Depths Inferred from Velocities Estimated by Remote Sensing: A Flow Resistance Equation-Based Approach to Mapping Multiple River Attributes at the Reach Scale

Abstract

Remote sensing of flow conditions in stream channels could facilitate hydrologic data collection, particularly in large, inaccessible rivers. Previous research has demonstrated the potential to estimate flow velocities in sediment-laden rivers via particle image velocimetry (PIV). In this study, we introduce a new framework for also obtaining bathymetric information: Depths Inferred from Velocities Estimated by Remote Sensing (DIVERS). This approach is based on a flow resistance equation and involves several assumptions: steady, uniform, one-dimensional flow and a direct proportionality between the velocity estimated at a given location and the local water depth, with no lateral transfer of mass or momentum. As an initial case study, we performed PIV and inferred depths from videos acquired from a helicopter hovering at multiple waypoints along a large river in central Alaska. The accuracy of PIV-derived velocities was assessed via comparison to field measurements and the performance of an optimization-based approach to DIVERS was quantified by comparing calculated depths to those observed in the field. We also examined the ability of two variants of DIVERS to reproduce the discharge recorded at a gaging station. This analysis indicated that the accuracy of PIV-based velocity estimates varied considerably from hover to hover along the reach, with observed vs. predicted R2 values ranging from 0.22 to 0.97 and a median of 0.57. Calculated depths were also reasonably accurate, with median normalized biases from −4% to 9.9% for the two versions of DIVERS, but tended to be under-predicted in meander bends. Discharges were reproduced to within 1% and 4% when applying the optimization-based technique to individual hovers or reach-aggregated data, respectively. The results of this investigation suggest that, in addition to the velocity field derived via PIV, DIVERS could provide a plausible, first-order approximation to the reach-scale bathymetry. This framework could be refined by incorporating hydraulic processes that were not represented in the initial iteration of the approach described herein.

Keywords

• depth
• bathymetry
• flow velocity
• discharge
• flow resistance
• roughness