Multi-scale variations of subglacial hydro-mechanical conditions at Kongsvegen glacier, Svalbard

. The flow of glaciers is largely controlled by changes at the ice-bed interface, where basal slip and sediment deformation drive basal glacier motion. Determining subglacial conditions and their responses to hydraulic forcing remains challenging due to the difficulty of accessing the glacier bed. Here, we monitor the interplay between surface runoff and hydro-mechanical conditions at the base of the Kongsvegen glacier in Svalbard. From spring (cid:58)(cid:58)(cid:58) July (cid:58) 2021 to summer (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) August 2022, we measure both subglacial water pressure and till strength. Additionally, we derive subglacial hydraulic gradient and radius 5 over a kilometre scale (cid:58) of (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) channelized (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) subglacial (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)

in the accumulation area, symptomatic for a surge-type glacier in its quiescent stage.Surface velocities recorded nearby the equilibrium line indicate that the glacier is accelerating since 2014, indicating the possibility for an imminent fast flow event :::: surge : (Fig. 1 b).
We conducted field campaigns to install and maintain a set of instruments at Kongsvegen starting in September 2020.
Borehole and surface instrumentation was 3 Methods

Borehole
On April 25 , 2021, we drilled a borehole near the long term equilibrium line (78 13' E, Fig. 1a) of Kongsvegen and placed instruments along the borehole and at its base.The borehole was drilled using a hot water drilling system, consisting of three high-pressure hot water machines (Kärcher HDS1000D), a 1/2 inch diameter high-pressure hose, a 2 m drill stem with a 2.3 mm diameter nozzle, a pulley, a tripod, and water tanks (three 1000-liter IBC tanks, Fig. 1d).Since the glacier was in winter conditions and liquid water was not available, ::: the water flowing out of the borehole was captured in an auxiliary hole for recycling (Fig. 1c).During drilling, the borehole water level started dropping :::: level :: of ::::: water :: in ::: the :::::::: borehole ::::: suggested the existence of a preferential drainage pathway ::: axis : in close proximity to this site.
At the bottom of the borehole, we installed a ploughmeter, i.e. a 1.4 m long steel rod equipped with strain gauges, to monitor mechanical conditions of the subglacial till (e.g.Humphrey et al., 1993;Iverson et al., 1994;Fischer and Clarke, 1994;Porter et al., 1997;Fischer et al., 1998Fischer et al., , 2001;;Murray and Porter, 2001;Boulton et al., 2001).The tip of the instrument penetrates into the till whereas its upper part remains in the borehole and is trapped in the ice.As the glacier moves across its bed, the ploughmeter tip is dragged through the sediment , and the device bends : , : which is sensed by the strain gauges.Strain on the ploughmeter is measured using a Wheatstone bridge for each pair of strain gauges in two perpendicular axes (Hoffmann, 1974).The exact insertion depth of the device into the till is unknown ::::::: uncertain.However, based on previous experiences with identical devices, we estimate the penetration depth to be around :: in ::: the ::::: range 10 to 40 cm : , which is sufficient to ensure that all strain gauges are immersed in subglacial material :: the ::::::::: subglacial :: till.Just above the upper end of the ploughmeter , :::::: (which : is : about 1 m above the glacier bed), we installed a vibrating wire pressure sensor (Geokon 4500SH, <2 kPa accuracy and 0.5 kPa resolution) to monitor ::::::::: subglacial water pressure, p. Sensor readings and data recording is :: are : performed using a Campbell Scientific CR1000X data-logger, recording data at one minute intervals.Ploughmeter readings ::::::::::: measurements : are converted to force F experienced by the instrument while being dragged through the sediment, based on a calibration performed :: F .:: To ::: do :: the :::::::::: conversion, ::: we :::::::: performed :: a ::::::::: calibration in the laboratory prior to field deployment.To perform the calibration, loads : : :::::: masses :: of :: 10 ::: kg ::: and ::: 50 :: kg :::::: (∼100 ::: and ::::: ∼500 ::: N) : have been applied to the ::: free ::: end :: of ::: the : horizontally fixed ploughmeter by hanging a known mass on its free end.We repeated these measurements in eight orientations (0 to 315 o • : every 45 o )using masses of 10 kg and 50 kg corresponding to loads of ∼100 and ∼500 N, respectively :: • ).After applying the calibration component-wise, we derive F from the X and Y : x :::: and : y : components using Pythagoras' theorem.
Then the velocities are averaged daily to reduce ::: the velocity uncertainties caused by the relatively low speed of the glacier.The Norwegian Mapping Authority's permanent network base station in Ny Ålesund is used as reference (baseline of ∼ 30 km).
The two velocity records are merged, i.e. we consider the velocity derived from KNG6 when available and the one from KNG7 for the rest of the period (the original records for KNG6 and KNG7 can be seen in the Appendix C).We apply a one-week moving median for KNG7 velocity to smooth the record especially during the winter period when the velocities are low.
Table 1.Scaling relationships between P and Q, S and Q, and R and Q : , for special cases, derived by Gimbert et al. (2016) and Nanni et al.

Context Relation Reference
Change in runoff occurring at constant hydraulic radius
These phase relationships are analysed ::::::: analyzed : at three different, glaciologically relevant time scales: seasonal, multi-day, and diurnal.To extract the corresponding components at these three time scales, we filtered the time series using a low-pass filter with cutoff at 20 days, a band-pass filter between four and eight days, and a band-pass filter between six hours and 36 hours, respectively.We subdivide the multi-day and diurnal time series into individual events based on Q variations.We define an event by two subsequent minima of Q within the bandwidth investigated.We normalize both Q and the subglacial variables by their respective maxima and subdivide the time into 50 equidistant steps.We choose the :::: The number of time steps was chosen empirically as the minimum number of data points that preserves the shape and characteristics of the event time series (see also Appendix B, Fig. B1).We synthesize the different responses of each subglacial variables : , :: X, : to changes in Q using a classification scheme (Fig. 2).Our workflow resembles that developed by Nanni et al. (2020) to understand sub-glacial  Our classification scheme is based upon the following metrics: the slope, : m, : of the linear regression between the subglacial variable X (with X being F , P , p, R or S) and Q (black line, Fig. 2); the squared residuals, RSS, between the linear regression and the X norm − Q norm hysteresis loop; θ whose sign indicates the direction of the hysteresis loop, :: θ.The spread of the data relative to the regression is quantified by :: the ::::::: squared :::::::: residuals (Appendix F, Fig. F1b): where r i are the residuals of the regression.
Events are classified according to the phase relationship between Q and the subglacial variable.We distinguish four classes, representing the following cases (Fig. 2): - To discriminate between linear and hysteresis relations, we use a threshold of RSS = 2, corresponding to a phase difference of about π/10 for two sinusoidal variations.Our analysis does not target a two member classification (steady-state or not), but a four member classification of phase relationships which are subsequently interpreted :::: This :::::::: threshold :::::: allows ::::: some :::::::: deviation
In response to temperature and rainfall variations, Q displays variations on several time scales (Fig. 3c and d  (iii) and being melt-dominated, the pronounced diurnal variability of Q reflects the diurnal :::::::: reflecting ::: the variability of surface energy balance.
At the beginning of the 2021 melt season, p is high, close to the overburden pressure ::: (3.2 ::::: MPa).As Q continues to increase, p decreases until it reaches its minimum values (∼2 MPa) after peak :: an :::::: abrupt ::::::: increase :: in Q marked by ( 2 : ).p increases again during the winter to reach a value (2.9 MPa) close to overburden pressure (3.2 MPa, ( :: 2.9 ::::: MPa, Appendix A, Fig. A1d).In the second year of the record, p remains high and increases to the overburden pressure in mid-July 2022 before decreasing again to levels close to its winter value (2.9 MPa) at the end of August .:::: 2022.: Similar to p, the force acting on the ploughmeter, F , shows different behaviors between the two melt seasons (Fig. 3g and h, dark red).During the melt season 2021, it : F : remains fairly stable until August 2021, when it suddenly undergoes :::::::: variations :: of large amplitude (∼150 N maximum amplitude) , ::: and : high-frequencyvariations.As the instrument site becomes snow-free around August 15 , 2021 (Fig. 3a), F gradually decreases towards the end of the melt season until it reaches its minimum value in early October 2021 (∼ 70 N).At the end of September :::: 2021 : occurs a major precipitation episode (Fig. 3c 4 ), with heavy rainfall going over to snowfall as the temperature dropped.F does not react to this event.After this precipitation event, F gradually increases until it stabilizes at ∼ 170 N in January 2022.Note that this value is almost twice the value observed before the melt season 2021 (∼ 90 N).
To interpret the responses of the subglacial drainage system and glacier dynamics to variations in runoff, Q, we analyze the data using a phase relationship analysis on seasonal (above 20 days, Sec.4.2), multi-day (four to eight days, Sec.4.3), and diurnal (six hours to 36 hours, Sec.4.4) time scales.

Analysis of seasonal variations
To examine the phase relationship between the subglacial variables and Q at the seasonal scale, all time series are low-pass filtered with a cut-off frequency of 20 days.We first describe the results obtained for the melt season 2021 and then for the melt season 2022.
As Q increases, this is followed by ::: we :::::: observe : an adjustment of S at constant R (Fig. 4a, 2).When Q decreases in August 2021, the preferential drainage axis evolves by adjusting R (constant S; Fig. 4a, 3).At the end of the melt season 2021, the trajectory of P is indicative of :: we ::::::: observe an adjustment of S (Fig. 4a, 4).The ::::::::::::: Simultaneously, : R − Q trajectory is parallel to the scaling relationships ::::::::: relationship : for channels evolving at steady-state (Fig. 4b) and we observe that the S − Q trajectory follows the steady-state relationship, though not always strictly parallel (Fig. 4c).We observe that the :: At ::: this ::::: time, : p − Q relationship is characterised :::::::::: characterized : by a clockwise hysteresis (Fig. 4d) indicating that the peak in p precedes the peak in Q.The linear relationship between F and p during the first half of the melt season indicates that the two subglacial variables are anti-correlated (Fig. 4e) and, at the end of the melt season, F −p trajectory shows a counter-clockwise hysteresis, indicating the ::: that the peak in F lags after the peak in p (Fig. 4e).
Similar as in 2021, the melt season 2022 can be divided into four regimes, but these phases describe different behaviours :::::::: behaviors.
At the beginning of the melt season, the preferential drainage axis evolves predominantly by adjusting R (Fig. 4f, 1), as observed in 2021.Then, the preferential drainage axis briefly leaves this regime to follow an evolution that is not described by the theoretical relations and that are neither governed by :::::::: indicative :: of ::::: either : constant R nor :: or constant S (Fig. 4f, 2).This is followed by a return to a regime indicative of predominant ::::: After ::: this :::::: period, ::: the :::::::::: preferential :::::::: drainage :::: axis :::::: follows :: a :::::: regime numbers refer to different periods described in the main text.The numbers do not correspond to the same periods between each panels and are unrelated to the periods identified by the circled numbers in Figure 3. ::: that :: is :::::::::::: predominantly :::::::: governed ::: by adjustment of S (constant R) for the remaining increase in runoff (Fig. 4f, 3).The runoff 345 decrease phase is not completely captured in the record because the records do not extend to the end of the melt season 2022.
However, for ::: For the period covered by data, we observe that the evolution of P is not indicative for neither : of :::::: either constant R nor : or : constant S (Fig. 4f, 4).We identify these four phases in the relationship of S and Q.During phases 1 and 3, the behavior is indicative of a preferential drainage axis evolving in equilibrium with Q (Fig. 4g and h, 1 and 3) and :::: while : during phases 2 and 4, the observed behavior more ::::::: behavior closely resembles that of a rigid-pipe (Fig. 4g and h, 2 and 4).As :::: Over season, p and Q are positively related even though the relationship displays some clockwise hysteresis (Fig. 4i).As for the melt season 2021, F and p are anti-correlated ::::: during ::: the :::: melt :::::: season :::: 2022 : (Fig. 4j).To understand the relationships on ::: the time-scales of weather variations, we filtered the time series with a band-pass filter, removing the variations with periods below four days and above eight days.Then, we applied our phase relationship classification scheme to each event (Fig. 5).We investigate the phase relationships between the subglacial variables (the force, F , the water pressure, p, the hydraulic radius, R, the hydraulic gradient, S) and the runoff, Q, for each event during the melt seasons in 2021 (eleven events) and 2022 (eight events, see Section 3.5).Similar phase relationships are observed during both melt seasons between (i) R and Q : , : and (ii) S and Q.During both melt seasons, R evolves in phase with Q (In-phase class, Fig. 5 a and c)and : .S :::::: evolves :: in ::::: phase ::::: with :: Q :::: only : at the beginning of the melt season 2021 (In-phase class, Fig. 5a).We cannot compare the relationship between S and Q at the beginning of the melt season 2022 as we have removed the events due to the inconsistency ::: due ::: to :::::::::::: inconsistencies : between the filtered data and the raw dataduring this period ::: and ::: raw ::::: data, ::::::::::: necessitating ::::

Analysis at multi-day scale
their :::::::: exclusion :::: from ::: the ::::::: analysis : (Appendix G, Fig. G1).For the remaining part of the season, the behaviour ::::::: behavior of S in response to Q is very similar in 2021 and 2022.During the first half of both melt seasons, S is first lagging after Q (Lagging class, Fig. 5a and c).During Q important excursions occurring in :: of : August 2021 (Fig. 5b 2 ) and July 2022 (Fig. 5d, 7 ), S precedes Q changes (Preceding class, Fig. 5a and b).In contrast to the phase relationships of R and S to Q, F do not show the same time-evolution across both melt seasonsbut : .F − Q phase relationship is sensitive to glacier acceleration.During high velocity episodes (Fig. 5b and d, 1 , 3 , 7 ), F systematically lags behind Q (Lagging class, Fig. 5a and c).Conversely, when velocity is low and stable during the melt season 2021 (Fig. 5b and d, from 1 to 3 ), F is anti-correlated with Q (Fig. 5a  and c).We do not have GNSS data in 2022 at this period to compare with the observations in 2021.behavior seen at the beginning of the melt season 2021 (Fig. 6a).In general, R evolves with Q similar to what is expected for a steady-state channel (Fig. 6b) whereas S shows a more complex behaviour ::::::: behavior that is difficult to disentangle (Fig. 6c).
The filtered time series are then subdivided into 95 events in 2021 and 84 events in 2022 (see Section 3.5) and we applied our phase relationship classification scheme.
The phase relationships between the subglacial variables (the force, F , the water pressure, p, the hydraulic radius, R, the hydraulic gradient, S) and Q on a diurnal time scale are displayed in Figure 7. Results indicate ::: We :::::: observe : that R and S show consistent phase relationships with Q during both melt seasons ::: the :::: melt :::::: seasons ::::: 2021 ::: and ::::: 2022, alternating between Lagging class and Preceding class, and Preceding class and Anti-phase class, respectively (Fig. 2).However, p − Q and F − Q phase relationships vary across all classes without an easily identifiable pattern (Fig. 7a-c).Except for during short episodes, p and F do not display pronounced diurnal variations (Appendix H, Fig. H1).Therefore, we focus on the analysis of diurnal variations on the responses of P , R and S.
During the 2021 melt season, we observe that R mostly varies in phase with Q (In-phase class, Fig. 7a).S is mostly anti-correlated with or precedes Q (Preceding class or Anti-phase class, Fig. 7a).
During the melt season 2022, we observe a shift from linear responses of R and S (In-phase class and Anti-phase class, Fig. 7c) towards more hysteretic responses (Preceding class and Lagging class, Fig. 7c) when Q shows the first significant increase in June (Fig. 7c and d, 6 ).::::: Before :::: this ::::: event, R varies with changes in Q before this event (In-phase class, Fig. 7c) but after, R lags behind Q (Lagging class, Fig. 7c).Similarly, S shifts regimes from being anti-correlated with Q before the episode ::::: event 6 (Anti-phase class, Fig. 7c) to a regime where S precedes Q after this period :::: event (Preceding class, Fig. 7c).
Due to the relatively low bed slope and the long distance between our borehole location and the glacier front, unpressurized drainage is unlikely to persist in these conditions and open flowpaths ::: and :::: open :::: flow ::::: paths are expected to close quickly (Nye, 1976).For a drainage axis with a fixed cross sectional area (rigid pipe), an increase in runoff, : Qresults , :: is :::::::: expected :: to ::::: result in increasing water pressure : , p : , that translates to a positive, linear p − Q relationship (In-phase class, Fig. 2).In this situation, we expect constant R, unaffected by variations in Q (not classified) ::: and :::::::::: concomitant :::::::::: acceleration :::::: events.Since we always measure p at the same location and the glacier terminus is fixed at sea-level, for a spatially homogeneous drainage system, we expect that variations in S are closely related to those of p.However, spatio-temporal complexity in the drainage system downstream of our borehole may lead to incoherent relations between local p and spatially integrated S. According to Röthlisberger's theory for ice-walled channels (Röthlisberger, 1972), the channel cross-section is determined by the ::: two : counter-acting processes of melt opening :: 1) ::::::: opening ::: by ::::::: melting : due to dissipation of potential energy and : 2) : creep-closure of the surrounding ice.In steady-state, these two processes balance each other, and a larger runoff would be :::: large ::::: runoff :: is : associated with a larger :::: large : channel, thus requiring lower :::::: causing ::: low : S and p (Schoof, 2010;Werder et al., 2013).This inverse p − Q relationship is one of the best-known characteristics of ice-walled drainage.Hence, we : In :::: this :::::::: situation, ::: the :::::: glacier ::::::: velocity :: is :::::::: expected :: to :::::: remain ::::::: constant :: or :::::::: decrease.:::: We interpret a negative, linear relationship (Anti-phase class, Fig. 2) between Q and p (and similar for S and Q), as indicative for steady-state drainage of a preferential drainage axis.This situation also entails that :: In ::: this :::::::::::: configuration, R increases with Q (In-phase class, Fig. 2).The evolution of the drainage system in response to Q typically is : is :::::::: typically transient between the two end-members described above, with a fixed cross sectional area referred to ::::::: evolving as rigid pipe on one hand, and a steady-state channel on the other one :::: hand.For transient evolution between these two endmembers, we expect a hysteretic behavior in the phase relationships between subglacial variables and Q. Evolution towards steady-state occurs with some time delay; if variations of the forcing term Q occur faster than this delay, the variations of R lag the variation :::::::: variations : of Q, resulting in a counter-clockwise hysteresis (Lagging class, Fig. 2).For such a transient evolution, R is smaller during the rising limb of Q than during the decline, emanating as :: its ::::::: decline, :::::::: resulting :: in : a counter-clockwise R − Q hysteresis (Lagging class, Fig. 2).At the same time, the larger R during the decline of Q requires a lower p to drive the flow, resulting in a clockwise hysteresis in the p − Q relation ::::::::: relationship : (Preceding class, Fig. 2).As stated above, we expect S to vary in a similar fashion as :::::::: similarly :: to p.The response of turbulent-water-flow-induced seismic power P to changes in Q is complex because it integrates the responses of both R and S, hence direct interpretation of the P − Q relations is difficult (Gimbert et al., 2016;Nanni et al., 2020).
Our interpretation scheme described here lets us expect two to three a ::::::: limited :::::: number :: of options for the classification of phase relations between each subglacial variable and Q. we observe that some events are classified outside the expected range (Figs. 5 and 7).The occurrence of such behavior may be attributed partly to artifacts introduced by the spectral filtering applied to the time series for the analysis.Although we manually checked the consistency between the unfiltered and filtered signals to remove the most apparent differences (see Section 3.5), some inconsistencies may still remain.Small shifts in timing of peaks may be amplified by normalizing the event time axis and hence lead to mis-classification of some events.In addition, the definition of the four classes is motivated by noticing that phase relations may be linearly positive or negative or exhibit some transitory stage (preceding or lagging).To account for uncertainties symptomatic for observations of natural systems, we allow some deviation from strictly linear behavior and accept RSS ≤2 still representing linear behavior.The choice of this threshold is motivated from visual impression of clustering of phase relations.

Subglacial drainage system evolution
The two observed melt seasons considerably differ in terms of duration : , :::::::: variability : and intensity (Fig. 3).Whereas in 2021, melting occurs over a relatively short period and yields low levels of water supply, in 2022, the melt season :::: 2022 : lasts longer and is characterized by higher temperatures and thus yields :::::: yielding ::: to higher water supply rates.This difference provides the opportunity to study the evolution of the subglacial drainage system in response to very different forcing.
The theoretical timescale of channel adjustment is usually longer (several days to weeks) than typical variations in Q (hours) (Röthlisberger, 1972).At short time scales, drainage pathways are then ::: thus : either overwhelmed when Q increases or partially filled when Q decreases : , : which results in a response similar to that of a rigid pipe (fixed cross-sectional area channel) rather than that of a steady-state channel (variable cross-section determined by the balance between melt opening and creep-closure to cope with runoff variations).We therefore expect a predominance of In-phase class for the p − Q and S − Q relationships over multi-day and diurnal time scales (Fig. 5a and 7a).The multi-day classifications of p − Q and S − Q relationships mainly support this view by displaying Lagging class and In-phase class behaviors (Fig. 5a), however; :::::::: however, on diurnal time scales (Fig. 7a), the picture is less clear .On these shorter time scales, we expect only minor variations of R, lagging those of Q (Lagging class).However, we observe mainly In-phase class behavior at both multi-day and diurnal time scales (Fig. 5a and 7a), suggesting that geometrical adjustment of the drainage system takes place already over short time scales; however this implies that the observed behaviors of p and S are caused by :::: likely :::: due :: to changes in hydraulic roughness since R already has adjusted ::::::::::::::: (Nanni et al., 2020).

Ambiguous interpretation from borehole and cryoseismic records
In the previous section, we interpreted the multi-variable record in terms of drainage system evolution in response to runoff (summarised :::::::::: summarized in Figure 9).We note that sometimes, interpretations derived from different records are ambiguous.
For instance, during the melt season 2021 , on a seasonal scale : , : the relationships between the cryoseismic record (P ) ::: with ::: Q, and derived variables (R and S) and :::: with Q, : yield a picture of a subglacial drainage system in equilibrium with Q.In contrast, the p − Q relationship based on the borehole record is symptomatic of a transient evolution where geometric adjustments lag variations in Q.Another example :: of ::: the ::::::::: ambiguity : is found in the analysis of diurnal variations in 2022 (Fig. 7b) where the cryoseismic records indicate a switch from an equilibrium to a transient evolution coinciding with a major increase in Q (Fig. 7d 6 ).The corresponding classification of the p − Q relation ::::::::: relationship : is less conclusive about a similar switch and exhibits variations over all classes with no clearly recognizable pattern.In this section, we discuss potential sources for these inconsistencies and how these may be resolved.

Till changes and glacier dynamics
In the Section 5.1 above, we have proposed an interpretation scheme based on the phase relationship between the force experienced by the ploughmeter, F , and the pore water pressure of the till :: in ::: the :: till ::::: layer, here taken as adequately represented by p.In this section, we explore subglacial processes that may explain the complex relationship observed between the subglacial hydrology (represented by the subglacial water pressure) and the mechanical properties of the till (represented by the force experienced by the ploughmeter) assuming a Coulomb-plastic rheology.We recall that for such a constitutive flow law for the till, a negative p − F relationship is expected (In-phase :::::::: Anti-phase : class).Over :: At : a seasonal scaleduring the melt seasons, the , : p−F relation ::::::::: relationship : displays a generally negative slope (Figs.4e and j and 8a).For a Coulomb-plastic material, an increase in pore water pressure results in a decrease in shear strength, which in turn would cause a decrease in F (Fig. 9).Furthermore, the observed anti-correlation between p and F is in good agreement 615 with the modeling results of Kavanaugh and Clarke (2006) for a Coulomb-plastic material, an interpretation that is in line with the findings of Fischer and Clarke (1994); Fischer et al. (1998Fischer et al. ( , 2001) ) at Trapridge glacier, Storglaciären and Unteraargletscher, respectively.However, during winter 2021/22, the p−F relationship exhibits a positive slope (Fig. 8a) which is unexpected for Coulomb-plastic rheology.Apparent-viscous behavior entails a velocity dependency of basal resistance, resulting in a positive p − F relationship.However, we do not observe glacier acceleration during the same period in winter 2021/22.Over shorter time scales, time series of p and F exhibit complex behavior: correlation (Fig. 8b), anti-correlation (Fig. 8c), and lagging after each configuration other occur (Fig. 8d).Applying our interpretation scheme suggests that during episodes similar to those displayed in Figure 8c, the inverse p − F correlation results from weakening of the sediment at times of high water pressure due to reduced effective pressure and vice versa, as expected for a near-Coulomb rheology (Fig. 9).However, a positive relationship between p and F as pictured in Figures 8b and d  The illustrated episodes apparently do not coincide with periods of high surface velocity.Similar p − F correlations have been observed previously (e.g., Murray and Porter, 2001;Rousselot and Fischer, 2007;Thomason and Iverson, 2008) but not extensively discussed.A range of mechanisms have been proposed to explain such behavior, such as :::: e.g., the sediments loaded towards their yield point (e.g., Murray and Porter, 2001), the state of the mechanical coupling between the ice and the till and its influence on pore-pressure variations (Iverson et al., 1995;Fischer and Clarke, 1997;Boulton et al., 2001;Mair et al., 2003;Iverson, 2010), the varying mobilisation :::::::::: mobilization of the till at depth (e.g., Iverson et al., 1998;Tulaczyk, 1999;Tulaczyk et al., 2001;Truffer et al., 2000;Truffer, 2004).However, a direct explanation on how these mechanisms would explain the correlation between F and p is not straightforward.We further point out that the attitude :::::: vertical ::::::: position of the ploughmeter relative to the till may have changed, for instance ::: e.g.: through changes in tilt or vertical position :::::::::: ploughmeter ::: tilt, but these effects cannot be disentangled from till behavior without further accompanying measurements.Such measurements will be subject for future ploughmeter deployments.
The relationship between the force experienced by the ploughmeter and the water pressure reveals complex till rheology ::::::: behavior.
As expected, the till behaves mainly ::::: mostly : as a Coulomb-plastic materialbut episodically, the p − F relation is indicative of deviating behavior.Such behavior may be caused by different mechanisms, e.g.till loading towards its yield strength, or variations in the mobilization of the till at depth, but we cannot exclude possible effects of changes in instrument-till coupling that may cause similar behavior.In future, additional measurements of instrument attitude : .:: In ::: the ::::: future, :::::::::: monitoring ::::::::: instrument :::::: vertical ::::::: position could help disentangling instrument behavior from till behavior and assessments of changes in till properties using seismic noise interferometry (Zhan, 2019) over a large area could complement the local ploughmeter record.

Figure 1 .
Figure 1.Study site and field methods.(a) Location of Kongsvegen ::::: glacier in Svalbard.The green star indicates the instrument site where data were collected and the red circles indicate the position of the GNSS KNG6 and KNG7 (Credits: NPI/Copernicus Sentinel data).(b) Annual surface velocity near the equilibrium line of Kongsvegen glacier from 2005 to 2022, with an acceleration around 2014 witnessing that this glacier is closer to a surge event(personal communication from J. Kohler).(c) Main borehole with the smaller secondary borehole where the return pump is installed.(d) Drilling installation.(e) Sediment sample recovered with a sediment sampling tool at the bottom of the borehole.

:
::::::: subglacial : hydrology on hard-bed glaciers, and by Javed et al. (2021) to study storm-induced hydrological conditions variations.The period of records is subdivided ; at a multi-day time scales into twelve events (melt season 2021, see Appendix D, Tab.D1) and eight events (melt season 2022, see Appendix D, Tab.D2); and at a diurnal time scale into 96 events (melt season 2021, see Appendix D, Tab.D3) and 85 events (melt season 2022, see Appendix D, Tab.D4).

Figure 2 .
Figure 2. Phase relationship classification for events.Below each class, the plots in the first row correspond to a representative event for this class with runoff (Qnorm) plotted in blue and one subglacial variable (Xnorm, with X being F , P , p, R or S) plotted in pink against time.The magnitude of the variables is normalised :::::::: normalized between 0 and 1 and the time is re-sampled into 50 time steps.The plots in the second row show the shape of the relationship between the two variables after classification.The solid color points refer to the mean behavior in this class, all individual events from the filtered time series are shown in shaded colors.The black line is the linear regression fitted to the scatter plot.Preceding class and Lagging class correspond to clockwise or anti-clockwise hysteresis (or time-lag) between the runoff, Q, and the observed variable, while In-phase class and Anti-phase class correspond to linear relationships.The color scale indicates chronology.
and b) control :: the : timing and volume of Q resulting from meltwater production or rainfall (Figure3c and d).We note that the dataset covers two very different melt seasons.While the 2021 melt season is short (67 days from July 1 , 2021 to September 6 , 2021), marked by low temperature oscillating around 0 o : • C and continuous low runoff (lower than 20 m 3 s −1 ), the 2022 melt season is long (at least 83 days because we do not capture the end of this melt season, from May 25 , 2022 to August 16 , 2022) marked by high temperatures (up to 7 o C) and ::: , blue line): (i) the seasonal time scale (>20 days) is marked by Q generally being limited to the melt season; (ii) the multi-day superimposed time scale (four to eight days), typically reflects weather variability (warm-spells, e.g., Fig. 3c 2 , or rainfall, e.g, Fig. 3c 4 );

Figure 3 .
Figure 3.Time series of physical quantities measured during the melt seasons 2021 (a, c, e, g) and 2022 (b, d, f, h).: (a-b) Temperature (black line), snow fall :: rate : (grey ::: gray : bars) and rainfall ::: rate (light blue) from CARRA/AROME-Artic (Schmidt et al., 2023).The three variables are extracted for the grid point closest to the borehole location.(c-d) Modelled :::::: Modeled : runoff (blue) and measured glacier surface velocity (red).Circled numbers refer to episodes described in the main text.(e-f) seismic power recorded at the surface of the glacier in the 3-10 Hz frequency band (yellow).(g-h) Borehole water pressure (green) and force acting on the ploughmeter (dark red).Blue shaded areas represent the melt seasons.Grey shaded areas represent periods of missing data.The complete uninterrupted record spanning from spring 2021 to the end of summer 2022 is presented in Appendix A, Fig. A1.

Figure 4 .
Figure 4. Relationships between two variables at the seasonal scale for the melt seasons 2021 and 2022.Color scales are scale ::::: scaled to the number of days in each melt seasons.Note that the variables R and S have been derived only from July 19 to August 31, 2021 and from May 25 to August 1, 2022 explaining that the color scale is not entirely represented (outside of these periods, runoff is too low to derive R and S, see Section 3.4.1.P , R and S are expressed in terms of relative changes to a reference stage, in our case on June 14, 2021, when Q ref = 0.2m 3 s −1 .(a) and (f) Relationships between scaled runoff (Q/Q ref ) and scaled turbulent-water-flow-induced seismic power (P/P ref ).The x-axis is in logarithmic scale.The superimposed lines show the relations derived by Gimbert et al. (2016) for a constant hydraulic gradient (pink lines, P ∝ Q 5/4 ) and for a constant hydraulic radius (purple curve, P ∝ Q 14/3 ).(b) and (g) Relationship between scaled runoff (Q/Q ref ) and scaled hydraulic radius (R/R ref ).Both x and y-axes are in logarithmic scale.Superimposed lines show the relations of steady-state preferential drainage axis evolution (Nanni et al. (2020), R ∝ Q 9/22 ).(c) and (h) Relationship between scaled runoff (Q/Q ref ) and scaled hydraulic gradient (S/S ref ).Both x and y-axes are in logarithmic scale.Superimposed lines show the relations of Nanni et al. (2020) for a preferential drainage axis at steady-state (black lines; S ∝ Q −2/11 ) and for a preferential drainage axis evolving as a fixed cross sectional area channel referred to as rigid pipe (red line; S ∝ Q 2 ).For the panels a to c and f to h, we interpret our observations as aligning with one of the scenarios detailed inGimbert et al. (2016);Nanni et al. (2020), where the slope of the hysteresis curve is parallel to the theoretical scaling.(d) and (i) Relationship between normalised ::::::::normalized water pressure and normalised ::::::::: normalized runoff.(e) and (j) Relation between normalised :::::::: normalized force and normalised :::::::: normalized : water pressure.Arrows indicate the direction of time and

Figure 5 .
Figure 5. Phase relationships between the subglacial variables (S, R, p and F ) and runoff (Q) at a multi-day time scale.:::: Panel : (a) shows the classification for the melt season 2021, and :::: panel : (b) for the melt season 2022.Grey fields refer to periods when data is missing and the vertical grey :::: gray lines delineate the events.Preceding class and Lagging class correspond to clockwise or anti-clockwise hysteresis between the runoff and the observed variable while classes In-phase class and Anti-phase class correspond to linear relationships.In addition, the time series of velocity (grey ::: gray line) and runoff (blue line) are super-imposed on each panel.Circled numbers refers to episodes described in Section 4.1.

Figure 6 .
Figure 6.Relationship between the subglacial variables (P/P ref , R/R ref , S/S ref ) and runoff (Q/Q ref ) during the two melt seasons at a multi-day time scale.The color scale indicates the timing during both melt seasons and is scaled according to the length of each season.(a)and (d) Relationship between scaled runoff (Q/Q ref ) and scaled turbulent-water-flow-induced seismic power (P/P ref ).The x-axis is in logarithmic scale.The superimposed lines show the relations derived by Gimbert et al. (2016) for a constant hydraulic gradient (pink lines, P ∝ Q 5/4 ) and for a constant hydraulic radius (purple curve, P ∝ Q 14/3 ).(b) and (e) Relationship between scaled runoff (Q/Q ref ) and scaled hydraulic radius (R/R ref ).Both, x and y-axis are in logarithmic scale.Superimposed lines show the relations for a steady-state channel evolution (Nanni et al. (2020) R ∝ Q 9/22 ).(c) and (f) Relationship between scaled runoff (Q/Q ref ) and scaled hydraulic gradient (S/S ref ).x and y axes are in logarithmic scale.Superimposed lines show the relations of Nanni et al. (2020) for a channel evolution (black lines; S ∝ Q −2/11) and for a channel evolving as a rigid-pipe of static cross-section (red line; S ∝ Q 2 ).

Figure 7 .
Figure 7. Phase relationships between the subglacial variables (S, R, p and F ) and runoff (Q) at a diurnal time scale.(a) Classes from the phase relationship classification per event for the melt season 2021 and (b) for the melt season 2022.Grey fields refer to periods when data is missing and the vertical grey :::gray : line delineate the events.In addition, the time series of velocity (grey ::: gray) and runoff (blue) are super-imposed on each panel.Circled numbers refer to episodes described in Section 4.1.
For p − Q and S − Q, we expect behaviors according to Preceding class, Inphase class or Anti-phase class; we expect R − Q to display either Lagging class or In-phase class behavior; F − p is expected to fall either in In-phase class or Anti-phase class, direct F −Q relations are not easily comprehended ::::::::::interpretable.In practice,

Figure 8 .
Figure 8.Comparison between the variations of water pressure p and ploughmeter force F (a) at the seasonal, and (b) to (d) multi-day time scales.(a) Relationship between p and F at the seasonal time scale.F and p are normalised :::::::: normalized : (min-max normalisation :::::::::: normalization) to be comparable.Blue-yellow and yellow-purple color scales indicate time during melt seasons and winter, respectively.(b) Evolutions of F (red ) and p (blue) for an event indicative of apparent viscous behavior (assuming that p is positively related to basal motion).Similar behaviour :::::: behavior has been observed also during other periods (e.g., from July 13, 2021 to July 22, 2021, and August 8, 2021 to August 17, 2021).The time of the event is normalised :::::::: normalized : over 50 time steps.(c) Evolutions of F (red) and p (blue) for an event indicative of Coulomb-plastic behavior.Similar behaviour ::::::: behavior has been observed also during other periods (e.g., from July 22, 2021 to July 31, 2021, from July 7, 2021 to August 8, 2021, and from July 11, 2022 to July 23, 2022).The time of the event is normalised :::::::: normalized : over 50 time steps.(d) Evolutions of F (red) and p (blue) that remain unclear as the interpretation scheme does not provide a clear indication of till rheology.Similar behaviour ::::::: behavior has been observed also during other periods (e.g., from September 15, 2021 to September 27, 2021, and from May 28, 2022 to June 6, 2022).The time of the event is normalised :::::::: normalized over 50 time steps.Simultaneous multi-day variations of F and p can be assessed only for five and two events during the melt seasons 2021 and 2022, respectively.All panels show normalized variations of F and p.

Figure 9 .
Figure 9. Sketch of the adjustment of hydro-mechanical conditions below Kongsvegen glacier to variations in runoff over the period from June 2021 to August 2022.(a) Hydraulic quantities, i.e. water pressure (p), hydraulic gradient (S), and hydraulic radius (R), used to characterize the evolution of the subglacial drainage system during the short and low intensity melt season of 2021, and the long and high intensity melt season of 2022.Our findings indicate that during the 2021 season, the subglacial drainage system adapted to runoff changes in steady-state, leading to an increase in its capacity over time.However, during the 2022 season, we observed a transient evolution of the drainage system in response to the continued and high-intensity input of runoff.As a result, the drainage capacity of the main drainage system was exceeded, causing water to leak into poorly connected areas of the bed increasing the water pressure, thereby triggering speed-up events.(b)The mechanical quantity, i.e., force (F ), was used to examine the rheological behavior of the till.The till rheology behaved mainly as a Coulomb-plastic material (anti-correlation between p and F ), but episodically showed deviating behavior (correlation between p and F ), the underlying mechanisms for which remain unclear.

Figure B1 .Figure C1 .
Figure B1.Pre-processing workflow applied to the time series.The original time-series (see Fig. 3 below) have been filtered at three timescales.The multi-day and diurnal filtered data have been inspected against the unfiltered data to remove spurious artefacts that can be created by the filtering technique (see also Appendix G, G1).We then segmented the recorded data into multiple events and normalised :::::::: normalized the magnitude and duration of each.

Table D3 .
Description of the 96 diurnal time scale events during the melt season 2021