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

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 center dot 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.