Towards affordable 3D physics-based river flow rating: application over the Luangwa River basin

Abstract. Uncrewed aerial vehicles (UAVs), affordable precise global navigation satellite system hardware, multi-beam echo sounders, open-source 3D hydrodynamic modelling software, and freely available satellite data have opened up opportunities for a robust, affordable, physics-based approach to monitoring river flows. Traditional methods of river discharge estimation are based on point measurements, and heterogeneity of the river geometry is not contemplated. In contrast, a UAV-based system which makes use of geotagged images captured and merged through photogrammetry in order to generate a high-resolution digital elevation model (DEM) provides an alternative. This UAV system can capture the spatial variability in the channel shape for the purposes of input to a hydraulic model and hence probably a more accurate flow discharge. In short, the system can be used to produce the river geometry at greater resolution so as to improve the accuracy in discharge estimations. Three-dimensional hydrodynamic modelling offers a framework to establish relationships between river flow and state variables such as width and depth, while satellite images with surface water detection methods or altimetry records can be used to operationally monitor flows through the established rating curve. Uncertainties in the data acquisition may propagate into uncertainties in the relationships found between discharge and state variables. Variations in acquired geometry emanate from the different ground control point (GCP) densities and distributions used during photogrammetry-based terrain reconstruction. In this study, we develop a rating curve using affordable data collection methods and basic principles of physics. The basic principal involves merging a photogrammetry-based dry bathymetry and wet bathymetry measured using an acoustic Doppler current profiler (ADCP). The output is a seamless bathymetry which is fed into the hydraulic model so as to estimate discharge. The impact of uncertainties in the geometry on discharge estimation is investigated. The impact of uncertainties in satellite observation of depth and width is also analysed. The study shows comparable results between the 3D and traditional river rating discharge estimations. The rating curve derived on the basis of 3D hydraulic modelling was within a 95 % confidence interval of the traditional gauging-based rating curve. The 3D-hydraulic-model-based estimation requires determination of the roughness coefficient within the stable bed and the floodplain using field observation at the end of both the dry and wet season. Furthermore, the study demonstrates that variations in the density of GCPs beyond an optimal number have no significant influence on the resultant rating relationships. Finally, the study observes that which state variable approximation (water level and river width) is more accurate depends on the magnitude of the flow. Combining stage-appropriate proxies (water level when the floodplain is entirely filled and width when the floodplain is filling) in data-limited environments yields more accurate discharge estimations. The study was able to successfully apply advanced UAV and real-time kinematic positioning (RTK) technologies for accurate river monitoring through hydraulic modelling. This system may not be cheaper than in situ monitoring; however, it is notably more affordable than other systems such as crewed aircraft with lidar. In this study the calibration of the hydraulic model is based on surface velocity and the water depth. The validation is based on visual inspection of an RTK-based waterline. In future studies, a larger number of in situ gauge readings may be considered so as to optimize the validation process.