River Discharge Estimation Using Imaged Critical Flow Phenomena

A wide variety of river science applications require remote estimation of discharge. Flow in steep rivers often approach critical flow (Froude number equal to one), as evidenced by trains of standing waves either perpendicular or at a high angle relative to the flow direction. Previous work has demonstrated that where such waves are present, water depth can be estimated without the need for a roughness coefficient such as Manning's n. We extend this prior work to remotely calculate river discharge. The wavelength of standing waves can be measured using high-resolution remote sensing imagery. Velocity can then be calculated from wavelength using the Kennedy wave equation. Assuming critical flow allows depth to be calculated using the modified Froude number equation, and with an additional measurement of imaged river width, river discharge can be computed directly as the product of these three values. We test this approach using high-resolution Google Earth imagery of rivers with standing waves near existing stream gages. We also demonstrate the utility of this approach by extracting a drainage area-to-discharge relationship for a large watershed. There are certain challenges with this approach, the greatest being the need for high resolution (meter-scale or better) imagery to see and measure standing waves. Such waves are also easily confused with wind waves, turbulence or other surface effects. Nevertheless, this approach offers promise for both estimating discharge in places without extensive gage networks, and also estimating discharge in archival imagery. Repeat imaging of the same areas might also be used to construct at-a-station and downstream hydraulic geometry relationships.