Modeling Sediment Transport in Ice‐Walled Subglacial Channels and Its Implications for Esker Formation and Proglacial Sediment Yields

Abstract

Sediment yields from glacierized basins are used to quantify erosion rates on seasonal to decadal timescales as well as conditions at the glacier bed, and eskers hold valuable information about past subglacial hydraulic conditions in their spatial organization, geometry, and sedimentary structures. Ultimately, eskers are a record of past glacio‐fluvial sediment transport, but there is currently no physical model for this process. We develop a 1‐D model of morphodynamics in semicircular bedrock‐floored subglacial channels. We adapt a sediment conservation law developed for mixed alluvial‐bedrock conditions to subglacial channels. Channel evolution is a function of melt opening by viscous heat dissipation from flowing water and creep closure of the overlying ice, to which we add the closure or enlargement due to sediment deposition or removal, respectively. We apply the model to an idealized land‐terminating glacier and find that temporary sediment accumulation in the vicinity of the terminus, or the formation of an incipient esker, is inherent to the dynamics of the channelized water flow. The alluviation of the bed combined with the pressurized channel flow produces unexpected patterns of sediment evacuation: We show that the direction of hysteresis between sediment and water discharge is not necessarily linked to a supply‐ or transport‐limited system, as has been hypothesized for proglacial sediment yields. We also find that the deposition of an incipient esker is a function of a compromise between water discharge and sediment supply, but perhaps more importantly, ice‐surface slope and the temporal pattern of water delivery to the bed.

A Model for the Formation of Eskers

“…Channel size evolves on a timescale of days to weeks, so it could apply roughly to summer conditions, but short-term fluctuations are known to lead to more complicated dynamics (Beaud et al, 2018). On the timescale of margin retreat, it must be some long-term average behavior that controls esker deposition, but it is not obvious that can be described by the quasi-steady theory developed here.…”

“…In this context we note the recent study of Beaud et al (2018), whose model includes similar ingredients to our own but concentrates on time-dependent evolution on shorter timescales. In this context we note the recent study of Beaud et al (2018), whose model includes similar ingredients to our own but concentrates on time-dependent evolution on shorter timescales.…”

A Numerical Model for Fluvial Transport of Subglacial Sediment

“…This suggests the diurnal variability in sediment access decreases beyond the initial peak in suspended sediment concentration early in the season (Williams, 1989). However, counterclockwise hysteresis is not observed in these model outputs as is sometimes observed in natural systems (e.g., Mao et al, 2014;Riihimaki et al, 2005) and in model outputs (Beaud et al, 2018). In the modeling framework presented here, this could be due to the relatively steep hydraulic gradients of the synthetic glacier ( Figure 2) that do not permit deposition of substantial amounts of sediment at the terminus that could permit counterclockwise hysteresis in these environments.…”

“…Estimates of hydraulic conditions at the glacier bed over subdaily timescales are needed to describe the ability of subglacial water to transport sediment (e.g., Beaud et al, 2018;Collins, 1990;Creyts et al, 2013;Walder & Fowler, 1994). This is because water discharge often varies diurnally, while the subglacial drainage system responds over longer timescales (e.g., Iken & Bindschadler, 1986).…”

“…The velocity of subglacial water is a function of the size of the subglacial conduits that the water flows through, the discharge of the water, and the gradient of the hydraulic potential. This is manifested in the Darcy-Weisbach relation for water flow through a pipe (Beaud et al, 2018;Carter et al, 2017;Creyts et al, 2013;Hewitt & Creyts, 2019;Ng, 2000;Walder & Fowler, 1994). In a warming climate, glacier melt and water discharge will temporarily increase (e.g., Huss & Hock, 2018), resulting in a greater capacity of subglacial water to transport sediment.…”