Going against the flow: Testing the hypothesis of pulsed axial glacier flow

Hypothesised lobe‐like flow of a temperate glacier in southeast Iceland, proposed from an analysis of ice surface crevassing patterns, is appraised from both empirical and theoretical perspectives. The hypothesis comprises the migration of individual lobes (or ‘pulses’) of ice through the glacier body, with central lobes migrating more rapidly along a narrow, central, ‘axial flow corridor’. Our alternative hypothesis is that crevasse patterns at this glacier reflect simple surface ice responses to stresses caused by flow over uneven bed topography. To substantiate our rejection of the lobe‐like, pulsed axial flow hypothesis, we provide: (a) evidence for a prominent transverse foliation that exhibits no evidence of shear of the required magnitude to support the hypothesis; and (b) an analysis of ice surface displacement, obtained by feature tracking, that shows a uniform flow field throughout the glacier tongue. We argue that caution needs to be exercised when interpreting glacier flow solely from crevasse patterns and observations of minor displacements along near‐surface fractures and other features. © 2018 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.


Introduction
propose that fracture (i.e. crevasse) patterns at Kvíárjökull (Fig. 1), a temperate glacier in southeast Iceland, indicate that flow since c. 1940 has proceeded as a series of independently moving lobes or 'pulses' of ice (Fig. 1d) originating in the upper glacier tongue.
These authors have used 'marked changes' in crevasse patterns to divide the glacier surface into 27 domains, which are claimed to be individual pulses of ice separated by shear zones. Perceived 'cross-cutting' relationships between domains, and the elongate nature of the central domains, is inferred to show that lobes within a narrow central corridor (or axis) 'bypass' packages of slowflowing or stationary marginal ice ( Fig. 1(b)). The conclusionthat flow can occur in discrete lobes that migrate independently through the glacier bodyprofoundly contradicts widely demonstrated patterns of glacier flow (e.g. Hooke, 1998;Cuffey and Patterson, 2010).
The work presented by Philips et al. (2017) sets a new standard for glacier fracture mapping. In addition, it is essential for the development of glaciological theory that, as in all fields of science, new methods are trialled that seek to challenge received wisdom. It is also essential that all new theories and methods are subject to rigorous testing, and that those found wanting are dismissed, or highlighted as deserving of further work. We set out to test the pulsed axial flow hypothesis of Phillips et al. (2017) because crevasse patterns are more commonly interpreted to reflect local tensile stresses caused by undulations at the glacier bed (see Discussion). In addition, Swift et al. (2006) have previously documented the presence of a glacier-wide, transverse, ogive-origin foliation at Kvíárjökull. This foliation is largely overlooked by Phillips et al. (2017), yet could provide strong supporting evidence for their theory if it can be shown that independently migrating lobes of ice have caused the foliation to be sufficiently offset.

Study Area and Methods
Kvíárjökull ( Fig. 1(a)) is a valley glacier fed by the Oraefajökull icecap via a steep icefall located c. 6 km from the glacier terminus. For this study, horizontal displacement of ice in the icefall and tongue was obtained by analysis of high-resolution (3 m) PlanetScope imagery (Planet Team 2017) using a normalised cross correlation algorithm that tracks movement of surface features (Kääb and Vollmer, 2000;Heid and Kääb, 2012). A limited structural survey (restricted to mapping open crevasse areas and notable examples of transverse foliation) was undertaken from an aerial photograph acquired in 2009 (shown in Fig. 1(b) and (c)), and mapped features were observed in the field in August 2007 and 2012. Band-ogives (e.g. Goodsell et al. 2002) are clearly visible in aerial and satellite images from the 1940s onwards (e.g. Phillips et al. 2017 and Fig.   1(a)), and thrusting along ogive-origin foliae has previously been observed in ice approaching the glacier terminus (Swift et al. 2006). These thrusts were argued by Swift et al. (2006) to originate from reactivation of shear along dark-ogive bands that contain a higher density of foliae (Goodsell et al. 2002) by a change in deviatoric stress that occurs as ice nears the adverse slope of the terminal overdeepening. Phillips et al. (2017) describe the mapped domains ( Fig. 1(b)) as a series of radially crevassed, teardrop-shaped regions of ice centred around ice-surface topographic highs, and interpret these to be a chronosequence of discrete lobes of ice produced in the upper tongue. The central lobes are more elongate and said to 'clearly cross-cut and truncate the relatively earlier developed teardrop-shaped [i.e. less elongate] lobes at the ice margins' (p. 14). Particular attention is given to Domain 27, a marginal domain ( Fig. 1(b)) that displays a rounded 'teardrop' shape and radial crevasse pattern. This domain is immediately upglacier of Domain 1 ( Fig. 1(b)), which has relatively low relief and an absence of surface crevassing. Small displacements on steeply dipping, closed fractures in Domain 27 lead Phillips et al. (2017) to conclude that Domain 27 is a discrete lobe that has overthrust slower moving ice in Domain 1. Small displacements (10s of centimetres) along crevasses are also used to conclude that a longitudinal crevasse zone adjacent to Domain 1 is a 'dextral shear zone' (see Fig. 1(b)), marking a deflection of the active ice flow corridor to the true-left (i.e. to the northern part of the frontal margin).

Results
Measured displacement of glacier ice (Fig. 2) is highest along a broad central zone, with maximum displacements occurring in the steep topography of the icefall, and decreases towards the glacier tongue and margins. Displacements therefore demonstrate a broadly uniform flow field that is characterised by 'plug-flow' across c. 60% of the glacier width ( Fig. 2(c)), with the majority of shear being restricted to ice at the lateral margins. Rapid changes in displacement that are perpendicular to flow, which might indicate longitudinal shear, are not apparent (Fig. 2(c)), meaning no discrete central (or 'axial' flow) corridor is observed. Mapped flowlines ( Fig. 2 indicate that flow near the terminus bends slightly to the true-right (i.e. the southern region of the terminus), and do not show evidence of dextral shear. Rather, the northern region appears almost to be stagnant (see Discussion). A small area (10s of m wide) of low displacement near the terminus ( Fig. 2(a)) possibly reflects localised mass loss caused by subglacial water flow, or resistance provided by a subglacial landform, such as an esker deposit. Debris-covered ice at the extreme lateral margins near the terminus Fig. 2(a) also exhibits low displacements.
Two prominent ice structures visible from aerial and satellite imagery and in the field are present along the length of the glacier tongue. The first is an arcuate transverse englacial foliation that originates from band-ogive foliation, which first appears below the icefall ( Fig. 1(a)). The second is a medial moraine that originates from a bedrock outcrop within the icefall ( Fig. 1(a)) and extends to the terminus. Band-ogive foliation continues to be visible along the tongue and is traceable across the glacier width ( Fig. 1, 3). Incorporation of debris into foliae associated with band-ogive formation (see Goodsell et al. 2002) is demonstrated by the concertina-style margins

Flow pattern of Kvíárjökull
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of the medial moraine structure and lateral edges of the glacier ( Fig. 1(c)). Bands become less clear in the lower tongue and terminus, but many distinct, occasionally debris-rich ogive-parallel foliae remain (Fig. 3). The reduced visibility of ogive bands in the lower tongue may be due to surface ablation, which diffuses sediment across the glacier surface, and removes upper layers of ice containing snow-filled crevasses that contribute to the lighter appearance of the 'winter' bands (Swift, 2015). morphology, but, rather than shearing, this appears to indicate shortening (giving rise to a concertina morphology; Fig. 1a) that is consistent with compressional flow near the terminus.

Crevasse patterns and glacier flow
Crevasses are tensional fractures that form at 90 degrees to the direction of maximum tension (Nye, 1952;Hambrey and Müller, 1978;Huddleston, 2015). They are typically a shallow surface phenomenon because the confining pressure imposed by surrounding ice sets a maximum depth limit that in temperate ice is about 25 to 30 m (Nye, 1957;Hambrey and Müller, 1978). (Waterfilled crevasses can exceed this, but do not occur on Kvíárjökull). Crevasses form relatively quickly under a specific local stress regime, and may close similarly rapidly as flow transports them into a new stress regime. The minimum extensional strain required for crevasse formation varies greatly, meaning the absence of crevassing does not necessarily indicate slow or stagnant flow (Hambrey and Müller, 1978;Cuffey and Patterson, 2010). Closed fractures are sometimes observed deep within the interior of glaciers but the origin of these is debated, and most documented examples are transverse features originating in areas of very rapidly extending ice flow, such as icefalls (e.g. Hambrey and Müller, 1978;Goodsell et al. 2002).
Their relatively shallow depth means crevasses have limited significance for glacier flow (Huddleston, 2015). Instead, horizontal stress coupling in ice below the depth limit for crevassing transmits internal forces over distances of several ice thicknesses, meaning glacier flow proceeds in the manner of a stiff fluid in which flow is dictated by the creep properties of ice. This precludes sharp longitudinal velocity gradients, and causes the drag exerted by bedrock at the glacier sides to restrain the flow at the glacier centre. Rapid shear is concentrated in thinner ice near the lateral margins and almost absent in thick ice near the glacier centre, as shown by field measurements of longitudinal velocity (Fig. 6) (Raymond, 1971). This general pattern is reinforced by patterns of basal water pressure that promote high rates of basal slip beneath thick ice in the centre. Studies show that slip accounts for typically greater than 65% (and frequently 80

Flow pattern of Kvíárjökull
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to 90%) of ice surface velocity across more than half the width of the glacier (Cuffey and Paterson, 2010). Flow within this central region is therefore nearly uniform (i.e. 'plug flow').
Longitudinal flow of ice in discrete, fast-moving, corridors or streams (but not 'lobes') is known to occur only in ice sheet systems. Such systems are sufficiently large to accommodate 'shear margins' of 5 to 10 km wide (e.g. Joughin et al. 2004 Complex crevasse patterns may occur as a result of the uneven character of glacial valleys and beds (e.g. Hambrey and Lawson, 2000;Cuffey and Patterson, 2010;Huddleston, 2015). Notably, longitudinal undulations in glacier beds give rise to alternating regions of transverse and longitudinal crevassing arising from longitudinal flow extension on areas of steeper bed and transverse extension due to flow compression on areas of less steep or negative bed slope, respectively (Nye 1952). Thus, short wavelength bed undulations will cause crevasse formation under rapidly alternating stress regimes, and therefore to contrasting crevasse patterns being 'overprinted'. Further, longitudinal and radial (or splaying) patterns are common at glacier termini where a widening valley enables ice flow to splay out laterally (e.g. Hambrey et al., 2005), or where ice flows past a valley constriction or promontory, or where it negotiates subglacial ridges or hills (Cuffey and Paterson, 2010). In the terminal area that includes Domains 27 and 1, rather than a discrete lobe centred on one high, orientations of radial and longitudinal crevasses that form a contiguous field indicate flow

Flow pattern of Kvíárjökull
This article is protected by copyright. All rights reserved. deflection by possibly several subglacial highs (Fig. 7(a)), before flow continues into Domain 1 where these crevasses close. These highs correlate with the upglacier termination of a diagonally oriented subglacial ridge mapped by Magnússon et al. (2012) (Fig. 7 (b)). The change in longitudinal crevasse orientation north of Domain 1, as ice approaches the terminus, reflects quasi-transverse extension of ice that overrides the ridge (Fig. 7 (a) and (b)). Displacement in this region (Fig. 2) indicates broadly uniform flow similar to that of other glaciers (e.g. Fig. 6) and does not provide evidence of longitudinal shear or lobe-like flow.
Displacement measurements (Fig. 2 (b)) also show that the central flowline of ice in the glacier tongue is not deflected to the true-left when approaching the terminus and that Domain 1 is not slow-moving or stagnant ice. Rather, the central flowline runs through Domain 27 into Domain 1, and ice meeting the subglacial ridge appears to slow and extend transversely. This general pattern is supported by patterns of deformation shown by ogive bands and ogive-origin foliae (see below), and displacements of prominent ice-surface debris accumulations (Fig. 7 (c)). An absence of crevasses and the low elevation of Domain 1 likely reflect high surface ablation rates and reduced basal drag in this location on account of flow entering a deep, terminal subglacial basin (Magnússon et al. 2012; Fig. 7(b)). An advance of the northern frontal margin at a time of no clear change in the position of the southern frontal margin is noted by Phillips et al. (2017) as further evidence that active ice flow is deflected to the true-left. However, such an advance could also have resulted from thermal insulation of the ice margin by large terminal debris accumulations that are not present in the southern region. Further, 2017 imagery confirms the continued presence near the ice-front of the 'rockfall' moraine (Fig. 2).
Coherent glacier-wide, transverse ogive-origin banding is also present throughout the region of proposed lobe-like and axial flow (e.g. Fig. 1(c)). Band-ogives are an arcuate glacier-wide foliation phenomenon commonly observed in glacier tongues where ice has navigated a steep icefall. Band-ogive formation reflects the compression of ice flow at the base of an icefall to produce an annual pair of lighter 'winter' and darker 'summer' bands comprising transverse foliae that dip steeply upglacier (Swift, 2015). Individual foliae are produced by the healing, rotation and shortening of crevasses formed within the icefall and by shearing at the base of the ice fall, a process that has been observed to entrain basal ice and debris, with folia in darker 'summer' bands appearing denser and more sediment-rich (Goodsell et al. 2002). Drag imposed by the valley bed and sides (see above; Fig. 6) causes ogive folia to rotate from being initially sub-vertical to being semi bed-parallel, and bands to become increasingly arcuate, with distance down-flow. Bands therefore form a series repeating arches that are convex in the direction of glacier flow and closely spaced near the ice margins and widely spaced near the centre of flow (see Fig. 8 and caption).
At Kvíárjökull, the integrity of ogive-origin foliation throughout the lower tongue and terminal region indicates an absence of internal longitudinal shear of the magnitude required to support the presence of discrete ice lobes and therefore support the pulsed axial flow hypothesis. It is also clear that, near the terminus, the deformation patterns shown by dark ogive banding and related transverse foliae show that active flow is directed towards the southern part of the frontal margin, an observation supported by feature tracking (Fig. 2). This means the crevasse-free ice surface in Domain 1 does not indicate stagnation, but likely indicates rapid ablation. Further, it is this flow pattern, rather than strike-slip at the edge of Domain 1, that likely explains the c. 260 m movement of the ice-cored esker between 2010 and 2014 (see Phillips et al., 2017). Further evidence of this general flow pattern and the integrity of the ogive-origin foliation throughout the lower tongue and terminal region is provided by observations of thrusting close to the terminus that apparently occurs along ogive-origin foliae (Swift et al. 2006) (Figs. 4 and 8). Phillips et al. (2017) speculate that the pulses of flow required to produce individual lobes are the result of a surge-type phenomenon linked to the temporary storage of ice behind subglacial Flow pattern of Kvíárjökull This article is protected by copyright. All rights reserved.

Surging as an analogue and links to surge mechanisms
bedrock highs beneath the upper tongue. Flowers et al. (2011) have indeed proposed a surge mechanism linked to the presence of a subglacial basin (i.e. overdeepening), but observations at surging glaciers demonstrate that surging in temperate ice leads to even greater plug-like flow because it is associated with uniformly high basal water pressures that produce widespread, rapid basal slip (e.g. Kamb et al. 1985). Surging ice has notto our knowledgebeen observed to flow in a corridor past non-surging or stagnant ice adjacent. Surging can produce certain lobe-like flow phenomena, specifically 'loop' or 'tear-drop' moraines (Post & LaChapelle, 1971), but these occur only where surging ice from one glacier displaces or strongly shears the ice of another glacier at a tributary-trunk junction. The images we present indicate no evidence of such lobe-like structures at Kvíárjökull. Nonetheless, it is possible that decadal scale changes in velocity at Kvíárjökull do occur, and that they may indeed be linked to the presence of subglacial basins that influence subglacial hydrological and sediment transfer processes (e.g. Turrin and Forster, 2014).

Conclusion
The motivation for the study by Phillips et al. (2017)  First, crucial aspects of crevasse formation and glacier flow are not given adequate consideration.
Crevasses form in response to near-surface stress in their immediate locality and close as glacier flow causes ice to move from one stress regime to another, whilst traces of shallow crevasse may be removed entirely by surface ablation. Crevasses cannot therefore be used to identify, unequivocally, discrete areas or packages of ice flow originating decades apart, or areas of historically stagnant ice. Moreover, flow of ice in discrete corridors or streams appears to occur Flow pattern of Kvíárjökull This article is protected by copyright. All rights reserved.
only in much larger ice sheet systems and lacks physical plausibility at the valley glacier scale.
Second, unequivocal evidence of shear of suitable magnitude at the boundaries of the proposed lobes is lacking. Even more importantly, the existence of such lobes is incompatible with glacierwide transverse ogive-origin foliae and thrusts observed in the glacier tongue.
A simpler explanation for the crevasse patterns at Kvíárjökull is the uneven nature of the glacier bed, which is indicated by published bed data. This explanation is supported by the unchanging nature and positions of crevasse patterns between 2009 (ARSF aerial photograph) and 2017 (PlanetScope imagery). Longer-term changes in crevasse patterns may nevertheless occur as a result of glacier thinning and thickening, and it is likely that subtle changes in patterns identified by Phillips et al. (2017) since 1940 reflect changes in mass balance that have affected ice thickness and velocity. In the absence of other evidence, these explanations are far more likely than those that invoke surge behaviour or, even, changes in the morphology of the bed.
Crevasse patterns should primarily be interpreted in view of valley and bed morphology, which determines local patterns of stress in surface ice, but in addition caution needs to be exercised when interpreting glacier surface structures because their behaviour cannot be extrapolated to ice behaviour at depth. For example, horizontal and vertical displacements along faults likely represent local movements on open crevasses or their traces in the context of the very different behaviour of surface ice. Such ice is not subject to large confining pressures or the transverse stress couplings that dictate the behaviour of ice within the body of the glacier below. In light of this, the 'sense of shear' that may be demonstrated by small displacements observed on such near-surface features must be considered insufficient to support broader theories of ice flow.
acknowledges support for fieldwork in Iceland from the Royal Geographical Society through awards SRG 20/12 (awarded to DAS) and SRG 18/07 (awarded to Simon J. Cook). Fieldwork in Iceland was conducted under permit from The Icelandic Centre for Research (Rannis). Eyjólfur Magnússon kindly supplied the glacier bed topography dataset. Robert G. Bryant and Jeremy C.
Ely are thanked for their advice during the preparation of an earlier version of this manuscript.
DAS also gratefully acknowledges discussions with David J. Graham. Mike Hambrey and one anonymous reviewer provided constructive and valuable reviews of an initial submission of this manuscript, and we are grateful for their time and insight.