A generalized framework for inferring river bathymetry from image-derived velocity fields

Abstract

Although established techniques for remote sensing of river bathymetry perform poorly in turbid water, image velocimetry can be effective under these conditions. This study describes a framework for mapping both of these attributes: Depths Inferred from Velocities Estimated by Remote Sensing, or DIVERS. The workflow involves linking image-derived velocities to depth via a flow resistance equation and invoking an optimization algorithm. We generalized an earlier formulation of DIVERS by: (1) using moving aircraft river velocimetry (MARV) to obtain a continuous, spatially extensive velocity field; (2) working within a channel-centered coordinate system; (3) allowing for local optimization of multiple parameters on a per-cross section basis; and (4) introducing a second objective function that can be used when discharge is not known. We also quantified the sensitivity of depth estimates to each parameter and input variable. MARV-based velocity estimates agreed closely with field measurements ($R^2=0.81$) and the use of DIVERS led to cross-sectional mean depths that were correlated with in situ observations ($R^2=0.75$). Errors in the input velocity field had the greatest impact on depth estimates, but the algorithm was not highly sensitive to initial parameter estimates when a known discharge was available to constrain the optimization. The DIVERS framework is predicated upon a number of simplifying assumptions — steady, uniform, one-dimensional flow and a strict, purely local proportionality between depth and velocity — that impose important limitations, but our results suggest that the approach can provide plausible, first-order estimates of river depths.