Subglacial drainage characterization from eight years of continuous borehole data on a small glacier in the Yukon Territory, Canada

The subglacial drainage system is one of the main controls on basal sliding, but remains only partially understood. Here we use an eight-year data set of borehole observations on a small, alpine polythermal valley glacier in the Yukon Territory to assess qualitatively how well the established understanding of drainage physics explains the observed temporal evolution and spatial configuration of the drainage system. We find that the standard picture of a channelizing drainage system that evolves towards higher effective pressure explains many features of the data set. However, our data set underlines the importance of 5 hydraulic isolation of parts of the bed. We observe how isolated portions of the bed systematically grow towards the end of the summer season, causing the drainage system to fragment into progressively more distinct subsystems. We conclude with an adaptation of existing drainage models that aims to capture the ability of parts of the bed to become hydraulically isolated due to basal cavities of finite size becoming disconnected from each other as they shrink.


Introduction
Basal sliding often accounts for about half of the observed surface speed of glaciers (e.g.Gerrard et al., 1952;Vivian, 1980;Boulton and Hindmarsh, 1987;Blake et al., 1994;Harper et al., 1998).The sliding rate typically shows a marked seasonal variation, with summer sliding speeds sometimes two or three times faster than winter averages (Nienow et al., 1998a;Sole et al., 2011;Ryser et al., 2014).These variations are controlled by the subglacial drainage system (Iken and Bindschadler, 1986;Gordon et al., 1998;Nienow et al., 1998b;Mair et al., 2001;Harper et al., 2005).However, the physical processes controlling the magnitude and timing of sliding rate variations are still incompletely understood.
The main variable linking subglacial drainage processes to basal sliding is effective pressure N , defined as the difference between normal stress at the bed and water pressure, where normal stress is usually taken to be equal to the overburden pressure.Increased basal water pressure reduces N and provides partial support for the weight of the glacier, reducing the contact surface with the underlying bedrock, and therefore enhancing basal sliding (Lliboutry, 1958;Hodge, 1979;Iken and Bindschadler, 1986;Fowler, 1987;Schoof, 2005;Gagliardini et al., 2007).A similar effect is observed on glaciers resting on a till layer, where a lower N reduces the yield stress of the till, and therefore also enhances basal sliding (Engelhardt et al., 1978;Iverson et al., 1999;Tulaczyk et al., 2000;Truffer et al., 2001).Conversely, large effective pressures enhance the mechanical coupling at the bed interface and therefore reduce sliding.
In contrast to channels, equilibrium in a linked cavity system is reached at lower effective pressure when Q increases: cavities have to grow to accommodate additional discharge, and this requires creep closure to be suppressed by a reduced effective pressure.Therefore, an increase in Q should decrease effective pressure, and speed the glacier up (Kamb, 1987;Schoof, 2010).
The formation of channels can be understood as an instability in drainage through a distributed network of channels, and can be expected to occur when water supply rates to the bed are sufficiently large (Schoof, 2010;Hewitt, 2011Hewitt, , 2013;;Werder et al., 2013).However, even then the formation of a well-developed arterial channel network requires time and may not be fully complete in a single summer melt season.
The relative scarcity of subglacial observations make it difficult to assess how common these phenomena are, and in some cases, the physical processes involved.In this paper, we take a holistic view of an eight-year data set of borehole water pressure records and surface conditions obtained from a small polythermal valley glacier in the Yukon Territory, Canada.This data set includes 311 boreholes with up to 150 being recorded simultaneously.We attempt to present a comprehensive picture of the evolution of the drainage system, incorporating all the main features of the borehole record.
Our aim in this paper is to assess qualitatively the extent to which established understanding of drainage physics is compatible with our observations, and where existing models are in conflict with those observations.We will then present a modification of a class of existing models intended to account for what appears to be the most significant missing physics: the development of hydraulically isolated patches of the bed (Hodge, 1979;Engelhardt et al., 1978;Murray and Clarke, 1995;Hoffman et al., 2016).
The paper is laid out as follows: in section 2, we describe the field site and observational methodology.An overview of our observations is given in section 3, with a physical interpretation presented in section 4. Motivated by our observations, we present the model modification in section 5, focusing on the dynamic organization of the drainage system into active and hydraulically isolated components.This will not provide a full account of the presented data set, which also includes surface speed and other variables.An in-deep study of the evolution of the subglacial drainage system structure and its relationships with measured surface speeds is ongoing and will be presented in upcoming papers.

Field site and methods
All observation presented were made on a small (4.28 km 2 ), unnamed surge-type alpine glacier in the St. Elias Mountains, Yukon Territory, Canada, located at 60 • 49' N, 139 • 8' W (Fig. 1).We will refer to the site as "South Glacier" for consistency with prior work (Paoli and Flowers, 2009;Flowers et al., 2011Flowers et al., , 2014;;Schoof et al., 2014).Surface elevation ranges from 1,960 to 2,930 m above sea level (asl), with an average slope of 12.6 • .The equilibrium line altitude (ELA) lies at about 2,550 m 5 (Wheler, 2009).Bedrock topography at the site has been reconstructed from extensive ground-penetrating radar (GPR) surveys (Wilson et al., 2013), reporting an average and maximum thickness of 76 m and 204 m respectively.Direct instrumentation and radar scattering (Wheler and Flowers, 2011;Wilson et al., 2013) reveal a polythermal structure with a basal layer of temperate ice.Exposed bedrock in the valley consists mainly of highly fractured Shield Pluton granodiorite (Dodds and Campbell, 1988;4 The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.Crompton et al., 2015).Borehole videos have also shown the presence of granodiorite cobbles in the basal ice, and highly turbid water near the bottom of freshly drilled boreholes.Frozen-on sediments and a basal layer of till of unknown depth are visible in some borehole imagery, and till thicknesses in excess of two meters are exposed near the snout.
Boreholes were drilled in the upper ablation area of the glacier, between 2,270 and 2,430 m asl (Fig. 1), covering an area of approximately 0.6 km 2 , with an average ice thickness of 63.4 m and a maximum of 100 m.No moulins are visible in or above this area.Instead, surface melt is routed into the glacier through abundant crevassess (Fig. 2).The basal layer of temperate ice in the study area extends up to 30-60 m above the bed.
An automatic weather station (AWS) operated at 2,290 m next to the lower end of the study area between July 2006and August 2015(MacDougall and Flowers, 2011) as part of simultaneous energy balance studies (Wheler and Flowers, 2011).
We use air temperatures (specifically positive air temperatures, meaning the maximum of measured temperature and 0 • C) and Positive Degree Days (PDD, defined in the usual way as the integral with respect to time over positive air temperatures) as the main proxy of the water input into the subglacial drainage system.Temperature estimates after the August 2015 removal of the on-glacier AWS were calculated by a calibrated linear regression of data from a second AWS operated since 2006 by the Geological Survey of Canada and the University of Ottawa 8.8 km to the Southwest, at an elevation of 1845 m. Between 2008 and2015, 311 boreholes were drilled to the bed (Schoof et al., 2014) and instrumented with pressure transducers (Fig. 1) providing continuous subglacial water pressure records, with up to 150 boreholes being recorded simultaneously.
The inclination of the boreholes was not measured, but the drilling technique used aims to ensure minimal deviations from vertical.A comparison with GPR data shows that borehole lengths were generally in agreement with ice thickness within a 6% margin (Wilson et al., 2013).Contact with the bed was deemed to have been established if water samples taken from the bottom of the holes showed significant turbidity.Otherwise, a borehole camera was used to assess bed contact visually; a significant number of additional, unsuccessful drilling attempts terminated at englacial cobbles near the bed.With only a few exceptions, sensors were installed only in holes that we were confident had reached the bed, and placed 10-20 cm from the bottom.Boreholes typically froze shut within one to two days, becoming isolated from the surface.The spatial distribution of new boreholes varied each year, not following a regular pattern.However, they were generally 15-60 m apart along cross-glacier lines, with lines 60-120 m apart.A map of all boreholes drilled is shown in Fig. 1.The region labelled as the "plateau" in Fig. 2 was re-drilled every year between 2011 and 2015.
Pressure data were acquired using Barksdale model 422-H2-06 and 422-H2-06-A and Honeywell model 19C200PG5K and SPTMV1000PA5W02 transducers.Each sensor was embedded in clear epoxy to provide mechanical strength and waterproofing.Most transducers installed from summer 2013 onwards were equipped with a Ray 010B ¼" brass piston snubber as protection against transient high-pressure spikes.Data were recorded by Campbell Scientific CR10, CR10X and CR1000 data loggers, set to log at intervals of 2 minutes during summer for CR10(X) loggers, switching to 20 minutes for the rest of the year, and at intervals of 1 minute for CR1000 loggers year-round.In the present paper, water pressure values will be reported in metres of water (the height of the water column that would produce that pressure).
During the summers of 2014 and 2015, a total of 10 custom-made digital sensor pods was installed in boreholes.These pods were built based on an ATMega328P microprocessor and communicated via the RS-485 protocol with custom-made data loggers built using the Arduino Mega open-hardware platform.The sensor pods recorded pressure, conductivity, turbidity, reflectivity in five spectral bands, tilt, orientation, movement, temperature, and confinement.The latter is a measure of the magnitude of the acceleration produced by an internal vibrating motor, used to assess whether the sensor was hanging freely in water, or tightly confined within solid walls.Seven of the digital sensors were installed in the same boreholes as the standard analogue transducers to assess data quality.
We have not used data from a stream gauge at the outlet of the glacier, maintained for part of the observation period by the Simon Fraser University glaciology group, for two reasons: first, several surface melt streams and at least one major lateral stream enter the glacier below the study site.Second, the instrumentation at the stream site was destroyed on multiple occasions by flood waters, and a continuous record is not available.overburden) water pressures, interrupted only during a 2-4 months period of summer activity starting in June-July (Fig. 3).
The onset of the active summer period (or "spring event") occurs during rapid thinning of the snowpack under high summer temperatures.After the spring event, 20% of sensors show a drop in diurnal running mean pressure, and most start displaying diurnal oscillations.
Pressure records alone do not allow us to determine the characteristics of water flow at the bed, and visual observations at the bottom of boreholes often fail due to the high turbidity of the water after drilling.However, in a few exceptional cases, we were able to observe water flow at the bed directly.We will describe the two most clear-cut cases.
On July 28th, 2013, while installing a sensor in the hole marked "Fast-Flow" in Fig. 2, strong periodic pulls were felt through the sensor cable, revealing a conduit with turbulent, fast flow in the bottom 50 cm of the borehole.This borehole was also the only one in which there was an audible sound of flowing water.The fast-flow hole was drilled at the very end of the field operations, and no further detailed on-site investigation was conducted.
The fast-flow borehole was 93 m deep, and drained at a depth of 87 m during drilling.On the first recorded diurnal pressure peak, the water reached a pressure of about 5.2 m (6% of ice overburden; we will consistently express pressures in metres of water in this paper).A water sample retrieved from the bottom showed moderate turbidity.Two pressure sensors were installed in this borehole 10 and 80 cm above the bed, the upper one with a snubber and the lower one without one.forming a cluster that extends some distance laterally across the glacier (see section 3.2).In the case of the fast-flow borehole, somewhat similar temporal pressure patterns were observed at a much larger distance downstream, as shown in panels e and g of Fig. 4" and less so in panel h, while a set of boreholes exhibiting very different variations close to those in panel d is shown in panels f.For reference, panel i shows the remaining pressure time series recorded in the same area, highlighting the diversity of pressure patterns observed.No systematic time lags were found between peaks on the fast-flow borehole and pressure peaks of boreholes displayed in panels e and g.

Panel c of
The grouping of boreholes into panels in Fig. 4 was done on the basis of spatial proximity in panel c, and on the basis of a commonality of diurnal pressure variations in the remaining panels, in particular, a commonality in how the amplitude of diurnal pressure variations changes in time.For instance, the similarity between the records in panel g should be obvious.
However, note that there can be subtler similarities: panels c, e and g at least partially share a period of larger diurnal amplitudes leading up to August 3rd, a hiatus lasting until August 10th punctuated by a diurnal pressure peak late on August 6th, and a period of renewed diurnal oscillations lasting until August 17th; this differs from the pattern of diurnal oscillations seen in panel h.Grouping boreholes in this way is partially a subjective measure, and we will present a more systematic clustering method (which has helped to guide the groupings here) in a separate paper (see also Gordon et al. (1998); Huzurbazar and Humphrey (2008)).
Several features stand out in the pressure record from the fast-flow borehole: sharp diurnal pressure peaks and a small time lag between peak surface temperatures and diurnal water pressure maxima (1-3 hours), as well as the general similarity between the pressure and temperature pattern.The correlation between the two, computed over a moving window, stayed above 0.8 for several days (Fig. 4b, grey shading).This high correlation was more pronounced late in the season, also coinciding with the water pressure dropping to atmospheric values at night.
A contrasting observation of water flow was made on July 23rd, 2014, when a clear water sample was retrieved from the bottom of a borehole ("Slow-flow" in Fig. 2) and the borehole camera was deployed.The resulting borehole video (see supplementary material) reveals a slowly flowing thin layer of turbid water at the borehole bottom overlaid with clear water, an unusual condition that allowed the observation, as the water in a bed-terminating hole is usually highly turbid due to the basal sediments disturbed by the drill jet.
The slow-flow borehole was 62 m deep, and the first recorded diurnal pressure peak reached 48 m (85% of ice overburden).
One pressure transducer with snubber was installed 6 cm above the bed. Figure 5c shows the pressure recorded in the slow-flow borehole (black line).Pressure records from three other boreholes in the same across-glacier line and one sensor downstream are shown in red in the same panel, while the record of a fifth borehole in the same line is shown in panel d.Note that there are four virtually indistinguishable records in panel c during July 23rd-25th (see also figure 6).After a data gap caused by a corrupted compact flash card, the records have become more dissimilar by August 2nd, but continue to exhibit common pressure variations.The pressure time series from the borehole that is part of the line immediately below the slow-flow hole by contrast has significantly higher mean water pressure and the diurnal pressure variations have a much smaller amplitude.We have included it in panel c because it is the only one in that lower line that matches one of the other pressure records in panel c well if we remove their means and scale them to have unit variance.As discussed above, the grouping into panels is somewhat    (S2), green (S3) and blue (S4).We have applied offsets to make the agreement between the records clearer.These are,in order,27,26,24,and 29 meters in (a),and 27,20,22,and 27 in (b).Note that the S2-S4 time series in panel (a) agree so well with each other that they are barely distinguishable.
Most boreholes showing diurnal pressure oscillations share the general features displayed by the slow-flow borehole, specifically 1) smooth pressure peaks and troughs, 2) pressure patterns well differentiated from the atmospheric temperature pattern, 3) mean pressures during periods with diurnal oscillations that lie between 55-120% of the overburden ice pressure (much higher than in the fast-flow hole), 4) peak pressures that typically lag peak temperatures by 2-8 hours and 5) patterns of temporal pressure variations that are often similar to neighbouring boreholes both in the along and across glacier direction.
On average, during summer, 71% of sensors showed the behaviour observed in the slow-flow borehole at some point, as assessed visually from the presence of smooth diurnal pressure oscillations.Only 8 boreholes (3% of the total, shown as red markers in Fig. 2) exhibited water pressures dropping to atmospheric pressure, one of the key characteristics of the fast-flow borehole.Six of them were found during the three years with the highest cumulative positive degree day count in the data set (2013: 437 • C days, 2009: 386 • C days, 2015: 297 • C days).These figures may however not be representative as drilling was concentrated in some areas.For this reason, we have selected 70 boreholes in two across-glacier profiles (blue markers in Fig. 2).Among those, 81% show a behaviour qualitatively similar to the slow-flow borehole, and 4% that of the fast-flow one.Note however that even these statistics remain biased, as borehole spacing along these lines is concentrated in areas that were of interest due to likely drainage activity, and crevassed areas are under-represented as sensors signal cables typically have a short life span there.
We emphasise that the borehole in which fast flow was observed initially displayed a relatively smooth diurnal cycle, and the statistics above are based on the identification of diurnal pressure oscillations reaching atmospheric pressure at night: it is therefore possible that more boreholes intersect conduits with fast-flowing ice, without the observed pressure records indicating as much.
The remaining 26% (or 15% of the two cross-glacier lines in Fig. 2) of boreholes do not show any significant diurnal pressure oscillations at any point during the year.These "isolated" boreholes usually show year-round mean pressures between 90-120% of the ice overburden pressure.Isolated boreholes frequently show a near-constant pressure signal, but not always, with some exhibiting difficult-to-interpret temporal variability.In 2016 there were 55 isolated sensors, allowing us to treat their  behaviour statistically.Despite only slight differences in mean pressures between winter and summer there is, however, a slow but statistically significant decrease in water pressure during summer, starting around the spring event and amounting to about 6% of the overburden pressure in total (Fig. 7).

Spatial patterns in water pressure variations
When the whole data set is viewed over a given time window during summer, it is often possible to identify multiple subsets of boreholes showing very similar temporal pressure variations within that subset (often recognizable by the way in which the amplitude of diurnal oscillations changes over time), but these temporal variations are different from other boreholes.One example of this phenomenon comes from the boreholes in Fig. 4f, where we can see a group of boreholes that display a very coherent signal but with a distinctive two-day period.The boreholes in panel f are directly adjacent to those in panel e, we have associated with the fast-flow borehole and which show a very different, diurnal pattern of pressure variations (see also panels c and g).Less clear-cut though indicative of the same phenomenon is Fig. 5, where we see boreholes in panels d-f that exhibit quite different diurnal pressure variations to those observed in the group associated with the slow-flow borehole in panel c. pressure signal that was qualitatively different from the atmospheric temperature signal (panel b) and the majority of other boreholes in the two areas (panel f).There was no consistent time lag between sensors in the plateau and downstream.However, there was a clear drop in amplitude of diurnal oscillations between the plateau and downstream sensors (panels c and d), where the latter showed amplitudes around 15-30% of those seen in the plateau.
Five of the sensors on the plateau were capable of conductivity measurements (panel g).We emphasize that, in general, the spatial patterning was recognizable only in the pressure records, and pressure oscillations were not associated with conductivity changes.Although all five sensors showed very similar temporal variations in pressure (panel c), the conductivity time series bear far less similarity to each other, with only a handful of abrupt conductivity changes common to three of the sensors (S2 and S4 marked in panel g).
The group of 14 boreholes in panel e of Fig. 8 also shares common diurnal pressure variation patterns, though this is not immediately clear as the mean pressures and amplitude of pressure variations varies significantly.Specifically, these variations are "inverted" versions of the pressure variations seen in panel b, with peaks becoming troughs and vice versa.These anticorrelated boreholes, in contrast to those in panels c and d, have smaller diurnal oscillations amplitudes, and the oscillations are super-imposed on a signal with near-constant running mean and high mean pressure, usually close to overburden.Therefore, if diurnal variations were filtered out, these pressure records would resemble the winter regime.At 15 meters spacing between boreholes, we do not observe sequences of boreholes smoothly transitioning from correlated to anti-correlated, in the sense that there appears to be no continuous change in phase and amplitude from borehole to borehole: we observe a sharp boundary between correlated and anti-correlated boreholes, or correlated boreholes and boreholes exhibiting no diurnal oscillations.Note that one of the records in panel f of Fig. 5 also anti-correlates strongly with the record in panel e of the same figure during the later part of the time window shown, and the record in panel d anti-correlates strongly with the record from the adjacent borehole S4 during August; anti-correlation of this kind is a common feature of the data set, often but not always involving boreholes in close proximity.
There is typically another set of boreholes that show very similar diurnal variations in water pressure super-imposed on near-constant or slowly changing diurnal running mean values.The diurnal variations for this set have very small amplitude (typically 0.2-0.6 m, exceptionally up to 6 m), and resemble a square-wave with super-imposed high-frequency variations.
Matching oscillations can be observed in multiple boreholes spread over large distances, both along and across the glacier, and both diurnal and much higher frequency features in the pressure signal are preserved between boreholes.An example from 2011 involving boreholes across the width of the study area, and recorded by different data loggers, is shown in Fig. 9. Clearly, the oscillations can be both correlated or anti-correlated with each other.Not shown in Fig. 9 is the longer-term evolution of water pressure in the same boreholes.While they share short-time-scale temporal variability, their long-term pressure variations are generally not well correlated.

Three-dimensional drainage structures
The pressure observations primarily give us a two-dimensional picture of the drainage system.The drilling process itself as well as borehole camera investigation provides additional information on englacial connections (Fountain et al., 2005;Harper The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.To make these visible in the same plot, we have applied offsets of 93,71,64,61,63,66 and 27 meters to the measured pressures.Three common high-frequency features are highlighted by grey vertical bands.et al., 2010).37% of all the boreholes drilled drained completely or partially during the drilling process, as did 39% of those in the cross-glacier lines marked as blue symbols in Fig. 2. For simplicity, we will give statistics for the entire data set in running text below, and the corresponding figure for the cross-glacier lines in parentheses.Of the boreholes that drained during drilling, only 14% (0%) drained when reaching the bed, and the remaining 86% (100%) drained at some point during the drilling process, suggesting connections to englacial conduits or voids.Such connections were also observed on multiple occasions using the borehole camera.Drainage events occurred during drilling at all depths, but more frequently at greater depths, with 60% (59%) happening in the lower half of the boreholes.This remains true for the 2012 drilling campaign, where the first sensors were installed before the spring event and observations are likely to reflect winter conditions.
During the borehole re-freezing process, 29% (11%) of the boreholes showed a pressure spike typically about 1.3 times overburden pressure, suggesting that freezing happened in a confined space.In total, 62% (73%) of these initially confined boreholes showed diurnal oscillations during the first week, suggesting that some degree of connection was developed with a drainage system experiencing diurnal varying water input.
In 2014 and 2015, three one-year-old boreholes were re-drilled, and the sensor was recovered (boreholes A, B and C in Fig. 2).During this process, we found that holes A and C had sections about 8-12 m long near the bed that had remained unfrozen for the entire year, suggesting that boreholes, as well as natural englacial conduits close to the bed, could remain open through the winter.In borehole A, the contact with the bed had erroneously been assumed after the initial drilling based on highly turbid water.However, borehole video footage after re-drilling showed that the original borehole had terminated at an isolated rock.
From the depth of nearby boreholes, we estimate that the sensor was installed approximately 4 m above the bed.Nonetheless, the diurnal water pressure oscillations recorded in borehole A continued to mimic other nearby bed-terminating boreholes that were drilled in 2014 and 2015, indicating a persistent connection.

Seasonal evolution
We have described the apparent spatial patterning of the drainage system above.This patterning is however not fixed but evolves over time.In Fig. 8b, it is clear that all 42 boreholes show very coherent temporal pressure variations at the start of the observation period.During late July and August, some the pressure variations in some of the boreholes become more distinct until, by late August, there is no longer a common signal and all boreholes show dissimilar temporal pressure variations.
In Fig. 8c, this emerging patterning is evident only in the more disordered appearance of the plot for later times.In Fig. 10, we show the 42 boreholes of Fig. 8b separated into subgroups.As in figures 4 and 5, the grouping is somewhat subjective; a paper on a more systematic clustering approach that has guided our choices here is in preparation.We have attempted to group boreholes whose diurnal water pressure oscillations during late July and early August closely resemble each other.
Even within these groupings, it is clear that boreholes can switch from having closely correlated pressure records to behaving independently and, less frequently, to being strongly correlated again (panels d-h in particular); For simplicity, we refer to boreholes as being "connected" while they exhibit the same temporal pattern of pressure variations, and as "disconnected" otherwise.For each grouping, we have computed a mean pressure displayed in black, including only the boreholes that are connected at a given time; in some cases, no boreholes were connected to each other, and we used the last borehole still to exhibit diurnal oscillations to define the set of connected boreholes.In that case, the black mean curve obscured the corresponding, coloured borehole pressure time series.These mean curves for each panel are re-plotted in the corresponding borehole marker colour in panel c.
The major dichotomy in Fig. 10 is between the groupings in panels d-g and i on one hand and panel k on the other.The distinctions between panels d-g in particular are more subtle, and generally relate to the absence or subdued nature of certain diurnal peaks in them: for instance, panels d-f all show diurnal oscillations on August 1st and 2nd, while the larger group in g does not; there are other examples close to the end of the summer season.For all groupings in panels d-g, it appears that the early season records resemble each other more closely than those late in the season, as was already evident in Fig. 8b, and that fewer boreholes have disconnected.
At a much smaller scale, a similar fragmentation of the drainage system is shown in Figs.5b and 6, where we see four boreholes that are initially very well connected during late July having become much less well connected in August, although with the diurnal pressure oscillations still showing some similarities between several of the boreholes.Interestingly, one borehole (S2, yellow) has ceased to exhibit oscillations by August, but is straddled by two that still do (S1 and S3, 15 m to either side), suggesting a relatively fine-scale structure to the drainage system locally.
In addition to spatial patterning, Figs. 8 and 10 hint at an overall evolution towards lower mean water pressures and larger diurnal oscillations.The seasonal evolution of the drainage system may be evident not only in its spatial extent, but also in the evolution of mean water pressure and its response to surface melt input.Perhaps the simplest measure of sensitivity to surface melt input is what we term the relative amplitude of pressure to temperature oscillations: we compute standard deviations of pressure time series from boreholes that exhibit diurnal oscillations at some point of the season, and also standard deviations of positive air temperatures (the maximum of air temperature and 0 • C).We compute these standard deviations over one- day running windows, and define the ratio of the two running standard deviations to be the relative amplitude of pressure to temperature variations.Taking the running standard deviation of air temperature as a marker of surface melt rate variability, the relative amplitude defined in this way gives an indication of how sensitive the drainage system is to variations in water input.
In Fig. 11, we see that the running standard deviation in pressure only vaguely tracks its temperature counterpart.However, the relative amplitude systematically increases during much of the season (Fig. 11c), except during an interval of colder weather 5 and surface snow around the beginning of August, while the mean water pressure also decreases (Fig. 11d).
Above, we have seen that boreholes can become disconnected from each other, going from a state in which they undergo synchronous and virtually identical pressure variations over time to a state in which borehole pressure appears to evolve independently.The reverse change also happens, though less frequently.The change from connected to disconnected and its reverse can take different forms.In a few cases, disconnection is gradual, with the boreholes continuing to exhibit similar diurnal pressure oscillations that progressively become more dissimilar in amplitude, phase and mean water pressure.The record from H1 in Fig. 8c (yellow line in panel c) is one such example.In most cases, however, the transition is abrupt, and the same is true of boreholes connecting with each other: a rapid change in water pressure can occur over the course of a few hours or less as a connection is established.We term such abrupt transitions "switching events", following Kavanaugh and Clarke (2000) .
Figure 6 shows multiple examples in the boreholes labelled S1-S4 in Fig. 5c, spaced 15 m apart.Perhaps unsurprisingly, the majority of switching events involving new connections seem to occur while water pressure is increasing or after a recent increase, while disconnections tend to occur as water pressure is falling (see Fig. 10c,d,f for several obvious examples), though the two are rarely symmetric, with disconnection usually occurring at a lower water pressure than the original connection.
The record from sensor D1 in Fig. 8c is one such example, where arrows labelled S1-S7 mark multiple switching events.The borehole originally disconnected from the main group on July 11th, but reconnects on several occasions during periods of high water pressure in the active drainage system, disconnecting when water pressure subsequently drops.Note that for the first two reconnections, S2 on July 21st and S4 on July 24th, the switching events are clearly associated with large drops in conductivity as seen in panel g, suggesting an inflow of melt water that has spent less time in contact with the bed.
Towards the end of the melt season, most boreholes have become disconnected from each other, and water pressure in them typically rises again towards overburden, remaining nearly constant through the winter.However, in some cases, we observe quasi-periodic pressure variations in winter as previously reported in Schoof et al. (2014).Figure 12 shows the winter pressure record for the two sensors installed in the fast-flow borehole, extending the summer record shown in Fig. 4c.As in other boreholes, we see water pressures rising at the end of the summer season.This is briefly interrupted during early September, when surface snow cover temporarily disappears, and a drop in water pressure occurs in the borehole, accompanied by the resumption of diurnal oscillations.This is followed once again by the termination of diurnal oscillations and a sharp rise in water pressure towards overburden once the surface becomes snow-covered again.Unlike in most other boreholes, that rise towards overburden is however interrupted by oscillations lasting from 2-12 days.During these oscillations, water pressure can drop rapidly to as little as a quarter of the overburden, followed by a slower rise in pressure back towards overburden, stabilization, and a renewed rapid drop.

Inter-annual variability
As observed in Fig. 3, there is large inter-annual variability in positive air temperatures and hence, presumably, in surface melting, both in terms of onset and intensity.In addition, we expect that differences in the snow-pack can also affect water delivery to the englacial system; presumably, a thicker snow-pack can store or refreeze surface melt water.Figure 13 shows a view of the study area from an automated camera on July 19th in 2012-2015.These images illustrate very significant differences in surface snow cover at the height of the summer melt season: the visible snow cover in each image is part of the remaining winter snowpack.
Alongside the inter-annual variability in temperature and snow cover, there are also significant season-to-season differences in the water pressure records.Differences in drilling objectives from season to season make year-to-year comparisons difficult  except in one part of the study area.Figure 14 shows a compilation of pressure records from a set of boreholes drilled in almost the same locations every year in the lower plateau area from 2012 to 2015, as indicated by two red polygons in Fig. 2.There are four boreholes (surrounding the fast-flow hole in Fig. 4) included here for 2013-2015 that were not drilled in 2012, and four that were drilled in 2012 but not in later years.Alongside air temperatures and snow cover, we also indicate the total PDD count prior to June 15th, and at the end of September.Also shown are the median of the dates on which diurnal oscillations 5 appear and disappear over all boreholes with functioning sensors (red lines).The latter are clearly a crude measure of drainage system evolution as they are biased by borehole locations and drilling dates.Despite these differences, the borehole pressure records clearly indicate some systematic differences, with a relative absence of diurnal pressure oscillations in 2012 and 2013, though accompanied by very low water pressures associated with the fast-flow borehole in 2013 (see also Fig. 4), and a larger number of "connected" boreholes with large-amplitude diurnal oscillations in 2015.We also note that we drilled new boreholes

Data quality
There are numerous mechanisms by which a sensor can become corrupted.An obvious cause is a damage to the signal cables, which is sometimes visible at the glacier surface due to crevasse opening.We have visually identified records that show signs of such corruption, such as large, random jumps in pressure between successive measurements, and large negative water pressures.
Transient high-pressure spikes (Kavanaugh and Clarke, 2000) are likely to have caused abrupt calibration changes in four All presented pressure values were computed from differential voltage readings using a linear transformation.The two corresponding constants are referred as the offset and the multiplier.Our reported measurements rely on pre-installation calibrations, and assume no change in calibration constants.
To assess data quality as well as drift in the offset and multiplier, eleven boreholes were equipped with two sensors, logged independently (see the supplementary material for details).These sensors recorded in total more than 13 years of duplicated data.Seven of the boreholes included a digital transducer, in which the measurement is made in the sensor, while the remaining sensors were analogue sensors, which rely on voltage measurements at the surface and can, therefore, be corrupted by damage to the signal cable introducing partial short circuits.Doubly-instrumented boreholes indicate that calibration drift can start developing 3-4 months after installation (in October-November), but differences in measured pressures always remain below 15 m even after two years.Therefore, they can only explain pressures readings around 120% above overburden for most boreholes, and a few analogue sensors in the data set reached values as high as 130-200 % of overburden.Test of the sensors extracted by re-drilling after one year also found that small offsets had developed, in all cases smaller than 3 m.Multiplier changes were also observed, but they account for an even smaller effect within the measured pressure range.The observation of a few sensors gradually drifting up to nearly 200% of overburden is therefore difficult to explain and may be due to errors in calibration or hard-to-diagnose sensor damage.We were not able to correct for this effect; one possible cause of large calibration errors developing could be permanent deformation of the sensing diaphragm by ice formation against it.
Instrumental accuracy and precision aside, our interpretation below will rely on water pressures having been measured at the bed, except in cases where the sensor is known to have been installed englacially (such as hole A in Fig. 2).Recall that sensors were typically installed 10-20 cm above the bed; we are relying on the connection to the bed not becoming closed off.
We observe that sensors in doubly-instrumented boreholes can start to exhibit independent pressure variations during winter, sometimes reverting to a common signal.One example can be seen in Fig. 12, where the red and blue curves are measured by two different sensors in the same hole.One possible explanation for the mismatched data could be the sensors becoming encased in ice during the winter, and thus separated from each other in the doubly-instrumented borehole, where the sensors are vertically offset from one another.
There is direct evidence for processes that could lead to sensors becoming enclosed in ice.Digital confinement data suggest that in some cases, as in Fig. 15, the termination/initiation of diurnal oscillations is associated with an increase/decrease in confinement: this is measured as the response of an accelerometer on board the sensor pod to an internal motor being activated, and expressed as one minus the ratio of the acceleration recorded by the sensor to the calibration acceleration recorded when freely hanging in water.Note that the fraction of boreholes showing diurnal variation in their second summer season decreases compared with the first, dropping from 71% in the first season to 58% in the second.This could also be a consequence of sensors becoming encased in ice or otherwise isolated from the bed.

Discussion
The seasonal evolution of the drainage system we observe is broadly consistent with existing ideas about drainage physics.
A drainage system forms annually, triggered abruptly by the delivery of melt water to the bed in a "spring event" (Iken and Bindschadler, 1986).The timing of the spring event varies significantly from year to year, taking place when most of the glacier surface is still snow covered, but always after the appearance of the first sizeable snow-free patches (Fig. 13, see also Nienow et al. (1998b)).This suggests that the development of drainage pathways through the surface snow cover is a precursor to water delivery to the bed, with the timing most likely dictated by snow depth, temperatures, and early season melt rates (see also Harper et al., 2005).After the spring event, most boreholes show strongly correlated diurnal pressure variations, suggesting extensive hydraulic connections, and at least a slight drop in water pressure.However, if compared with late-season diurnal pressure fluctuations, these early season pressure oscillations have smaller amplitudes and lower correlation with the inferred surface melt rates, suggesting a relatively inefficient drainage system.We will refer to this initial state of the subglacial drainage system as stage 1.Note that the "stages" identified here are not the same as the "phases" discussed in Schoof et al. (2014), who focused only on the later part of the melt season and the subsequent winter; for instance, phase 2 in Schoof et al. (2014) corresponds to the transition from stage 2 to 3 here.
Later in the season, the drainage system becomes more focused, in what we will call stage 2.During this stage, the mean water pressure in the system drops, and the magnitude of diurnal pressure variations increases (see Fig. 11, also Harper et al. (2002)).Different parts of bed still exhibit diurnal oscillations but cease to be mutually well-connected, as also observed by Fudge et al. (2008).We will refer to the parts of the bed that remain internally well-connected as hydraulic subsystems (Fig. 4 panels f and g, Fig. 5 panels c and f, and Fig. 10d-h, j and k are examples of this behaviour, with panels d-g in the latter sharing many features but appearing quite distinct from panel k).Subsystems progressively shrink, shutting down drainage over an increasing fraction of the bed.At most boreholes, the drainage shut-down is marked first by the sudden disappearance of diurnal cycles in a switching event, often followed by a sustained increase in pressure that takes approximately one to a few weeks to stabilize at a value close to overburden.
In high-melt years, the fragmentation of the drainage system can be extreme.Figure 4 shows only a handful of boreholes exhibiting diurnal oscillations towards the end of stage 2. Our data suggest these boreholes may align with down-glacier drainage axes.Had we sampled the glacier bed differently, we could have had no boreholes showing diurnal oscillations during this period.This widespread drainage shut-down around highly focused drainage subsystems would explain why the end of The systematic increase throughout stages 1 and 2 of the relative amplitude of diurnal pressure and inferred melt oscillations (Fig. 11), and the correlation with positive temperatures (Figures 4 and 10) is consistent with an increase in the drainage system efficiency.
A widespread termination of diurnal oscillations in the remaining connected holes is typically triggered by a marked drop in meltwater supply, usually coincident with a snowfall event.We label this as the start of stage 3 in Figs. 4 and 8, 10;in Fudge et al. (2008), this is referred to as the "fall event" (though their data makes connections with snow fall less easy to establish).
The termination of diurnal oscillations is often followed by a rise in borehole pressures towards overburden, marking the beginning of the winter pressure regime, where pressure variations are no longer closely correlated, suggesting an absence of hydraulic connections.
The shrinking and fragmentation process during stage 2, and possibly the onset of stage 3, may, however, be partially reversed by brief episodes in which the reconnection of at least some boreholes is observed.These reconnection episodes are often associated with strong increases in meltwater supply, usually on hot days when temporary snow cover clears.During 2015, snow events during late July and early August led to several episodes in which most boreholes shown in Fig. 8 appeared to disconnect from each other, pressures in them not only ceasing to exhibit diurnal oscillations but also evolving independently.
These episodes ended with surface snow cover disappearing and melt supply resuming, leading to widespread and often abrupt reconnection at high basal water pressures.
Similarly, we cannot exclude the possibility that highly focused drainage subsystems remain open during the early parts of stage 3: the borehole array cannot sample all conduits directly, and we are only certain of having intersected a main conduit in one instance.That conduit, the 2013 "fast-flow" borehole, remained at close to atmospheric pressure for nine days at the start of stage 3 (Fig. 4).Subsequently, water pressure started to rise, but even then, the disappearance of snow cover and continued melting led to a pressure drop and renewed diurnal pressure oscillations correlated with surface temperatures from September 1st to 6th (Fig. 12).
The spatial evolution of the drainage system is consistent with the drainage system becoming channelized during the melt season.By this, we mean the formation of individual Röthlisberger-type ("R") channels, incised into the base of the ice by dissipation-driven melting (Röthlisberger, 1972).Formation of channels should cause the mean water pressure to drop, as the focusing of water discharge causes larger channel wall melt rates that have to be offset by faster creep closure, driven by larger effective pressures (Nye, 1976;Spring and Hutter, 1982).It can also account for the increased sensitivity of the pressure response to the inferred melt input.The clustering of boreholes into drainage subsystems indicates good hydraulic connections between them.However, as channels cannot coexist stably in close proximity (e.g.Schoof, 2010;Hewitt, 2011), it is unlikely that all boreholes that sample the same drainage subsystem are located in R-channels, or in an R-channel at all.A more obvious explanation is that in stage 2, each independent subsystem contains a channel surrounded by a distributed drainage system consisting of linked cavities or a similar conduit configuration (Kamb, 1987;Fowler, 1987;Schoof, 2010;Hewitt, 2011).Such a distributed system is consistent with the observation of slow-moving water in the 2014 slow-flow borehole.In addition, the existence of narrow R-channels within those systems is also consistent with the finding of the 2013 fast-flow borehole in stage 2.
Pressure records alone are insufficient to determine if there is water flow and whether a sensor is in a channel or a distributed system, even if the distributed system is hydraulically well-connected.The pressure record shown in Fig. 4 is the one record of which we know that it almost certainly reflects pressure variations in a channel.We know that highly turbulent flow occurred in the bottom 50 cm of the borehole, which we take to be the height of the channel, but its width is unknown.The first week of that time series resembles the smooth pressure variations observed in many other boreholes (albeit at fairly low water pressures), while it develops very distinct features later: water pressure drops to atmospheric at night, and there are unusually small time lags relative to and very high correlation with inferred surface melt rates.
The 2013 fast-flow borehole does not connect hydraulically to other nearby ones that lie along an across-glacier line (Fig. 4d), but appears to connect to a narrow set of boreholes extending 500 m downslope (Fig. 4 e and g).The pressure time series from those boreholes differ somewhat from that measured in the channel, so there is probably a narrow distributed system close to the channel, the width of that system being less than the 15 m borehole spacing.
These observations are consistent with a highly developed channel with higher water discharge that has become hydraulically isolated from the neighbouring bed: the high effective pressures in the channel would favour the closure of cavities or other connections at the bed.
The 2013 season was marked by high net inferred melt: the total PDD at the end of that season exceeded the PDD for 2014 and 2015 by 46% or more (Fig. 14).The high inferred melt rates are consistent with channelization reaching an end-member state.The rapid flow of water in the borehole also made identification easier; it is unclear if a smaller channel would have been as easy to identify.
Using the channel end-member feature of diurnal oscillations with pressure doping to atmospheric at night, we have identified seven other boreholes where the drainage system is likely to have evolved into a well-developed channel (Fig. 2 Late in the season, the shut-down of the now well-developed basal drainage system during a period of dwindling inferred melt supply is consistent with high effective pressures causing the closure of subglacial connections, especially as disconnection events often occur at low observed water pressures.Different boreholes appear to become hydraulically isolated from each other during this process.We interpret the subsequent evolution of pressure records after disconnection as reflecting the response of an isolated water pocket in the borehole, presumably containing a fixed (or nearly fixed) volume of water exposed to the ambient stress field.Initially, creep closure will reduce any volume still occupied by air in the borehole and pressure can rise gradually; The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.once there is no air space left, changes in water pressure must reflect the pressure required to maintain the borehole volume constant (assuming no further freezing) while the borehole may still deform under anisotropic stress conditions.Intuitively, we would expect the borehole to become flattened perpendicular to the direction of greatest compressive stress, requiring a larger borehole pressure to maintain a constant volume, which could account for the slow rise observed in water pressure, and possible for slightly above-overburden values.Importantly, the pressure in an isolated borehole should depend on its shape and can, therefore, differ from borehole to borehole; abrupt creation of new storage volume for instance due to crevasse propagation could also lead to abrupt changes in pressure in isolated boreholes.
During winter, a handful of boreholes exhibited large-scale aperiodic pressure oscillations as detailed in Schoof et al. (2014) and shown in Fig. 12.We have previously hypothesized that these multi-day winter oscillations indicate ongoing drainage in a few locations, with the oscillations driven by the interaction between conduit growth and distributed water storage in smaller water pockets, basal crevassess and moulins; such oscillations could be triggered when water supply drops below a critical value in combination with a steady background water supply (Schoof et al., 2014).Winter oscillations are common in boreholes that showed end-member channel behaviour at the end of the summer, as it is the case for our 2013 fast-flow borehole as seen in Fig. 12, and borehole D in Schoof et al. (2014).However, similar winter oscillations can occur also in boreholes that were isolated or belonged to distributed drainage systems during the previous summer.

Interannual variability
The timing of spring events and speed at which the evolution of drainage system occurs appears to be linked systematically to the availability of meltwater.Cool, snowy summers are most obviously linked to a poorly developed drainage system with weak diurnal cycles (2012) and poor correlations between boreholes, as well as the absence of a sharp spring event (Fig. 14).
The spatial structure of the drainage system also varies from year to year.The plateau area reliably has drainage activity, though upstream area pattern in Fig. 2 does not directly agree with the observed drainage structure (Fig. 10), but is merely suggestive.Channel formation is influenced by pressure gradients controlled by surface and bed topography.However, changes in water supply geometry and the instability inherent in channel growth and competition between emerging channels implies that channels need not form in the same location every year, as evidenced in our failure to find in 2014 and 2015 a channel at the 2013 fast-flow borehole location.

Challenges to current subglacial drainage models
Boreholes do not only disconnect from or reconnect to each other during the summer: a significant number of boreholes never connect at all.Others disconnect from the drainage system as it becomes more focused and fragment into subsystem during stage 2. Some boreholes even disconnect and reconnect multiple times (figures 6, 8 and 10).
There is typically a very clear distinction between connected holes showing a similar response to the diurnal input, and disconnected ones that do not.Within a given drainage subsystem, there is typically no gradual phase shift or diminution of oscillation amplitudes from borehole to borehole, as would be expected if the drainage system were a diffusive system with a The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.finite diffusivity (Hubbard et al., 1995): effectively, our data suggest that, if the distributed system is diffusive, its diffusivity is very high, or zero where the system has become disconnected.This observation contrasts with the interpretation of data in Hubbard et al. (1995), who identify a gradual phase shift and decay in amplitude of diurnal pressure oscillations away from an inferred subglacial channel location.In our view, the "phase lag" in their Fig. 5, can however also be interpreted as showing diurnal switching of their borehole 40 from being wellconnected with their boreholes 29 and 35 to being disconnected.The latter interpretation would be consistent with Murray and Clarke (1995), and with Fig. 6 here also showing an example of switching events with similar characteristics on South Glacier.
Pressure measurements at South Glacier therefore suggest that the distributed parts of each drainage subsystem are hydraulically well-connected, with all connected boreholes showing almost identical pressure variations.The limited electrical conductivity and turbidity measurements however also indicated that relatively little water might actually flow in the distributed system: unlike in the data in Hubbard et al. (1995), there are no diurnal variations in electrical conductivity.With a hydraulically well-connected system, this has to correspond to a low water storage capacity, so that substantial variations in water pressure need not be accompanied by the similarly large changes in stored water.Alternatively, that storage capacity could be relatively localized, so that water need not flow everywhere.
While there are typically insignificant cross-glacier differences in diurnal pressure response within well-defined drainage subsystems, the same is not true in the down-glacier direction, even where we believe a hydraulic connection can be identified.
The pressure time series along the inferred channel system in Fig. 4 (panels c, e and g) are merely suggestive of a hydraulic connection, but hardly identical.The amplitude of pressure variations decreases markedly downstream from the fast-flow borehole, which would be consistent with a diffusive system, though it is unclear whether the change in amplitude occurs along the length of the channel, or within a putative distributed system flanking the channel, since the holes further downglacier most likely did not sample the channel directly.Importantly, however, there is no systematic phase lag accompanying the decrease in amplitude, as would be predicted by a diffusion model (Hubbard et al., 1995).
We have referred to boreholes that cease to exhibit diurnal pressure variations as having disconnected.Connection and disconnection typically manifest themselves very abruptly in time (Fig. 6, see also Fig. 5 of Murray and Clarke (1995)).Usually, disconnection occurs during a drop in water pressure in the subsystem, and reconnection during an increase (figures 6 and 8).This is consistent with connection or disconnection resulting from viscous creep closing connections between individual cavities within the distributed system (Kamb, 1987).Disconnection could also be the result of cavities shrinking while remaining connected, if the borehole simply terminates on an ice-bed contact area between connected cavities and those contact areas are systematically larger than the ∼ 10 cm diameter of our boreholes.It however seems unlikely that this effect, which should be random, would lead to a recognizable spatial structure of narrow drainage regions flanked by increasing large disconnected regions.Instead, we would expect a random distribution of apparently connected and disconnected boreholes.
The anti-correlated signals we observe in our data (Fig. 8e) have previously been explained by a mechanical load transfer mechanism, where the ice around a pressurized conduit redistributes normal load, reducing the normal stress over neighbouring areas of the bed.Therefore unconnected water pockets in those areas would experience a drop in water pressure (Murray and Clarke, 1995;Gordon et al., 1998;Lefeuvre et al., 2015).A 3D full Stokes model presented by Lefeuvre et al. (2018) supports The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.this interpretation, and suggest that the anti-correlation pattern depends on the bed slope, which can be one of the factors affecting the observed distribution of borehole displaying this behaviour.Boreholes exhibiting those anti-correlated pressures must then be effectively isolated, so that a change in normal stress mainly causes changes in the pressurization of the borehole rather than water exchange.The load transfer mechanism is consistent with our observations.Note that we observe anti-correlated signals in boreholes that are not immediately adjacent to boreholes showing a correlated signal (purple and blue markers in Fig. 8).It would be difficult to explain the anti-correlated signal in these boreholes by normal load transfer over larger distances, when other isolated boreholes nearby show no such behaviour.This suggests that the connected drainage system can contain fine structure (either as channels or narrow regions of distributed drainage) with lateral extents smaller than the ∼ 15 m borehole spacing.The same is indicated by the formation of disconnected "islands" in lines of otherwise connected boreholes at the same spacing as see in Fig. 6 for the August observation period.
We have referred to a borehole as isolated when observations suggest that there is effectively no water transport into or out of the borehole on a diurnal timescale.However, the evolution of the mean water pressure in disconnected boreholes is consistent with a residual amount of water leakage into the connected drainage system: during the summer, that mean pressure gradually decreases.The end of the monotonic increase in water pressure of disconnected boreholes observed in Fig. 7, coincides with the spring event, followed by a slow decrease.The large sample obtained in summer 2016 supports this trend up to a 99% confidence despite the large variability of the observations.As in Hoffman et al. (2016), such a slow evolution could be accounted for by flow through a relatively impermeable till aquifer underlying a much more effective but less pervasive interfacial drainage system, and the magnitude of that leakage could have a significant impact on basal sliding rates if disconnected areas act as sticky spots.
Widespread bed hydraulic isolation in winter is supported by high recorded water pressures and the marked pressure drop at the spring event observed in 20% of boreholes.In contrast, theories based on a remnant "distributed" system would ordinarily suggest relatively low water pressures in winter (Schoof, 2010;Hewitt, 2013).Although it is possible that some boreholes do not connect because they were not properly drilled to the bed, we believe that the existence of persistently disconnected areas is robust.Non-spatially biased samples suggest that up to 15% of the bed could remains unconnected year round.The existence of such unconnected holes, and the possibility of dynamic connection and disconnection, represents a challenge to existing drainage models, which typically assume pervasive connections at the bed.
In addition to conduits at the bed interface, englacial conduits are known to exist inside temperate glaciers (Fountain and Walder, 1998;Nienow et al., 1998b;Harper et al., 2010).However, it is unclear whether they allow mostly vertical water transport, or if horizontal water transport over significant distances is also possible through them.Frequent drainage events during drilling (also observed by Iken and Bindschadler (1986)) suggest the existence of a large number of englacial conduits, and borehole re-drilling observations show that upward conduits can remain open through the winter season in a layer extending several meters above the bed.However, we have no evidence of significant along-glacier drainage in winter, while we know that englacial connections can remain.This suggests that the englacial connections remain isolated from each other during winter.It is unclear if they can connect in summer and establish an englacial drainage system capable of supporting significant down-glacier drainage.The persistence of conduits through winter is most likely related to the basal layer of temperate ice The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.(Wilson et al., 2013), and hydraulic isolation preventing creep closure.The apparent ubiquity of englacial conduits suggests a need to assess their role in downstream water transport in future; if significant, this represents another area of improvement for drainage models.

Mechanically connected boreholes
Strong correlations over long distances were observed in boreholes displaying all the features of isolated boreholes except a superimposed low-amplitude diurnal pressure variations with high-frequency variations (Fig. 9).From their wide spatial distribution, it appears impossible for them to be connected by hydraulic conduits.As such conduits would need an extremely high diffusivity to preserve the observed high-frequency features over large distances (>500 m as seen in Fig. 2).Moreover, a high diffusivity is at odds with the diverging evolution of smoothed borehole water pressures in the same holes.
These signals do not seem to be instrumental artifacts, and in many cases were recorded by independent data loggers.We have also considered effects due to induction on non-twisted signal cable coils, temperature, or solar irradiation.However, in those cases, such signals should also be superimposed on records from distributed drainage systems, contrary to our observations.Possible explanations must be related to periodic large-scale stress changes in the ice compressing isolated boreholes whose volume must remain constant, thereby eliciting an instant water pressure response.The most likely cause of such largescale stress changes would appear to be the occurrence of periodic diurnal basal slip events as suggested by Andrews et al. (2014).

Data interpretation
We generally assume that the sensors at the bottom of boreholes measure the water pressure at the bed.However, this may not always be the case if the sensor becomes encased in ice, is connected to an englacial conduit, or if the borehole did not reach the bed or has penetrated into the basal till.
It is likely that with time, some sensors can become encased in ice, as suggested by the fact that older sensors are less likely to show diurnal oscillations, and by confinement data showing in some cases a correlation with the initiation/termination of diurnal pressure oscillations (Fig. 15).For this reason, old isolated sensors were often decommissioned before they ceased to produce a signal.
Although the upper end of the boreholes typically freezes shut within few days, the abundance of englacial conduits described above opens the possibility that the sensors could connect to an englacial conduit through the lower portion of the borehole while it is still open.In such a case, the pressure record could at least partially reflect the evolution of englacial conduits instead of the basal drainage system.
Alternatively, in the absence of englacial connections, a sensor in a borehole that fell short of the bed would appear as isolated, even if the underlying bed is not.However, we believe this is not a common situation due to the strict procedures followed to assess whether a borehole reached the bed or not (see section 2).
Observations by Hart et al. (2015) using wireless pressure sensors installed across the basal till layer in a glacier in Norway showed that, while a sensor in the ice-till interface shows clear diurnal variations, another one placed a short distance away The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.inside the till layer can show a signal very similar to our isolated boreholes.This could be a problem affecting some of our sensors, as borehole drilling could eventually penetrate the till.Nevertheless, the lifespan of a sensor buried in the till ought to be short if there is differential motion between ice and till, causing the signal cable to tear.Indeed, one sensor that was accidentally installed directly on the bed with limited (1 m) cable slack, rather than suspended just above the bed, survived for only just over a month, and showed uncharacteristic high-frequency noise superimposed on a smooth diurnal oscillation (see the lowest curve in Fig. 4g).
We also reiterate that calibration drifts may affect in-situ sensors over time, and differences in measured water pressure may not be reflective of an actual pressure gradient between two boreholes (section 3.6); consequently, we have taken similarity in response to diurnal forcing as our indicator of connections, rather than looking directly at the evolution of pressure differences.

Modelling
Our data show that the glacier bed not only contains regions that remain disconnected from the subglacial drainage system during the melt season, but that those regions can evolve in time, and that disconnection from or reconnection to the drainage system can be quite abrupt.By itself, that insight is not new.Previous observational studies (Murray and Clarke, 1995;Gordon et al., 1998;Andrews et al., 2014;Meierbachtol et al., 2016) have pointed out the same set of phenomena.Most models in their present form (Schoof, 2010;Hewitt, 2011;Schoof et al., 2012;Hewitt et al., 2012;Hewitt, 2013;Werder et al., 2013;Bueler and van Pelt, 2015) however do not capture them: water can flow everywhere in the domain, although the permeability of the distributed system varies with position and over time.The expected signature of the distributed system in borehole records is then a progressive decrease in amplitude of diurnal oscillations away from subglacial channels, with a corresponding phase lag (see Fig. 8 of Werder et al. 2013): the sheet behaves as a diffusive system, in which the diffusivity varies smoothly in space and time and evolves as sheet thickness does (see also Hubbard et al., 1995).This contrasts with the possibility of abrupt disconnection from the drainage system that appears to be the main feature of our field data, rather than a slow, diffusive attenuation of pressure signals.
The only exception is the model of Hoffman et al. (2016), which contains a 'weakly connected' component that exchanges water with the active remainder of the drainage system through highly inefficient connections.Diurnal pressure variations in that weakly connected system are primarily due to the effect of ice motion rather than through the exchange of water, as we have also inferred for the groups of boreholes in our data that show common, mechanically transferred pressure variations (Fig. 9).The spatial extent of individual weakly connected parts of the bed is however left unresolved in Hoffman et al. (2016), and water exchange with the distributed system occurs locally, as is also the case in dual-porosity models (de Fleurian et al., 2014).Instead of prescribing the physics by which the connection between distributed and weakly connected systems evolves, a simple linear increase in the exchange coefficient is assumed to occur during the summer.
Here we take a different approach and try to construct a model that can resolve connected and unconnected (or weakly connected) regions explicitly, and track their evolution.Our basic premise is the following: models of distributed drainage (Hewitt, 2011;Schoof et al., 2012;Werder et al., 2013;Bueler and van Pelt, 2015) typically describe a system of cavities, and The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.model the mean cavity size at any given location.Crucially, these cavities are assumed to connect whenever they have non-zero size.Here, we replace that assumption by a percolation limit: cavities only form a connected system once they have reached a critical size.We describe the implementation of such a limit in the context of a discrete network-based model for subglacial drainage, and discuss the relatively straightforward equivalent continuum formulation in the supplementary material.

Model Formulation
We assume an arbitrary network of conduits connecting nodes labelled by a single index i; the edge connecting nodes i to j is identified by the double index ij.The basic set-up of the model, with a handful of alterations identified below, proceeds as in Schoof (2010).
Along each network edge ij, we assume one 'R'-conduit that can behave either as a Röthlisberger (R) channel or a cavity, as in Schoof (2010), with average cross-section S R,ij .To mimic the sheet of Werder et al. (2013) and avoid the pitfall of having to resolve every basal conduit, we also assume there are n c − 1 'K'-conduits that behave only as cavities, and are not subject to enlargement by melting.We denote their average cross-sectional area by S K,ij .The conduits evolve according to Here Q R,ij is discharge from node i to j in the R-conduit, and Ψ R,ij the hydraulic gradient along the R-conduit, u is sliding velocity, h R the size of bed obstacles supporting cavity formation, and S R0 is a cavity-size cut-off at which further conduit enlargement drowns out bed obstacles.P e,ij is the effective pressure driving conduit closure (related to N i as described by equation 1h below), and c 1 , c 2 are the same constants as in Schoof et al. (2014).Subscripts K refer to equivalent quantities for the K-conduits.
We associate a nominal effective pressure N i with each node, defined as overburden minus basal water pressure.Hydraulic potential Φ i at each node and hydraulic gradient along the conduits are then given by where Φ 0,i = ρ i gs i + (ρ w − ρ i )gb i is the geometrical contribution to hydraulic potential, ρ i and ρ w being the densities of ice and water, g acceleration due to gravity, s i and b i ice surface and bed elevation at the node.L ij is the length of the network edge and T ≥ 1 is the tortuosity of the K-conduits, relative to the R-conduits.In a departure from previous models, we assume a percolation cut-off for flow along the conduits, and write cavities, such a threshold is easy to justify: while S K may be the average cross-sectional area of cavities along the network edge, the local cavity size will naturally vary as bed obstacles are uneven, and it is natural to expect that cavities with non-zero size may fail to connect.We apply the threshold equally to the R-conduit as it can act as either a channel or a cavity, and a cut-off must apply self-consistently in its cavity state.A node that is connected to others purely by conduits that are all below the percolation threshold is then hydraulically disconnected from the drainage system.
At each node, water can be stored in englacial void space connected to the node, with volume storage capacity per unit water pressure V p (see also Werder et al., 2013;Schoof et al., 2014;Brinkerhoff et al., 2016).Water can also be supplied externally to each node at a locally-defined rate m i , and flows along network edges through R-or K-conduits, or possibly through a permeable porous substrate if the conduits are closed.To account for conservation of mass, we also associate half the volume of water stored in a conduit between two nodes with each node, and likewise account for half the water created by wall melting in an R-conduit as water supply to each node.Consequently we impose where k leak represents the possibility of a substrate (till) with non-zero permeability.Sums over j are taken over nodes connected to node i.
To close the model, we need to relate the conduit effective pressure P e,ij to the nominal effective pressures N i at network nodes, we write this in the form where the sum is over all node indices k in the network, and G ijk is a suitable positive averaging kernel that satisfies k G ijk = 1; in our network model below we put G ijk = 1/2 if k = i or k = j and G ijk = 0 otherwise for simplicity; this is however a surprisingly key assumption (see also the Supplementary Material).Suppose we have k leak = 0 and no hydraulic connection at all between adjacent nodes.This can lead to arbitrarily large effective pressure gradients.The usual assumption of cavity formation models (Fowler, 1987;Schoof, 2005;Gagliardini et al., 2007) breaks down, namely that adjacent cavities are subject to the same nominal effective pressure, defined as overburden pressure (or far field normal stress) minus a common water pressure.The rate of opening or closing of a cavity is unlikely to be a function of its own nominal effective pressure alone, and is likely to be affected by stresses around other nearby cavities (and hence dependent on their nominal effective pressure: the observation of anti-correlated water pressure records in our data set indicating a load transfer of overburden onto highly pressurized parts of the bed (Murray and Clarke, 1995) also supports this assumption.We try to capture this load transfer effect by the averaging kernel G above.
More practically, if conduit opening and closing were driven by a local effective pressure variable alone, then the generalization of our model to a distributed sheet (Werder et al., 2013) would result in disconnected parts of the bed potentially never reconnecting.In order for a disconnected region to reconnect, sheet thickness in the disconnected region needs to change.
On the absence of leakage through the substrate, the only way that can happen in a way that is driven by the hydrology of the connected regions is through a non-local sheet closure term, or through the sliding velocity u.We expand on this in the supplementary material, but note here that conduit closure must involve a non-locally defined effective pressure in order for our percolation model to function as intended, allowing for expansion as well as the contraction of a connected region at the bed.
A key component that the model above continues to miss is the ability to open conduits due to overpressurization of the system (Schoof et al., 2012;Hewitt et al., 2012;Bueler and van Pelt, 2015;Dow et al., 2016).While not necessary to explain switching events during the main melt season, this is likely to be key in establishing a drainage system at the start of the melt season: unlike existing sheet models, in which a distributed system always exists and can simply be expanded through water supply in the spring, the percolation limit model above allows the system to shut down completely, and rapid re-establishment through a spring event is likely to require overpressurization.We discuss the extension of the approach in Schoof et al. (2012) and Hewitt et al. (2012) further in the supplementary material.

Results
We show results here for the evolution of a drainage system supplied through discrete moulins, focusing on time-dependent water input to a fully developed, channelised drainage system .A list of model parameters is given in Table 1; unlike in Hoffman varies over several days, with mean water supply rates also varying over several days; the dominant period of the cycle is the same for each moulin but the ratio of diurnal amplitude to mean water supply is chosen randomly (while maintaining positive water supply rates at all times), and we have allowed for slight phase shifts between moulins.The time series of water supply to all moulins are shown in panel c of Fig. 16.
Figure 16 shows two snapshots of a four-week drainage cycle, corresponding to the maximum and minimum extent of the connected drainage system during that period.Panels a4 and b4 indicate the connected regions in each case in blue.Also indicated there are two squares that we treat as synthetic borehole grids.A video showing the continuous evolution of conduit sizes, effective pressure and connectivity is included in the supplementary material.
Time series for water pressure in these borehole grids are shown in Fig. 17.The character of diurnal pressure signal propagation is qualitatively more in line with that in our field data than, for instance, the equivalent Fig. 8 in Werder et al. (2013): switching events as well as clear differentiation into drainage subsystems are visible, while there is considerably less diffusive attenuation and development of phase lags.The synthetic time series however also provide a note of caution.As expected, connections usually happen during times of decreasing mean effective pressure, with the opposite true for disconnection events.In Fig. 17, all boreholes in panels e and f as well as two boreholes rendered in pink in g ultimately connect to the same channel, though a superficial assessment would not necessarily identify that.

Conclusions
While winter pressure record suggests that most boreholes remain isolated during that period, the rapid spring increase in water supply produced when the water storage capacity of the snowpack is overwhelmed, leads to the sudden activation of an extensive and well connected distributed drainage system.During this period, the majority of boreholes show similar diurnal pressure variations and experience modest water transport (see section 3.1).
Over time, water transport becomes concentrated in some areas, and probably becomes channelized: water flow ends up focused in R-channels surrounded by a distributed drainage system that carries relatively low water fluxes.Borehole water pressure data in most cases do not allow the direct identification of channels, in fact, in most cases, our borehole array probably fails to intersect the narrow R-channels.However, in one instance we were able to confirm the existence of a channel from direct observation in a borehole in which the lowermost 50 cm were occupied by turbulent water flow.
The increase in effective pressure associated with channelizations leads to the progressive shut-down of drainage activity of the surrounding distributed drainage system, possibly due to basal cavities becoming isolated from each other as they shrink The Cryosphere Discuss.under the effect of a larger effective pressure.In long and hot enough seasons, most of the bed can become disconnected, concentrating drainage in narrow pathways.The eventually complete shut-down of the entire drainage system at the end of the summer season is presumably the result of low water supply: high effective pressure and low dissipation rate in channels allow basal conduits to close.This appears to be strongly linked with the appearance of fresh snow cover, rather than the arrival of low temperatures alone (see section 4).
Most of the observations are consistent with borehole data from other sites.However, the density of boreholes at South Glacier has allowed us to identify, in particular, the prevalence of "switching events", through which the drainage system focus, and the isolated areas enlarge.Such isolated areas always exist, even during the spring event, with isolation sometimes being reversed.Isolated parts of the bed are necessary to account for many aspects of our data, including anti-correlation between boreholes pressure time series, above-overburden pressure, and the occurrence of strongly correlated high-frequency pressure variations in sets of widely spaced boreholes (see section 4.3).As in Hoffman et al. (2016), our data suggest that isolated areas need not be completely isolated, but can experience slow leakage into the active drainage system (see section 4.2).
In view of the above, perhaps the main shortcoming of most current models is their inability to account for the evolution of an isolated or weakly connected component (Hoffman et al., 2016).This ability can however be incorporated in the current modelling framework as a percolation threshold, assuming that cavities only form a connected system once they reach a critical size.We have implemented this approach in a simple model, allowing us to reproduce qualitatively some of the main features of our data set: a sharply-defined drainage subsystems with insignificant diffusive pressure signal attenuation and the existence of isolated areas (See section 5.1).
However, the ability of the system to fully shut-down requires the incorporation of other physical process that could allow the reactivation of the drainage system during the spring event, something that is probably accomplished by over-pressurization.
The model also requires a more careful treatment of normal stress redistribution, in particular in association with isolated and closely spaced cavities of very different water pressures.In the future, we hope that it will be possible to test models like the one presented here or more sophisticated versions of it, against detailed borehole data sets such as that from South Glacier.

Figure 1 .
Figure 1.WorldView-1 satellite image of South Glacier taken on September 2nd, 2009.Borehole positions are marked according to the year of drilling, showing the most recent year in repeatedly drilled locations.Time lapse camera positions, Automatic Weather Station (AWS) approximate equilibrium line (ELA) are also indicated.The inset map shows the general location in the Yukon.The white box corresponds to the area shown in Fig. 2. Note that the different symbols indicating years of borehole drilling are used systematically through the text.

Figure 2 .
Figure 2. Detailed map of the study area.The following symbols indicate specific boreholes: those used for non spatially-biased statistics (blue symbols), displaying behaviour similar to the fast-flow hole in Fig. 4 (red symbols), re-drilled ones (light blue symbols), and those used in Fig. 9 (orange symbols), the 2014 slow-flow borehole in Fig. 5 (yellow triangle), and the location of the Automatic Weather Station (yellow circle).The red outlines encompass all the boreholes displayed in figure 14, shown here using coloured and white markers.Black lines indicate major crevassess, blue lines surface streams.Contours show surface elevation, blue shading ice thickness.Grey shading indicates the upstream area calculated as in panel b of Fig. 2 in Schoof et al. (2014).
cycle and water flow Despite a large diversity of borehole pressure records, a few general patterns are easy to identify.The most common is the contrast between an inactive winter regime and an active summer period.During winter, most sensors show stable, high (near 6 The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 3 .
Figure 3. Example pressure time series recorded in one borehole (D in Fig. 2) from 2011 to 2015 (blue line).Daily PDD values are shown as a red line, annual cumulative positive degree days as orange shading, and fresh snow cover determined from time lapse imagery as light blue shading.The fading blue at the end of the winter indicates the appearance of larger snow-free patches and the filling of a perennial supraglacial pond in the study area, rather than the complete disappearance of the winter snowpack.Green dots indicate the count of boreholes drilled each day.
Fig. 4 shows the pressure recorded in the fast-flow borehole for the first 33 days after installation.Panel d shows the pressure records in three boreholes along the same line across the glacier at 15 m spacing.The lack of similarity between the fast-flow hole pressure record and those from other nearby boreholes differs from the behaviour of most boreholes that display diurnal pressure oscillations: typically, such boreholes show a signal similar to one or more neighbouring boreholes, The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 4 .
Figure 4. Locations and pressure time series of the boreholes associated with the fast-flow borehole during the summer of 2013.(a) The map uses the same scheme as Fig. 2, but omits the upstream area shading.(b) Temperatures (grey) and fresh snow cover determined from time lapse imagery (light blue shading, fading colour indicates partial cover).(c) Pressure in the fast-flow borehole (red) and its correlation with temperature in grey, computed for any given time over a 3-day running window.Note that two sensors were installed in the fast-flow borehole, offset vertically from each other by 70 cm.(d-i) Pressure records from other boreholes marked on the map.The colour of plots corresponds to borehole marker colours on the map; the same convention is used in all subsequent figures.Symbol shapes represent drilling years as in Fig. 2, uncoloured (grey) markers correspond to boreholes with active sensors during the displayed period whose pressure time series are not shown in the figure.

Figure 5 .
Figure 5. Locations and pressure time series of the boreholes associated with the slow-flow borehole on July and August 2014, with the same plotting scheme as Fig. 4 (see corresponding caption).Panel c shows pressure in the slow-flow borehole (black) and three other boreholes in the same line.The remaining panels show pressure time series from other nearby holes as indicated by the line and borehole marker colours.The time series from boreholes S1-S4 are shown in more detail in Fig. 6..

Figure 7 .
Figure 7. Mean water pressure computed over a 1-day running window for each of the 55 sensors that did not display diurnal oscillations during 2016, shown in black.For legibility, we have subtracted the mean over all sensors and the time window shown.The blue line shows the mean over all the black lines at a given time (i.e. over all the sensors) and the bootstrap confidence intervals (Efron and Tibshirani, 1993) of 90 and 99% (dark and light pink shading, respectively).Gray shading represent the period over which the initiation of diurnal oscillations was observed in connected boreholes, and the red vertical line is the median time at which diurnal oscillations first appeared in the 70 boreholes that did experience such oscillations during 2016.

Figure 3 of
Figure 3 of Schoof et al. (2014) also shows an example of the same phenomenon during July and August 2011: borehole B in that figure is, in fact, one of a group of 5 that exhibit almost identical diurnal water pressure oscillations that are quite distinct from those in boreholes A1-A6 in the same figure.The spatial patterning of the drainage system into distinct subsets becomes much clearer when a dense borehole array with good spatial coverage is available.During the summer of 2015, there were 88 boreholes with active sensors on the plateau indicated in Fig.2, and 66 further downstream.The corresponding pressure records are presented in Fig.8.Between June 26th and August 27th, 42 boreholes on the plateau (panel c) and 11 boreholes downstream (panel d) showed a highly coherent

Figure 8 .
Figure 8. Locations and pressure time series from all 82 boreholes on the plateau area and 20 boreholes down-glacier during June-August 2015, plotted using the same scheme as Fig. 4. (b) Temperatures (grey) and fresh snow cover (light blue shading), (c) Pressure in 42 boreholes on the plateau that share similar diurnal water pressure variations during at least part of the observation period.The highlighted time series are from boreholes D1 (black) and H1 (yellow line).Both boreholes are indicated on the map.S1-S7 indicate 'switching events' in the D1 record (see section 3.4).(d) Boreholes downstream of the plateau showing similar pressure variation to those in (b).(e) Pressure records that are anti-correlated to those on panels (c)-(d).(f) Pressure records from the remaining boreholes on the map, (g) Conductivity records from the six digital sensors included in panel b.

Figure 9 .
Figure9.Relative pressure variations in 7 boreholes (orange symbols in Fig.2) displaying common small amplitude diurnal oscillations with high-frequency content during August 2011.To make these visible in the same plot, we have applied offsets of93, 71, 64, 61, 63, 66 Fig. 10i, shows the pressure record in borehole A and the point at which the re-drilling took place.The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 10 .
Figure 10.Locations and pressure time series of all 42 boreholes shown in Fig. 8b, grouped according to the similarities between their diurnal pressure variations in July-August 2015, same plotting scheme as in Fig. 4. (a) The map area is indicated as a box in figure 8a.Grey shading is the upstream area shown in Fig. 2 (b) Air temperature (grey) and fresh snow cover (light blue).(d-k) borehole pressure time series, colour of plots corresponds to colour of borehole marker on the map.Black lines are the mean pressure in each panel, computed only over those boreholes that are "connected" at a given time (see main text); the black lines frequently obscure one of the borehole time series.(c) The black "mean" curves from panels (d-k), plotted in the corresponding borehole marker colour.The maximum cross-correlation coefficients, allowing for time lags of up to six hours, between all pressure records and air temperature computed over a moving three-day window is shown in dark grey.

Figure 11 .
Figure 11.Relative amplitudes of pressure and temperature diurnal oscillations from May to September 2015.(a) Positive air temperature (grey), and its standard deviation over a 1-day running window (red).(b) Standard deviation of pressure over a 1-day running window (thin black lines) for each borehole in the plateau area, and the mean of these standard deviations (blue) with bootstrap confidence intervals of 90 % (dark pink) and 99% (light pink).(c) Ratio between pressure and temperature standard deviations shown in (a) and (b), computed only where standard deviation of air temperature is non-zero.(d) Mean pressure computed over a 1-day running window.Light blue shading represents fresh snow on the glacier surface.

Figure 12 .
Figure 12.Extended pressure time series from the 2013 fast-flow borehole (Fig. 4).(a) air temperature (grey) and fresh snow cover (light blue).(b) Pressure recorded by two sensors installed 10 cm and 80 cm above the bed (red and blue respectively).

Figure 13 .
Figure 13.Photographs of the study area taken on July 19th, 2012-2015, as indicated in each panel.
10 in 2014-2015 in the location of the 2013 fast-flow hole without encountering more evidence of turbulent water flow.20 The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 14 .
Figure 14.Overview of pressures variations on the lower portion of the plateau area from 2012 to 2015.Each panel includes air temperature (grey), coverage of fresh snow (light blue), and vertical red lines displaying the median date of initiation and termination of diurnal oscillations on all active sensors each year.Cumulative positive degree days are displayed for the begin and end of the shown interval.

5
of the recorded pressure time series.From 2013 onwards, most sensors were equipped with snubbers, and only one sensor displayed this issue afterwards.In all four cases, instantaneous offsets were manually identified and corrected.21TheCryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 15 .
Figure 15.Confinement data (grey) and pressure (blue) for one of the digital sensors in Fig. 8b from July 2015 to September 2016.
The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.diurnal oscillations in most boreholes precedes the decline in inferred meltwater supply and pro-glacial river runoff as observed byHarper et al. (2002) andFudge et al. (2005).The distinct response of different subsystems to the same surface conditions must be the result of peculiarities of each subsystem.The amplitude of the diurnal pressure cycle typically varies over periods of several days, but the temporal pattern of amplitude variations differs between subsystems, and generally, does not reproduce corresponding variations in diurnal melt amplitude (Fig.10here and Fig.3ofSchoof et al. (2014)).
, red symbols), in all cases during the second half of July or first days of August during years with relatively high cumulative PDD, which ought to favour channel formation.Their locations loosely match zones with high up-stream areas (Fig 2, dark shading).

)
Here c 3 is the same constant as inSchoof et al. (2012), and α and β are constant exponents as inWerder et al. (2013), while S P R and S P K are the constant thresholds that conduit sizes must reach before water can flow in the conduits.For linked The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.
Fig. 16, the size of each dot scaled to the instantaneous water supply.Each moulin undergoes a diurnal cycle whose amplitude , https://doi.org/10.5194/tc-2017-270Manuscript under review for journal The Cryosphere Discussion started: 19 January 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 16 .
Figure 16.Snapshots of drainage system evolution.Column 1: SR conduit size.Column 2: SK conduit size.Column 3: effective pressure, black lines are 100 m surface contours, grey lines 100 m bed contours.Column 4: connectedness of conduits, indicated in blue if SR,ij > SP R or SK,ij > SP K along a given edge, in white otherwise.Red dotes indicate moulin locations, size of dot scaled with instantaneous water supply.Rows a and b show solutions at t = 7.8 days and 20.6 days, respectively.Panel c: water supply time series for all moulins in the domain.

Figure 17 .
Figure 17.A synthetic borehole grid.(a-c): enlargements of the inset box in Fig. 16(a4) at times t = 3.9 (a), 7.8 (b) and 20.6 (c) days.Superimposed on the blue connectivity map is SR conduit size, plotted using the same colour scheme as indicated by the colour bar in column 1 in Fig. 16 .Also shown are the locations of 16 synthetic boreholes, colour-coded by row, (d-g).Effective pressure time series from the boreholes, grouped according to borehole symbols: circles (d), diamonds (e), triangles (f), crosses (g).Each time series is colour-coded by row.