Christina M. Leonard | Geology Reports

USGS2026

Estimating discharge from undular hydraulic jumps: Feasibility assessment based on flume experiments

Rapids are common in steep rivers, often forming where flow transitions from supercritical (Froude number, Fr > 1) to subcritical ( Fr < 1) through a hydraulic jump. When upstream Fr is supercritical but close to 1, this transition may occur as an undular hydraulic jump, exhibiting a train of stationary waves downstream of the jump toe. Previous studies proposed a method to estimate discharge using only UHJ wave spacing and channel width combined with a wave dispersion equation for large water depths relative to the UHJ wavelength. This method is based on the hypotheses that, by their presence, UHJs indicate near-critical flow conditions ( Fr ≈ 1) and that wave celerity c is equal to and opposite the cross-sectionally averaged flow velocity U . However, these hypotheses have not been thoroughly tested. We used data from published UHJ flume experiments to test the hypotheses that Fr ≈ 1 and c = U , compare the deep-water and general wave dispersion equations, and evaluate the accuracy of discharge estimates. In these experiments, the stationary waves exhibited shallow depths relative to wavelength and flow was subcritical ( Fr < 1) when averaged across multiple wavelengths. Additionally, wave celerity more closely approximated the surface flow velocity than U . By using a Fr representative of actual conditions and applying a coefficient to correct for c ≠ U , the accuracy of the discharge estimates improved. This finding suggests that the critical flow-based method is robust and can produce reliable streamflow estimates if the remotely observed wave trains are correctly interpreted as UHJs, without requiring in situ measurements.

Water Resources Research↗

USGS2025

Toward an efficient framework for remote sensing of river bathymetry: Comparing sensors and algorithms on an inaccessible proglacial river in Alaska

Remote sensing can provide reliable information on river depths and this approach might be particularly valuable in areas that are difficult to survey via conventional field methods. In this study, we assessed the potential to map the bathymetry of an inaccessible proglacial river in Alaska from both aerial orthophotos and a multispectral satellite image. In addition, we evaluated a variety of depth retrieval algorithms with different input data requirements, including some methods that require field measurements of water depth for calibration and other techniques that can be applied even when such field data are not available. These approaches might enable more efficient use of remote sensing methods by resource management agencies. Our results suggest that bathymetric mapping along the turquoise-colored river we examined was not only feasible but highly accurate ( R 2 up to 0.94) for both types of image data. Algorithms that use paired observations of depth and reflectance to train depth retrieval models were the most accurate, with errors on the order of 15%–20% and little or no bias. Alternative techniques based on hydraulic and statistical concepts also led to strong agreement between predicted and observed depths but were more susceptible to systematic biases toward under- or over-estimation of depth. In contrast to clear-flowing streams, bathymetric mapping in this environment was enabled by a direct relationship between the depth and brightness of the water due to scattering by suspended sediment. In selecting an appropriate depth retrieval method, a compromise might need to be reached between the level of field effort invested and the accuracy of the resulting image-derived bathymetry. Standalone software for implementing these techniques is freely available.

Alaska↗