A Drone‐Borne Method to Jointly Estimate Discharge and Manning's Roughness of Natural Streams
Filippo Bandini, Beat Lüthi, Salvador Peña‐Haro, Chris Borst, Jun Liu, Sofia Karagkiolidou, Xiao Hu, Grégory Guillaume Lemaire, Poul Løgstrup Bjerg, Peter Bauer‐Gottwein
Abstract
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.