# Non-linear dynamics of United States streamflow dataset

## TL;DR

This paper provides a detailed U.S. streamflow dataset with fractal and chaos metrics to study water flow dynamics across different time scales.

## Contribution

The dataset introduces fractal and chaos metrics for streamflow data across multiple resolutions and flow regimes.

## Key findings

- Streamflow data is analyzed using fractal and chaos metrics like Hurst exponents and Lyapunov exponents.
- Gauges are clustered into three dynamic-behavior groups using fuzzy C-means clustering.
- The dataset includes raw and processed time series with location metadata for 2899 stations.

## Abstract

Comprehensive hydrological dataset containing daily, weekly, monthly, quarterly, and annual streamflow time series with corresponding fractal and chaos metrics for three flow regimes (maximum, average, and minimum) for 2899 gauging stations across the United States and Puerto Rico. Time series are available from January 1, 1970, to December 31, 2023, in five temporal resolutions in raw and filtered formats (where negative, zero, and missing data were interpolated). A suite of fractal and chaos metrics is included with data and contains Hurst exponents, detrended fluctuation analysis, multifractality, wavelet transform modulus maxima (with varying bands and modulus methods), sample entropy, recurrence quantification analysis, and Lyapunov exponents. Gauges were grouped via fuzzy C-means clustering into three dynamic-behavior groups, with a matrix of membership probabilities. Gauge metadata including corrected latitudinal and longitudinal coordinates is included. The resulting dataset includes raw and processed time series, computed fractal and chaos metrics, cluster assignments, and location metadata for each station. These data enable researchers and water resources managers to benchmark streamflow dynamics across scales, support the evaluation of hydrological models or resources, perform regional classification, and develop machine-learning applications.