Drought’s Chemical Footprint: Decoding Nonlinear Dependencies in River Ion Dynamics via Cross-Correlation and Chaos Theory

This study presents a novel application of chaotic dynamics and nonlinear time series analysis, specifically Lyapunov exponents (LE), phase space reconstruction, and cross-correlation, to investigate the complex interdependence between hydrological drought and water quality in Iran’s Helle River (1970–2020). By integrating the streamflow drought index (SDI) with key water quality parameters, we reveal varying levels of drought sensitivity: acidity showed no dependence; potassium low; and bicarbonate and calcium medium; while sodium, magnesium, and chlorine exhibited high dependence on drought conditions. Notably, positive correlations were found between the SDI’s LE and bicarbonate (0.28), calcium (0.31), magnesium (0.52), sodium (0.53), and chlorine (0.54), indicating increasing chaotic behavior in water quality under drought stress. The negative weak correlation for acidity (−0.05) further highlights parameter-specific responses. These findings significantly advance understanding of nonlinear hydrological processes and demonstrate that drought amplifies chemical variability in river systems through chaotic dynamics. The proposed framework enhances early warning capabilities and sustainable water resource management, offering international relevance for drought-prone regions facing climate variability, particularly in agriculture and industrial water supply.