The hydrology of subglacial overdeepenings: A new supercooling threshold formula

Abstract

Overdeepenings are a hallmark glacial landform of broad geomorphologlogical and glaciological interest. Their formation mechanism has not yet been fully uncovered, but subglacial drainage is likely a key factor. One prominent hypothesis states that the depth of an overdeepening stabilizes at the supercooling threshold. This threshold is reached when the adverse bed slope terminating an overdeepening is sufficiently large to shut down the efficient, channelized drainage system. Classic theory puts this threshold at a ratio of bed to surface slope of −1.6. Here I extend that theory by taking into account that downstream water pressure can be below overburden pressure. The new formula agrees well with results from one‐ and two‐dimensional subglacial drainage models. Applying it to observations of 147 overdeepenings from alpine glaciers and ice sheets shows that the depth of overdeepenings rarely exceeds the new supercooling threshold. Thus, this work supports the stabilizing hypothesis.

On the morphological characteristics of overdeepenings in high‐mountain glacier beds

“…Mean adverse slopes have a maximum around 10°-20°, which largely exceeds the glacier-surface slope of <5°-10°considered critical for overdeepening formation (cf. Frey et al, 2010) and hence is in many cases above the critical slope ratio (1.6 times the surface slope) for supercooling and channel closure as commonly mentioned in the literature (Hooke, 1991;Alley et al, 2003;Cook and Swift, 2012;Werder, 2016). Maximum adverse slope is most frequently around 25°-30°, which in some cases could be high enough for sub-glacial lake formation (Clarke, 2005;Cook and Swift, 2012).…”

“…This figure is available in colour online at wileyonlinelibrary.com/journal/espl depths for the Swiss and Peruvian samples. Furthermore, the range for deeper overdeepenings is far above the critical slope (1.6 times the glacier surface slope or about 10°-20°in the case of mountain glaciers) so far often assumed for supercooling and channel closure along the adverse slopes of overdeepenings (Alley et al, 2003;Cook and Swift, 2012; but see also Werder, 2016).…”

“…The present study attempts to analyse quantitative data about the morphological characteristics of glacial overdeepenings by using high-resolution glacier-bed models and measured bathymetries of newly formed lakes. The question is investigated whether such data may have the potential to be used for calibrating numerical models of glacial erosion (Herman et al, 2011;Egholm et al, 2012) and for testing hypotheses of stabilizing feedbacks associated with the erosion of glacial overdeepenings (Alley et al, 2003;Hooke, 1991;Werder, 2016).…”

Modeling Antarctic subglacial lake filling and drainage cycles

“…At all stages of the model runs, water can flow up the adverse slope of the overdeepening; this is because water pressures at the rim of the overdeepening are slightly below overburden due to the presence of small channels. Combined with higher pressures in the lake, this cre-ates a gradient that allows water to flow up the reverse slope (Werder, 2016). The relative difference between the pressure in the lake and at the top of the adverse slope is a key driver for how much water can exit the lake.…”

A Numerical Model for Fluvial Transport of Subglacial Sediment

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where Q sc is the sediment transport capacity (see equation below), l is a sediment uptake e ‐folding length required for sediment discharge to adjust to transport capacity (e.g., Phillips & Sutherland, ), and H lim is a maximum till thickness (Table ) prescribed to prevent unbounded till deposition in places such as overdeepenings (e.g., Alley et al, ; Creyts et al, ; Werder, ). σ is a sigmoidal function of till height H and it is used for a smooth transition over H =2Δ σ −1 ±Δ σ −1 in equation 10c.…”