceptible to severe and extreme droughts than previously estimated by lighter-tailed models.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eModel validation: The discovery of an observed drought event (SPI-3 = -2.155) that exceeds the theoretical 100-year return level (-2.090) within a 44-year record strongly validates the GEV model\u0026rsquo;s capacity to capture exceptionally rare climatic extremes.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eInfrastructure Standards: Based on the return level analysis, the 50-year drought level (SPI-3 \u0026le; \u0026minus; 2.001) is recommended as the minimum design standard for critical regional water infrastructure to mitigate catastrophic potential.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eCumulative risk: Risk analysis reveals a high probability (58%) of experiencing a 50-year drought within a 44-year period, and a 26% cumulative risk of a 100-year event over a standard 30-year planning horizon, necessitating urgent updates to safety margins.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFuture research should implement non-stationary GEV models with climate covariates (e.g., NAO index, AMO) and Regional Frequency Analysis (Hosking and Wallis, 1997) across multiple CHIRPS grid pixels to reduce parametric uncertainty and provide spatially coherent drought return levels for the wider Tafna watershed.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of competing interest\u003c/h2\u003e \u003cp\u003eThe authors have no competing interests to declare that are relevant to the content of this article.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding Information\u003c/h2\u003e \u003cp\u003eNo funding was received for conducting this study.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eN.M. and A.M.: Conceptualization, methodology, investigation, software, supervision, formal analysis, data collection - curation, writing\u0026mdash;original draft, writing\u0026mdash;review \u0026amp; editing. N.Za. and A.M.: Formal analysis, methodology, writing - review \u0026amp; editing. K.A.: Methodology, supervision \u0026amp; software.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAbi K (2018) A review of the climate change funding under the UNFCCC: With reference to the case of Algeria. J Adv Economic Res 3:320\u0026ndash;338. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://asjp.cerist.dz/en/article/66583\u003c/span\u003e\u003cspan address=\"https://asjp.cerist.dz/en/article/66583\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAchite M, Simsek O, Sankaran A, Katipoğlu OM, Caloiero T (2024) Analyzing the dynamical relationships between meteorological and hydrological drought of Wadi Mina basin, Algeria using a novel multiscale framework. Stoch Env Res Risk Assess 38:1935\u0026ndash;1953. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00477-024-02663-w\u003c/span\u003e\u003cspan address=\"10.1007/s00477-024-02663-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAchour K, Meddi M, Zeroual A, Bouabdelli S, Maccioni P, Moramarco T (2020) Spatio-temporal analysis and forecasting of drought in the plains of northwestern Algeria using the standardized precipitation index. J Earth Syst Sci 129:42. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s12040-019-1306-3\u003c/span\u003e\u003cspan address=\"10.1007/s12040-019-1306-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdeola OM, Masinde M, Botai JO, Adeola AM, Botai CM (2021) An analysis of precipitation extreme events based on the SPI and EDI values in the Free State Province, South Africa. Water 13:3058. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/w13213058\u003c/span\u003e\u003cspan address=\"10.3390/w13213058\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAnghel CG, Ianculescu D (2025) Application of the GEV distribution in flood frequency analysis in Romania: An in-depth analysis. Climate 13:152. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/cli13070152\u003c/span\u003e\u003cspan address=\"10.3390/cli13070152\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAttou AK, Baba-Hamed K, Bouanani A (2025) Developing a method to model extreme rainfall events using drought indices in northern Algeria under climate change. H2Open J 8:313\u0026ndash;335. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2166/h2oj.2025.003\u003c/span\u003e\u003cspan address=\"10.2166/h2oj.2025.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBougara H, Hamed KB, Borgemeister C, Tischbein B, Kumar N, Baba K (2023) A comparative assessment of meteorological drought in the Tafna basin, Northwestern Algeria. J Water Land Dev. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.24425/jwld.2021.139018\u003c/span\u003e\u003cspan address=\"10.24425/jwld.2021.139018\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBouraoui S, Medjerab A (2022) A spatiotemporal approach in detecting and analyzing hydro-climatic change in Northwest Algeria. Eng Technol Appl Sci Res 12:9632\u0026ndash;9639\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBurnham KP, Anderson DR (2002) : Model selection and multimodel inference: A practical information-theoretic approach (2nd ed.). \u003cem\u003eSpringer\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/b97636\u003c/span\u003e\u003cspan address=\"10.1007/b97636\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCeppi A, Achite M, Toubal AK, Caloiero T (2025) Mapping drought characteristics in northern Algerian basins using the ERA5-Land dataset. Sci Rep 15:10720. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-025-95418-8\u003c/span\u003e\u003cspan address=\"10.1038/s41598-025-95418-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChite M, Bazrafshan O, Wałęga A, Azhdari Z, Krakauer N, Caloiero T (2022) Meteorological and hydrological drought risk assessment using multi-dimensional copulas in the WadiOuahrane Basin in Algeria. Water 14:653. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/w14040653\u003c/span\u003e\u003cspan address=\"10.3390/w14040653\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDjellouli F, Bouanani A, Babahamemed K (2016) Climate change: Assessment and monitoring of meteorological and hydrological drought of Wadi El Hammam Basin (NW-Algeria). J Fundamental Appl Sci 8:1037\u0026ndash;1053\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFunk C, Peterson P, Landsfeld M, Pedreros D, Verdin J, Shukla S, Husak G, Rowland J, Harrison L, Hoell A, Michaelsen J (2015) The climate hazards infrared precipitation with stations\u0026mdash;A new environmental record for monitoring extremes. Sci Data 2:150066. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/sdata.2015.66\u003c/span\u003e\u003cspan address=\"10.1038/sdata.2015.66\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhenim AN, Megnounif A (2013) Ampleur de la s\u0026eacute;cheresse dans le bassin d'alimentation du barrage Meffrouche (Nord-Ouest de l\u0026rsquo;Alg\u0026eacute;rie). Physio-G\u0026eacute;o 7:35\u0026ndash;49\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHadri A, Ndiaye AS, Khadir L, Jaffar O, Zamzami HA, El Khalki EM, Amazirh A, Bouchaou L, Chehbouni A (2024) Spatio-temporal analysis of meteorological drought return periods in a Mediterranean arid region, the center of Morocco. J Water Clim Change 15:4573\u0026ndash;4595. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2166/wcc.2024.192\u003c/span\u003e\u003cspan address=\"10.2166/wcc.2024.192\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHamlaoui-Moulai L, Mesbah M, Souag-Gamane D, Medjerab A (2013) Detecting hydro-climatic change using spatiotemporal analysis of rainfall time series in Western Algeria. Nat Hazards 65:1293\u0026ndash;1311. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11069-012-0411-2\u003c/span\u003e\u003cspan address=\"10.1007/s11069-012-0411-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHayes M, Svoboda M, Wall N, Widhalm M (2011) : The Lincoln Declaration on Drought Indices: Universal meteorological drought index recommended. Drought Mitigation Cent Fac Publications, 14. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://digitalcommons.unl.edu/droughtfacpub/14\u003c/span\u003e\u003cspan address=\"http://digitalcommons.unl.edu/droughtfacpub/14\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHosking JRM, and James R. Wallis (1997) Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, Cambridge\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhaldi A (2005) : Impacts of drought on the groundwater flow regime in the limestone massifs of Western Algeria: Tlemcen\u0026ndash;Saida Mountains. Ph.D. thesis, University of Oran\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLadji H, Benrachdi K, Djoumad S (2019) Analysis of climatic drought using drought indices in Algiers region. Algerian J Environ Sci Technol 5:1062\u0026ndash;1071\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcKee T, Doesken N, Kleist J (1993) : The relationship of drought frequency and duration to time scales. \u003cem\u003eProc. Eighth Conf. on Applied Climatology\u003c/em\u003e, Anaheim, CA\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeddi M (2009) Annual variability of precipitation of the northwest of Algeria. S\u0026eacute;cheresse 20:57\u0026ndash;65\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeddi M, Hubert P (2014) : Impact de la modification du r\u0026eacute;gime pluviom\u0026eacute;trique sur les ressources en eau du nord-ouest de l'Alg\u0026eacute;rie. IAHS Publ, 229\u0026ndash;235\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeddi M, Bouabdelli S, Hallouz F, Rahmouni A, Taibi S, Zeroual A (2024) Impacts of climate change on drought in northern Algeria. Hydroclimatic Extremes in the Middle East and North Africa. Elsevier, pp 101\u0026ndash;128. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/B978-0-12-824130-1.00019-9\u003c/span\u003e\u003cspan address=\"10.1016/B978-0-12-824130-1.00019-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMega N, Medjerab A (2016) Study of climatic drought in Algerian high plateaus using standardized precipitation index and MODIS observations. J Appl Remote Sens 10:046002. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1117/1.JRS.10.046002\u003c/span\u003e\u003cspan address=\"10.1117/1.JRS.10.046002\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMellak S, Souag-Gamane D (2020) Spatio-temporal analysis of maximum drought severity using Copulas in Northern Algeria. J Water Clim Change 11:68\u0026ndash;84. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2166/wcc.2020.070\u003c/span\u003e\u003cspan address=\"10.2166/wcc.2020.070\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMerabti A, Darouich H, Paredes P, Meddi M, Pereira LS (2023) Assessing spatial variability and trends of droughts in Eastern Algeria using SPI, RDI, PDSI, and MedPDSI. Water 15:626. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/w15040626\u003c/span\u003e\u003cspan address=\"10.3390/w15040626\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNedjraoui D, B\u0026eacute;drani S (2008) : La d\u0026eacute;sertification dans les steppes alg\u0026eacute;riennes: Causes, impacts et actions de lutte. VertigO, 8. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://journals.openedition.org/vertigo/5375\u003c/span\u003e\u003cspan address=\"http://journals.openedition.org/vertigo/5375\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNekkacheGhenim A, Megnounif A (2011) Caract\u0026eacute;risation de la s\u0026eacute;cheresse par les indices SPI et SSFI (Nord-Ouest de l\u0026rsquo;Alg\u0026eacute;rie). LJEE 18:59\u0026ndash;67\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRezzoug C, Merzougui T, Bouchiba A (2025) Wastewater treatment technologies and challenges in Algeria and their future prospects. Discover Sustain 6:884. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s43621-025-01731-7\u003c/span\u003e\u003cspan address=\"10.1007/s43621-025-01731-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTramblay Y, Adlouni SE, Servat E (2013) Trends and variability in extreme precipitation indices over Maghreb countries. Nat Hazards Earth Syst Sci 13:3235\u0026ndash;3248. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5194/nhess-13-3235-2013\u003c/span\u003e\u003cspan address=\"10.5194/nhess-13-3235-2013\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWilhite DA, Glantz MH (1985) Understanding the drought phenomenon: The role of definitions. Water Int 10:111\u0026ndash;120\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWorld Meteorological Organization (2012) : \u003cem\u003eStandardized Precipitation Index User Guide\u003c/em\u003e. WMO-No. 1090\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYahiaoui A, Toua\u0026iuml;bia B, Bouvier C (2009) Frequency analysis of the hydrological drought regime: Case of Oued Mina catchment in western Algeria. Revue Nat et Technologie 1:3\u0026ndash;15. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://asjp.cerist.dz/en/article/41191\u003c/span\u003e\u003cspan address=\"https://asjp.cerist.dz/en/article/41191\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZiari A, Medjerab A (2024) Impact of drought in Northeastern Algeria: Comparative study of the SPI and SPEI indices. Revista de Gest\u0026atilde;o \u0026ndash; RGSA 18:e06591. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.24857/rgsa.v18n9-078\u003c/span\u003e\u003cspan address=\"10.24857/rgsa.v18n9-078\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Extreme Value Theory, Meteorological Drought, Fréchet Distribution, Standardized Precipitation Index, North-West Algeria","lastPublishedDoi":"10.21203/rs.3.rs-9204781/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9204781/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe 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\u0026ndash;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\u0026thinsp;=\u0026thinsp;0.2843), which indicates a heavy-tailed Fr\u0026eacute;chet 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 \u0026le; -2.001) formally crosses the threshold for an extreme event. Furthermore, the occurrence of an observed drought (SPI-3 \u0026le; -2.155) more severe than the calculated 100-year return level (SPI-3 \u0026le; -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.\u003c/p\u003e","manuscriptTitle":"Extreme Value Analysis of Meteorological Drought in Tlemcen, North-West Algeria: Evidence of a Heavy-Tailed Fréchet Distribution Using the SPI-3 Index","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-31 19:26:24","doi":"10.21203/rs.3.rs-9204781/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8643faee-ce53-47c3-acc6-332f85ab35c0","owner":[],"postedDate":"March 31st, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Rejected","date":"2026-04-29T18:37:02+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-29T18:53:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-31 19:26:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9204781","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9204781","identity":"rs-9204781","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}