Statistical Perspectives on Mediterranean Precipitation: Power-Law Insights in Hydro-Climatology

Statistical Perspectives on Mediterranean Precipitation: Power-Law Insights in Hydro-Climatology | 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 Statistical Perspectives on Mediterranean Precipitation: Power-Law Insights in Hydro-Climatology Hasan TATLI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6177610/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract This study investigates precipitation variability across the Mediterranean Basin (MB) with a specific focus on power-law relationships as a framework for understanding climatological patterns. Using National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR) reanalysis monthly data from 1990 to 2024, the research employs statistical analyses and clustering techniques to unravel the spatial and temporal complexities of precipitation in the region. The findings highlight a strong power-law relationship between mean precipitation and its standard deviation, with an R² value of 0.75 demonstrating high explanatory power. This relationship indicates that variability increases nonlinearly with mean rainfall. This scaling behavior highlights how regions with higher precipitation experience greater absolute variability but proportionally less relative fluctuation. Such insights offer a quantitative framework for understanding precipitation dynamics in the MB and their dependence on climatic and physical geographic factors. The spatial analysis reveals a pronounced north-south gradient in precipitation distribution. Northern regions, influenced by orographic effects, receive annual precipitation exceeding 900 mm, while southern areas, dominated by subtropical high-pressure systems, often receive less than 300 mm. The study identifies seven distinct precipitation regimes through k-means clustering, with regimes varying in mean precipitation, variability, and skewness. Coastal clusters exhibit intermediate precipitation characteristics shaped by mesoscale systems, while arid regions display high interannual variability and increased propensity for extreme events. The analysis also shows a positive correlation between skewness and kurtosis. This indicates that regions with asymmetric rainfall distributions are prone to extreme precipitation events. Furthermore, the negative logarithmic relationship between mean precipitation and coefficient of variation (CV%) highlights increased variability in drier areas. Coastal North Africa and the eastern Mediterranean are identified as hotspots for intense, short-duration rainfall due to their elevated skewness values (> 2). This research integrates power-law scaling, statistical variability, and spatial clustering to provide a comprehensive climatological assessment of precipitation in MB. The findings advance our understanding of regional rainfall patterns and offer critical insights for water resource management, disaster risk reduction, and climate adaptation strategies. Climatic Drivers Cluster Analysis Mediterranean NCEP/NCAR Power-Law Precipitation Variability Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. INTRODUCTION The Mediterranean Basin (MB) stands as a quintessential exemplary of climatic complexity, a geographically intricate region spanning the confluence of Europe, Africa, and Asia, where atmospheric, oceanic, and terrestrial processes converge to shape a precipitation regime of exceptional variability and dynamism. This transitional domain, bridging temperate and subtropical latitudes, harbors a diverse spectrum of ecosystems—from the moist, temperate forests of its northern highlands to the parched, arid expanses of its southern desert rendering it a critical nexus of ecological, hydrological, and socio-economic significance (Lionello et al. 2012 ; Mariotti et al. 2015 ). The MB’s precipitation patterns, modulated by an array of multiscale forcing mechanisms, offer a rich proving ground for advancing the science of climate dynamics, a field that has long illuminated the intricate interplay of physical processes governing regional climates. Within the Köppen-Geiger climate classification framework, the MB is predominantly delineated by "Csa" (hot-summer Mediterranean) and "Csb" (warm-summer Mediterranean) regimes, encapsulating a seasonal dichotomy of arid, thermally intense summers juxtaposed against mild, precipitation-rich winters (Kottek et al. 2006 ; Taşoğlu et al. 2024 ). This archetypal characterization, while broadly instructive, masks a profound spatial heterogeneity inherent to the region. Northern montane zones, such as those encompassing the Alps and Balkans, exhibit temperate characteristics with elevated precipitation totals, starkly contrasting the semi-arid and arid conditions that prevail across the southern lowlands of North Africa and the Middle East (Massoud et al. 2020 ). This variability is intricately coupled to the region’s pronounced topographical gradients, which induce localized effects such as orographic precipitation enhancement on windward slopes—where ascending air masses undergo adiabatic cooling and condensation—and pronounced rain-shadow desiccation on leeward descents (Smith, 1979 ). These geophysical interactions underscore the necessity of integrating high-resolution spatial analyses with synoptic-scale atmospheric dynamics to fully elucidate MB’s precipitation climatology, a challenge that lies at the heart of contemporary climate dynamics research. The MB’s precipitation dynamics are distinguished by substantial interannual and decadal variability, a consequence of both intrinsic oscillatory modes within the climate system and extrinsic anthropogenic perturbations, as meticulously documented in global assessments (IPCC, 2021 ). This variability imposes a pressing imperative for a sophisticated understanding of precipitation processes—not merely as an academic pursuit but as a foundational requirement for addressing critical societal challenges, including the optimization of water resource management, the sustenance of agricultural productivity, and the mitigation of hydrometeorological hazards (Rebora et al. 2013 ; Serkendiz et al. 2023 ). Positioned at the interface of temperate and subtropical climate zones, the MB is acutely susceptible to the cascading impacts of anthropogenic climate change, amplifying its status as a pivotal domain for rigorous scientific inquiry (Sarkar, 2022). This susceptibility is further exacerbated by its geographic proximity to regions already grappling with severe hydrological stress, such as parts of North Africa and the eastern Mediterranean, where water scarcity threatens both human livelihoods and ecosystem stability (del Pozo et al. 2019 ; Serkendiz et al. 2023 ). Consequently, the MB serves as a natural laboratory for probing the nonlinear responses of precipitation to climatic forcings, a pursuit that resonates deeply with the objectives of climate dynamics scholarship. Precipitation across the MB exhibits a pronounced spatiotemporal heterogeneity, governed by a multifaceted ensemble of forcing mechanisms that span planetary-scale atmospheric teleconnections, regional topographic influences, and localized mesoscale convective instabilities. A robust north-south gradient dominates the annual precipitation climatology, with northern sectors—such as the Alpine forelands and Balkan highlands—accruing significantly greater totals than the arid expanses of the southern MB, including North Africa and the Levant (Xoplaki et al. 2004 ; Lionello et al. 2012 ). This distribution is temporally modulated, with the preponderance of rainfall concentrated during the boreal winter, driven by the incursion of mid-latitude cyclonic systems and their attendant frontal boundaries, which transport moisture from the Atlantic and Mediterranean Sea (Tramblay and Somot, 2018 ). Orographic forcing emerges as a linchpin of spatial variability, whereby moisture-laden air masses, impinging upon mountain ranges like the Alps, Balkans, and Atlas Mountains, are forced to ascend, triggering adiabatic cooling, condensation, and precipitation amplification on windward slopes (Roe, 2005 ). Conversely, leeward descents engender aridity through foehn-like drying processes, a phenomenon starkly manifest in the rain-shadow zones south of these topographic barriers (Smith, 1979 ; Rotunno et al. 1988 ). These terrain-induced effects, interacting with synoptic-scale flows, generate a mosaic of microclimatic regimes, necessitating advanced analytical frameworks to disentangle their contributions to regional precipitation patterns. Large-scale atmospheric circulation patterns exert a commanding influence over MB precipitation dynamics, with the North Atlantic Oscillation (NAO) serving as a principal modulator of interannual variability across the region (Tatli and Menteş, 2019 ; Jones et al. 2003 ). During its positive phase, characterized by an intensified Azores High and a deepened Icelandic Low, storm tracks are displaced poleward, frequently suppressing precipitation across the MB through enhanced subsidence and reduced cyclonic activity (Trigo et al. 2004 ; Nicault et al. 2008 ). In contrast, the negative NAO phase redirects cyclonic trajectories equatorward, fostering increased moisture advection and rainfall totals across the region. Complementary teleconnection patterns, such as the East Atlantic/Western Russia (EA/WR) pattern and the Arctic Oscillation (AO), further regulate cyclone intensity, frequency, and positioning, amplifying precipitation fluctuations on seasonal to decadal scales (Krichak and Alpert, 2005 ). Beyond these synoptic drivers, mesoscale processes, Including sea-breeze convergence driven by land-sea thermal contrasts and localized convective systems triggered by surface heating—contribute significantly to precipitation variability, particularly along coastal margins and during the summer months (Krichak et al. 2002 ). In summer, the dominance of the subtropical anticyclone generally suppresses widespread precipitation yet permits sporadic convective bursts in the eastern MB and North Africa, fueled by high surface temperatures and atmospheric instability (Galanaki et al. 2018 ). This seasonal oscillation between wintertime frontal precipitation and summertime convective episodes underscores the MB’s climatological intricacy, demanding a nuanced approach to its analysis. The Mediterranean Sea itself functions as a critical thermodynamic regulator, with its surface temperatures (SSTs) modulating the flux of sensible and latent heat into the overlying atmosphere, thereby influencing precipitation processes (Lionello et al. 2012 ). Elevated SSTs enhance convective available potential energy (CAPE), intensifying mesoscale convective systems and facilitating the genesis of Mediterranean cyclones, or "medicanes"—hybrid systems blending tropical and extratropical characteristics—that deliver torrential rainfall and gale-force winds (Emanuel, 2005 ; Miglietta et al. 2019). This oceanic-atmospheric coupling, intertwined with topographic and circulatory influences, necessitates an integrated, multiscale perspective to fully decipher the MB’s precipitation behavior. Compounding these natural dynamics, anthropogenic climate change introduces profound perturbations, with observational evidence indicating a secular decline in mean annual precipitation across the southern and eastern MB, concomitant with rising temperatures and an escalating frequency of extreme hydroclimatic events (IPCC, 2021 ; Diffenbaugh and Giorgi, 2012 ; Zittis et al. 2019 ; Kelley et al. 2015 ). These shifts precipitate more frequent and severe droughts, imperiling water availability, agricultural productivity, and ecosystem integrity across arid subregions (Spinoni et al. 2021 ; Dai, 2011 ). Simultaneously, northern zones experience an intensification of extreme precipitation events, elevating the risks of flash flooding, landslides, and associated socio-economic disruptions (Rebora et al. 2013 ; Mastrantonas et al. 2021 ; Kundzewicz et al. 2014 ; Barredo, 2009 ). Such transformations, driven by poleward displacements of mid-latitude storm tracks, enhanced SST-driven convection, and altered teleconnection phasing, exemplify the nonlinear feedback that climate dynamics seeks to unravel (Trenberth et al. 2003 ; Coumou and Rahmstorf, 2012 ; Shepherd, 2014 ; Collins et al. 2013 ; Lehmann and Coumou, 2015 ; Pendergrass et al. 2017 ; Pendergrass & Knutti, 2018 ). The field of climate dynamics, as exemplified by the rigorous and transformative scholarship published in Climate Dynamics, has profoundly advanced our understanding of MB precipitation through meticulous observational syntheses, reanalysis datasets, and numerical modeling efforts (e.g., Xoplaki et al. 2004 ; Lionello et al. 2012 ; Tramblay and Somot, 2018 ). These contributions have elucidated the roles of teleconnections, orography, and oceanic influences in shaping regional hydro-climatology, providing a robust foundation upon which this study builds. However, a significant subset of prior analyses has relied on linear statistical frameworks—such as simple regression or anomaly correlations—that may inadequately capture the nonlinear scaling of precipitation variability and extremes, phenomena central to the MB’s response to both natural and anthropogenic forcings (Fatichi et al. 2012 ). Precipitation variability often exhibits power-law behavior, wherein the standard deviation scales nonlinearly with the mean, reflecting the interplay of stochastic processes, convective thresholds, and synoptic forcing—a dynamic that linear models may oversimplify (Koutsoyiannis, 2005 ; Pendergrass and Knutti, 2018 ). This limitation is particularly acute in the MB, where the coexistence of arid, highly variable southern regimes and wetter, orographically modulated northern regimes suggests scale-dependent precipitation characteristics that defy linear assumptions. This investigation seeks to address these gaps by deploying power-law scaling relationships and k-means clustering techniques, integrated with the long-term NCEP/NCAR reanalysis dataset (1990–2024), to probe the nonlinear dynamics of MB precipitation with unprecedented statistical rigor. Our approach builds upon the legacy of Climate Dynamics by extending beyond traditional linear methodologies to uncover the scale-dependent behaviors of precipitation variability, their spatial manifestations, and their physical drivers. Specifically, we hypothesize that precipitation variability follows a power-law relationship with mean precipitation, wherein regions of higher mean rainfall exhibit greater absolute variability but reduced relative fluctuations—a pattern with profound implications for understanding extreme events and climatic resilience. By concerning this analysis with spatial clustering, we aim to delineate distinct precipitation regimes across the MB, linking their statistical properties to underlying climatic and geophysical controls. This dual methodology not only honors the field’s tradition of integrating statistical and physical insights but also pushes the boundaries of hydroclimatic analysis in a region of global significance. Our investigation is structured around the following specific objectives: To analyze the spatial distribution of long-term annual precipitation across MB, employing high-resolution statistical mapping to delineate zones of elevated and diminished precipitation and their geophysical underpinnings. To evaluate an ensemble of statistical metrics—standard deviation, coefficient of variation (CV%), skewness, and kurtosis—to quantify the magnitude, frequency, and asymmetry of precipitation extremes across diverse MB subregions. To explore nonlinear relationships between mean precipitation and variability metrics through power-law scaling, elucidating scale-dependent patterns and their implications for the physical processes governing precipitation dynamics. To apply k-means clustering techniques to identify distinct precipitation regimes, assessing their spatial coherence, statistical signatures, and linkages to topographic and atmospheric drivers. To assess the influence of large-scale atmospheric circulation patterns, notably the NAO, on modulating MB precipitation variability across interannual to decadal timescales, leveraging correlation and composite analyses. To provide quantitative insights into the impacts of climate change on precipitation patterns and extremes, integrating statistical findings with observed trends to inform regionally tailored adaptation strategies. In summary, the MB encapsulates a confluence of climatic, geographic, and atmospheric processes that render its precipitation regimes both exceptionally intricate and acutely responsive to global change. This study builds upon the rich legacy of climate dynamics research, as exemplified by Climate Dynamics, to deploy power-law scaling and spatial clustering in revealing the nonlinear behaviors and regional heterogeneity of MB precipitation. By integrating these cutting-edge statistical methods with a 34-year reanalysis dataset, our investigation seeks to deepen scientific comprehension of scale-dependent precipitation dynamics while offering actionable insights for managing water resources, bolstering agricultural systems, and mitigating disaster risks across this vital region. In doing so, it aims to contribute to the ongoing evolution of climate dynamics as a discipline capable of addressing the complex challenges posed by a warming world. 2. METHODOLOGY AND DATA 2.1 Study Area and Datasets The Mediterranean Basin, spanning approximately 30°N to 45°N latitude and 10°W to 50°E longitude, serves as the primary focus of this study. However, to encompass a broader perspective, the study area has been expanded to extend northward to 60°N, while maintaining the western and eastern boundaries. This expanded region encompasses a wide range of climatic zones, transitioning from the temperate climates of the northern latitudes to the arid conditions prevalent in the southern regions, particularly in the Sahara Desert and parts of the Middle East. Within this diverse landscape, several key geographic features significantly influence regional climate. The northern Mediterranean region is characterized by the presence of the Alpine and Balkan Mountains ranges. These mountainous regions experience notably higher levels of precipitation due to orographic effects, where moisture-laden air masses are forced to ascend the mountain slopes, leading to condensation and subsequent rainfall. In contrast, the southern Mediterranean region is dominated by arid conditions, with minimal precipitation throughout the year. Finally, the coastal zones bordering the Mediterranean Sea experience relatively higher precipitation compared to the inland areas. This increased precipitation is attributed to the proximity of these coastal regions to moisture sources, such as the Mediterranean Sea itself, and the influence of sea breezes. These sea breezes, generated by the differential heating of land and sea, transport moisture inland, contributing to higher precipitation levels along the coast. This comprehensive study of the Mediterranean Basin provides a valuable opportunity to investigate the intricate interplay between climatic gradients and the influence of both local and large-scale atmospheric processes. The methodology and data employed in this study, as detailed in subsequent sections, provides a robust foundation for a thorough analysis of precipitation variability and its underlying driving factors across this diverse and dynamic region. The utilization of sophisticated statistical techniques and a high-resolution reanalysis dataset ensures that the findings of this study offer a robust understanding of precipitation patterns and their contributing factors within the Mediterranean Basin. This study employs a rigorous quantitative methodology to investigate the spatial and temporal precipitation patterns across the Mediterranean Basin. The analysis integrates statistical methods, spatial analysis techniques, and utilizes a comprehensive reanalysis dataset. This section details the data sources, computational methods, and analytical approaches employed in this research. The study utilizes the NCEP/NCAR reanalysis dataset, specifically, the daily atmospheric variables with a spatial resolution of 1.875° by 1.875°, spanning the period from 1990 to 2024. The data is accessed through the National Oceanic and Atmospheric Administration (NOAA) website. This dataset provides a globally gridded representation of atmospheric variables, including precipitation (Kalnay et al. 1996 ). The temporal resolution of the dataset includes monthly aggregated data derived from daily records. Key variables analyzed include monthly mean precipitation, standard deviation, CV%, skewness, and kurtosis. The NCEP/NCAR reanalysis integrates data from various sources, including surface stations, radiosondes, and satellites, using an advanced data-assimilation system to ensure spatiotemporal consistency. It is important to acknowledge the inherent limitations of the utilized data. While the NCEP/NCAR reanalysis dataset provides valuable atmospheric insights, it is subject to biases and uncertainties, particularly in regions with limited observational data coverage, such as North Africa and the Middle East. While robust for broad-scale analyses, this dataset may not capture fine-scale precipitation patterns due to its coarse resolution, particularly in regions with complex topography, such as the Alps and the Atlas Mountains. In addition, the time interval analyzed (1990 to 2024) reflects a period influenced by anthropogenic climate change, and thus observed trends may be a combination of natural variability and climate change impacts, necessitating cautious interpretation of the results. However, the combination of statistical, spatial, and clustering analyses provides a comprehensive assessment of precipitation dynamics across the Mediterranean Basin. 2.2 Methodology To quantify precipitation variability, several statistical metrics were computed. The mean precipitation µ was determined as the arithmetic average of all recorded precipitation values over the analysis period, represented by the following expression: $$\:\mu\:=\left(1/N\right)*\varSigma\:\left(Pᵢ\right)\:$$ 1 where Pᵢ represents the monthly precipitation totals (in mm) and N is the total number of monthly observations over the time period of analysis. The standard deviation σ quantifies the dispersion of precipitation values around the mean, reflecting the extent of variability in precipitation across time, and it is calculated using the formula: $$\:\sigma\:=\sqrt{\left(1/N-1\right)\varSigma\:{\left(Pᵢ-\mu\:\right)}^{2}}$$ 2 The CV% provides a normalized measure of variability, expressed as a percentage of the mean, computed as: $$\:CV\%\:=\:\left(\sigma\:\:/\:\mu\:\right)\:100$$ 3 Skewness (γ 1 ) is employed to measure the asymmetry of the precipitation distribution, calculated using the formula: $$\:{\gamma\:}_{1}=\frac{N}{(N-1)(N-2)}\sum\:{\left(\frac{{P}_{j}-\mu\:}{\sigma\:}\right)}^{3}$$ 4 Positive skewness indicates a longer tail towards higher precipitation values, often associated with extreme events. Kurtosis (γ₂) assesses the “tailedness” of the distribution, with higher kurtosis values pointing to more frequent extreme events and a sharper peak in the distribution. It is calculated using the formula: $$\:{\gamma\:}_{2}=\left\{\frac{N(N-1)}{(N-1)(N-2)(N-3)}\sum\:{\left(\frac{{P}_{j}-\mu\:}{\sigma\:}\right)}^{4}\right\}-\frac{3{\left(N-1\right)}^{4}}{(N-2)(N-3)}$$ 5 Spatial analysis of precipitation patterns was performed using Geographic Information Systems (GIS) tools, facilitating the generation of distribution maps and highlighting spatial gradients such as the influence of coastal proximity, orographic effects, and atmospheric circulation. Scatter plots were utilized to investigate relationships between key variables, including mean precipitation, standard deviation, skewness, and kurtosis. To identify distinct precipitation regimes, the k -means clustering algorithm was applied. This method categorizes the dataset into groups with similar characteristics, enabling a clearer understanding of regional precipitation variability. The optimal number of clusters was determined by the “gap statistic method” (Tibshirani et al. 2001 ), which compares the within-cluster dispersion to a reference distribution and determines the number of clusters for which the increase in within-cluster variance plateaus. The gap statistic ( Gapₖ ) for k clusters is calculated as: $$\:Gapₖ=Enlog\left(Wₖ\right)-log\left(Wₖ\right)$$ 6 where Wₖ is the within-cluster dispersion for k clusters, and E n {log ( Wₖ )} is the expectation under a null hypothesis. The k value for which Gapₖ is the largest with respect to the next k value is then considered the optimal number of clusters. In this study, the gap statistic identified seven distinct clusters. Curve fitting functions, including power-law and quadratic equations, were fitted to quantify relationships between long-term annual precipitation and variability metrics using the scikit-learn (scikit-learn.org) and statsmodels (statsmodels.org) libraries in Python. These models were used to better understand patterns of precipitation and the relative role of climatic mechanisms. 3. RESULTS This section delves into a comprehensive analysis of precipitation patterns across the Mediterranean Basin (MB) utilizing the NCEP/NCAR reanalysis dataset spanning the period 1990–2024. Our findings illuminate the intricate interplay of various factors, including geographic features, atmospheric dynamics, and climatic controls, that collectively shape the spatial and temporal variability of precipitation within this region. Precipitation, being a critical determinant of water availability and a crucial factor influencing the functioning of regional ecosystems, warrants a thorough understanding of its patterns and drivers. To effectively convey these findings, this section incorporates a series of eleven figures. These meticulously crafted visualizations provide a robust and nuanced representation of our results, enabling a deeper understanding of the complex relationships between different factors and their impact on precipitation patterns across the Mediterranean Basin. Through detailed interpretations of these figures, we aim to provide a clear and insightful narrative of the key findings and their implications for the region. This study begins by examining the spatial distribution of long-term annual precipitation across MB, as visualized in Fig. 1 . This map serves as a foundational representation of rainfall patterns, clearly illustrating a north-south gradient in precipitation. The northern regions, notably the Alps and Dinaric Alps, exhibit significantly higher annual precipitation, often exceeding 900 mm. This elevated precipitation is primarily attributed to orographic lifting, where air masses are forced to ascend mountainous terrain, leading to cooling, condensation, and subsequent rainfall (e.g., see Göbel et al. 2023 ). In contrast, the southern MB, encompassing North Africa and the Middle East, experiences significantly lower precipitation, typically below 300 mm. This aridity is primarily due to the dominance of subtropical high-pressure systems, characterized by descending air and suppressed convection. These patterns align with previous observational studies (e.g., see Lin et al. 2022 ) and theoretical analyses of large-scale atmospheric dynamics (e.g., see Giorgi et al. 2021 ). Coastal areas within MB generally exhibit higher precipitation compared to inland regions. This coastal enhancement is attributed to the convergence of sea breezes, driven by differential heating between land and sea, which increases atmospheric instability and promotes precipitation. Figure 1 highlights the north-south precipitation gradient, emphasizing the role of orography and latitude. It is important to note that Fig. 1 represents long-term annual and therefore may not fully capture the considerable temporal variability in rainfall observed across the region. The analysis delves deeper into the relationship between mean precipitation and its variability, as quantified by the standard deviation, as depicted in Fig. 2 . This scatter plot reveals a positive, albeit non-linear, relationship between long-term monthly mean precipitation and its standard deviation. Locations with higher mean precipitation generally exhibit higher standard deviations, indicating greater temporal variability. However, the relative variability (standard deviation divided by mean) tends to decrease with increasing mean precipitation. This observation aligns with previous research findings (e.g., see Gudmundsson et al. 2021). A power-law relationship indicates that precipitation variability increases with mean rainfall, but at a diminishing rate, reflecting complex climate dynamics. This non-linearity reflects the complex nature of rainfall formation, consistent with findings by studies exploring the dynamics of extreme precipitation events (e.g., see Donat et al. 2016 ). Furthermore, the increasing scatter of data points at higher mean precipitation values suggests that rainfall in these regions is likely generated by a diverse array of atmospheric processes, including convective storms, frontal systems, and orographic lifting. This implies that the specific mechanisms driving precipitation can vary significantly between events. These findings emphasize the crucial role of both mean precipitation and its variability in shaping regional climate patterns. The analysis highlights a scale-dependent nature of rainfall variability within the MB, where relatively small changes in mean precipitation can lead to substantial variations in total precipitation amounts, particularly in areas with lower mean values. This suggests that precipitation in drier regions may be characterized by larger interannual fluctuations compared to wetter regions. Figure 7 further corroborates this finding, illustrating a similar power-law relationship between mean annual precipitation and its standard deviation (y = 0.7851x 0.6123 , R² = 0.7497). This consistency across both monthly and annual timescales strongly suggests that the relationship between mean precipitation and variability is a fundamental characteristic of the precipitation regime within the MB. This also implies that the underlying mechanisms influencing this relationship operate across different temporal scales. Notably, the increased dispersion of data points at higher annual precipitation values, mirroring the pattern observed in Fig. 2 , further emphasizes the diverse range of processes contributing to high annual precipitation totals, including large-scale cyclonic activity, mesoscale convective systems, and localized orographic effects. To understand the occurrence of extreme precipitation events, the analysis investigates the spatial distribution of skewness coefficients, presented in Fig. 3 a. Positive skewness values, prevalent across much of the MB, indicate that the tails of the precipitation distributions are skewed towards higher values, making extreme events more likely. Notably, coastal regions of North Africa and parts of the eastern Mediterranean exhibit considerably higher skewness values, suggesting a greater propensity for short periods of intense rainfall. This spatial pattern strongly suggests the influence of localized mesoscale and convective mechanisms, particularly in areas of high surface temperatures and instability, aligning with findings by Galanki et al. (2018) on thunderstorm activity in the eastern Mediterranean. Figure 3 b further elucidates the relationship between skewness coefficients and long-term annual precipitation. This figure demonstrates that the propensity for extreme precipitation is not solely determined by the overall levels of annual rainfall. High skewness values are often observed in areas with relatively low annual rainfall, indicating that factors beyond annual precipitation totals influence the occurrence of extreme events. The contrasting examples of the Alpine region (high annual precipitation, moderate skewness) and coastal North Africa (lower annual rainfall, high skewness) highlight the heterogeneity of precipitation regimes across the MB and the diverse mechanisms driving rainfall formation. Figure 6 , depicting the relationship between skewness and kurtosis in monthly precipitation distributions, provides crucial insights. The strong quadratic relationship (R² = 0.984) between these two parameters underscores the interconnectedness between the asymmetry and tail heaviness of rainfall distributions, consistent with the findings of Wilks ( 2011 ) and von Storch and Zwiers ( 2002 ). This strong correlation suggests a common underlying mechanism driving the formation of extreme precipitation events. The analysis then examines the spatial variability of the CV%, a measure of relative precipitation variability, as shown in Fig. 4 . Arid and semi-arid regions, particularly in North Africa and the Middle East, exhibit high CV% values, indicating high interannual variability. In these regions, the timing and amount of rainfall can fluctuate significantly from year to year, posing significant challenges for water management. These results are consistent with the findings of Dai ( 2011 ) and Zittis, et al. ( 2019 ). Conversely, northern and coastal regions generally show lower CV% values, implying a more consistent precipitation regime. Figure 5 shows a negative logarithmic relationship between mean annual precipitation and CV% (y = -48.13ln(x) + 270.42, R² = 0.837), This figure further illustrates the findings from Fig. 4 . This means that as precipitation increases, the relative variability of rainfall tends to decrease. This negative correlation is consistent with the findings of Koutsoyiannis (2006). Furthermore, the stabilization of CV% values at higher mean precipitation levels indicates that areas with more rainfall have comparatively lower variability, and that they also tend to be more consistent from year to year. This underscores the dual nature of precipitation in the MB, with lower mean rainfall and more unpredictable patterns in the south, compared with the more consistent and higher rainfall amounts in the north. This result underscores the dual nature of precipitation variability in the MB and further confirms that wetter areas tend to have more predictable rainfall. To further elucidate these findings, we turn to Fig. 8 , which shows the relationship between skewness and CV%, which shows that locations with higher skewness also tend to show higher CV%, further reinforcing the idea that areas subject to extreme events are also subject to highly erratic rainfall amounts across time. This finding also demonstrates that the processes that tend to increase variability also tend to increase the tendency toward extreme events, which shows how these two characteristics are linked in the MB. As described by von Storch and Zwiers ( 2002 ), the CV% and skewness is both important aspects of precipitation, and that these two are linked by the underlying physical and climatic mechanisms. The interpretation of Figs. 4 , 5 , and 8 , together highlights the need to evaluate both average conditions, the variability of rainfall, and the tendency towards extreme events as different, but related, aspects of a full analysis of regional climate in the MB. To conclude, we bring together the analysis of skewness and kurtosis with a spatial representation of distinct precipitation regimes, using Fig. 9 , Fig. 10 , and Fig. 11 . In Fig. 9 , the quadratic relationship between skewness and kurtosis (y = 1.3004 x ² + 0.4047 x − 0.7592, R² = 0.984), which underscores that locations with extreme precipitation events also tend to have longer tails in their distributions, and it highlights the role of extremes in shaping the statistical attributes of precipitation. Building upon this understanding, we use Fig. 10 to justify our clustering approach by illustrating the results of the gap statistic method, which identified 7 as the optimal number of clusters. These results provide a statistical basis for the analysis of the precipitation regimes, and to then produce the spatially explicit visualization in Fig. 11 . Figure 11 , which shows the spatial distribution of the seven distinct precipitation clusters that were identified using a k-means clustering algorithm, can be understood as a synthesis of the various precipitation characteristics that we have analyzed up until this point. This map integrates findings from previous figures and reveals that spatial variability in precipitation is not simply determined by latitude. The northern clusters, which are distributed across the Alps, Balkans, and parts of Turkey, are characterized by high mean precipitation (as shown in Fig. 1 ), relatively low interannual variability (as shown in Fig. 4 ), and moderate skewness values (as seen in Fig. 3 a and 3 b). This is consistent with the understanding that precipitation in these areas is strongly influenced by synoptic-scale atmospheric systems, such as mid-latitude cyclones, and the orographic lifting of air masses over complex terrain, as shown in Lionello et al. ( 2012 ). In these regions, precipitation is more consistent and reliable, and less prone to short periods of intense rainfall. The southern clusters, spanning North Africa and the Middle East, exhibit low mean precipitation (as seen in Fig. 1 ), high interannual variability (as shown in Fig. 4 ), and high skewness values (as shown in Fig. 3 a and 3 b), with the relationship between these aspects further characterized by the quadratic form shown in Fig. 9 . This shows that rainfall is not only lower in the south, but also more sporadic and prone to extreme events. The main underlying physical mechanisms that generate this rainfall regime are convective processes and the influence of subtropical high-pressure systems (Galanaki et al. 2018 ). Finally, coastal clusters exhibit intermediate characteristics, influenced by the interaction of sea-breeze convergence, orographic effects, and mesoscale cyclonic systems. The gradient of rainfall and variability between the coastal regions, the north, and the south are further corroborated by Fig. 5 , which shows the relationship between mean precipitation and CV%. In total, Fig. 11 reveals that the underlying dynamics of precipitation in MB are regionally distinct, and they are a result of multiple climate mechanisms. Overall, this underscores the need for localized approaches to adaptation and planning. This comprehensive analysis of Fig. 11 , when combined with all the other results, underscores the complex spatial and temporal patterns in MB, and it demonstrates the interplay of geographical, atmospheric, and climatic factors, including the effects of large-scale circulation and local thermodynamic systems. 4. CONCLUSIONS This study provides a comprehensive analysis of precipitation patterns across the MB, utilizing the NCEP/NCAR reanalysis dataset from 1990 to 2024. Acknowledging the inherent limitations of the reanalysis data, including potential biases and uncertainties, the study provides valuable insights into the spatial and temporal dynamics of precipitation within this complex region. A key finding is the stark contrast in precipitation patterns between the mountainous north, influenced by orographic effects, and the arid south, dominated by subtropical high-pressure systems. The north, characterized by mountainous terrain, experiences higher annual precipitation due to orographic lifting, while the south, dominated by arid conditions, receives significantly less rainfall. Coastal regions, influenced by sea breezes and cyclonic activity, exhibit higher precipitation compared to inland areas. The analysis reveals crucial relationships between mean precipitation and its variability. A power-law relationship was observed between mean precipitation and standard deviation, indicating that while variability increases with mean precipitation, it does so at a decreasing rate. This non-linearity suggests that the underlying mechanisms driving precipitation variability may exhibit scale-dependent behavior. For instance, in regions with lower mean precipitation, small changes in the mean may have a more pronounced effect on variability compared to regions with higher mean precipitation. This observation has significant implications for understanding the dynamics of extreme events and their potential impacts. Furthermore, the analysis highlights the prevalence of extreme precipitation events, particularly in regions with high skewness values, such as coastal areas of North Africa and the eastern Mediterranean. These regions are more prone to intense, short-duration rainfall events, emphasizing the need for robust flood risk management strategies. The study also demonstrates a strong inverse relationship between long-term annual precipitation and CV%, indicating that regions with lower average rainfall exhibit higher interannual precipitation variability. This finding underscores the vulnerability of drier regions to water-scarcity and highlights the need for effective water resource management strategies in these areas. This inverse relationship aligns with contemporary research on hydrological extremes (e.g., see Xiong and Yang, 2024 ), which emphasizes the importance of understanding the interplay between different aspects of precipitation variability, including extreme events (e.g., see Donat et al. 2016 ). Finally, the application of clustering techniques identified seven distinct precipitation regimes, each characterized by unique spatial and temporal patterns. For instance, coastal clusters exhibit intermediate precipitation influenced by sea breezes, while southern clusters are characterized by high variability and arid conditions. These clusters reflect the influence of diverse climatic and geographic factors, including Atlantic cyclones, subtropical air masses, and convective activity. This study highlights the critical need to evaluate spatial and temporal precipitation variability for effective regional planning, including extreme events, when assessing regional climate within the MB. The findings have significant implications for water resource management, agriculture, and ecosystem health across the Mediterranean region. Future studies could explore higher-resolution datasets, socio-economic impacts, and predictive modeling of extreme events. Declarations Conflicts of Interest The author declares no conflicts of interest Ethical Approval Not Applicable. Consent to Publish Not Applicable. Consent to Publish Not applicable. Funding The author declares that no funds, grants, or other support were received during the preparation of this manuscript. Author Contributions H. 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International Journal of Climatology , 24 (8), 925-944. Türkeş, M., & Tatlı, H. (2011). Use of the spectral clustering to determine coherent precipitation regions in Turkey for the period 1929–2007. International Journal of Climatology , 31 (14), 2055-2067. Vicente-Serrano, S. M., Quiring, S. M., Peña-Gallardo, M., Yuan, S., & Domínguez-Castro, F. (2020). A review of environmental droughts: Increased risk under global warming? Earth-Science Reviews , 201 , 102953. Von Storch, H., & Zwiers, F. W. (2002). Statistical Analysis in Climate Research . Cambridge University Press. Wilks, D. S. (2011). Statistical Methods in the Atmospheric Sciences . Academic press. Xiong, J., & Yang, Y. (2024). Climate Change and Hydrological Extremes. Current Climate Change Reports , 11 (1), 1. Xoplaki, E., González-Rouco, J. F., Luterbacher, J., & Wanner, H. (2004). Wet season Mediterranean precipitation variability: influence of large-scale dynamics and trends. Climate dynamics , 23 , 63-78. Zittis, G., Hadjinicolaou, P., Klangidou, M., Proestos, Y., & Lelieveld, J. (2019). A multi-model, multi-scenario, and multi-domain analysis of regional climate projections for the Mediterranean. Regional Environmental Change , 19 (8), 2621-2635. Cite Share Download PDF Status: Under Review Version 1 posted Editor invited by journal 05 Mar, 2026 Reviewers agreed at journal 02 Apr, 2025 Reviewers invited by journal 02 Apr, 2025 Editor assigned by journal 09 Mar, 2025 First submitted to journal 07 Mar, 2025 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. 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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-6177610","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":437415057,"identity":"eea429e1-20c0-4ec5-b4a2-74e200fa79d6","order_by":0,"name":"Hasan TATLI","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtklEQVRIiWNgGAWjYHACxgMJFVAmDzHqeRiYGQ4knEFokSBOC2MbKVrs2c8fOPBwnp2c7owExgdv2xjqzBsI2cKTzHAgcVuysdmNBGbDuW0MEjIHCDoMrAWIbiSwSfMCtRB0GQ//Y6CWOWAt7L+J0yIBsqUBYgszcVpuPDY4kHAM6JczD5sl55yTkJxBSAt7f+LDhz9q7OTMjicf/PCmzIafcCgjAGMDAzHRMgpGwSgYBaOACAAAP5w75lgOHioAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-1960-0618","institution":"Çanakkale Onsekiz Mart University: Canakkale Onsekiz Mart Universitesi","correspondingAuthor":true,"prefix":"","firstName":"Hasan","middleName":"","lastName":"TATLI","suffix":""}],"badges":[],"createdAt":"2025-03-07 10:56:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6177610/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6177610/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81254613,"identity":"76fd31eb-7466-478e-9617-c347ea76b00c","added_by":"auto","created_at":"2025-04-24 04:10:29","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":99922,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distribution of long-term annual precipitation (1990–2024): This map shows the variation in annual precipitation across the Mediterranean Basin, derived from NCEP/NCAR reanalysis data. It emphasizes the regional differences in precipitation patterns.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/815c741d66fd74809b33d332.jpg"},{"id":81255734,"identity":"99e1d6a7-e26d-4442-ba56-bca918cc6441","added_by":"auto","created_at":"2025-04-24 04:26:29","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":45361,"visible":true,"origin":"","legend":"\u003cp\u003eThe relationship between long-term monthly mean precipitation and standard deviation: This scatter plot demonstrates the power-law relationship between monthly mean precipitation and its variability. The analysis shows that variability increases with higher precipitation levels, but at a diminishing rate, with heteroscedasticity observed at higher precipitation values.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/f84176f8214f6f3a22c404d1.jpg"},{"id":81255064,"identity":"72cf4c07-85e7-44b6-b768-3bce3d75d6c4","added_by":"auto","created_at":"2025-04-24 04:18:29","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":148046,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e Skewness coefficients overlaying long-term annual precipitation patterns: The map illustrates the spatial distribution of skewness coefficients across the Mediterranean Basin. The analysis highlights regions prone to extreme precipitation events, with coastal North Africa and the Eastern Mediterranean displaying the highest skewness values. \u003cstrong\u003e(b)\u003c/strong\u003e Contours of skewness coefficients in green lines and their relation to long-term annual precipitation in black lines: An expanded view showcasing regional differences in precipitation distribution asymmetry, emphasizing the influence of climatic and topographic factors.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/82dfe5c49cac344d1cffd7bd.jpg"},{"id":81254621,"identity":"92477002-30af-43fc-8f4e-b9023e5126a3","added_by":"auto","created_at":"2025-04-24 04:10:29","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":139123,"visible":true,"origin":"","legend":"\u003cp\u003eCoefficient of variation CV% of annual precipitation: This map shows spatial variability in CV% across the Mediterranean Basin. Arid regions demonstrate high interannual variability, whereas northern and coastal areas exhibit more stable precipitation patterns.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/9c9701b623b2bf5906ac3a51.jpg"},{"id":81254620,"identity":"46239f17-e654-4981-bba9-d04a8011ba9b","added_by":"auto","created_at":"2025-04-24 04:10:29","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":42880,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between mean annual precipitation and coefficient of variation: This scatter plot shows a logarithmic decline in CV% as mean precipitation increases. The analysis highlights greater variability in arid regions and stabilization in wetter zones.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/ea23d8e90c08442cc1076db2.jpg"},{"id":81255069,"identity":"44ba66ee-976c-41c3-8ef8-ffddffade774","added_by":"auto","created_at":"2025-04-24 04:18:29","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":45845,"visible":true,"origin":"","legend":"\u003cp\u003eThe relationship between skewness and kurtosis of monthly precipitation distributions: A scatter plot illustrating a strong quadratic relationship, where higher skewness is associated with increased kurtosis. The findings suggest that extreme precipitation events play a key role in shaping the distribution tails.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/474ff21840f2987dfdd8d5b0.jpg"},{"id":81255951,"identity":"be566d6b-b4e8-4687-92d8-57c6a2bbe333","added_by":"auto","created_at":"2025-04-24 04:34:29","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":49306,"visible":true,"origin":"","legend":"\u003cp\u003ePower-law relationship between long-term annual precipitation and standard deviation: A scatter plot showing variability scaling with long-term annual precipitation. The results highlight the nonlinear nature of precipitation variability and the influence of climatic mechanisms.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/6eed169dc02442ddf24ded25.jpg"},{"id":81255068,"identity":"87c440f3-fe29-4b3c-ae78-f299321141df","added_by":"auto","created_at":"2025-04-24 04:18:29","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":34603,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between skewness and coefficient of variation (CV%): The scatter plot demonstrates the quadratic relationship between skewness and CV%, highlighting increased variability in regions with highly asymmetric precipitation distributions.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/69dbce5c2227cf455f6f19ce.jpg"},{"id":81255737,"identity":"14235cd9-f24a-4aca-bcdc-59adf952a284","added_by":"auto","created_at":"2025-04-24 04:26:29","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":37996,"visible":true,"origin":"","legend":"\u003cp\u003eQuadratic relationship between skewness and kurtosis of monthly total precipitation: This scatter plot demonstrates the strong correlation between skewness and kurtosis. The results highlight the influence of asymmetric precipitation distributions on the occurrence of extreme rainfall events in the Mediterranean Basin.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/4c5b746ed4d2e7b5e666fdeb.jpg"},{"id":81254623,"identity":"50a9aa83-dc2d-41c6-94d7-b647773852c4","added_by":"auto","created_at":"2025-04-24 04:10:29","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":33663,"visible":true,"origin":"","legend":"\u003cp\u003eDetermination of the optimal number of clusters for the analytical framework based on the gap statistic method: This method compares the observed within-cluster dispersion to that expected under a null reference distribution, providing a robust criterion for cluster validation. The analysis identifies seven clusters as the most suitable configuration.\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/31f224aca5ab8bafd67cde28.jpg"},{"id":81254626,"identity":"bffbbf7b-02a1-4b40-a127-5fefb75c285c","added_by":"auto","created_at":"2025-04-24 04:10:29","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":138843,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distribution of distinct monthly precipitation clusters across the Mediterranean Basin: The analysis applied the k-means clustering method using NCEP/NCAR Reanalysis data from 1990 to 2024. Larger, red-colored numbers within the clusters enhance the visual ordering of the cluster groups. This figure visually represents the spatial patterns of monthly precipitation variability within the Mediterranean region.\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/d12086de57f240772a73ce40.jpg"},{"id":81256185,"identity":"cca314b6-e0d5-4630-98a0-45dc77fc7348","added_by":"auto","created_at":"2025-04-24 04:42:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1381509,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6177610/v1/3e1b80c9-7d9c-48b7-93a0-4c59ae4297b4.pdf"}],"financialInterests":"","formattedTitle":"Statistical Perspectives on Mediterranean Precipitation: Power-Law Insights in Hydro-Climatology","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003eThe Mediterranean Basin (MB) stands as a quintessential exemplary of climatic complexity, a geographically intricate region spanning the confluence of Europe, Africa, and Asia, where atmospheric, oceanic, and terrestrial processes converge to shape a precipitation regime of exceptional variability and dynamism. This transitional domain, bridging temperate and subtropical latitudes, harbors a diverse spectrum of ecosystems\u0026mdash;from the moist, temperate forests of its northern highlands to the parched, arid expanses of its southern desert rendering it a critical nexus of ecological, hydrological, and socio-economic significance (Lionello et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Mariotti et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The MB\u0026rsquo;s precipitation patterns, modulated by an array of multiscale forcing mechanisms, offer a rich proving ground for advancing the science of climate dynamics, a field that has long illuminated the intricate interplay of physical processes governing regional climates.\u003c/p\u003e \u003cp\u003eWithin the K\u0026ouml;ppen-Geiger climate classification framework, the MB is predominantly delineated by \"Csa\" (hot-summer Mediterranean) and \"Csb\" (warm-summer Mediterranean) regimes, encapsulating a seasonal dichotomy of arid, thermally intense summers juxtaposed against mild, precipitation-rich winters (Kottek et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Taşoğlu et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). This archetypal characterization, while broadly instructive, masks a profound spatial heterogeneity inherent to the region. Northern montane zones, such as those encompassing the Alps and Balkans, exhibit temperate characteristics with elevated precipitation totals, starkly contrasting the semi-arid and arid conditions that prevail across the southern lowlands of North Africa and the Middle East (Massoud et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This variability is intricately coupled to the region\u0026rsquo;s pronounced topographical gradients, which induce localized effects such as orographic precipitation enhancement on windward slopes\u0026mdash;where ascending air masses undergo adiabatic cooling and condensation\u0026mdash;and pronounced rain-shadow desiccation on leeward descents (Smith, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1979\u003c/span\u003e). These geophysical interactions underscore the necessity of integrating high-resolution spatial analyses with synoptic-scale atmospheric dynamics to fully elucidate MB\u0026rsquo;s precipitation climatology, a challenge that lies at the heart of contemporary climate dynamics research.\u003c/p\u003e \u003cp\u003eThe MB\u0026rsquo;s precipitation dynamics are distinguished by substantial interannual and decadal variability, a consequence of both intrinsic oscillatory modes within the climate system and extrinsic anthropogenic perturbations, as meticulously documented in global assessments (IPCC, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This variability imposes a pressing imperative for a sophisticated understanding of precipitation processes\u0026mdash;not merely as an academic pursuit but as a foundational requirement for addressing critical societal challenges, including the optimization of water resource management, the sustenance of agricultural productivity, and the mitigation of hydrometeorological hazards (Rebora et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Serkendiz et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Positioned at the interface of temperate and subtropical climate zones, the MB is acutely susceptible to the cascading impacts of anthropogenic climate change, amplifying its status as a pivotal domain for rigorous scientific inquiry (Sarkar, 2022). This susceptibility is further exacerbated by its geographic proximity to regions already grappling with severe hydrological stress, such as parts of North Africa and the eastern Mediterranean, where water scarcity threatens both human livelihoods and ecosystem stability (del Pozo et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Serkendiz et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Consequently, the MB serves as a natural laboratory for probing the nonlinear responses of precipitation to climatic forcings, a pursuit that resonates deeply with the objectives of climate dynamics scholarship.\u003c/p\u003e \u003cp\u003ePrecipitation across the MB exhibits a pronounced spatiotemporal heterogeneity, governed by a multifaceted ensemble of forcing mechanisms that span planetary-scale atmospheric teleconnections, regional topographic influences, and localized mesoscale convective instabilities. A robust north-south gradient dominates the annual precipitation climatology, with northern sectors\u0026mdash;such as the Alpine forelands and Balkan highlands\u0026mdash;accruing significantly greater totals than the arid expanses of the southern MB, including North Africa and the Levant (Xoplaki et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Lionello et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). This distribution is temporally modulated, with the preponderance of rainfall concentrated during the boreal winter, driven by the incursion of mid-latitude cyclonic systems and their attendant frontal boundaries, which transport moisture from the Atlantic and Mediterranean Sea (Tramblay and Somot, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Orographic forcing emerges as a linchpin of spatial variability, whereby moisture-laden air masses, impinging upon mountain ranges like the Alps, Balkans, and Atlas Mountains, are forced to ascend, triggering adiabatic cooling, condensation, and precipitation amplification on windward slopes (Roe, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Conversely, leeward descents engender aridity through foehn-like drying processes, a phenomenon starkly manifest in the rain-shadow zones south of these topographic barriers (Smith, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1979\u003c/span\u003e; Rotunno et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). These terrain-induced effects, interacting with synoptic-scale flows, generate a mosaic of microclimatic regimes, necessitating advanced analytical frameworks to disentangle their contributions to regional precipitation patterns.\u003c/p\u003e \u003cp\u003eLarge-scale atmospheric circulation patterns exert a commanding influence over MB precipitation dynamics, with the North Atlantic Oscillation (NAO) serving as a principal modulator of interannual variability across the region (Tatli and Menteş, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Jones et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). During its positive phase, characterized by an intensified Azores High and a deepened Icelandic Low, storm tracks are displaced poleward, frequently suppressing precipitation across the MB through enhanced subsidence and reduced cyclonic activity (Trigo et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Nicault et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). In contrast, the negative NAO phase redirects cyclonic trajectories equatorward, fostering increased moisture advection and rainfall totals across the region. Complementary teleconnection patterns, such as the East Atlantic/Western Russia (EA/WR) pattern and the Arctic Oscillation (AO), further regulate cyclone intensity, frequency, and positioning, amplifying precipitation fluctuations on seasonal to decadal scales (Krichak and Alpert, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Beyond these synoptic drivers, mesoscale processes,\u003c/p\u003e \u003cp\u003eIncluding sea-breeze convergence driven by land-sea thermal contrasts and localized convective systems triggered by surface heating\u0026mdash;contribute significantly to precipitation variability, particularly along coastal margins and during the summer months (Krichak et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). In summer, the dominance of the subtropical anticyclone generally suppresses widespread precipitation yet permits sporadic convective bursts in the eastern MB and North Africa, fueled by high surface temperatures and atmospheric instability (Galanaki et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). This seasonal oscillation between wintertime frontal precipitation and summertime convective episodes underscores the MB\u0026rsquo;s climatological intricacy, demanding a nuanced approach to its analysis.\u003c/p\u003e \u003cp\u003eThe Mediterranean Sea itself functions as a critical thermodynamic regulator, with its surface temperatures (SSTs) modulating the flux of sensible and latent heat into the overlying atmosphere, thereby influencing precipitation processes (Lionello et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Elevated SSTs enhance convective available potential energy (CAPE), intensifying mesoscale convective systems and facilitating the genesis of Mediterranean cyclones, or \"medicanes\"\u0026mdash;hybrid systems blending tropical and extratropical characteristics\u0026mdash;that deliver torrential rainfall and gale-force winds (Emanuel, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Miglietta et al. 2019). This oceanic-atmospheric coupling, intertwined with topographic and circulatory influences, necessitates an integrated, multiscale perspective to fully decipher the MB\u0026rsquo;s precipitation behavior. Compounding these natural dynamics, anthropogenic climate change introduces profound perturbations, with observational evidence indicating a secular decline in mean annual precipitation across the southern and eastern MB, concomitant with rising temperatures and an escalating frequency of extreme hydroclimatic events (IPCC, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Diffenbaugh and Giorgi, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Zittis et al. \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Kelley et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). These shifts precipitate more frequent and severe droughts, imperiling water availability, agricultural productivity, and ecosystem integrity across arid subregions (Spinoni et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Dai, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Simultaneously, northern zones experience an intensification of extreme precipitation events, elevating the risks of flash flooding, landslides, and associated socio-economic disruptions (Rebora et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Mastrantonas et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Kundzewicz et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Barredo, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Such transformations, driven by poleward displacements of mid-latitude storm tracks, enhanced SST-driven convection, and altered teleconnection phasing, exemplify the nonlinear feedback that climate dynamics seeks to unravel (Trenberth et al. \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Coumou and Rahmstorf, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Shepherd, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Collins et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Lehmann and Coumou, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Pendergrass et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Pendergrass \u0026amp; Knutti, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe field of climate dynamics, as exemplified by the rigorous and transformative scholarship published in Climate Dynamics, has profoundly advanced our understanding of MB precipitation through meticulous observational syntheses, reanalysis datasets, and numerical modeling efforts (e.g., Xoplaki et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Lionello et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Tramblay and Somot, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). These contributions have elucidated the roles of teleconnections, orography, and oceanic influences in shaping regional hydro-climatology, providing a robust foundation upon which this study builds. However, a significant subset of prior analyses has relied on linear statistical frameworks\u0026mdash;such as simple regression or anomaly correlations\u0026mdash;that may inadequately capture the nonlinear scaling of precipitation variability and extremes, phenomena central to the MB\u0026rsquo;s response to both natural and anthropogenic forcings (Fatichi et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Precipitation variability often exhibits power-law behavior, wherein the standard deviation scales nonlinearly with the mean, reflecting the interplay of stochastic processes, convective thresholds, and synoptic forcing\u0026mdash;a dynamic that linear models may oversimplify (Koutsoyiannis, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Pendergrass and Knutti, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). This limitation is particularly acute in the MB, where the coexistence of arid, highly variable southern regimes and wetter, orographically modulated northern regimes suggests scale-dependent precipitation characteristics that defy linear assumptions.\u003c/p\u003e \u003cp\u003eThis investigation seeks to address these gaps by deploying power-law scaling relationships and k-means clustering techniques, integrated with the long-term NCEP/NCAR reanalysis dataset (1990\u0026ndash;2024), to probe the nonlinear dynamics of MB precipitation with unprecedented statistical rigor. Our approach builds upon the legacy of Climate Dynamics by extending beyond traditional linear methodologies to uncover the scale-dependent behaviors of precipitation variability, their spatial manifestations, and their physical drivers. Specifically, we hypothesize that precipitation variability follows a power-law relationship with mean precipitation, wherein regions of higher mean rainfall exhibit greater absolute variability but reduced relative fluctuations\u0026mdash;a pattern with profound implications for understanding extreme events and climatic resilience. By concerning this analysis with spatial clustering, we aim to delineate distinct precipitation regimes across the MB, linking their statistical properties to underlying climatic and geophysical controls. This dual methodology not only honors the field\u0026rsquo;s tradition of integrating statistical and physical insights but also pushes the boundaries of hydroclimatic analysis in a region of global significance.\u003c/p\u003e \u003cp\u003eOur investigation is structured around the following specific objectives:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTo analyze the spatial distribution of long-term annual precipitation across MB, employing high-resolution statistical mapping to delineate zones of elevated and diminished precipitation and their geophysical underpinnings.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTo evaluate an ensemble of statistical metrics\u0026mdash;standard deviation, coefficient of variation (CV%), skewness, and kurtosis\u0026mdash;to quantify the magnitude, frequency, and asymmetry of precipitation extremes across diverse MB subregions.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTo explore nonlinear relationships between mean precipitation and variability metrics through power-law scaling, elucidating scale-dependent patterns and their implications for the physical processes governing precipitation dynamics.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTo apply k-means clustering techniques to identify distinct precipitation regimes, assessing their spatial coherence, statistical signatures, and linkages to topographic and atmospheric drivers.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTo assess the influence of large-scale atmospheric circulation patterns, notably the NAO, on modulating MB precipitation variability across interannual to decadal timescales, leveraging correlation and composite analyses.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTo provide quantitative insights into the impacts of climate change on precipitation patterns and extremes, integrating statistical findings with observed trends to inform regionally tailored adaptation strategies.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eIn summary, the MB encapsulates a confluence of climatic, geographic, and atmospheric processes that render its precipitation regimes both exceptionally intricate and acutely responsive to global change. This study builds upon the rich legacy of climate dynamics research, as exemplified by Climate Dynamics, to deploy power-law scaling and spatial clustering in revealing the nonlinear behaviors and regional heterogeneity of MB precipitation. By integrating these cutting-edge statistical methods with a 34-year reanalysis dataset, our investigation seeks to deepen scientific comprehension of scale-dependent precipitation dynamics while offering actionable insights for managing water resources, bolstering agricultural systems, and mitigating disaster risks across this vital region. In doing so, it aims to contribute to the ongoing evolution of climate dynamics as a discipline capable of addressing the complex challenges posed by a warming world.\u003c/p\u003e"},{"header":"2. METHODOLOGY AND DATA","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Study Area and Datasets\u003c/h2\u003e \u003cp\u003eThe Mediterranean Basin, spanning approximately 30\u0026deg;N to 45\u0026deg;N latitude and 10\u0026deg;W to 50\u0026deg;E longitude, serves as the primary focus of this study. However, to encompass a broader perspective, the study area has been expanded to extend northward to 60\u0026deg;N, while maintaining the western and eastern boundaries. This expanded region encompasses a wide range of climatic zones, transitioning from the temperate climates of the northern latitudes to the arid conditions prevalent in the southern regions, particularly in the Sahara Desert and parts of the Middle East.\u003c/p\u003e \u003cp\u003eWithin this diverse landscape, several key geographic features significantly influence regional climate. The northern Mediterranean region is characterized by the presence of the Alpine and Balkan Mountains ranges. These mountainous regions experience notably higher levels of precipitation due to orographic effects, where moisture-laden air masses are forced to ascend the mountain slopes, leading to condensation and subsequent rainfall. In contrast, the southern Mediterranean region is dominated by arid conditions, with minimal precipitation throughout the year.\u003c/p\u003e \u003cp\u003eFinally, the coastal zones bordering the Mediterranean Sea experience relatively higher precipitation compared to the inland areas. This increased precipitation is attributed to the proximity of these coastal regions to moisture sources, such as the Mediterranean Sea itself, and the influence of sea breezes. These sea breezes, generated by the differential heating of land and sea, transport moisture inland, contributing to higher precipitation levels along the coast.\u003c/p\u003e \u003cp\u003eThis comprehensive study of the Mediterranean Basin provides a valuable opportunity to investigate the intricate interplay between climatic gradients and the influence of both local and large-scale atmospheric processes. The methodology and data employed in this study, as detailed in subsequent sections, provides a robust foundation for a thorough analysis of precipitation variability and its underlying driving factors across this diverse and dynamic region. The utilization of sophisticated statistical techniques and a high-resolution reanalysis dataset ensures that the findings of this study offer a robust understanding of precipitation patterns and their contributing factors within the Mediterranean Basin.\u003c/p\u003e \u003cp\u003eThis study employs a rigorous quantitative methodology to investigate the spatial and temporal precipitation patterns across the Mediterranean Basin. The analysis integrates statistical methods, spatial analysis techniques, and utilizes a comprehensive reanalysis dataset. This section details the data sources, computational methods, and analytical approaches employed in this research.\u003c/p\u003e \u003cp\u003eThe study utilizes the NCEP/NCAR reanalysis dataset, specifically, the daily atmospheric variables with a spatial resolution of 1.875\u0026deg; by 1.875\u0026deg;, spanning the period from 1990 to 2024. The data is accessed through the National Oceanic and Atmospheric Administration (NOAA) website. This dataset provides a globally gridded representation of atmospheric variables, including precipitation (Kalnay et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). The temporal resolution of the dataset includes monthly aggregated data derived from daily records. Key variables analyzed include monthly mean precipitation, standard deviation, CV%, skewness, and kurtosis. The NCEP/NCAR reanalysis integrates data from various sources, including surface stations, radiosondes, and satellites, using an advanced data-assimilation system to ensure spatiotemporal consistency.\u003c/p\u003e \u003cp\u003eIt is important to acknowledge the inherent limitations of the utilized data. While the NCEP/NCAR reanalysis dataset provides valuable atmospheric insights, it is subject to biases and uncertainties, particularly in regions with limited observational data coverage, such as North Africa and the Middle East. While robust for broad-scale analyses, this dataset may not capture fine-scale precipitation patterns due to its coarse resolution, particularly in regions with complex topography, such as the Alps and the Atlas Mountains. In addition, the time interval analyzed (1990 to 2024) reflects a period influenced by anthropogenic climate change, and thus observed trends may be a combination of natural variability and climate change impacts, necessitating cautious interpretation of the results. However, the combination of statistical, spatial, and clustering analyses provides a comprehensive assessment of precipitation dynamics across the Mediterranean Basin.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Methodology\u003c/h2\u003e \u003cp\u003eTo quantify precipitation variability, several statistical metrics were computed. The mean precipitation \u0026micro; was determined as the arithmetic average of all recorded precipitation values over the analysis period, represented by the following expression:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\mu\\:=\\left(1/N\\right)*\\varSigma\\:\\left(Pᵢ\\right)\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ePᵢ\u003c/em\u003e represents the monthly precipitation totals (in mm) and \u003cem\u003eN\u003c/em\u003e is the total number of monthly observations over the time period of analysis. The standard deviation σ quantifies the dispersion of precipitation values around the mean, reflecting the extent of variability in precipitation across time, and it is calculated using the formula:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\sigma\\:=\\sqrt{\\left(1/N-1\\right)\\varSigma\\:{\\left(Pᵢ-\\mu\\:\\right)}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe CV% provides a normalized measure of variability, expressed as a percentage of the mean, computed as:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:CV\\%\\:=\\:\\left(\\sigma\\:\\:/\\:\\mu\\:\\right)\\:100$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eSkewness (γ\u003csub\u003e1\u003c/sub\u003e) is employed to measure the asymmetry of the precipitation distribution, calculated using the formula:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\gamma\\:}_{1}=\\frac{N}{(N-1)(N-2)}\\sum\\:{\\left(\\frac{{P}_{j}-\\mu\\:}{\\sigma\\:}\\right)}^{3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ePositive skewness indicates a longer tail towards higher precipitation values, often associated with extreme events. Kurtosis (γ₂) assesses the \u0026ldquo;tailedness\u0026rdquo; of the distribution, with higher kurtosis values pointing to more frequent extreme events and a sharper peak in the distribution. It is calculated using the formula:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\gamma\\:}_{2}=\\left\\{\\frac{N(N-1)}{(N-1)(N-2)(N-3)}\\sum\\:{\\left(\\frac{{P}_{j}-\\mu\\:}{\\sigma\\:}\\right)}^{4}\\right\\}-\\frac{3{\\left(N-1\\right)}^{4}}{(N-2)(N-3)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eSpatial analysis of precipitation patterns was performed using Geographic Information Systems (GIS) tools, facilitating the generation of distribution maps and highlighting spatial gradients such as the influence of coastal proximity, orographic effects, and atmospheric circulation. Scatter plots were utilized to investigate relationships between key variables, including mean precipitation, standard deviation, skewness, and kurtosis. To identify distinct precipitation regimes, the \u003cem\u003ek\u003c/em\u003e-means clustering algorithm was applied. This method categorizes the dataset into groups with similar characteristics, enabling a clearer understanding of regional precipitation variability. The optimal number of clusters was determined by the \u0026ldquo;gap statistic method\u0026rdquo; (Tibshirani et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), which compares the within-cluster dispersion to a reference distribution and determines the number of clusters for which the increase in within-cluster variance plateaus. The gap statistic (\u003cem\u003eGapₖ\u003c/em\u003e) for \u003cem\u003ek\u003c/em\u003e clusters is calculated as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:Gapₖ=Enlog\\left(Wₖ\\right)-log\\left(Wₖ\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eWₖ\u003c/em\u003e is the within-cluster dispersion for \u003cem\u003ek\u003c/em\u003e clusters, and E\u003cem\u003en\u003c/em\u003e {log (\u003cem\u003eWₖ\u003c/em\u003e)} is the expectation under a null hypothesis. The \u003cem\u003ek\u003c/em\u003e value for which \u003cem\u003eGapₖ\u003c/em\u003e is the largest with respect to the next \u003cem\u003ek\u003c/em\u003e value is then considered the optimal number of clusters. In this study, the gap statistic identified seven distinct clusters.\u003c/p\u003e \u003cp\u003eCurve fitting functions, including power-law and quadratic equations, were fitted to quantify relationships between long-term annual precipitation and variability metrics using the \u003cem\u003escikit-learn\u003c/em\u003e (scikit-learn.org) and \u003cem\u003estatsmodels\u003c/em\u003e (statsmodels.org) libraries in Python. These models were used to better understand patterns of precipitation and the relative role of climatic mechanisms.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. RESULTS","content":"\u003cp\u003eThis section delves into a comprehensive analysis of precipitation patterns across the Mediterranean Basin (MB) utilizing the NCEP/NCAR reanalysis dataset spanning the period 1990\u0026ndash;2024. Our findings illuminate the intricate interplay of various factors, including geographic features, atmospheric dynamics, and climatic controls, that collectively shape the spatial and temporal variability of precipitation within this region. Precipitation, being a critical determinant of water availability and a crucial factor influencing the functioning of regional ecosystems, warrants a thorough understanding of its patterns and drivers.\u003c/p\u003e \u003cp\u003eTo effectively convey these findings, this section incorporates a series of eleven figures. These meticulously crafted visualizations provide a robust and nuanced representation of our results, enabling a deeper understanding of the complex relationships between different factors and their impact on precipitation patterns across the Mediterranean Basin. Through detailed interpretations of these figures, we aim to provide a clear and insightful narrative of the key findings and their implications for the region.\u003c/p\u003e \u003cp\u003eThis study begins by examining the spatial distribution of long-term annual precipitation across MB, as visualized in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e. This map serves as a foundational representation of rainfall patterns, clearly illustrating a north-south gradient in precipitation.\u003c/p\u003e \u003cp\u003eThe northern regions, notably the Alps and Dinaric Alps, exhibit significantly higher annual precipitation, often exceeding 900 mm. This elevated precipitation is primarily attributed to orographic lifting, where air masses are forced to ascend mountainous terrain, leading to cooling, condensation, and subsequent rainfall (e.g., see G\u0026ouml;bel et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn contrast, the southern MB, encompassing North Africa and the Middle East, experiences significantly lower precipitation, typically below 300 mm. This aridity is primarily due to the dominance of subtropical high-pressure systems, characterized by descending air and suppressed convection. These patterns align with previous observational studies (e.g., see Lin et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and theoretical analyses of large-scale atmospheric dynamics (e.g., see Giorgi et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eCoastal areas within MB generally exhibit higher precipitation compared to inland regions. This coastal enhancement is attributed to the convergence of sea breezes, driven by differential heating between land and sea, which increases atmospheric instability and promotes precipitation.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e highlights the north-south precipitation gradient, emphasizing the role of orography and latitude. It is important to note that Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e represents long-term annual and therefore may not fully capture the considerable temporal variability in rainfall observed across the region.\u003c/p\u003e \u003cp\u003eThe analysis delves deeper into the relationship between mean precipitation and its variability, as quantified by the standard deviation, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e. This scatter plot reveals a positive, albeit non-linear, relationship between long-term monthly mean precipitation and its standard deviation.\u003c/p\u003e \u003cp\u003eLocations with higher mean precipitation generally exhibit higher standard deviations, indicating greater temporal variability. However, the relative variability (standard deviation divided by mean) tends to decrease with increasing mean precipitation. This observation aligns with previous research findings (e.g., see Gudmundsson et al. 2021).\u003c/p\u003e \u003cp\u003eA power-law relationship indicates that precipitation variability increases with mean rainfall, but at a diminishing rate, reflecting complex climate dynamics. This non-linearity reflects the complex nature of rainfall formation, consistent with findings by studies exploring the dynamics of extreme precipitation events (e.g., see Donat et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFurthermore, the increasing scatter of data points at higher mean precipitation values suggests that rainfall in these regions is likely generated by a diverse array of atmospheric processes, including convective storms, frontal systems, and orographic lifting. This implies that the specific mechanisms driving precipitation can vary significantly between events.\u003c/p\u003e \u003cp\u003eThese findings emphasize the crucial role of both mean precipitation and its variability in shaping regional climate patterns. The analysis highlights a scale-dependent nature of rainfall variability within the MB, where relatively small changes in mean precipitation can lead to substantial variations in total precipitation amounts, particularly in areas with lower mean values. This suggests that precipitation in drier regions may be characterized by larger interannual fluctuations compared to wetter regions.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e7\u003c/span\u003e further corroborates this finding, illustrating a similar power-law relationship between mean annual precipitation and its standard deviation (y\u0026thinsp;=\u0026thinsp;0.7851x\u003csup\u003e0.6123\u003c/sup\u003e, R\u0026sup2; = 0.7497). This consistency across both monthly and annual timescales strongly suggests that the relationship between mean precipitation and variability is a fundamental characteristic of the precipitation regime within the MB. This also implies that the underlying mechanisms influencing this relationship operate across different temporal scales. Notably, the increased dispersion of data points at higher annual precipitation values, mirroring the pattern observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e, further emphasizes the diverse range of processes contributing to high annual precipitation totals, including large-scale cyclonic activity, mesoscale convective systems, and localized orographic effects.\u003c/p\u003e \u003cp\u003eTo understand the occurrence of extreme precipitation events, the analysis investigates the spatial distribution of skewness coefficients, presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003ea. Positive skewness values, prevalent across much of the MB, indicate that the tails of the precipitation distributions are skewed towards higher values, making extreme events more likely. Notably, coastal regions of North Africa and parts of the eastern Mediterranean exhibit considerably higher skewness values, suggesting a greater propensity for short periods of intense rainfall. This spatial pattern strongly suggests the influence of localized mesoscale and convective mechanisms, particularly in areas of high surface temperatures and instability, aligning with findings by Galanki et al. (2018) on thunderstorm activity in the eastern Mediterranean.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003eb further elucidates the relationship between skewness coefficients and long-term annual precipitation. This figure demonstrates that the propensity for extreme precipitation is not solely determined by the overall levels of annual rainfall. High skewness values are often observed in areas with relatively low annual rainfall, indicating that factors beyond annual precipitation totals influence the occurrence of extreme events. The contrasting examples of the Alpine region (high annual precipitation, moderate skewness) and coastal North Africa (lower annual rainfall, high skewness) highlight the heterogeneity of precipitation regimes across the MB and the diverse mechanisms driving rainfall formation.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e6\u003c/span\u003e, depicting the relationship between skewness and kurtosis in monthly precipitation distributions, provides crucial insights. The strong quadratic relationship (R\u0026sup2; = 0.984) between these two parameters underscores the interconnectedness between the asymmetry and tail heaviness of rainfall distributions, consistent with the findings of Wilks (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) and von Storch and Zwiers (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). This strong correlation suggests a common underlying mechanism driving the formation of extreme precipitation events.\u003c/p\u003e \u003cp\u003eThe analysis then examines the spatial variability of the CV%, a measure of relative precipitation variability, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Arid and semi-arid regions, particularly in North Africa and the Middle East, exhibit high CV% values, indicating high interannual variability. In these regions, the timing and amount of rainfall can fluctuate significantly from year to year, posing significant challenges for water management. These results are consistent with the findings of Dai (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) and Zittis, et al. (\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Conversely, northern and coastal regions generally show lower CV% values, implying a more consistent precipitation regime.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows a negative logarithmic relationship between mean annual precipitation and CV% (y = -48.13ln(x)\u0026thinsp;+\u0026thinsp;270.42, R\u0026sup2; = 0.837), This figure further illustrates the findings from Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e. This means that as precipitation increases, the relative variability of rainfall tends to decrease. This negative correlation is consistent with the findings of Koutsoyiannis (2006). Furthermore, the stabilization of CV% values at higher mean precipitation levels indicates that areas with more rainfall have comparatively lower variability, and that they also tend to be more consistent from year to year. This underscores the dual nature of precipitation in the MB, with lower mean rainfall and more unpredictable patterns in the south, compared with the more consistent and higher rainfall amounts in the north. This result underscores the dual nature of precipitation variability in the MB and further confirms that wetter areas tend to have more predictable rainfall.\u003c/p\u003e \u003cp\u003eTo further elucidate these findings, we turn to Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e8\u003c/span\u003e, which shows the relationship between skewness and CV%, which shows that locations with higher skewness also tend to show higher CV%, further reinforcing the idea that areas subject to extreme events are also subject to highly erratic rainfall amounts across time. This finding also demonstrates that the processes that tend to increase variability also tend to increase the tendency toward extreme events, which shows how these two characteristics are linked in the MB. As described by von Storch and Zwiers (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), the CV% and skewness is both important aspects of precipitation, and that these two are linked by the underlying physical and climatic mechanisms. The interpretation of Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e, \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e, and \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e8\u003c/span\u003e, together highlights the need to evaluate both average conditions, the variability of rainfall, and the tendency towards extreme events as different, but related, aspects of a full analysis of regional climate in the MB.\u003c/p\u003e \u003cp\u003eTo conclude, we bring together the analysis of skewness and kurtosis with a spatial representation of distinct precipitation regimes, using Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e9\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e10\u003c/span\u003e, and Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e11\u003c/span\u003e. In Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the quadratic relationship between skewness and kurtosis (y\u0026thinsp;=\u0026thinsp;1.3004\u003cem\u003ex\u003c/em\u003e\u0026sup2; + 0.4047\u003cem\u003ex\u003c/em\u003e \u0026minus;\u0026thinsp;0.7592, R\u0026sup2; = 0.984), which underscores that locations with extreme precipitation events also tend to have longer tails in their distributions, and it highlights the role of extremes in shaping the statistical attributes of precipitation. Building upon this understanding, we use Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e10\u003c/span\u003e to justify our clustering approach by illustrating the results of the gap statistic method, which identified 7 as the optimal number of clusters. These results provide a statistical basis for the analysis of the precipitation regimes, and to then produce the spatially explicit visualization in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e11\u003c/span\u003e, which shows the spatial distribution of the seven distinct precipitation clusters that were identified using a k-means clustering algorithm, can be understood as a synthesis of the various precipitation characteristics that we have analyzed up until this point. This map integrates findings from previous figures and reveals that spatial variability in precipitation is not simply determined by latitude. The northern clusters, which are distributed across the Alps, Balkans, and parts of Turkey, are characterized by high mean precipitation (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e), relatively low interannual variability (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e), and moderate skewness values (as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). This is consistent with the understanding that precipitation in these areas is strongly influenced by synoptic-scale atmospheric systems, such as mid-latitude cyclones, and the orographic lifting of air masses over complex terrain, as shown in Lionello et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). In these regions, precipitation is more consistent and reliable, and less prone to short periods of intense rainfall. The southern clusters, spanning North Africa and the Middle East, exhibit low mean precipitation (as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e), high interannual variability (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e), and high skewness values (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), with the relationship between these aspects further characterized by the quadratic form shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e9\u003c/span\u003e. This shows that rainfall is not only lower in the south, but also more sporadic and prone to extreme events. The main underlying physical mechanisms that generate this rainfall regime are convective processes and the influence of subtropical high-pressure systems (Galanaki et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFinally, coastal clusters exhibit intermediate characteristics, influenced by the interaction of sea-breeze convergence, orographic effects, and mesoscale cyclonic systems. The gradient of rainfall and variability between the coastal regions, the north, and the south are further corroborated by Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e, which shows the relationship between mean precipitation and CV%. In total, Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e11\u003c/span\u003e reveals that the underlying dynamics of precipitation in MB are regionally distinct, and they are a result of multiple climate mechanisms. Overall, this underscores the need for localized approaches to adaptation and planning.\u003c/p\u003e \u003cp\u003eThis comprehensive analysis of Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e11\u003c/span\u003e, when combined with all the other results, underscores the complex spatial and temporal patterns in MB, and it demonstrates the interplay of geographical, atmospheric, and climatic factors, including the effects of large-scale circulation and local thermodynamic systems.\u003c/p\u003e"},{"header":"4. CONCLUSIONS","content":"\u003cp\u003eThis study provides a comprehensive analysis of precipitation patterns across the MB, utilizing the NCEP/NCAR reanalysis dataset from 1990 to 2024. Acknowledging the inherent limitations of the reanalysis data, including potential biases and uncertainties, the study provides valuable insights into the spatial and temporal dynamics of precipitation within this complex region.\u003c/p\u003e \u003cp\u003eA key finding is the stark contrast in precipitation patterns between the mountainous north, influenced by orographic effects, and the arid south, dominated by subtropical high-pressure systems. The north, characterized by mountainous terrain, experiences higher annual precipitation due to orographic lifting, while the south, dominated by arid conditions, receives significantly less rainfall. Coastal regions, influenced by sea breezes and cyclonic activity, exhibit higher precipitation compared to inland areas.\u003c/p\u003e \u003cp\u003eThe analysis reveals crucial relationships between mean precipitation and its variability. A power-law relationship was observed between mean precipitation and standard deviation, indicating that while variability increases with mean precipitation, it does so at a decreasing rate. This non-linearity suggests that the underlying mechanisms driving precipitation variability may exhibit scale-dependent behavior. For instance, in regions with lower mean precipitation, small changes in the mean may have a more pronounced effect on variability compared to regions with higher mean precipitation. This observation has significant implications for understanding the dynamics of extreme events and their potential impacts.\u003c/p\u003e \u003cp\u003eFurthermore, the analysis highlights the prevalence of extreme precipitation events, particularly in regions with high skewness values, such as coastal areas of North Africa and the eastern Mediterranean. These regions are more prone to intense, short-duration rainfall events, emphasizing the need for robust flood risk management strategies.\u003c/p\u003e \u003cp\u003eThe study also demonstrates a strong inverse relationship between long-term annual precipitation and CV%, indicating that regions with lower average rainfall exhibit higher interannual precipitation variability. This finding underscores the vulnerability of drier regions to water-scarcity and highlights the need for effective water resource management strategies in these areas. This inverse relationship aligns with contemporary research on hydrological extremes (e.g., see Xiong and Yang, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), which emphasizes the importance of understanding the interplay between different aspects of precipitation variability, including extreme events (e.g., see Donat et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFinally, the application of clustering techniques identified seven distinct precipitation regimes, each characterized by unique spatial and temporal patterns. For instance, coastal clusters exhibit intermediate precipitation influenced by sea breezes, while southern clusters are characterized by high variability and arid conditions. These clusters reflect the influence of diverse climatic and geographic factors, including Atlantic cyclones, subtropical air masses, and convective activity.\u003c/p\u003e \u003cp\u003eThis study highlights the critical need to evaluate spatial and temporal precipitation variability for effective regional planning, including extreme events, when assessing regional climate within the MB. The findings have significant implications for water resource management, agriculture, and ecosystem health across the Mediterranean region. Future studies could explore higher-resolution datasets, socio-economic impacts, and predictive modeling of extreme events.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of Interest\u003c/h2\u003e \u003cp\u003eThe author declares no conflicts of interest\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eEthical Approval\u003c/h2\u003e \u003cp\u003eNot Applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to Publish\u003c/strong\u003e \u003cp\u003eNot Applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to Publish\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThe author declares that no funds, grants, or other support were received during the preparation of this manuscript.\u003c/p\u003e\u003ch2\u003eAuthor Contributions\u003c/h2\u003e \u003cp\u003eH. TATLI independently executed all phases of this research as the sole investigator, encompassing the conceptualization of the study, preparation of materials, data collection and analysis, as well as the development of software utilizing Python.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eData sets generated during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBarredo, J.I. (2009). Normalised flood losses in Europe: 1970\u0026ndash;2006. \u003cem\u003eNatural Hazards and Earth System Sciences, 9\u003c/em\u003e(1), 97\u0026ndash;104. \u003c/li\u003e\n\u003cli\u003eCollins, M., Knutti, R., Arblaster, J., Dufresne, J.-L., Fichefet, T., Friedlingstein, P., Gao, X., Gutowski, W. J. Johns, T., Krinner, G., Shongwe, M., Tebaldi, C., Weaver, A. J., \u0026amp; Wehner, M. (2013). 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A multi-model, multi-scenario, and multi-domain analysis of regional climate projections for the Mediterranean. \u003cem\u003eRegional Environmental Change\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(8), 2621-2635.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Climatic Drivers, Cluster Analysis, Mediterranean, NCEP/NCAR, Power-Law, Precipitation Variability","lastPublishedDoi":"10.21203/rs.3.rs-6177610/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6177610/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates precipitation variability across the Mediterranean Basin (MB) with a specific focus on power-law relationships as a framework for understanding climatological patterns. Using National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR) reanalysis monthly data from 1990 to 2024, the research employs statistical analyses and clustering techniques to unravel the spatial and temporal complexities of precipitation in the region.\u003c/p\u003e \u003cp\u003eThe findings highlight a strong power-law relationship between mean precipitation and its standard deviation, with an \u003cem\u003eR\u0026sup2;\u003c/em\u003e value of 0.75 demonstrating high explanatory power. This relationship indicates that variability increases nonlinearly with mean rainfall. This scaling behavior highlights how regions with higher precipitation experience greater absolute variability but proportionally less relative fluctuation. Such insights offer a quantitative framework for understanding precipitation dynamics in the MB and their dependence on climatic and physical geographic factors.\u003c/p\u003e \u003cp\u003eThe spatial analysis reveals a pronounced north-south gradient in precipitation distribution. Northern regions, influenced by orographic effects, receive annual precipitation exceeding 900 mm, while southern areas, dominated by subtropical high-pressure systems, often receive less than 300 mm. The study identifies seven distinct precipitation regimes through k-means clustering, with regimes varying in mean precipitation, variability, and skewness. Coastal clusters exhibit intermediate precipitation characteristics shaped by mesoscale systems, while arid regions display high interannual variability and increased propensity for extreme events.\u003c/p\u003e \u003cp\u003eThe analysis also shows a positive correlation between skewness and kurtosis. This indicates that regions with asymmetric rainfall distributions are prone to extreme precipitation events. Furthermore, the negative logarithmic relationship between mean precipitation and coefficient of variation (CV%) highlights increased variability in drier areas. Coastal North Africa and the eastern Mediterranean are identified as hotspots for intense, short-duration rainfall due to their elevated skewness values (\u0026gt;\u0026thinsp;2).\u003c/p\u003e \u003cp\u003eThis research integrates power-law scaling, statistical variability, and spatial clustering to provide a comprehensive climatological assessment of precipitation in MB. The findings advance our understanding of regional rainfall patterns and offer critical insights for water resource management, disaster risk reduction, and climate adaptation strategies.\u003c/p\u003e","manuscriptTitle":"Statistical Perspectives on Mediterranean Precipitation: Power-Law Insights in Hydro-Climatology","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-24 04:10:24","doi":"10.21203/rs.3.rs-6177610/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvited","content":"Water Resources Management","date":"2026-03-05T07:11:46+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-04-02T12:22:18+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-02T12:06:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-10T02:08:22+00:00","index":"","fulltext":""},{"type":"submitted","content":"Water Resources Management","date":"2025-03-08T01:17:00+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8c794bbd-a9a2-4396-895a-08c1083a0d52","owner":[],"postedDate":"April 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-04-24T04:10:25+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-24 04:10:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6177610","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6177610","identity":"rs-6177610","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}