Remote sensing of stream depths with hydraulically assisted bathymetry (HAB) models

This article introduces a technique for using a combination of remote sensing imagery and open-channel flow principles to estimate depths for each pixel in an imaged river. This technique, which we term hydraulically assisted bathymetry (HAB), uses a combination of local stream gage information on discharge, image brightness data, and Manning-based estimates of stream resistance to calculate water depth. The HAB technique does not require ground-truth depth information at the time of flight. HAB can be accomplished with multispectral or hyperspectral data, and therefore can be applied over entire watersheds using standard high spatial resolution satellite or aerial images. HAB also has the potential to be applied retroactively to historic imagery, allowing researchers to map temporal changes in depth. We present two versions of the technique, HAB-1 and HAB-2. HAB-1 is based primarily on the geometry, discharge and velocity relationships of river channels. Manning’s equation (assuming average depth approximates the hydraulic radius), the discharge equation, and the assumption that the frequency distribution of depths within a cross-section approximates that of a triangle are combined with discharge data from a local station, width measurements from imagery, and slope measurements from maps to estimate minimum, average and maximum depths at a multiple cross-sections. These depths are assigned to pixels of maximum, average, and minimum brightness within the cross-sections to develop a brightness–depth relation to estimate depths throughout the remainder of the river. HAB-2 is similar to HAB-1 in operation, but the assumption that the distribution of depths approximates that of a triangle is replaced by an optical Beer–Lambert law of light absorbance. In this case, the flow equations and the optical equations are used to iteratively scale the river pixel values until their depths produce a discharge that matches that of a nearby gage. R 2 values for measured depths versus depths estimated by HAB-1 and HAB-2 are 0.51 and 0.77, respectively, in the relatively simple Brazos River, Texas. R 2 values for HAB-1 and HAB-2 are 0.46 and 0.26, respectively, in the Lamar River, a complex mountain river system in Yellowstone National Park. Although the R 2 values are moderate, depth maps and crosssections derived from the HAB techniques are consistent with typical stream geomorphology patterns and provide far greater