Spatial Patterns of Peak Flow Quantiles Based on Power-Law Scaling in the Mississippi River Basin

This study explores the spatial variability of peak flows for different drainage area sizes in the Mississippi River Basin (MRB) based on the power-law relation between flood quantiles (Q p ) and drainage areas (A) expressed as \( {Q}_p={\upalpha}_p{A}^{\uptheta_p} \). The aim is to reveal consistent regional flood patterns within the MRB. The authors use 5137 streamflow gauges with peak flow records and the USGS Hydrologic Unit Code (HUC) catchment organization framework to estimate the scaling parameters (α p and θ p ) at multiple spatial disaggregation levels, including the complete Mississippi River Basin (MRB), six major MRB sub-regions (HUC-2), and finally 84 medium-scale catchments (HUC-4). The analysis at the HUC-4 level exposes remarkable regional flood patterns in θ p and α p , which are used to estimate peak flows at 2.33 and 100 years of return periods at multiple spatial scales including 1, 100, 1000, and 10,000 km2 drainage areas. The results expose a peak flow quantile relation that varies as a function of region and drainage area, demonstrating that the regions with the higher peak flows quantiles are varying with respect to the watershed size along the MRB. Mainly, we found that the cluster of higher floods extends from the center to the eastern MRB for drainage areas from 1 to 10,000 km2. Conversely, the clusters of lower 2.33-year floods are preserved in the western MRB for the same range of drainage areas. The results presented in this study demonstrate that the flood-producing mechanisms are varying with respect to the drainage area size and regions, providing a starting point for a quantitative description of physical processes that dominate the variability of flood-producing mechanisms, a critical step in the design of parsimonious continental scale hydrological models.