Towards affordable 3D physics-based river flow rating: application over the Luangwa River basin
Authors: Samboko Hubert T. , Schurer Sten , Savenije Hubert H. G. , Makurira Hodson , Banda Kawawa , Winsemius Hessel 
Published: August 2023

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.