Fig. 3: Regional Long-Term Annual Peak Streamflow (> 60 years).

a Regional trends for all USGS sites, b reference-only sites, and d non-reference sites. a, b, and d displays the Regional Average Mann-Kendall Z values, which assess the statistical significance of the trends by considering all individual sites within each HUC-2 region. A Z value < −1.96 or > 1.96 indicates statistically significant regional trends, with higher magnitudes of Z reflecting greater confidence in the trend (refer to Methods for details). Panels (c) and (e) depict the same data as Fig. 2, but is restricted to the reference and non-reference sites, respectively. Open circles indicate insignificant trends with the color representing the direction of the trend slope (blue for positive, red for negative, and grey for zero), while upward and downward arrows represent statistically significant (p-value < 0.05) increasing and decreasing trends, respectively, based on a non-parametric method. Regional trends are quantified using the Regional Average Mann–Kendall (RAMK) normalized Z-score, which is computed from the sum of site-level Mann–Kendall statistics (including both significant and non-significant sites) across the region (See Method). The regional trend significance thus reflects the net balance of increasing and decreasing site-level trends. Magnitude of trends are expressed as a percentage of the standard deviation over 60 years, where 100% change equates to one standard deviation change in this period. The reference sites include both the HCDN and GAGES-II reference sites, and the non-reference sites include the GAGES-II non-reference and other USGS sites.