Large-scale hydrologic and hydraulic modeling efforts require accurate, compact representation of the shape and flow properties of rivers. However, quantifying and representing rivers at these scales has remained elusive due to observational and computational limitations. We address this challenge by (1) leveraging increasingly widespread high-resolution topographic data to fully describe at-a-reach and downstream hydraulic geometry and longitudinal patterns of variability and (2) compactly summarizing these findings into predictable, reach-scale attributes. This scalable analytical framework for representing river corridors advances our fundamental scientific understanding of rivers and yields research-supported tools for improving national, high-fidelity flood inundation forecasting efforts.