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

*Corresponding author for this work

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Abstract

Image cross‐correlation techniques, such as Particle Image Velocimetry (PIV), can estimate water surface velocity (vsurf) of streams. However, discharge estimation requires water depth and the depth‐averaged vertical velocity (Um). The variability of the ratio Um/vsurf introduces large errors in discharge estimates. We demonstrate a method to estimate vsurf 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 meters per time is performed by informing a camera pinhole model; the range from the pinhole to the water surface is measured by the drone‐board radar. For approximately uniform flow, Um is a function of the Gauckler‐Manning‐Strickler coefficient (Ks) and vsurf. We implement an approach that can be used to jointly estimate Ks and discharge by informing a system of 2 unknowns (Ks and discharge) and 2 non‐linear equations: i) Manning's equation ii) mean‐section method for computing discharge from Um. This approach relies on bathymetry, acquired in‐situ a‐priori, and on UAS‐borne vsurf and water surface slope measurements. Our joint (discharge and Ks) estimation approach is an alternative to the widely used approach than relies on estimating Um as 0.85·vsurf. 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 in discharge of 19.1% compared to in‐situ discharge measurements. Ks estimates showed a mean absolute error of 3.2 m1/3/s compared to in‐situ measurements.
Original languageEnglish
JournalWater Resources Research
ISSN0043-1397
DOIs
Publication statusAccepted/In press - 2021

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