Liquid water content (wetness) within glacier ice is known to strongly
control ice viscosity and ice deformation processes. Little is known about
wetness of ice on the outer flanks of the Greenland Ice Sheet, where a
temperate layer of basal ice exists. This study integrates borehole and radar
surveys collected in June 2012 to provide direct estimates of englacial ice
wetness in the ablation zone of western Greenland. We estimate
electromagnetic propagation velocity of the ice body by inverting reflection
travel times from radar data. Our inversion is constrained by ice thickness
measured in boreholes and by positioning of a temperate–cold ice boundary
identified in boreholes. Electromagnetic propagation velocities are
consistent with a depth-averaged wetness of
As ice flows outward from the centre of the Greenland Ice Sheet (GrIS), heat is added at the base of the ice column. This heat is due to geothermal heat flux from the bed, strain heating in ice, and basal friction in places where sliding occurs. Several ice sheet flow models depict that in western Greenland enough heat is eventually added to develop a fully temperate layer of basal ice (e.g. Brinkerhoff et al., 2011; Lüthi et al., 2015; Meierbachtol et al., 2015); however substantial modelling uncertainty exists regarding the spatial extent and vertical dimensions of the warm basal layer. Limited borehole temperature observations have confirmed a temperate basal layer in western Greenland that is tens of metres to well over 100 m thick (Lüthi et al., 2002; Ryser et al., 2014; Harrington et al., 2015). This layer potentially plays a key role in deformational motion of the ice sheet.
Measurement of the GrIS's surface motion has become relatively commonplace, and basal sliding speed can be partitioned from surface velocity as the residual after modelled deformational velocity has been removed. An accurate representation of ice viscosity is a fundamental ingredient for reliable numerical simulations of deformational velocity. The viscosity of ice at the melting point is highly dependent on the liquid water fraction (wetness) of the ice (Duval, 1977). Incorporation of wetness properties into numerical models can therefore result in substantial modifications to simulation output (e.g. Greve, 1997; Hubbard et al., 2003; Aschwanden et al., 2012). Unfortunately, due to a lack of observational evidence for constraining the water content of the ice, poorly constrained modelling decisions must be made regarding the water content and therefore viscosity of the GrIS temperate basal layer.
Direct measurement of in situ ice wetness is not straightforward, as field samples would somehow need to be collected and then measured in an unaltered condition. Several studies (conducted outside of Greenland) have therefore utilized ground-penetrating radar's (GPR) strongly sensitive propagation velocity to volumetric water content to make non-invasive estimates of englacial water content (e.g. Macheret et al., 1993; Bradford and Harper, 2005; Murray et al., 2007; Bradford et al., 2009). A drawback of radar-based studies is that the water in grain-scale and macro-scale inclusions cannot be distinguished or partitioned since the propagation speed of the radar is dependent on the bulk properties of the ice–water mixture. In addition, measuring radar propagation velocity in a thick ice sheet setting such as Greenland requires a cumbersome data collection scheme, with large and variable antenna separations that are not logistically attainable from airborne platforms at present.
The development of a temperate basal layer of ice along the outer flanks of the GrIS is predicted by models and confirmed by observation. Here we provide a key observation of the volumetric liquid water content of the temperate basal layer, an important constituent of the layer's rheological properties. We integrate multiple datasets, including (1) direct measurement of ice thickness and ice temperature from instrumented boreholes extending to the bed of the ice sheet, (2) common-offset GPR transects acquired with three different frequencies, and (3) a common-source-point multi-offset GPR survey (equivalent geometry to a single shot gather in seismic data). Our purpose is to quantify the liquid water content of a basal temperate layer spanning a reach between boreholes by employing a geophysical inversion of the GPR data with constraints from borehole data.
The study was conducted in western Greenland,
The three boreholes drilled at S3 had an average depth of 461 m with a
standard deviation of 4 m, and the four boreholes drilled at S4 had an
average depth of 698 m with a standard deviation of 8 m (Table S1,
Supplement). The GPR transect between borehole sites has less than 30 m of
surface elevation difference but more than 200 m of bed elevation change as
it extends from a relative high ridge to the centre of a bed trough (Fig. 2).
The radar transects start at S3 and run in a nearly straight line to within
120 m of S4, where we encountered a large, deeply incised stream which we
could not cross (Fig. 1b). Temperature data were recorded with a string of
temperature-sensing semiconductor chips spaced at 20 m intervals from the
ice surface. Data were retrieved from the chips via laptop computer 3 months
after the temperature strings were placed in the boreholes, allowing time for
the chips to equilibrate to the ice temperature. Thus, measured temperatures
are representative of the time of retrieval. Temperature profiles from both
borehole sites indicate that the ice near the surface is about
Common-offset radar profiles collected with 10 MHz
Acquisition parameters for GPR surveys collected for this study.
We collected three common-offset GPR profiles and
a common-source-point multi-offset GPR survey between borehole sites S3 and
S4. Data were collected using a custom GPR system deployed on the ice
surface. The transmitter consisted of a Kentech pulser which sends a
Bradford et al. (2013) point out that the polarity mode of the GPR survey can have large effects on the propagation velocity of the EM wave in wet, fractured ice. By comparing the nearest offset common-source trace (TM mode) to the coincident 2.5 MHz common-offset trace (TE mode), we find no significant discrepancy in the travel time to the bed or to the internal reflection at 3584 ns; from this we conclude that fracture alignment is not greatly influencing our measurements.
Present at the surface during data collection were ridges up to
Common-offset data were acquired by manually stepping both antennae forward while maintaining a constant spacing between the transmitting and receiving antennas (antenna offset). The antennas were held stationary for the duration of acquisition for each trace, which included stacking 128 traces at each location. Although this resulted in a time-consuming survey, we successfully avoided spatial aliasing while allowing for enough stacking to achieve a signal-to-noise ratio high enough to allow interpretation of the data. For the common-source-point multi-offset GPR survey, the transmitting antenna was left stationary near S3 for the duration of the acquisition as the receiving antenna was manually stepped toward S4. As the receiving antenna was stepped away from the transmitting antenna, the recorded signal strength diminished as a function of the spherical spreading and signal attenuation. Thus, the threshold level for triggering was manually reduced with greater offset. The amplitude of each trace was also normalized to the airwave during processing of the common-source-point profile to account for system variability that accompanied the reduction of the triggering threshold.
The common-source-point multi-offset survey that we use in this study is
preferable to common-midpoint (CMP) surveys for regions where reflecting
surfaces, including internal layering and the bed, are not planar surfaces.
This is because CMP surveys assume that the point of reflection for each
offset is invariant; thus residual move-out correction must be employed in
regions where the reflecting surfaces are not parallel with the survey
surface. This, in turn, requires a priori knowledge of the magnitude of the
dip angle for all reflecting surfaces. However, the survey setup and
inversion used in this study do not require residual move-out correction or a
priori knowledge of the magnitude of the dip angle since the dip of
reflecting surfaces is solved for in the inversion. Further, as described in
Brown et al. (2012), the inversion used in this analysis is not subject to
normal move-out (NMO) assumptions such as small offset-to-depth ratios and
small velocity gradients over reflection boundaries; velocity/depth models
derived from CMPs are most commonly determined through semblance analysis and
the Dix inversion (Dix, 1955) of solving for layer velocities, which
Average electromagnetic (EM) propagation velocity of the glacial ice was
measured using two separate methods.
A direct comparison between the two-way travel time of the GPR bed
reflection and the measured depths of the boreholes. We calculate the average
EM propagation velocity at each borehole location with a simple two-way
travel time vs. depth relationship: Here, A ray-based travel time inversion (Zelt and Smith, 1992) of the
common-source-point multi-offset data is constrained by the direct move-out of
the surface wave and borehole temperature and depth measurements. This
inversion employs a forward-ray-tracing model to determine the travel time of a
reflected wave from the transmitter to the receiver based on an input
velocity/depth model; in each iteration of the inversion, the velocity/depth
model is adjusted using a dampened least-squares method. We solved the
ray-based travel time inversion with a two-layer model, which allows us to
constrain vertical variations in the GPR propagation velocity structure of
the ice column. This inversion technique employs a model space that mimics
the ice thickness at our field site, which has a nearly flat surface on the
scale of the 2.5 MHz GPR and a bed dip angle that exceeds 14
The ray-based travel time inversion requires an initial 2-D velocity model, which we constrained with the apparent bed geometry derived from our common-offset radar profiles, the measured borehole depths, and the boundary between the upper cold ice layer and the lower temperate ice layer which was measured with the borehole-derived vertical temperature profiles at S3. The input velocity model geometry is based on unmigrated common-offset GPR data since migration of the data does not affect the geometry of the profiles in the region where bed reflections are modelled (see Supplement). We used the interfacial surface wave velocity measured with the common-source-point multi-offset survey to further constrain our travel time inversion.
The initial velocity model consists of two layers with homogenous velocity distribution. We use the deepest continuous layer observed in the common-offset GPR data to extend the cold–temperate boundary toward S4 in our initial velocity model. Using this layer as an initial model boundary is arbitrary to an extent; however, we chose this layer as our model boundary since this layer is coincident with the temperate–cold ice boundary observed in the borehole temperature profile at S3 when the depth is calculated using the measured surface wave velocity. This does not indicate that the reflection is due to a boundary between cold and temperate ice or that the boundary between cold and temperate ice is coincident across the profile. Thus, the depth of the modelled cold–temperate layer boundary is allowed to vary in our inversion in places where direct measurements of temperature do not exist. We employ the travel time inversion by solving for the depth of the upper layer while holding the velocity constant before solving for the bulk velocity of the lower layer and the depth to the bed. Our travel time inversion solution is further constrained by the average EM propagation velocity of the ice column as measured at the boreholes and the measured thickness of the glacier at the two borehole sites at the ends of the transect.
Ice wetness value results calculated at S3 and S4 using the methods described in the text.
Electromagnetic wave propagation velocity through wet ice is dependent on
many physical properties of the medium, including the size, shape, and
orientation of the water bodies within the ice as well as impurity
concentration of both ice and water; unfilled porosity (air bubbles trapped
within ice); frequency range of the EM signal; and the polarity mode of the
survey. There are several mixing models that approximate the relationship
between EM propagation velocity, including the Looyenga (1965) mixing model
and the Complex Refractive Index Model (CRIM) (Wharton et al., 1980). Both of
these mixing models have been used to approximate the wetness of glacial ice
in previous studies with reasonable results (e.g. Bradford and Harper, 2005;
Murray et al., 2007). Herein we estimate wetness calculated from the two-phase
form of both the CRIM equation and the Looyenga (1965) equation.
To apply these equations, we assume that (1) randomly aligned cold glacial
ice has an EM phase velocity of 1.685
The two-phase CRIM equation for water inclusions in ice is
For wet ice, the Looyenga (1965) equation takes the form
We report the wetness values derived from both equations in Table 2, but we restrict our discussion to the results from the two-phase CRIM equation since it yields more conservative values for liquid water content.
The bed reflection is imaged in common-offset profiles at all three
frequencies (Fig. 2); it is most apparent in the 2.5 MHz data and most
precise in the 10 MHz data. For this reason, we use the 10 MHz data to
determine the TWT of the bed reflection. These data show that the TWT to the
bed reflection increases from S3 to S4 by 2.75
Fence plots
All of the common-offset GPR profiles also imaged internal layering
throughout the ice body, although the signal-to-noise ratio of the deeper
layers diminished at higher frequencies. It is apparent in the 10 MHz
profile that the internal reflection horizons within the upper 30 % of
the ice all approximately double in depth from S3 to S4. The internal
reflectors in the lower 70 % of the ice, including the lowest continuous
reflection, increase in depth by
In all three common-offset profiles, various unidentified sources of noise and occasional errors in timing due to difficulties in triggering off of the airwave created both coherent and non-coherent noise in the data. The most apparent noise recorded in our surveys were coherent “ghost” signals observed in the 5 and 2.5 MHz data (Fig. 2b and c). The source of this coherent noise is unknown, as it is not explainable by off-nadir englacial reflections, surface expressions of cracks, or surface streams or pools of water, nor is it seen in all of the radar profiles. Noise due to triggering errors is most prominent in the 5 MHz data (Fig. 2b). These noise features in the data can be ignored as they do not interfere with the interpretation of the data.
Borehole depth measurements show that the ice thickness increases from
461
We can further constrain this estimate by assuming that the liquid water in
the ice is not uniformly distributed across the ice thickness. The surface
arrival slope of the common-source-point multi-offset profile shows that the
EM velocity in the near surface (within the upper tens of metres) is
1.69
The result of the travel time inversion reveals a bulk EM propagation velocity
of 1.48
The ray-based travel time inversion is only valid over the region where rays are present; thus much of the transect has no constraint on the depth of the temperate layer or the ice wetness. However, since the borehole temperature measurements reveal that the temperate layer is the same thickness at both S3 and S4, we infer that the temperate layer thickness is fairly uniform across the profile.
The temperate basal layer present along the outer flanks of the GrIS arises from geothermal heating and flow mechanisms acting on cold ice moving outward from centre of the ice sheet. These warming processes differ from other temperate glacier settings where ice is warmed to the melting point during ice diagenesis related to surface melt and infiltration. This begs the question of how the water content of the warm basal layer in Greenland differs from other measurements of temperate ice. Various non-radar-based methods for estimating ice water content have suggested liquid water content of temperate glaciers ranging from 0.0 to 3.0 % (e.g. Raymond and Harrison, 1975; Vallon et al., 1976) . Studies employing GPR propagation velocity for wetness measurement have reported liquid water content values ranging from 0.0 to 7.6 % (e.g. Macheret et al., 1993; Moore et al., 1999; Murray et al., 2000; Gusmeroli et al., 2012). Although values of up to 9.1 % have been reported (Macheret and Glazovsky, 2000), most measurements indicate wetness of less than 4 %. Our results of 2.9–4.6 % for the mean wetness across the 130–150 m thick basal warm layer are thus slightly high end but not out of range compared to other estimates for temperate ice.
Our results are higher than the estimate by Lüthi et al. (2002) of 2 % water content at the cold ice–temperate layer interface at a site in the Jakobshavn region of Greenland. The latter was based on an observationally constrained model of refreezing at the layer boundary, whereas ours are averaged over the full thickness. Whether the higher water content we observe in the temperate layer represents grain-scale water or a mix of grain-scale and macro-scale bodies is not known. Harrington et al. (2015) documented vertical growth of the temperate layer along a flow line transect. They argued that the only mechanism for expanding the temperate layer vertically was through basal crevassing. If this is indeed the case, an important fraction of our measured water content is likely located in macro-scale basal crevasses. Our radar has not provided obvious imaging of any such crevasses, but our methods were not targeted to their detection.
The water content we observe in Greenland's temperate basal layer is substantially higher than the 1 % typically employed as a maximum cutoff in ice sheet models (e.g. Greve, 1997; Aschwanden et al., 2012). A drainage function is applied at this threshold to represent drainage of water in excess of 1 % through crevasses, cracks, and grain boundaries (Greve, 1997). This conceptualization, however, is limited to the grain-scale water content and has no accommodation of water storage in drainage features, whereas our results represent liquid water potentially existing at all scales.
While the cold layer may not have grain-scale water, our common-offset imaging of englacial hyperbolas implies macro-scale water bodies are present in this layer. Point reflectors in similar data have been interpreted either as near-surface crevasses (presumably the same as water-filled voids) or surface crevasses that are off-axis from the radar profile (Catania et al., 2008). The hyperbolic diffractions in our common-offset data are unlikely to result from a distant near-surface source, since the theoretical and measured radiation pattern of a dipole antenna (Arcone, 1995) greatly limits this possibility: the relative signal strength of off-nadir, near-surface reflections would be weak compared to reflections generated at nadir, and we do not observe that. Rather, the diffractions observed in our profiles are strong, indicating that they likely arise from near-nadir discontinuities. Similar hyperbolic returns in the cold ice layer of polythermal glaciers have been observed prior to any seasonal melt and have been interpreted as metre-scale water bodies persisting through the winter (e.g. Pälli et al., 2002). Therefore, our working hypothesis is that the cold layer contains sparse large water inclusions up to several hundred metres below the surface, perhaps generated in a crevassed area about 3 km up-flow from the site. Further, since our estimates of liquid water content are derived under the assumption of negligible water content in the upper layer, our wetness values for the temperate layer would be slightly high if the englacial bodies that produce the point reflections seen in the common-offset radar data contained non-negligible volumes of liquid water.
Warm ice near the bed requires a lower activation energy than cold ice to initiate creep of the polycrystalline structure. Furthermore, laboratory measurements reveal that the strain rate of ice triples as the grain-scale wetness increases from relatively dry conditions of 0.01 % to the modestly wet value of 0.8 % (Duval, 1977). That all of the water we observe is in macro-scale features and none exists at the grain scale is unlikely since water is known to accumulate at grain boundaries in temperate ice (e.g. Shreve et al., 1970; Nye and Frank, 1973). It follows that the temperate layer should contain sufficient grain-scale liquid water to permit enhanced strain rates. Further, the impact of water located in macro-scale features such as basal crevasses on ice rheology has not been quantified but is also likely to soften the ice.
With a soft basal layer, partitioning of surface velocity into sliding and deformation components would attribute enhanced deformation in the temperate layer to basal sliding processes, unless the enhanced creep is explicitly accounted for. Borehole observations have attributed 44–73 % of winter motion to basal sliding (Lüthi et al., 2002; Ryser et al., 2014); however, tilt sensors do not freeze in place within the temperate layer to yield reliable readings, thus making the distinction between motion due to high straining of the temperate layer and motion due to sliding processes ambiguous.
A final implication of our results relates to Greenland's ice thickness and
volume. Airborne radar has been deployed for decades to image the GrIS's
internal layers and bedrock topography, and these data have been used to
generate high-resolution digital elevation models of the ice sheet bed (e.g.
Bamber et al., 2013). Depth conversion of the airborne radar data typically
employs Eq. (1) with assumptions about the radar velocity, namely that the
velocity is constant and the conversion from TWT to depth assumes a bulk
permittivity of 3.15. Our direct comparisons of TWT to borehole depths
demonstrate the radar propagation speed in this region of the GrIS is
influenced by liquid water in the basal temperate layer of ice. Neglecting
the temperate layer and solving Eq. (1) using just the propagation speed of
cold ice could overestimate ice thickness by 20 m at S3 and 15 m at S4.
This would be equivalent to a 4.3 and 2.1 % overestimate of ice thickness at
S3 and S4, respectively. In our study area we find that potential error due
to applying Eq. (1) with a fixed cold-ice velocity would scale inversely with
thickness of the ice since the basal temperate layer has constant thickness.
However, in practice we found the opposite occurred – that the ice thickness
was underestimated in the interpretation of the airborne radar data. For
example, near S3 the IceBridge data show a TWT of 4.4545
Our integration of ground-based radar data with information collected in
boreholes reveals a two-layer thermo-hydrologic structure of varying
thicknesses in the ablation zone of western Greenland. Our results are based
on study of a
The ice mass is best described as a two-layer stratified system, with a cold upper layer overlying a warm temperate layer above the bed. The boundary between the two layers corresponds to a thermal transition from cold ice to temperate ice having liquid water. The temperate layer maintains nearly constant thickness of about 130–150 m as the total ice thickness increases by 50 % over a bedrock trough. The cold layer contains rare point reflectors hundreds of metres below the surface, which are likely water filled and perhaps generated in an icefall above the study reach. If we further assume that the upper cold ice layer has negligible wetness, the temperate basal layer has a water content of 2.9–4.6 %. This range is substantially higher than the cutoff value typically used in ice sheet models, although the fraction of our measured range located in macro-scale features such as basal crevasses is unknown.
The borehole temperature data and their availability are
described in Harrington et al. (2015). Ground-based radar data and processing
files are included in the Supplement. The ray-based inversion code (rayinvr)
is available at:
The authors declare that they have no conflict of interest.
This work was funded by SKB-Posiva-NWMO through the Greenland Analogue Project and NSF (Office of Polar Programs–Arctic Natural Sciences grant no. 0909495). We thank Joseph MacGregor, Achim Heilig, and two anonymous reviewers for their comments, which greatly improved the manuscript. Edited by: M. Tedesco Reviewed by: A. Heilig, J. MacGregor, and two anonymous referees