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.