Fully non-contact discharge measurement in shallow streams via physics-based water-surface image analysis

Noncontact image-based velocimetry methods provide a flexible, cost-effective, and safe alternative to standard river discharge measurement techniques, but require prior knowledge of the bathymetry and suitable tracer distributions. Image wave velocimetry (IWV) approaches estimate the flow velocity and water depth simultaneously without artificial tracers, but have a low spatial resolution and lack robustness. Here, we extend a previous IWV approach to reconstruct the spatial distribution of surface velocity and depth across a river and estimate the water discharge. We introduce a novel physics-informed approach that integrates the IWV analysis with an entropy-based framework, improving the resolution and robustness of the reconstructions. Testing in a shallow stream showed a 10% error in discharge for the extended IWV method, which improved to 4% with the combined IWV-entropy method. The results of this initial case study suggest that IWV methods can be used to measure the discharge of shallow rivers without requiring any contact with water.