Glaciology - Seasonal Evolution of the Hydrological System

‘Over the course of a melt season, a valley glacier’s hydrological system often evolves from one that is predominantly “distributed”, to one that is mostly “channelized”.’ Discuss.

Fiona Fang, Trinity Hall, 11/2024

The evolution of a valley glacier’s subglacial hydrological system during melt seasons from a “distributed” to a “channelized” configuration is a fundamental process that shapes glacier dynamics. Generally, at the onset of the melt season, subglacial drainage is characterized by a “distributed” network—tortuous and widespread across the glacier bed, with low-velocity flow through water films, linked cavities, braided canals, and groundwater pathways. As meltwater input increases, however, the system shifts toward a “channelized” configuration, where high-velocity flow is concentrated in a few large, efficient channels, which can be Rothlisberger (R-type) channels that incises up into ice or Nye channels that incise down into rocks or sediments (Sharp, 2005; Benn and Evans, 2010). This transition is documented by borehole measurements, GPS, seismic data, and dye tracing experiments. However, variations between glaciers are also observed, which can be explained by factors such as snowpack distribution, weather conditions, englacial drainage pathway availability, and bed type. Understanding this evolution is crucial, as it drives seasonal variations in basal sliding rates, with summer velocities often doubling or tripling those of winter (Rada and Schoof, 2018). Understanding this evolution can also help us better predict glacier behaviours with the intensified and lengthened of melt season under global warming.

Subglacial system evolution occurs through the expansion and contraction of conduits, described by Schoof (2010) in the following equation:

\[\frac{dS}{dt} = c_1 Q \Psi + u_b h - c_2 N^n S\]

The rate of the channels enlarge is governed by wall melting due to heat dissipation in the water flow, calculated in equation (1) as c1QΦ, where c1 is a constant, Q is discharge, and Φ is hydraulic potential. In contrast, distributed systems, characterized by slower water flow, experience negligible heat dissipation, making this mechanism less relevant for their enlargement (Rada and Schoof, 2018). For cavities, for example, the primary method of enlargement is through increased glacier sliding rates; the faster the sliding rate, the larger the gap, with the opening rate given in equation (1) as ubh, where ub is the speed of ice at bed and h is the height of cavity. Though enlarging through different mechanisms, both systems close due to creep deformation, which is controlled by effective pressure (N), i.e. difference between ice overburden pressure (pi) and water pressure (pw). In equation (1), the closure rate is calculated as c2Nn*S, where c2 and n being constants related to the latent heat of fusion and ice viscosity.

Seasonal evolution in the drainage system primarily reflects changes in melting, sliding, and creeping, all driven by the input of meltwater (Sharp, 2005). The introduction of meltwater raises the water level at the source, enhancing the pressure gradient and thereby increasing the velocity of water flow. Consequently, discharge tends to increase in both types of drainage systems, leading to a rise in basal sliding rates for cavity systems and wall melting rates for channelized systems. In the former, conduits expand proportionally less than the increase in discharge (Q), while in the latter, conduits expand proportionally more than the rise in Q. According to the relationship V=Q/S, water velocity (V) will increase in cavity systems but decrease in channel systems as Q changes. Therefore, effective pressure (N) in cavity systems is proportional to Q, whereas in channel systems, it inversely relates to Q, as shown in Figure 1. As Q increases, N initially decreases in cavity systems until it reaches a critical point, Qc ( Qc= where α=5/4). When mean discharge levels exceed Qc , the system transitions from a cavity-dominated configuration to a channel-dominated configuration, forming a set of large, well-defined channels fed by smaller, separated cavities (Schoof, 2010).

Figure 1 Steady state Q-N relationship, from Schoof (2010)

This model provides a foundation for understanding seasonal evolution. Before the melt season, the drainage system is under-developed, dominated by non-arborescent distributed networks. Dye-tracing experiments show that dye poured down moulins emerges diffusely at the glacier terminus, indicating slow and relatively inefficient transport (Figure 2b, Benn and Evans, 2010). The initial penetration of water to the glacier bed increases the separation between the ice and substrate, particularly downstream from where it reaches the beds (Mair et al., 2002). This results in an accumulation in stored water at the bed, as indicated by vertical uplift of glacier surfaces (eg. Sugiyama and Gudmundsson, 2004). As the meltwater and therefore discharge increase, water backs up in the drainage system, water pressures tend to rise (Sharp, 2005). With sustained high surface inputs over summer, discharge eventually surpasses the critical threshold Qc, marking the transition from distributed to channelized network. Since the water pressure in larger channels is lower than the smaller ones, these major channels also expand at the expense of nearby smaller ones (Schoof., 2010).

The transition from a distributed to a channelized system can lead to changes in water pressure, velocity, and diffusivity, with observed variations in these parameters reflecting this evolution. First, water pressure initially increases as cavities enlarge, and then drop gradually when with the growth of channels. This aligns with observations such as the borehole measurement of Haut Glacier d’Arolla, Switzerland by Gordon et al. (1998). Similarly, a 2-year-long seismic and in-situ measurement of Glacier d’Argentière (French Alps) reports 6-fold increase hydraulic pressure from spring to summer, followed by comparable decrease towards autumn (Nanni et al., 2020). Such change in water pressure, however, is not always slow and gradual throughout the melt season, as observed intermittently by Gimbert et al. (2016) at Mendenhall Glacier, Alaska. This is explained as the failure of variations in channel size in keeping pace with discharge changes over short time scales. Second, water velocity increases from spring to summer and then gradually declines as meltwater input decreases at the end of the ablation season. For instance, GPS measurements of an outlet glacier in western Greenland during the 2008 melt season showed a 70–100% increase in horizontal glacier motion velocity from winter levels after melt onset, with speeds gradually returning to below-winter values by summer’s end, despite isolated high-velocity events persisting throughout the summer (Bartholomew et al., 2010). This pattern indicates that water pressure lowers and basal sliding reduces at the start of the melt season, with the reverse occurring at the season’s close. Thirdly, the diffusivity or dispersion of channels decreases as the system transitions from a distributed to an arborescent network, a change detectable through dye-tracing experiments. At the beginning of the melt season, tracers emerge at the glacier terminus in diffuse waves, but after transitioning to a channelized system, they appear in a single, sharp-peaked slug (figure 2a; Benn and Evans, 2010). Similar pattern is observed by Nienow, Sharp and Willis (1998) in their study of Haut Glacier d’Arolla (figure 3). Finally, although these findings suggest widespread subglacial evolution during the melt season, it is important to note that this transition does not occur simultaneously across all parts of the glacier. As the snowline retreats, this efficient drainage system expands up-glacier, as observed by Nienow et al. (1998) on Haut Glacier d’Arolla, Switzerland, and by Rawlins et al., (2023) on Humboldt Glacier, northern Greenland.

Figure 2 The relationship between dye concentration and time since injection, from Benn and Evans (2010) Figure 3 The relationship between dye concentration and time since injection, from Nienow et al. (1998)

From these evidence, we can observe that during the melt season, subglacial systems typically undergo an evolution from distributed to channelized drainage. However, pattern of this transition varies between glaciers and across different years, influenced by several key factors. Firstly, the rate of transition depends on the end-of-winter snowpack distribution and the timing of its complete melt. This is because that snow, with its high albedo, melts relatively slowly in comparison to glacier ice, and therefore acts as a potential storage site for water (Sharp, 2005, p. 8). When snow cover disappears, a sudden release of water stored in the snowpack can lead to flooding (Flowers and Clarke, 2002). Meanwhile, the melt rates increase with the reduced near-surface water storage. (Benn and Evans, 2010, p. 78). Secondly, meteorological conditions at the glacier surface are also essential. Particularly, rainstorms can be a major stimulus to channel growth, controlling the exact timing of the transition from the ‘slow’ to ‘fast’ system, which varies from year to year (Gordon et al., 1998; Benn and Evans, 2010). Under current global warming, more frequent rain events are predicted to result from a northward shift of storm tracks over the next century (Schuenemann and Cassano, 2010). This might lead to more frequent and earlier transitions from the “slow” to “fast” drainage system beneath glaciers, accelerating glacier melt and movement. The third factor impacting the transition rate is the ease with which water can penetrate to the bed. Where drainage pathways from surface to bed are not immediately available, water is stored in supraglacial lakes, channels, and crevasses at the start of the melt season, and may be delivered to the bed very suddenly (Flowers and Clarke, 2000). This affects whether the system’s evolution is gradual or episodic. Where crevasses and moulins are distributed widely across a glacier, this can be a relatively smooth process. Where they are sparsely distributed, however, the process can be more episodic, with large areas of glacier bed developing channelized drainage in relatively short periods of time (Sharp, 2005, p. 9). Fourthly, patterns of subglacial system evolution differ between soft-bedded and hard-bedded glaciers. While most models are based on studies of hard-bedded glaciers, soft-bedded glaciers have unique characteristics, particularly their ability to store water within the subglacial system itself (e.g., in till, braided systems, or “ponds”). As a result, unlike hard-bedded glaciers, which experience most of their discharge during the melt season due to a channelized subglacial system, soft-bedded glaciers can experience speed-up events throughout the year, especially in winter (Hart et al., 2022).

In conclusion, the seasonal evolution of a valley glacier’s subglacial system from a predominantly “distributed” to a “channelized” configuration is a dynamic and complex process that is critical to understanding glacier hydrology and dynamics. This transition is driven by increased meltwater input, and would lead to changes in water pressure, velocity, diffusivity, and transport efficiency. In reality, the evolution dynamics varies from glacier to glacier, impacted by factors such as snowpack distribution, meteorological conditions, and subglacial bed characteristics. Further research can focus on how the intensified and prolonged melt season driven by current global warming affects this hydrological evolution. 

Supervisor Feedback: Very well done Fiona this shows an excellent process understanding and I like the way you discussed theory and the empirical evidence. Also, very good that you found different work to reference to that mentioned in the lecture slides. A 5th point you could have mentioned in your factors affecting evolution is the difference between temperate, polythermal and cold glaciers. And perhaps a 6th could be whether the glaciers are debris covered or not.

Bibliography

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