Multifractal assessment of hydroclimatic variability in Midwest Brazil using the hydroclimatic balance index (HBI): a comparison with the standardized precipitation index (SPI)

Abstract This study investigates the multifractal characteristics of hydroclimatic variability in the capital cities of Midwest Brazil using monthly precipitation (ppt) and actual evapotranspiration (aet) data from the TerraClimate dataset (1958–2024). A 12-month standardized hydroclimatic balance index (HBI), analogous to the Standardized Precipitation Evapotranspiration Index (SPEI), was constructed to represent dry–wet conditions under a water-balance framework. Multifractal Detrended Fluctuation Analysis (MFDFA) was applied to quantify scaling behavior, persistence, and variability heterogeneity. Results reveal pronounced multifractal dynamics across all capitals, with generalized Hurst exponents ranging from 0.87 to 0.98, indicating strong long-range dependence in hydroclimatic fluctuations. Singularity spectrum width (Δα) varied spatially, with Campo Grande and Goiânia exhibiting the highest multifractal strength. Comparative analysis shows that precipitation displays stronger intermittency than evapotranspiration, confirming rainfall variability as the primary driver of hydroclimatic complexity. Linear trend analysis of annual series revealed weak and statistically non-significant tendencies, whereas multifractal metrics captured substantial structural variability. Sub-period comparison (1958–1990 vs. 1991–2024) suggests increased persistence and intermittency in recent decades, indicating intensification of hydroclimatic variability. The findings highlight the relevance of complexity-based drought diagnostics for tropical continental regions under climate variability and change.