Deciphering hydrological drought controls on atrak river discharge predictability: a multiscale dynamic assessment

Hydrological drought, a persistent challenge in Iran, profoundly impacts water resources, particularly river discharge patterns critical for effective management. This study aims to quantify how hydrological drought shapes the chaotic, multiscale, and predictable dynamics of Atrak River discharge from 1978 to 2018, using an integrated approach of chaos theory, multifractal analysis, and cross-correlation techniques. Daily discharge data and monthly drought indices were used, with monthly data applied for dynamic analysis. Cross-correlation revealed drought intensifies sensitivity to initial conditions and randomness, with delayed effects (lag = 2 months for Lyapunov Exponent [LE]-SDI; lag = -3 for Approximate Entropy [ApEn]-SDI). Sensitivity analysis showed outlier removal shifts CC lags and directions, reduces LE by 74.5% on average, and narrows multifractal spectra (Δα smaller, left-truncation delayed to 41 years), confirming cleaner detection of intrinsic chaos. Autocorrelation-adjusted CC (prewhitening) yielded non-significant p-values (> 0.05) at all lags, indicating apparent delays partly reflect serial dependence. Bootstrap resampling (B = 1000) showed high LE uncertainty in short (31-point) segments, decreasing with longer series, and more chaotic months post-outlier removal. Sample Entropy validated ApEn, confirming moderate-to-low irregularity and seasonal predictability (lowest in June, highest in January). Multifractal spectra revealed a 41-year flood cycle and 25-year drought cycle. These findings improve drought and discharge forecasting models, enabling precise water allocation and reservoir management strategies to mitigate drought impacts in Iran.