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·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.