Quantifying Hydraulic Geometry and Whitewater Coverage for Steep Proglacial Streams to Support Process-Based Stream Temperature Modelling

Abstract

At-a-station hydraulic geometry (AASHG) relationships describe the dependence of a river's width, mean depth and mean velocity on discharge at a given location, and are typically modelled as power-law functions. They are often used when modelling stream temperature under unsteady flow conditions. Deriving AASHG relationships is challenging for steep proglacial streams due to the combination of complex morphology and velocity distributions, and rapidly varying flow. The objective of this study was to combine tracer injections with drone-based photogrammetry to derive AASHG relationships for a steep proglacial channel and to quantify whitewater coverage and its relationship with discharge to support process-based stream temperature modelling. Velocity–discharge and width–discharge relationships were reasonably well characterised using power-law functions, but varied amongst sub-reaches. Whitewater coverage as a fraction of total stream surface area generally exceeded 50% for the range of flows sampled, and exhibited a statistically significant positive relationship with discharge, which varied amongst sub-reaches. For the range of flows captured during drone flights, the relationship could be represented by a linear function. However, an asymptotic model would be required to extend the relationship to higher flows. The magnitude of whitewater coverage indicates that the albedo of the stream should be substantially higher than values typically used in stream temperature models, and the relationship with discharge means that ongoing glacier retreat, and the associated reduction in summer discharge, should result in lower albedo and higher downstream warming rates, reinforcing the effects of decreasing velocity and mean depth as flows decline.