Abstract
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 $Fr$ (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≈1 $Fr\approx 1$, 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 (R2 ${R}^{2}$ = 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.
Plain Language Summary
In some rivers with relatively steep slopes, regularly spaced standing waves can occur where the channel narrows or steepens, forming rapids. These waves remain stationary because the downstream velocity of the flow is equal and opposite to the upstream velocity of the waves. We refer to this balance as critical flow and under these conditions the depth and velocity of the water and the spacing of the waves are uniquely related to one another. These conditions form the basis of a remote sensing approach to estimating discharge, which is the volume of water flowing along the river per unit time. This study introduces a method for calculating discharge based on measurements of wavelength and channel width that can be made using widely available images. We compared the resulting estimates to independent measurements made using field‐based techniques at nearby gaging stations. We found strong agreement between traditional measurements and critical flow‐based estimates derived from 82 Google Earth images. This new technique could provide accurate discharge information for rivers where critical flow occurs, many of which are not measured regularly as part of current gage networks.
Key Points
Standing waves in rivers indicate unique hydraulic conditions that allow depth and velocity to be inferred from the spacing of the waves
Critical flow theory can be used to calculate discharge based on measurements of wavelength and width made using readily available images
Discharges estimated via the critical flow approach for 82 images agreed closely with discharges recorded at gaging stations (R2 ${R}^{2}$ = 0.98)