Şimşek et al. (2026) Multifractal characterization of meteorological droughts in Türkiye’s mediterranean region using visibility graph approaches

Identification

• Journal: Stochastic Environmental Research and Risk Assessment
• Year: 2026
• Date: 2026-02-01
• Authors: Oğuz Şimşek, Halil Karahan, Thomas Plocoste, S. Adarsh
• DOI: 10.1007/s00477-026-03176-4

Research Groups

• Faculty of Engineering, Civil Engineering Department, Harran University, Sanliurfa, Türkiye
• Boyabat Vocational School of Higher Education, Construction Department, Sinop University, Sinop, Türkiye
• KaruSphere Laboratory, Department of Research in Geoscience, Les Abymes, Guadeloupe, FWI, France
• Department of Civil Engineering, TKM College of Engineering, Kollam, India

Short Summary

This study introduces a novel framework based on visibility graph (VG) and its upside-down variant (UDVG) to assess the multifractal structure of meteorological droughts in Türkiye’s Mediterranean region. It finds that the Standardized Precipitation Evapotranspiration Index (SPEI) consistently displays stronger multifractality than the Standardized Precipitation Index (SPI), and the UDVG framework is more sensitive to low-amplitude, persistent droughts, offering complementary insights for early warning systems.

Objective

• To present an alternative framework for the multifractal description of droughts using Visibility Graph (VG) and its variants.
• To compare multifractal properties of Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) across diverse temporal scales.
• To investigate the added value of the Upside-Down Visibility Graph (UDVG) scheme for characterizing drought dynamics.

Study Configuration

• Spatial Scale: Türkiye’s Mediterranean region, encompassing 24 meteorological stations with elevations ranging from 2 meters to 1344 meters.
• Temporal Scale: Data from 1970 to 2022 (53 years), with drought dynamics examined across time scales from 1 month to 24 months, focusing on 3-, 6-, and 12-month series for multifractal analysis.

Methodology and Data

• Models used:
  • Visibility Graph (VG) and Upside-Down Visibility Graph (UDVG) for network construction.
  • Multifractal analysis using the Sandbox method for Rényi dimensions (Dq) and the Chhabra–Jensen method for singularity spectra (f(α) vs. α).
  • Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) as drought indicators.
  • Potential Evapotranspiration (PET) calculated using the Thornthwaite method for SPEI.
  • Inverse Distance Weighting (IDW) for spatial interpolation.
• Data sources:
  • Monthly precipitation and average temperature data from 24 stations operated by the General Directorate of Meteorology of the Republic of Türkiye.
  • Data period: 1970–2022.

Main Results

• Drought indices (SPI and SPEI) predominantly exhibit stochastic rather than chaotic behavior, validating the use of multifractal tools, except for a few 1-month cases.
• SPEI consistently displays stronger multifractality than SPI across the region, confirming the significant role of evapotranspiration in drought variability.
• The UDVG framework reduced the multifractal spread (ΔDq = D₀ – D₂) by approximately 30% compared to VG (mean ΔDq = 0.49 vs. 0.72), highlighting its sensitivity to low-amplitude, persistent droughts.
• VG is better suited for identifying high-magnitude wet–dry fluctuations (extreme wet conditions), while UDVG effectively captures low-amplitude fluctuations, which can serve as early indicators of long-term drought disasters.
• Drought dynamics are characterized by positive asymmetry, indicating that multifractality is dominated by large fluctuations (severe or sudden changes) rather than small ones.
• SPEI exhibits a more pronounced imbalance between extreme and moderate fluctuations and a broader multifractal spectrum (W) than SPI, suggesting increased intermittency and complexity due to evapotranspiration effects.

Contributions

• Introduces a novel integrated visibility graph–based multifractal (VGMF) framework, combining VG and UDVG, for the multifractal description of drought indices.
• Provides a dual-network approach that offers complementary perspectives on drought dynamics, distinguishing between high-amplitude (wet) and low-amplitude (persistent dry) regimes.
• Demonstrates the added value of the UDVG scheme in characterizing subtle, low-amplitude drought dynamics, which are crucial as early indicators for developing agricultural or hydrological droughts.
• Confirms that SPEI captures a higher level of complexity and nonlinearity than SPI, underscoring the importance of incorporating evapotranspiration effects in drought assessment.
• Offers a framework with potential to support the development of enhanced early warning systems and adaptation strategies for Mediterranean-type climates by providing a more nuanced understanding of drought evolution.

Funding

No funding was received to perform this research work.

Citation

@article{Şimşek2026Multifractal,
  author = {Şimşek, Oğuz and Karahan, Halil and Plocoste, Thomas and Adarsh, S.},
  title = {Multifractal characterization of meteorological droughts in Türkiye’s mediterranean region using visibility graph approaches},
  journal = {Stochastic Environmental Research and Risk Assessment},
  year = {2026},
  doi = {10.1007/s00477-026-03176-4},
  url = {https://doi.org/10.1007/s00477-026-03176-4}
}