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Fluvial geomorphic analyses frequently require knowledge of bankfull channel geometries, which are thought to be related to characteristic stream discharges. However, relating bankfull geometry to characteristic discharge is challenged by spatially limited stream discharge measurements, which may also lack extensive temporal records. Because of these limitations, discharge is commonly assumed to scale linearly with watershed drainage area. Here we evaluate the assumption of a linear relationship between discharge and drainage area for watersheds across the United States and Canada with limited anthropogenic disturbance. Using machine-learning to objectively cluster hydrologically similar gauges, we find that discharge scales linearly with drainage area for most of North America. However, regions with low average runoff efficiency tend to have non-linear discharge scaling. In regions with non-linear discharge scaling, bankfull channel dimensions increase more rapidly with drainage area than in regions with linear discharge scaling. These results suggest that the recurrence interval of the characteristic discharge that sets channel geometry may be larger in regions where discharge scales non-linearly with drainage area compared to those regions where linear discharge scaling applies. [Display omitted] • Discharge scales linearly with drainage area for the majority of the United States and Canada. • Regions with non-linear discharge scaling demonstrate strong empirical trends with runoff efficiency. • Bankfull channel dimensions increase more rapidly with drainage area in regions with non-linear discharge scaling. [ABSTRACT FROM AUTHOR]