Heuristic measurement of river bathymetry in proglacial braided streams using SfM-MVS photogrammetry and statistical approaches

The quantification of river bathymetry and its change through time is a primary challenge in fluvial geomorphology. Whilst there has been a very rapid development of methods for measuring exposed river morphology, inundated zones remain a problem. The development of cheap UAV platforms and SfM-MVS photogrammetry have been particularly important as these allow low cost, high resolution, and repeat surveys. Researches have now shown that provided that there is a signal of water depth then it is also possible to map inundated areas by adopting, for example, two media refraction correction if there is sufficient bed texture in the imagery. The main problem arises, however, when the water is so turbid that the river bed is not visible in imagery. This is the case for braided rivers in proglacial margins where high rates of glacial erosion create high suspended sediment concentrations and also morphodynamically active braided rivers. In this paper we test a new and simple hypothesis to predict water depth distribution based upon heuristic reasoning: that our experience of braided river environments allows us to make a series of qualitative statements about where water will be deeper and where it will be shallower; and that if we can quantify them, we can model the water depths associated with inundated zones.

The simplest statement is that water depth increases with distance away from the nearest river bank; and it is likely to do so more rapidly when the total wetted width is lower. A more rapid increase is also likely on the outer bank of curved sections; and conversely, a slower increase is likely on the inner bank. In a braided river, streamline convergence is likely to lead to deeper water; streamline divergence is likely to lead to shallow water. On this basis, we ought to be able to model water depths in a shallow braided river on the basis of: (1) distance from the nearest bank; (2) local channel width; (3) total inundated width (given a braided river is multi-channel); (4) local curvature magnitude and direction; and (5) planform streamline convergence/divergence. We measure these parameters for a shallow braided proglacial stream (Glacier d’Otemma, south-western Swiss Alps) with high suspended sediment concentrations. Over the summers of 2020 and 2021 we acquired high resolution UAV-based imagery, as well as spatially distributed GPS data of water depths. We used resultant ortho-imagery to extract these parameters and to calibrate predictive models of water-depth based upon multivariate statistical modelling. The independent validation data suggest that between 50% and 75% of the variance in water depths can be reconstructed and confidence in estimated depths are of the order of +/- 0.10m. Finally, we integrate these water depths and their uncertainty into elevation data derived using SfM-MVS photogrammetry for the exposed areas to produce digital elevation models with spatially dependent uncertainty. Comparison of these DEMs shows that they can be used to visualize quantitative geomorphological changes and that the associated uncertainties in volume of change estimates are sufficiently low to be used in sediment budget studies.