Remote Sensing of River Discharge Based on Critical Flow Theory

Critical flow theory provides a physical foundation for inferring discharge from measurements of wavelength and channel width made from images. In rivers with hydraulically steep local slopes greater than $\sim$0.01, flow velocities are high and the Froude number $Fr$ (ratio of inertial to gravitational forces) can approach 1.0 (critical flow) or greater. Under these conditions, undular hydraulic jumps (UHJ's) can form as standing wave trains at slope transitions or constrictions. The presence of UHJ's indicates that mean $Fr\approx 1$, implying that the velocity and depth of the flow and the spacing of the waves are uniquely related to one another. Discharges estimated from 82 Google Earth images agreed closely with discharges recorded at gaging stations ($R^2$ = 0.98), with a mean bias of 1% $\pm$ 11%. This approach could provide reliable discharge information in many fluvial environments where critical flow occurs, which tend to be underrepresented in gage networks.