Regional Patterns of Streamflow Persistence, Complexity, and Chaos Indicators within the United States

Raczynski, K., Grala, K., Baran-Gurgul, K., Cartwright, J. H., & Dyer, J. (2026). Regional Patterns of Streamflow Persistence, Complexity, and Chaos Indicators within the United States. Journal of Hydrology: Regional Studies. 64, 103184. DOI:https://doi.org/10.1016/j.ejrh.2026.103184.

Abstract

Study Region Streamflow records from 3135 gauging stations across the United States and Puerto Rico (1970–2023) were analyzed. Daily discharge was aggregated into non-overlapping calendar weekly, monthly, quarterly, and annual series; within each period Qmin, Qavg, and Qmax were computed as the minimum, mean and maximum of daily discharge, respectively. Study Focus Streamflow integrates climatic, hydrological, and anthropogenic influences. This study characterizes how memory, complexity, and chaos indicators in streamflow vary across regions, flow regimes, and time scales. Fractal and multifractal analyses, recurrence-quantification metrics, and largest Lyapunov exponents are computed for each gauge and aggregation scale, then summarized with fuzzy C-means clustering to derive regional dynamical regimes. New Hydrological Insights for the Region Hurst exponents mostly between 0.75 and 0.95 indicate widespread long-range dependence, strongest for Qmin. Multifractality intensifies with temporal aggregation and is greatest for Qmax, reflecting enhanced variability in extremes. Recurrence analysis reveals a trade-off between strong recurrence structure and high dynamical complexity, with Qavg comparatively stable across scales. Positive largest Lyapunov exponents suggest low-dimensional chaos embedded within persistent dynamics. Clustering of multifractality and recurrence metrics yields three coherent regimes: a high-persistence, low-entropy regime in the western and central United States (including Alaska), a transitional regime in the Great Plains and Appalachia, and a higher-entropy regime in the northeastern and Gulf Coast areas (including Puerto Rico). Taken together, these typologies support region-specific forecasting and water-management strategies under climate and land-use change by indicating where persistence-dominated dynamics favor long-memory model structures and where higher entropy implies shorter predictability horizons and a stronger role for probabilistic or ensemble forecasting.