Multifractal characterization of meteorological droughts in Turkiye's mediterranean region using visibility graph approaches

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 Turkiye's Mediterranean region. Using the Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) from 24 stations (1970-2022), we examined drought dynamics across time scales ranging from 1 to 24 months. The analysis shows that except for a few one-month cases, drought indices exhibit predominantly stochastic rather than chaotic behaviour, validating the use of multifractal tools. VG and UDVG approaches were then applied to 3-, 6-and 12-month series, and multifractal spectra were computed via the sandbox and Chhabra-Jensen methods. Results indicate that SPEI consistently displays stronger multifractality than SPI, confirming the added role of evapotranspiration in drought variability. The UDVG framework reduced the multifractal spread (Delta Dq = D-0-D-2) by similar to 30% compared to VG (mean Delta Dq = 0.49 vs. 0.72), highlighting its sensitivity to low-amplitude, persistent droughts. In contrast, VG emphasises high-magnitude wet-dry fluctuations. This dual-network approach therefore provides complementary perspectives: VG is better suited to identifying extreme wet conditions, while UDVG can capture low amplitude fluctuations, which are cautionary sign leading to long term drought and its small changes can be early indicators of drought disasters. Overall, the proposed VG/UDVG-based multifractal framework provides novel insights into drought complexity and has the potential to support the development of early warning systems and adaptation strategies in Mediterranean-type climates.