A Drone‐Borne Method to Jointly Estimate Discharge and Manning's Roughness of Natural Streams

Abstract Image cross‐correlation techniques, such as particle image velocimetry (PIV), can estimate water surface velocity ( v surf ) of streams. However, discharge estimation requires water depth and the depth‐averaged vertical velocity ( U m ). The variability of the ratio U m / v surf introduces large errors in discharge estimates. We demonstrate a method to estimate v surf from Unmanned Aerial Systems (UASs) with PIV technique. This method does not require any ground control point (GCP): the conversion of velocities from pixels per frame into length per time is performed by informing a camera pinhole model; the range from the pinhole to the water surface is measured by the drone‐borne radar. For approximately uniform flow, U m is a function of the Gauckler‐Manning‐Strickler coefficient ( K s ) and v surf . We implement an approach that can be used to jointly estimate K s and discharge by informing a system of two unknowns ( K s and discharge) and two nonlinear equations: i) Manning's equation and ii) mean‐section method for computing discharge from U m . This approach relies on bathymetry, acquired in situ a priori, and on UAS‐borne v surf and water surface slope measurements. Our joint (discharge and K s ) estimation approach is an alternative to the widely used approach that relies on estimating U m as 0.85· v surf . It was extensively investigated in 27 case studies, in different streams with different hydraulic conditions. Discharge estimated with the joint estimation approach showed a mean absolute error of 19.1% compared to in situ discharge measurements. K s estimates showed a mean absolute error of 3 m 1/3 /s compared to in situ measurements.