Formation and interpretation of eskers beneath retreating ice sheets

The retreat of the ice sheets during the Pleistocene left large and spectacular subglacial features exposed. Understanding these features gives us insight into how the ice sheets retreated, how meltwater influenced retreat, and can help inform our understanding of potential future rates of ice sheet retreat. Among these features, eskers, long sinuous ridges primarily composed of clastic sediments, lack a detailed explanation of how surface melt rates and ice sheet retreat rates influence their growth and spatial distribution. Here, we develop a theory for esker formation based on the initial work of Rothlisberger modified for sediment transport and inclusion of surface meltwater forcing. The primary subglacial ingredients include water flow through subglacial tunnels with the addition of mass balances for sediment transport. We show how eskers when water flow slows below a critical stress for sediment motion. This implies that eskers are deposited in a localized region near the snout of the ice sheet. Our findings suggest that very long eskers form sequentially as the ice front retreats. The position of the esker follows the path of the channel mouth through time, which does not necessarily coincide with the instantaneous route of the feeding channel. However, in most cases, we expect those locations to be similar. The role of surface meltwater and the climatology associated with the forcing is crucial to the lateral spacing of the eskers. We predict that high surface melt rates lead to narrower catchments but that the greater extent of the ablation area means that channels are likely larger. At the same time, for a given channel size (and hence sediment flux), the size of a deposited esker depends on a margin retreat rate. Hence, the size of the eskers is related delicately to the balance between surface melt rates and margin retreat rates. We discuss how our theory can be combined with observed esker distributions to infer the relationship between these two rates and help understand the melt history of ice sheets.