The Katahdin Esker

Introduction

Many landforms left by continental ice sheets owe their origin to thermal conditions at the glacier bed. Among these are thrust features¹ (Moran and others, 1980); periglacial landforms dating from the last interstadial, such as patterned ground (Kleman and Borgström, 1994) and tors (Kleman and Hättestrand, 1999); ribbed moraines² formed at boundaries between zones of thawed and frozen bed (Hättestrand and Kleman, 1999); and eskers.

Eskers are straight to somewhat sinuous ridges of stratified gravel deposited by water flowing in subglacial conduits. Water in such conduits flows in a direction that is determined only partly by the bed topography. Gradients in the pressure of the ice against the bed play an important role (Shreve, 1972). These pressure gradients explain some otherwise puzzling aspects of observed esker paths such as the tendency for eskers to be up on valley sides and to cross divides at their lowest points (Hooke, 2005, Figs. 8.24, 8.25).

In a subglacial conduit, shear in the viscous flowing water generates heat that melts conduit walls. Sediment in the basal ice is thus released into the water. The wall melting is offset by closure of the conduit, driven by pressure in the ice that is slightly higher than that in the water (Röthlisberger, 1972; Shreve, 1972). The resulting continuous supply of sediment quickly overloads the water, so some of it is deposited, forming the esker.

To study eskers, with particular reference to the Katahdin esker in Maine, we (Hooke and Fastook, 2007) used Fastook's numerical model of the Laurentide Ice Sheet. The model ice sheet is driven by climate. Past temperatures and winter precipitation are estimated from the GRIP (Greenland) ice core δ¹⁸O record (Fig. 1). The model was tuned so that the ice margin at 15.6 ka (15,600 calendar years ago) corresponded reasonably with a well-known massive 15.6 ka moraine in eastern Maine, the Pineo Ridge moraine (Fig. 2). The model was then tested by comparing other predicted margin locations and predicted basal and marginal temperatures with those suggested by field data.

Modeled and observed margins are in reasonable agreement, considering the uncertainties in both, especially prior to about 15 ka (Fig. 2). Modeled temperatures suggest arctic to subarctic conditions prior to ~15 ka, consistent with glaciotectonic thrust blocks and permafrost features on Cape Cod, and permafrost features in the Connecticut River Valley. The Pineo Ridge moraine, and also the 16.5 ka Pond Ridge moraine (Kaplan, 1999), appear to have been formed during short cold reversals recorded in the Greenland ice core (Fig. 1).

Esker segments

Many eskers were formed in segments (e.g. Donner 1965; Ashley and others, 1991). Along the 150 km Katahdin esker, an ideal ~5 km-long segment begins as a relatively small ridge. The ridge increases in size downflow, resulting in a tadpole shape (Fig. 3). The (tadpole) head reflects a period of time during which the margin position was relatively stable. We attribute the increase in size to: (1) melt rates on conduit walls that increase near the margin, thus releasing more sediment, and (2) to melt rates that exceed closure rates beneath the thinner ice near the margin, resulting enlargement of the conduit and thus in a decrease in water velocity. This part of the Laurentide margin terminated in the sea, so material that was flushed past the portal was deposited in submarine fans. As the margin retreated, successive segments were formed. The head of each younger segment, together with its associated fan, laps onto and buries the tail of the previous one.

Left unexplained by this conceptual model is why segments link up as nicely as they do.

Can eskers be built by subglacial meltwater alone?

The basal melt rate predicted by our model rises from 0 at the margin to 5 or 6 mm/yr within a few kilometers (Fig. 4). It then declines gradually. By integrating this melt rate over the drainage area of the Katahdin esker, we estimated that the discharge at the margin from this source would have been only 1.2 m³/s. This flow could have moved the material found in the esker. However, it would have resulted in melting of only ~11 m of ice per year from the conduit walls. Sediment concentrations in basal ice of continental ice sheets are generally less than ~10%. If this was true of the Laurentide Ice Sheet, such melt rates would have been too low to release enough sediment to build esker segments of the observed size in the time available. Water from the surface would have been required.

Why do segments line up?

Surface meltwater can reach the glacier bed through moulins that form when water-filled crevasses propagate to the bed (Glen, 1952; Weertman, 1973; Zwally and others, 2002). However, new moulins would not necessarily form in precisely the right place to result in a continuous esker. Rather, one would expect to see barbs representing situations in which water reached the bed offset laterally from the esker path. The next segment to develop would then join the earlier one some distance down flow from the base of the moulin that initiated the earlier one.

Where ice above a thawed bed is below the pressure melting point, heat is conducted upward into the ice. This loss reduces the heat available for melting of conduit walls and releasing debris, and thus may play a significant role in determining where eskers form. The heat loss is proportional to the temperature gradient in the basal ice, β_o. Our model predicts that β_o increases rapidly with distance from the margin, especially after the ice sheet begins to retreat, (Fig. 5).

On a bed beneath such cold ice, subglacial water is likely distributed in a network of broad low anastomosing channels. If the roof of one of these channels begins to melt upward, deepening the flow, the resulting increase in discharge would result in an increase in energy dissipation in this channel. Under temperate ice (ice that is everywhere at the pressure melting point) this dissipation would result in further melting. Owing to this positive feedback, the resulting conduit would probably become "sharply arched" and an esker could form (Shreve, 1972). Beneath cold ice, however, such a perturbation in conduit height increases β_o. This is because the roof of an arched conduit must remain at the pressure melting point, so temperature contours immediately above the conduit are deflected upward while those far above the conduit are not affected (Fig. 6). The resulting increased heat loss will inhibit melting of the conduit roof, and may prevent formation of an esker.

Geomorphic implications

In summary, eskers may form near the margin because temperature gradients in the basal ice further up glacier prevent development of arched conduits with melting walls (that supply sediment). Water may reach the bed through moulins further from the margin, but it then probably spreads out in a distributed drainage system.

¹ Slabs of sediment or bedrock, sometimes 100s of meters in extent, that became frozen to the base of the glacier relatively near the margin and were then sheared 10s to 100s of meters down glacier.

² Closely-spaced moraines with intervening troughs. If the troughs are closed by sliding the moraines together, they appear to form a continuous sheet. This suggests that the moraines were formed by pull-apart of the sheet.

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