Scale issues in hydrology arise because different hydrological processes are dominant at different regional scales. Recent hydrological research suggests that the geographic scale (size) of watersheds may influence the behavior of hydraulic geometry exponents (b and f, but not m values) of stream channels. Hence, the working hypothesis of this study is that variations of hydraulic geometry exponents are not random, but that there are systematic changes as a function of geographic scale as well as of water basin and channel physical and environmental characteristics (predictor variables).

To support this analysis, 43 subbasins in the Potomac River Basin ranging in size from 0.38 square miles to 1,642 square miles and representing a broad spatial diversity of predictor variables within the watershed were selected for study. Research goals were to attempt, via empirical correlations, to discern relationships between a geographic scale factor and b, f, and m values, to investigate the roles of predictor variables on b, f, and m values, and their statistical significance, and to identify the most influential predictor variables and the complexity of fluvial physical processes via stepwise multi-variable regressions.

Statistical evidence was found that there is a relationship between geographic scale and hydraulic geometry exponents. In every selected predictor variable case, investigation of the correlations between b, f, and m with a single selected predictor variable in a scale context resulted in a noticeable improvement over the correlations of the hydraulic exponents with each individual predictor variable alone. The research shows that, under higher discharges, the behavior of b, f, and m mainly result in higher m and f, with a slight increase in cross-sectional area (f with negative b) in a scale context.