Morphology, flow dynamics and evolution of englacial conduits in cold ice

Meltwater routing through ice masses exerts a fundamental control over glacier dynamics and mass balance, and proglacial hydrology. However, despite recent advances in mapping drainage systems in cold, Arctic glaciers, direct observations of englacial channels and their flow conditions remain sparse. Here, using terrestrial laser scanning (TLS) surveys of the main englacial channel of cold‐based Austre Brøggerbreen (Svalbard), we map and compare an entrance moulin reach (122 m long) and exit portal reach (273 m long). Analysis of channel planforms, longitudinal profiles, cross‐sections and morphological features reveals evidence of spatial variations in water flow conditions and channel incision mechanisms, and the presence of vadose, epiphreatic and phreatic conditions. The entrance reach, located at the base of a perennial moulin, was characterized by vadose, uniform, channel lowering at annual timescales, evidenced by longitudinal grooves, whereas the exit portal reach showed both epiphreatic and vadose conditions, along with upstream knickpoint migration at intra‐annual timescales. Fine‐scale features, including grooves and scallops, were readily quantified from the TLS point cloud, highlighting the capacity of the technique to inform palaeoflow conditions, and reveal how pulses of meltwater from rainfall events may adjust englacial conduit behaviour. With forecasts of increasing Arctic precipitation in the coming decades, and a progressively greater proportion of glaciers comprising cold ice, augmenting the current knowledge of englacial channel morphology is essential to constrain future glacier hydrological system change.

Terrestrial laser scanning (TLS) has been used to map the complex, fine (millimetre)-scale morphology of bedrock channels (e.g. Lague et al., 2013) and inaccessible areas of cave systems (e.g. Buchroithner et al., 2009;Gallay et al., 2015;Oludare Idrees & Pradhan, 2016). TLS has also been used to yield high-resolution digital elevation models of glacier surfaces (e.g. Fischer et al., 2016;Hopkinson, 2004;Schwalbe et al., 2008), to measure and monitor ice surface changes in ice-coated bedrock caves (Gašinec et al., 2012;G omez-Lende & Sánchez-Fernández, 2018) and, recently, to reconstruct digitally an englacial channel reach (Kamintzis et al., 2018). As an approach, TLS offers an improvement on traditional speleological surveying techniques through markedly increasing the level and resolution of recorded detail, and reducing time spent in high-risk environments owing to more rapid (minutes to hours) data acquisition (Heritage & Large, 2009). The locational precision and density of TLS point clouds retrieved from ice surfaces, however, depend on the physics and optical properties of the ice, with up to $50% return loss and a typical accuracy of 7 mm (Kamintzis et al., 2018). Nonetheless, the technique offers the potential to record the fine-scale morphology of englacial channels and explore its hydraulic significance.
Here, to explore the morphology and associated palaeoflow conditions of an englacial channel, we present the results of TLS surveys of the entrance and exit reaches (hereafter referred to as moulin and portal reaches, respectively) of such a flow pathway in Austre Brøggerbreen, Svalbard. Morphological features within each reach at millimetre to decametre scale are described, and subsequently combined, for the first time, to infer the flow conditions and evolution of the drainage channel. We assess the capacity for high-resolution mapping of englacial drainage features to inform models of englacial channel change, and suggest broader, regional implications relating to potential transition between englacial and subglacial drainage pathways through cold-ice glacier margins.  (Jennings et al., 2015) that coalesce to form an $1.25 km-wide, low-gradient tongue. Austre Brøggerbreen is <100 m thick (Björnsson et al., 1996), thinning at $0.6 m w.e. a À1 (Barrand et al., 2010;James et al., 2012) and has a surface velocity of <3.0 m a À1 (Hagen et al., 1993;Hagen & Liestøl, 1990).
Two contrasting englacial conduit reaches were selected for investigation in this study: extending down-glacier of the channel entrance at Moulin A (the moulin reach) and extending up-glacier from the channel emergence at the ice margin (the portal reach) (Figure 1).
The moulin reach has been mapped by traditional surveying techniques six times since 1998 (Myreng, 2015;Vatne, 2001;Vatne & Irvine-Fynn, 2016;Vatne & Refsnes, 2003), during which time it changed from a gently sloping conduit to a 45 m-deep vertical moulin descending to a near-horizontal channel. Moulin A is fed by a single supraglacial stream that is 1-2 m wide and 1 m deep, with typical discharges of 0.2-0.4 m 3 s À1 (Holtermann, 2007;Myreng, 2015). The meltwater emerging at the ice-marginal portal is sourced from an $7 km 2 area comprising the eastern and central portions of the glacier (Porter et al., 2010). Dye-tracing studies have confirmed that perennial Moulins A and B (Figure 1) are both linked hydrologically to the portal (Holtermann, 2007;Myreng, 2015;Vatne, 2001), and GPR surveys have indicated the conduit from Moulin B may be only partially water filled during the melt season (Stuart et al., 2003). In 2009, meltwater was observed upwelling from the portal onto the glacier surface near the ice margin. Subsequent thinning of the glacier at the ice margin and incision by the emerging portal stream resulted in the portal transitioning from a waterfall at the glacier margin in 2013, to meltwater emerging at the head of a >10 m-deep, 170 m-long trench that extended into the glacier interior in 2016 ( Figure 1). Meltwater discharge from the portal is estimated to be typically 1-2 m 3 s À1 (Hodson et al., 2002;Porter et al., 2010).

| Field surveying
High-resolution TLS surveys of Moulin A (March 2016) and the portal (March 2017) reaches were completed using a FARO Focus 3D X 330 phase-shift scanner, following methods described by Kamintzis et al. (2018). Laser scanning parameters for each survey are presented in Table 1. The smooth, shiny, clean ice surface, and its optical Horizontal spacing between scans (m) 2-9 6 -26 Scanner height above channel floor (m) properties, reduced the quality of nadir laser scan point cloud data (see Kamintzis et al., 2018), and this limited the coherence and regularity of returns describing the suite of englacial channel features detailed further in Section 3. GPS coordinates were recorded at the glacier surface around Moulin A using a differential GPS (0.61 m horizontal precision, 1.68 m vertical precision) and at the portal using a handheld GPS (1.98 m horizontal precision, 2.00 m vertical precision) to georeference the TLS survey datasets. Photographs were taken at each scan site and detailed notes of ice structure and sedimentological features within the conduits were recorded.

| Data processing
Following Kamintzis et al. (2018), the TLS point clouds were postprocessed using FARO SCENE software. Post-processing involved scan georeferencing, target-based registration (mean registration accuracy in Table 1) and automatic noise filtering. Further manual noise filtering was completed for the 2017 scan data to remove the scanner tripod legs from the point clouds using Technodigit 3DReshaper software.

| Extraction of channel morphology and analysis
Two-dimensional channel morphologies, in planform and cross-section, were extracted from the processed point clouds using Rhino 3D software with the Veesus Arena4D point cloud plugin. The 'slice' tool was used to take a section either horizontally or vertically through the point cloud, and a line of best fit was digitized manually through these points to represent the channel shape.

| RESULTS
The fine spatial resolution of the point clouds, and the reconstruction of the channel walls, roof and inaccessible conduit areas, revealed numerous morphological features at sub-reach (decametre to subcentimetre) scales. Details of specific features observed and the extraction of associated data and analyses are presented in Table 2. Longitudinal grooves.
Each ridge and groove may indicate either former channel beds or channel-forming water-level positions.
Digitization of groove ridges along the conduit length using cross-sections.

Rhino3D
Measurement of groove height (vertical distance between groove ridges) and depth (maximum horizontal distance between the groove ridge and trough), calculation of groove area in straight channel section.

(5A)
Moulin A Continuous concave depressions on the order of centimetres to tens of centimetres, comprising irregularly shaped, polygonal hollows surrounded by crests. Crests transverse to the water flow direction were more prominent than longitudinal crests.

Directional intermediate scallops
that denote the direction of water flow (Richardson & Carling, 2005 Moulin A Concave depressions on the order of centimetres to tens of centimetres, comprising hollows surrounded by parabolic, convex-upstream crests arranged in horizontal lines.

Directional en echelon scallops
that denote the direction of water flow (Richardson & Carling, 2005).

Digitization of scallop crests.
ArcMap; FARO SCENE Measurement of scallop length (distance between scallop crests parallel to water flow direction). Use of ScallopEx (Woodward & Sasowsky, 2009) to determine recent stream velocity using average channel width at 3 m above the channel floor.

Portal
Continuous concave depressions on the order of centimetres to tens of centimetres, comprising roughly equidimensional hollows with parabolic, convex-upstream crests located on the conduit walls and roof upstream of the knickpoint.

Digitization of scallop crests.
ArcMap; FARO SCENE Measurement of scallop length (distance between scallop crests parallel to waterflow direction). Use of ScallopEx (Woodward & Sasowsky, 2009) to determine recent stream velocity using average channel width upstream of the knickpoint at 1 m above the channel floor.

Portal
Horizontally bedded sediment entrained within and overlying water-ice banks extending downstream from meander apexes on the inside bank.
-FARO SCENE, photography Visual assessment of sediment location, measurement of differing sediment band height above channel floor.

(7C)
Portal Flat, angular, irregularly shaped plates of sediment-rich water ice, found both in isolation on the conduit roof and entrained in frozen slush covering the base of raised passageways.
-FARO SCENE Measurement of long a-axis and c-axis (thickness).

(6A, 7D)
Portal Linear cavern raised above the roof and laterally offset from main channel upstream of the knickpoint.

Rhino3D
Measurement of raised passageway height, measurement of raised passageway floor height above main channel floor.

(6, 7E)
Portal Abrupt increase in gradient of the conduit longitudinal profile.

Knickpoint.
Digitization of centre and sides of knickpoint longitudinal profile.

Rhino3D
Measurement of the knickpoint height and width at the lip, calculation of the knickpoint gradient.

Portal
Series of downstream-dipping, highly prominent, curvilinear protrusions and associated underlying grooves, located on the true-right conduit wall, orientated semi-parallel to the active knickpoint and channel floor. Protruding small-scale ridges or larger-scale ledges transitioned to less prominent quasi-horizontal ridges observed to run along substantial lengths of the conduit.
Each protruding curvilinear ridge represents a knickpoint scar, reflecting former locations of the knickpoint face, knickpoint lip and channel floor, providing a record of knickpoint migration and channel bed lowering ( Table   4).
Digitization of top of protrusion where it meets conduit wall.

Rhino3D
Measurement of horizontal and vertical distance between knickpoint lip positions, calculation of knickpoint face gradient.  Table 2.

| Longitudinal grooves
The channel walls along the moulin reach were characterized by con-  (Table 3).

| Portal reach morphology
In 2017, the portal reach extended up-glacier from the exit in a southwest direction (Figures 6a and b).

| Raised passageways
Upstream of the knickpoint, there was also evidence of a raised passageway $2 m above the surveyed channel floor (Figures 6a and 7d).
This upper level was offset laterally (Figure 5c) and was only visible in F I G U R E 4 Schematic summarizing groove height and horizontal depth, highlighting the observed symmetry of the channel walls along the moulin reach, using an exemplar conduit crosssection for illustrative reference; mean heights and depths were derived from 72 cross-sectional measurements.
channel sections where it intersected the main channel obliquely.
Where the raised passageway was not visible, a sediment-rich suture line was observed at the top of the conduit walls on the inside of the meander bends. A frozen, sediment-rich slush-like veneer also covered the raised passageway floor and extended onto the roof of the main conduit between cross-sections 2 and 3 ( Figure 6b). Assuming the visible sections of the raised passageway are from a sediment-rich suture line of a single continuous feature, it has a lower sinuosity (S = 1.04) than that of the main channel upstream of the knickpoint (S = 1.18). The maximum recorded height of the upper, raised level was 3.5 m. The downstream end of the upper level opened out into the gallery (Figures 6 and 7d). Full dimensions and geometry of the raised passageway were not retrievable because sections were not always visible from the scanner survey positions.
Downstream of Scar 6, $18 m upstream of the portal exit, the series of five knickpoint scars was more morphologically pronounced: the scars were characterized by broad sub-horizontal and dipping glacier ice 'ledges' on the channel's true right, which protruded by up to $1.5 m horizontally from the channel wall. These exaggerated scar forms exhibited a downstream dip of between 19 and 57 (Table 4) and extended from $2.5 m to between 3.1 and 4.1 m above the floor, where the ledges became horizontal. Ledge protrusion decreased upstream to form a ridge that was morphologically more similar to the longitudinal ridges observed in the moulin reach.

| DISCUSSION
From the combination of fine and coarse-resolution TLS records, we here explore the palaeoflow conditions, the spatial arrangement of

| Indicators of palaeoflow conditions
The fine-scale morphological data highlighted two key sources of palaeoflow information in both the moulin and the portal reaches: grooves and scalloping. The longitudinal grooves are interpreted in terms of alternating periods of vertical and lateral incision, reflecting discharge fluctuations, analogous to the grooves observed in supraglacial stream channel walls (Marston, 1983;Pinchak, 1972). and recirculation (Curl, 1974), with scallop dimensions being inversely proportional to flow velocity (Allen, 1971;Goodchild & Ford, 1971;Loehr, 2012). No significant difference in scallop length between Grooves 1 and 2 in the moulin reach (see Section 3.1.2 and Table 3) suggests similarity in the last two periods of dominant meltwater fluxes, consistent with our interpretation of regular, annual groove formation. Following Curl (1974) and Woodward & Sasowsky (2009), we used mean en echelon scallop diameter (D) to estimate water velocity (u): ffiffi ffi τ ρ in which τ is shear stress, ρ is water density, W is the channel width or diameter, D 32 is the Sauter mean of measurements of D, A is a shape constant of 1 for parallel channel walls or 1.5 for a circular conduit shape and B D is a roughness constant defined by the geometry of the scallops. Water velocities within the portal reach since 2013 derived from scallop lengths are presented in Table 5. Crudely estimating an annual maximum (bankfull) cross-sectional area, we also evaluate peak discharges (Table 5). In our estimation, flow depth is constrained by the observed groove spacing of the order of 1 m, which itself accords with observations of supraglacial channel water depth during peak summer-season melt entering Moulin A (Holtermann, 2007;Myreng, 2015). Following the same approach, but assuming the channel upstream of the knickpoint was full (phreatic), scallop lengths yield recent water velocities (assumed to be in 2016) of 0.46 m s À1 , and a maximum estimated discharge of 3.79 m 3 s À1 .
The velocity and discharge values calculated from scallop geometry are consistent with those estimated previously for the englacial channel between Moulin A and the portal. Throughflow velocities from Moulin A in July of 2014 (i.e. Groove 3) were $0.17 m s À1 (Myreng, 2015), and other summer-season estimates have reported $0.19 m s À1 (Holtermann, 2007) to 0.4 m s À1 (Hagen et al., 1991).
Discharge into Moulin A has been estimated to be 0.2-0.6 m 3 s À1 (Holtermann, 2007;Myreng, 2015), and 0.4-4.0 m 3 s À1 emerging at the portal (Hodson et al., 1997). While of the same order of magnitude, subtle disparities between other observations and our estimates are readily ascribed to three causes of uncertainty: first, the discrete snapshots of throughflow or emergence velocity and discharge do not necessarily characterize the channel-forming, or seasonally dominant, discharge regime. Second, scallops preferentially form in response to the upper 5% of discharge (Murphy, 2019) and, consequently, velocity and discharge estimates derived from scallop length or diameter may be overestimated (Springer & Wohl, 2002). Third, our estimates are based on en echelon scallops along straight channel sections, and overlook flow acceleration or deceleration in meander bends where scallop geometries may differ (Lagasse et al., 2004;Leopold & Wolman, 1960;Myreng, 2015).
We examined the runoff record for the Bayelva catchment, within which Austre Brøggerbreen is located (NVE, 2019; Figure 8). Discharge fluctuations at the portal of Austre Brøggerbreen, despite being an order of magnitude lower, typically parallel those recorded at the Bayelva station (Porter et al., 2010). Of note is the apparent discrepancy between the scallop-derived discharge estimates for Grooves 1-3 (2013Grooves 1-3 ( -2015 in the moulin reach and the Bayelva discharge record indicating, in contrast, an elevated discharge throughout the summer season in 2013 compared to 2014 and 2015. To explain this discrepancy, we hypothesize that, at inter-annual timescales, the englacial channel may vary between phreatic and vadose conditions that modify the throughflow of water. Evidence for this is the change in morphology in the portal reach where, at high discharges, the narrow, low channel section upstream of the knickpoint (Figures 4a and 5b) may impede water flow (Schuler et al., 2004), thereby causing phreatic conditions. The semi-elliptical morphology of the channel upstream of the knickpoint (Figure 6d) indicates that the conduit was occasionally water filled (Audra & Palmer, 2011;Gulley & Benn, 2007;Palmer, 1991), consistent with observations of pressurized outflow observed in 2009. This is supported by the directional scalloping of the conduit roof, denoting turbulent but unidirectional water flow under conduit-full conditions (Richardson & Carling, 2005).
The Bayelva discharge record (Figure 8) also indicates distinct pulses of elevated discharge, likely related to precipitation events common during the summer season (Hodson, Gurnell, Tranter, et al., 1998a;Hodson, Gurnell, Washington, et al., 1998b). Such pulses may cause hydraulic damming and flow modulation (Schuler et al., 2004), resulting in intra-seasonal, transient phreatic (or epiphreatic; see White, 1988) conditions. The water-ice plates  (Hubbard et al., 2004;Jennings et al., 2015). This deposition, together with the sloping ice banks on which sediment was deposited, indicates active channel meandering with flow concentration on the outer meander bank and lateral variations in heat transfer across the channel (Karlstrom et al., 2013). The tilt in channel cross-section towards the inside of meander bends indicates enhanced melt on lower parts of the outer conduit walls in the absence of conduit-full conditions. It is probable that meandering and deposition has occurred under relatively low water levels, as typically experienced towards the end of the ablation season.

| Implications for Austre Brøggerbreen's drainage system
Our results are consistent with the inferred absence of subglacial drainage at Austre Brøggerbreen (see Hodson et al., 1997Hodson et al., , 2002Vatne, 2001). Unpressurized conditions have previously been assumed throughout the glacier's englacial drainage system (Stuart et al., 2003;Vatne, 2001). In contrast, the evidence we present implies the occurrence of both atmospheric and conduit-full  The portal reach appears to be adjusting rapidly to the local base level via upstream knickpoint migration. It is likely that, over time, this process will continue to propagate upstream within the conduit, as  Clayton, 1964;Egli et al., 2021;Paige, 1956). The associated hydraulic (re)activation of parts of the glacier bed under certain circumstances could impart a dynamical response for cold ice (e.g. Rippin et al., 2005), although this is less likely for Austre Broggerbreen but is a process perhaps relevant elsewhere. Such changes would have an impact on the sediment and solute fluxes released to the glacier's forefield (e.g. Hodson et al., 2004;Hodson & Ferguson, 1999).
At the coarser scale, our observations support the notion that englacial channels within cold ice can respond to hydrological forcing at inter-annual and intra-annual timescales. The inferred rapidity of channel adjustment indicates that drainage pathways in cold ice can and do evolve, in contrast to their characterization as static, 'relict' features (Hodgkins, 1997), and may incise to a subglacial location (Baelum & Benn, 2011;Gulley, Benn, Müller, & Luckman, 2009a;Gulley, Benn, Screaton, & Martin, 2009b;Naegeli et al., 2014;Temminghoff et al., 2019). Under forecasts for warmer and longer Arctic melt seasons (Post et al., 2019), and projections of glacier thinning to result in more extensive areas of cold ice across the region (Delcourt et al., 2013;Irvine-Fynn et al., 2011;Østby et al., 2017;Wilson & Flowers, 2013), increasing meltwater fluxes may accelerate cut-and-closure channel formation (Gulley, Benn, Müller, & Luckman, 2009a) and the subsequent englacial drainage evolution (e.g. Vatne & Irvine-Fynn, 2016), which may ultimately lead to incision to the glacier bed. Our study highlights the need to better resolve the conditions that result in vadose, epiphreatic and phreatic flow conditions, and the modes and rates of channel change associated with these intra-and inter-annual variabilities. With evidence of increasing rainfall events in Arctic settings (e.g. Bintanja & Andry, 2017;McCrystall et al., 2021) and that cold ice may also be pervasive in some lower-latitude glaciers (e.g. Reinardy et al., 2019;Ryser et al., 2013), improving constraints on the flow regimes and evolution of englacial channels in such thermal conditions is relevant to furthering understanding of the hydrology of glaciers both inside and outside the Arctic region.

| CONCLUSIONS
To date, englacial drainage systems have been mapped using geophysical and speleological techniques, with a lack of quantitative detail of fine-scale features. To address this, we used TLS surveys to retrieve detailed 3D models of channel morphology along the entrance (moulin) and exit (portal) reaches of a principal englacial drainage channel at Austre Brøggerbreen, Svalbard. At the coarser scale, the geometry of the conduit supported existing understanding of the progression of cut-and-closure channels in many Arctic glaciers, with vadose incision and knickpoint migration rapidly adjusting the channel towards a local base level, and perhaps the glacier bed. At the finer scale, our data allowed the measurement of grooves and scallops on the ice-channel walls, from which incision rates and palaeoflow conditions could be resolved for the first time. These small-scale morphological features are instrumental in resolving transient epiphreatic switches between vadose and phreatic conditions within sections of the englacial channel at intra-and inter-annual timescales in response to changes in meltwater runoff. We suggest that both conceptual and numerical models of englacial channel evolution through cold glacier ice may be enhanced by including micromorphological data to describe flow conditions, to improve understanding of the hydrological response of glaciers in a warming, wetter Arctic climate. and helpful photographs. We also thank three anonymous reviewers for their constructive comments and recommendations that improved the final version of this paper.

AUTHOR CONTRIBUTIONS
TDLI-F and JEK conceived and designed the study. JEK, SJAJ, PRP and JPPJ conducted the fieldwork and data collection. JEK processed and analysed the data with assistance from JPPJ. JEK and TDLI-F wrote the manuscript. TOH led manuscript editing. All authors contributed to the final editing and revision of the paper.

DATA AVAILABILITY STATEMENT
Data are not publicly available but can be requested by contacting the corresponding author.