RiverEye Bathymetry Retrievals (REBaR): A Remote Sensing Approach to Bathymetry and Discharge Estimation in Rivers

We describe an inversion technique for water depth estimation in riverine environments which exploits the balance between surface pressure gradient and bottom friction (proportional to velocity) in open channel flow. This technique provides information on relative bathymetry and cross-section shape, but not absolute depths. Two methods for scaling the inversion results to absolute depth are described. We compare inversion results against direct bathymetry measurements, and discharge estimates against an in situ streamgage.

The inversion is demonstrated using a dataset obtained along a 500 m long reach of the Colorado River near Ehrenberg, AZ from a small aircraft. A mid-wave infrared camera captured images of the river surface for velocity processing, while a bathymetric lidar made direct measurements of water depth.

We obtain surface velocities using a cross-correlation algorithm on a regular grid. After identifying the river banks and setting appropriate boundary conditions (no slip velocity condition, zero depth), we apply our inversion algorithm starting from an initial guess of the bathymetry (e.g. a flat bottom) and the measured surface velocity field, forming a mass conserving streamfunction. A modified universal krigging technique is used to interpolate results and update the bathymetry guess. A change tolerance or maximum number of iterations are used as stopping criteria.

Relative depths are scaled either using the maximum channel depth or by estimating the channel roughness (Manning's n) and the surface energy gradient to obtain the hydraulic radius at specific cross-sections. The entire reach or individual cross-sections are normalized so their maximum depth is 1, and results are scaled by the maximum depth or the cross-section hydraulic radius estimate. Results (attached figure) demonstrate the inversion resolves the general cross-section shape while the hydraulic radius scaling at individual cross-sections works well to obtain absolute depth estimates. Mean absolute error between inversion results and lidar bathymetry was 8% averaged over the reach. Discharge estimates using the surface velocity and lidar bathymetry or the inversion results were approximately 1% of the streamgage discharge value.