Long-Range Dependence, Multifractality, and Trends of Drought Across Multiple Accumulation Periods in Türkiye Derived From SPEI

Abstract

Drought is a scale-dependent, memory-driven process, yet its temporal persistence and complexity remain poorly understood relative to its intensity and frequency. This study presents an integrated, scale-aware assessment of drought dynamics across Türkiye using the Standardized Precipitation Evapotranspiration Index (SPEI), derived from ERA5-Land precipitation and potential evapotranspiration data spanning 1975–2022. Monthly SPEI series at four accumulation scales (1, 3, 6, and 12 months) were analyzed using Detrended Fluctuation Analysis (DFA) and Multifractal DFA (MFDFA) to quantify persistence and complexity, complemented by ordinary least squares regression, the Mann–Kendall test, and Sen's slope estimator to assess trend direction, significance, and magnitude. DFA scaling exponents increased systematically from near-random values (α = 0.49–0.59) at SPEI-1 to strongly persistent, memory-dominated dynamics (α = 1.06–1.23) at SPEI-12, while MFDFA revealed a parallel intensification of multifractal complexity, with spectrum widths (Δα) expanding from 0.03–0.20 to 0.21–0.65 across the same range of scales. Trend analyses uncovered spatially limited and largely insignificant drying at short time scales, evolving into widespread, statistically significant negative trends (p < 0.05) at SPEI-6 and SPEI-12, with the steepest declines identifying several basins as persistent long-term drought hotspots, while only one basin exhibited a significant wetting trend. These findings establish that drought in Türkiye is governed by scale-dependent persistence and multifractal heterogeneity rather than short-term randomness, underscoring the inadequacy of short-timescale indices for long-term risk assessment and highlighting the need for persistence- and complexity-informed drought monitoring frameworks.