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ABSTRACT. Hydraulic roughness exerts an important but poorly understood control on water pressure in subglacial conduits. Where relative roughness values are <5%, hydraulic roughness can be related to relative roughness using empirically-derived equations such as the Colebrook-White equation. General relationships between hydraulic roughness and relative roughness do not exist for relative roughness >5%. Here we report the first quantitative assessment of roughness heights and hydraulic diameters in a subglacial conduit. We measured roughness heights in a 125 m long section of a subglacial conduit using structure-from-motion to produce a digital surface model, and hand-measurements of the b-axis of rocks. We found roughness heights from 0.07 to 0.22 m and cross-sectional areas of 1-2 m 2 , resulting in relative roughness of 3-12% and >5% for most locations. A simple geometric model of varying conduit diameter shows that when the conduit is small relative roughness is >30% and has large variability. Our results suggest that parameterizations of conduit hydraulic roughness in subglacial hydrological models will remain challenging until hydraulic diameters exceed roughness heights by a factor of 20, or the conduit radius is >1 m for the roughness elements observed here.

Flow resistance in mountain streams is important for assessing flooding hazard and quantifying sediment transport and bedrock incision in upland landscapes. In such settings, flow resistance is sensitive to grain‐scale roughness, which has traditionally been characterized by particle size distributions derived from laborious point counts of streambed sediment. Developing a general framework for rapid quantification of resistance in mountain streams is still a challenge. Here we present a semi‐automated workflow that combines millimeter‐ to centimeter‐scale structure‐from‐motion (SfM) photogrammetry surveys of bed topography and computational fluid dynamics (CFD) simulations to better evaluate surface roughness and rapidly quantify flow resistance in mountain streams. The workflow was applied to three field sites of gravel, cobble, and boulder‐bedded channels with a wide range of grain size, sorting, and shape. Large‐eddy simulations with body‐fitted meshes generated from SfM photogrammetry‐derived surfaces were performed to quantify flow resistance. The analysis of bed microtopography using a second‐order structure function identified three scaling regimes that corresponded to important roughness length scales and surface complexity contributing to flow resistance. The standard deviation σz of detrended streambed elevation normalized by water depth, as a proxy for the vertical roughness length scale, emerges as the primary control on flow resistance and is furthermore tied to the characteristic length scale of rough surface‐generated vortices. Horizontal length scales and surface complexity are secondary controls on flow resistance. A new resistance predictor linking water depth and vertical roughness scale, i.e.  H/σz, is proposed based on the comparison between σz and the characteristic length scale of vortex shedding. In addition, representing streambeds using digital elevation models (DEM) is appropriate for well‐sorted streambeds, but not for poorly sorted ones under shallow and medium flow depth conditions due to the missing local overhanging features captured by fully 3D meshes which modulate local pressure gradient and thus bulk flow separation and pressure distribution. An appraisal of the mesh resolution effect on flow resistance shows that the SfM photogrammetry data resolution and the optimal CFD mesh size should be about 1/7 to 1/14 of the standard deviation of bed elevation. © 2019 John Wiley & Sons, Ltd.

Flow resistance in subglacial conduits regulates the basal water pressure and sliding speeds of glaciers by controlling drainage efficiency and conduit enlargement and closure. Flow dynamics within subglacial conduits, however, remain poorly understood due to limited accessibility. Here we report the results of the first computational fluid dynamics simulations of flow within a realistic subglacial conduit beneath Hansbreen, a polythermal glacier in Svalbard, Norway. The simulated friction factor is 2.34 ± 0.05, which is around 5 to 230 times greater than values (0.01-0.5) commonly used in glacier hydrological modeling studies. Head losses from sinuosity and cross-sectional variations dominate flow resistance (∼ 94%), whereas surface roughness from rocks and ice features contributes only a small portion (∼6%). Most glacier hydrology models neglect head losses due to sinuosity and cross-sectional variations and thus severely underestimate flow resistance, overestimating the conduit peak effective pressure by 2 times and underestimating the conduit enlargement area by 3.4 times, respectively.Plain Language Summary Subglacial conduits drain meltwater from polar ice sheets, thus directly regulating the ice sheet sliding speed through basal flow resistance and water pressure inside the conduits. Despite their importance, our understanding of subglacial conduits is extremely limited due to difficulties of observing them and their interiors with either remote sensing or in situ exploration. Simplified models have been proposed for the hydraulics inside these conduits. A key problem in these models is the lack of scientific support in parameterizing the flow resistance. Currently, the resistance is parameterized but has not been validated due to the accessibility issues. To narrow this knowledge gap, we performed three-dimensional computational fluid dynamics simulations based on a millimeter-scale resolution model of an actual subglacial conduit in the Arctic. For the first time we give a direct and physics-based estimation of the flow resistance in an actual subglacial conduit and highlight the important contributions of the cross-sectional variations and longitudinal sinuosity. We further demonstrate the impacts of our simulated flow resistance on subglacial hydrodynamics and ice sheet dynamics. Key Points:• For the first time, flow resistance in a real subglacial conduit is quantified using CFD and structure-from-motion photogrammetry • Flow resistance in subglacial conduits is dominated by sinuosity and cross-sectional variations, not surface roughness from rocks and ice • Most glacier hydrology models severely underestimate flow resistance and significantly misrepresent subglacial flow and ice dynamics Supporting Information:• Supporting Information S1