Introduction
Basal water beneath the Greenland Ice Sheet (GrIS) influences and is
influenced by, the dynamics and thermodynamics of the overlying ice. A
lubricated bed is a necessary condition for basal sliding, which can be
responsible for up to about 90 % of the ice surface velocity
. Constraining the spatial distribution of basal water
is important, therefore, for understanding the dynamic state of the overlying
ice and its sensitivity to external forcing. A reliable estimate of the
presence of basal water can also be used as a boundary condition or as a
constraint in numerical modelling and to evaluate model performance and is,
as a consequence, an attractive objective.
The spatial distribution of basal water beneath the GrIS is known to arise
from an interplay of different physical processes including surface melt
(e.g. ), basal melting due to geothermal heat (e.g.
), frictional and shear heating (e.g.
), and transport processes (surface, englacial and
subglacial), which redistribute water (e.g. ).
There are, however, limited observational constraints on the ice-sheet-scale
distribution of basal water, and the relationship with other glacial and
subglacial properties is therefore largely unexplored and speculative. The
lack of unambiguous information about basal water arises primarily because
there are only a few existing observations of subglacial lakes
. By contrast, the
Antarctic Ice Sheet currently has over 400 identified subglacial lakes
, some of which have been found to be actively draining
and recharging. Instead, there is evidence that basal water beneath the GrIS
exists in smaller pools as wet sediment
and as part of channelised networks
.
The basal temperature distribution of the GrIS determines where basal water
can exist and requires basal temperatures at or above the pressure melting
point (PMP) for ice (herein “thawed”). Direct basal temperature
measurements are, however, sparse. At the majority of the interior boreholes
– Camp Century, Dye 3, GRIP, GISP2 and NEEM – basal temperatures indicate
frozen beds
,
with the thawed bed at NorthGRIP being an exception . Toward
the ice-sheet margins boreholes generally indicate thawed beds
. Indirect methodologies for discriminating frozen and
thawed beds (ice-sheet model predictions, radiostratigraphy and surface
properties) were recently combined by to produce a
frozen-thawed likelihood map for beds beneath the GrIS. Key predictions were
that the central ice divides and west-facing slopes generally have frozen
beds, the southern and western outlet glaciers have a thawed bed, and
basal thaw extends east from NorthGRIP over a large fraction of the
north-eastern ice sheet.
Spatially variable geothermal heat flux (GHF) influences the basal
temperature distribution ,
hydrology and flow features in
the interior of the GrIS. Notably, the onset of the Northeast Greenland Ice
Stream (NEGIS) is predicted to arise from basal melting that is attributed to
locally elevated GHF , which, in turn, has recently
been attributed to the path of the Iceland hotspot track
. As with basal temperature, the sparsity of
borehole measurements limits direct inference of GHF (which is related to the
vertical gradient of basal temperature). Instead, a range of geophysical
techniques including tectonic , seismic
and magnetic models have
been used to map GHF beneath the ice sheet. These models, however, differ
greatly in the predicted spatial distribution for GHF and also in the
absolute values . Due to the relationship between basal
melt and GHF, basal water observations can be used to further refine and
cross-validate GHF models .
In principle, airborne radio-echo sounding (RES) surveys provide the
information and spatial coverage to infer the presence of basal water at
the ice-sheet scale. Bed-echo reflectivity is the most commonly used
diagnostic for this purpose (e.g. )
and is based on the prediction that, across a range of subglacial
materials, wet glacier beds have a higher reflectivity than dry or frozen
beds . However, due to
uncertainty and spatial variation in radar attenuation (an exponential
function of temperature ) bed-echo reflectivity is
subject to spatial bias and can be ambiguous when mapped over larger
regions . In order to mitigate
spatial bias from radar attenuation, bed-echo scattering properties – including
the specularity (a measure of the angular distribution of energy and,
consequently, the smoothness of the bed at a radar-scale wavelength)
and the bed-echo abruptness (a
waveform parameter) – have also been
employed in basal water detection. Although attenuation independent, use
of some bed-echo scattering properties to discriminate basal water can be
prone to ambiguity and can potentially lead to false-positive detection of
smoother bedrock as water .
In this study we introduce a RES diagnostic for basal water that is
specifically tuned to be suitable for an ice-sheet-scale assessment of basal
thaw. The RES diagnostic, which we term “bed-echo reflectivity variability”,
detects wet–dry transitions in bed material and acts as a form of edge
detector. The technique is demonstrated to be insensitive to radar
attenuation, thus reducing the likelihood of false-positive identification of
basal water at the ice-sheet scale. Moreover, it also only requires local
radiometric power calibration and thus enables different Operation IceBridge
RES campaigns, using different radar system settings (e.g. peak transmit
power, antenna gain), to be combined and mapped. However, a limitation of the
technique is that it provides sufficient (not necessary) conditions for
basal water, and the detected subset of basal water corresponds to sharp
horizontal gradients in the bed dielectric.
The primary geographical focus of the study is to compare the spatial
relationship between predicted basal water and up-to-date analyses for the
basal thermal state and GHF
beneath the GrIS. We observe new
predictions for basal water predominantly in the northern and eastern ice
sheets, which spatially correlate with elevated GHF recently inferred by
. We then compare basal water and bed topography
, which enables us to identify likely subglacial flow
paths and storage locations beneath the contemporary ice sheet. Finally, with
a view toward improving our understanding of the influence of basal water
on ice-sheet motion, we compare the relationship between basal water and
ice surface speed .
(a) Ice-penetrating radar flight tracks for different CReSIS radar
systems. (b) Effective coverage for good-quality radar bed echoes
(corresponding to peak power 10 dB above noise floor). (c) Summary of key
GrIS landmarks: temperature boreholes, major drainage basin boundaries
and major regions of fast-flow identified from ice
surface speed . Abbreviations in (c)
correspond to
Camp Century (CC), Humboldt (Hu), Petermann (Pe),
Ryder (Ry), Northeast Greenland Ice Stream (NEGIS),
north-western margins (NWM), Jakobshavn Isbræ (JI),
Kangerlussuaq (Ka), Helheim (He) and Ikertivaq
(Ik). The projection is a polar stereographic north (70∘ N,
45∘ W) and is used in all future plots.
Methods
Radio-echo sounding data and bed-echo analysis
The airborne RES data used in this study were collected by the Center for
Remote Sensing of Ice Sheets (CReSIS) over the time period 2003–2014. The
data were taken using a succession of radar instruments: Advanced Coherent
Radar Depth Sounder (ACORDS), Multi-Channel Radar Depth Sounder (MCRDS),
Multi-Channel Coherent Radar Depth Sounder (MCoRDS), Multi-Channel Coherent
Radar Depth Sounder: version 2 (MCoRDS v2), mounted on three airborne
platforms: P-3B Orion (P3), DHC-6 Twin Otter (TO) DC8, Douglas DC-8 (DC8)
. The flight-track coverage, subdivided by the radar system, is
shown in Fig. a with the seasonal breakdown: ACORDS 2003 P3 and
2005 TO; MCRDS 2006 TO, 2007 P3, 2008 TO and 2009 TO; MCoRDs 2010 P3 and 2010
DC8; MCoRDs v2 2011 TO, 2011 P3, 2012 P3, 2013 P3, 2014 P3. More details on
the track lengths and data segmentation can be found in
. The vast majority of the data were collected in the
months March–May.
The various radar system details and signal processing steps are described in
detail in previous works . The centre-frequency of the radar systems is either 150 MHz
(ACORDS and MCRDS) or 195 MHz (MCoRDs and MCoRDS v2), and, after accounting
for pulse-shaping and windowing, the depth-range (vertical) resolution can
vary from ∼4.3 to 20 m in ice. The along-track (horizontal) resolution
also varies between field seasons and is typically ∼30 or 60 m. The
radar-echo strength profiles (CSARP, level 1B data) employ fixed fast-time
gain where the receiver gain is constant for each recorded pulse, which
enables consistent interpretation of bed-echo power on a season-by-season
basis. Whilst transmitted power can differ between seasons, since we consider
local variability, offsets between seasons do not matter, which enables the combination
of inter-seasonal data. Pre-2003 CReSIS data use
manual gain control and hence these seasons are not included.
The procedure used to extract bed-echo power is similar to
, , and aggregates power over bed-echo
fading (i.e. performs a depth-range integral). Briefly, the procedure
consists of the following steps. Firstly, CReSIS ice thickness (level 2)
picks were used as an initial estimate for the depth-range bin of the peak
bed-echo power. Secondly, a local retracker was used to locate the true
depth-range bin for peak bed-echo power. Thirdly, the power was aggregated by
a discrete summation over the bed-echo envelope (both before and after the
peak). The summations were truncated when the power was 10 dB or less than
the peak to ensure that the integral consisted of a dominant peak
associated with a dominant reflecting facet. The chosen signal-to-noise (SNR)
threshold of 10 dB in this study is less strict than the ∼17 dB
threshold used in and was required to extend
the effective coverage to some interior regions in southern Greenland.
Additionally, in this study we did not apply along-track averaging of level 1B
data that was done previously in . Finally,
again, to ensure a suitable SNR, a quality control measure was imposed such
that peak bed-echo power must be 10 dB above the noise floor. This results in
the effective coverage shown in Fig. b, which shows good-
(SNR>10 dB) and poor- (SNR≤10 dB) quality bed-echoes. The poor
quality bed echoes include a spatially coherent coverage gap in the southern
interior, high-altitude data and some marginal regions.
The rationale for use of aggregated bed-echo power (over peak power) is that
it serves to reduce bed-echo power variability due to roughness and thus
better enables comparison with the specular bed-echo reflectivity values that
are used to infer bulk material properties . Additionally,
since roughness scattering loss is frequency dependent ,
aggregated power serves as a pragmatic way to best combine bed-echo power
measurements from the 195 and 150 MHz radar systems. This is supported by
the observed ∼ 1 dB greater scattering loss (estimated here by the dB
difference between peak and aggregated power) for the 195 MHz systems at
crossover points.
Key landmarks of the GrIS that are used in the data
description – temperature boreholes, drainage basin boundaries and major
fast flow regions – are shown in Fig. 1c.
Bed-echo power, attenuation correction and bed-echo reflectivity
The bulk material properties of glacier beds, including the
presence of basal water, can, in principle, be inferred from the reflectivity
of the bed echo . The reflectivity, [R],
is obtained from solving the decibel form of the bed-echo power equation
[P]=[S]-[G]+[R]-[L]-[B],
where [P] is the bed-echo power (in this case the aggregated bed-echo
power, which mitigates for scattering losses from the ice–bed interface),
[S] is the system performance, [G] is the geometric correction, [L] is
the attenuation loss in ice, and [B] is the loss due to birefringence (ice
fabric anisotropy), and the notation [X]=10log10X is assumed
. Rough surface losses from transmission through the
air–ice interface (e.g. ) also influence the
radar power budget and are discussed in more detail in Sect. .
The geometric correction for a specular reflector can be defined by
[G]=2[2(s+h/ϵice)],
where s is the aircraft height and h is the ice thickness and
ϵice=3.15 is the relative dielectric permittivity of ice to
give the geometrically corrected bed-echo power
[Pg]=[P]+[G],
(e.g. ). For the majority of the CReSIS data used (2006
TO onward) s and h are known and Eq. () can be applied exactly.
For the 2003 P3 and 2005 TO seasons only h is known and s=500 m is
assumed (approximately the mean aircraft height). This approach is
justifiable since in this study we are interested in local (length scale
∼5 km) power variation, where s varies slowly. It is assumed that
variation in [S] and [B] is also negligible
(again, approximations that
are strengthened by consideration of local power
variation); then Eq. () reduces to
[Pg]=[R]-[L].
Finally, setting [L]=2<N>h gives
[Pg]=[R]-2<N>h,
where <N> (dB km-1) is the (one-way) depth-averaged attenuation rate
.
A fundamental ambiguity in bed-echo reflectivity analysis is that there are
two unknowns in Eq. (): <N> and [R]. Two approaches are
typically used to determine <N>: (i) forward modelling using estimates of
attenuation as a function of englacial temperature (e.g.
) and (ii) empirical determination
using the linear regression of bed-echo power and ice thickness (e.g.
). Attenuation follows an Arrhenius
(exponential) relationship with temperature and a linear dependence on the
concentration of ionic impurities: primarily hydrogen (H+)
but also chlorine (Cl-), and ammonium
(NH4+)
. On an ice-sheet
scale, the uncertainty when forward modelling <N> is so high that it can
be prohibitively challenging to accurately calibrate [R]
. This is due to both
uncertainty in ice-sheet model temperature fields, the ionic concentrations,
and the tuning of the parameters in the Arrhenius equation
. Empirical determination of <N> using
bed-echo power is also subject to sources of potential bias. In particular,
the regression methods can be ill-posed when there is rapid spatial variation
in attenuation , or when there is a thickness-correlated
distribution in bed-echo reflectivity .
We will later demonstrate that, unlike absolute values of [R], local
variability in bed-echo reflectivity is highly insensitive to modelled values
of <N> (Sect. ). However, despite acting as a very weak
constraint, an initial estimate for ice-sheet-scale variation in <N> is
still necessary to calculate reflectivity variability. The estimate for <N>
relies on previous work by and uses the M07 Arrhenius
equation , the Greenland Ice Sheet Model (GISM)
temperature field from as updated in
, depth-averaged ionic concentrations from the GRIP ice
core , and the Greenland ice thickness data set in
. The temperature field derives from a full 3-D
thermomechanical simulation over several glacial-interglacial cycles and
resolves the flow on a model resolution of 5 km, which causes some smoothing
of the temperature field in narrow outlet glaciers near to the coast. In the
calculation of <N> the temperature field was firstly interpolated to a 1 km
resolution, then vertically scaled using the 1 km representation of the
ice thickness. The geothermal heat flux in GISM was
initially taken from but further adjusted with Gaussian
functions around the deep ice core sites to match observed basal
temperatures. Vertical temperature profiles are within 1–2 ∘C when
compared to available in situ measurements.
Using this model framework, it is that predicted that <N> varies by a
factor ∼5 over the GrIS, ranging from ∼6 dB km-1 in the
colder northern interior to ∼30 dB km-1 toward the warmer
south-western margins (refer to Fig. 5a in for a spatial plot).
Calculating bed-echo power and reflectivity variability
In this study we use simple standard deviation measures to
quantify the variability of bed-echo power and reflectivity along the
flight tracks, denoted by σ[Pg] and σ[R]. The
numerical calculation is analogous to how topographic roughness (the rms
height) is calculated from bed elevation profiles , and
assumes an along-track window of length 5 km evaluated at 1 km intervals
(taking the standard deviation of all the points within the window). The
choice of horizontal length scale was chosen for consistency with the basal
thermal state mask by , which was deemed an appropriate
scale for integration of radar data with thermomechanical models at the
ice-sheet scale. At this 5 km length scale, high values of reflectivity
variability – a diagnostic for wet–dry transitions (also, see
Sect. ) – act as a form of edge detector. The rationale for using
this approach (rather than a conventional edge detector) is that it does not
impose that a single along-track transition is present, which is desirable
when aiming to also detect multiple smaller water bodies relative to the
window size.
Since this application of along-track variability is a non-standard approach
to bed-echo data analysis, we now take a closer look at the statistical
properties. The formula for σ[Pg] follows from the variance of
Eq. () and is given by
σ[Pg]=σ[R]2+σ[L]2-2σ[R],[L],
where σ[L] is the standard deviation in attenuation loss, and
σ[R],[L] is the covariance of bed-echo reflectivity and attenuation
loss. Using [L]=2<N>h and assuming <N> can be approximated as constant
(justifiable at the 5 km length scale that is considered); then Eq. () becomes
σ[Pg]=σ[R]2+4<N>2σh2-4<N>σ[R],h,
where σh is the standard deviation of ice thickness and
σ[R],h is the covariance of bed-echo reflectivity and ice
thickness. Equations () and () consider the variability
of log-transformed variables (i.e. the dB or additive form of the radar power
equation). This differs from the variability of the linear variables
(i.e. the multiplicative form of the radar power equation) expressed in log space.
The first advantage to our use of log-transformed variables is that we can
better separate the variability contributions into separate components. The
second advantage is that we can make a clearer connection to the dB
reflection amplitudes that are typically used in radioglaciology
. This includes prior applications that have
considered the distribution and standard deviation of dB reflection
amplitudes in the context of water detection (e.g.
).
Example flight-track profiles for bed-echo power and variability,
[Pg] and σ[Pg], bed-echo reflectivity and variability,
[R] and σ[R], attenuation loss and variability, [L],
σ[L] and ice thickness, h. Example (a), left panel, is
from the north-central interior of the ice sheet and (b), right panel,
is from the north-western margins (locations both shown in Fig. ).
The threshold that is later used for water detection, σ[R]>6 dB,
is indicated by the dashed pink line and applies to the right axis. The
values for [R] are relative with zero mean. The variability measures
are all calculated at a 5 km length scale with 1 km posting.
In regions where σ[R],[L]≈0 (bed-echo reflectivity has
negligible covariance with attenuation loss), Eqs. () and
() are approximated by
σ[Pg]≈σ[R]2+σ[L]2,≈σ[R]2+4<N>2σh2,
and the loss component of σ[Pg] is solely modulated by
σ[L] which is proportional to the product <N>σh. Whilst
an approximation (in certain circumstances the second and third terms on the
right-hand side of Eqs. () and () can be of
comparable magnitude), this scenario provides an intuitive way to understand
the interrelationship between σ[Pg], σ[R] and
σ[L].
Two example profiles for [Pg], σ[Pg], [R],
σ[R], [L], σ[L] and h are shown in
Fig. . Figure a is an example
from the interior of the ice sheet where σ[L] is relatively low and
h is thick (∼2.8 km). Subsequently the profiles for
σ[Pg] and σ[R] are very similar in appearance, with
the most notable difference at a distance of ∼360 km where there is higher
σ[Pg] due to the subglacial trough. The peaks in σ[R]
are later related to wet–dry bed material transitions in Sect. .
It is also important to note that σ[R] can be
greater than σ[Pg] (e.g. at a distance of ∼342 km), which is an
effect that can be explained by the covariance between attenuation loss/ice
thickness and bed-echo reflectivity in Eqs. () and
(). Figure b is a representative example from
toward the ice-sheet margins, where σ[L] is higher due to more rapid
variation in h (more complex bed topography) and higher values of <N>
(warmer ice). In this case, σ[Pg] is noticeably greater than
σ[R], with the differences largely attributable to higher
σ[L] as anticipated by Eq. (). The examples in
Fig. highlight that, at this length scale, higher values
of σ[R] arise primarily due to a large single transition in [R].
However, there are also instances where multiple transitions result in local
variability peaks (e.g. at distance ∼380–385 km along Fig. a).
When calculating σ[Pg], σ[R] and σ[L],
bed-echo coverage gaps within a 5 km bin (see Fig. b) were
accounted for by neglecting bins where less than half the data corresponded
to good bed echoes. The effects of this filtering step are demonstrated in
Fig. b, where, aligned with the deep subglacial trough at
distance ∼1324 km, there are along-track gaps in σ[Pg],
σ[R] and σ[L].
It is important to clarify the difference between the use of bed-echo power
and reflectivity variability in this study from previous radioglaciology
studies . These studies
focused on the statistical distribution of the peak echo power as a result
of phase modulation by interfacial roughness. By contrast, in this study we
suppress roughness effects by performing a depth integral for power over the
echo envelope (Sect. ). We are therefore able to focus on power
variability that is a result of along-track changes in the bed dielectric.
Spatial distributions for (a) bed-echo power variability
σ[Pg], (b) attenuation loss variability σ[L], (c)
bed-echo reflectivity variability σ[R] and (d) ice thickness, h.
Zoomed-in panels with flight-track data at true buffer size (5 km) are shown
for the north-central ice sheet (pink bounding box, containing profile in
Fig. a) and north-western margins (black bounding box,
containing profile in Fig. b). The profiles are
indicated in bold green in the ice thickness zoomed-in panels. In panels (a–c)
higher variability data is stacked on top of lower variability data, which
acts to emphasise higher variability. The zoomed-in panels all have the same
scale (×8 the resolution of the ice-sheet-scale plots).
Distributions for bed-echo power and reflectivity variability
Spatial distributions for the variability measures: σ[Pg],
σ[L], σ[R] are shown in Fig. a, b, c along
with ice thickness in Fig. d. In
general, σ[Pg] has a strong ice thickness dependence and
increases toward the margins where ice is thinner. The attenuation
correction, which primarily acts to reduce the component of
σ[Pg] that is attributable to σ[L], results in a more
uniform ice-sheet-scale distribution of σ[R] than
σ[Pg]. Notably, there are localised patches of higher
σ[R] present in both marginal and interior regions (which are later
attributed to the presence of basal water). The ice-sheet-scale trends in
σ[Pg] and σ[L]=2<N>σh may be related to
spatial variation in <N> and bed
roughness (which correlates with σh).
Frequency distributions for (a) bed-echo power variability,
σ[Pg] (corresponding to Fig. a); (b) bed-echo
reflectivity variability, σ[R] (corresponding to Fig. c).
Later in the study σ[R]>6 dB is used as the threshold criteria for
diagnosing the presence of basal water.
The two zoomed-in regions in Fig. include the flight-track profiles
in Fig. . (north-central ice sheet, pink bounding box;
north-western margins, black bounding box). These examples serve to further
illustrate the spatial interrelationship between σ[Pg],
σ[R] and σ[L] in a typical interior region with lower
σ[L] and a typical marginal region with higher σ[L]. Its
is clear that the interior example has very similar spatial distributions for
σ[Pg] and σ[R], whereas the marginal example has
higher σ[Pg] associated with the higher σ[L] that
occurs in the subglacial troughs and more complex topography toward the edge
of the ice sheet. The marginal example also demonstrates that the power
variability associated with the subglacial troughs is largely removed for σ[R].
The corresponding frequency distributions for σ[Pg] and
σ[R] are shown in Fig. . Both demonstrate a strong
positive-skew, with a long-tail extending to higher values. The mean and
standard deviation for σ[Pg] is greater than σ[R].
This is consistent with the commonly observed result that making an
attenuation correction to [Pg] acts to reduce the overall decibel range
for [R] (e.g. ), hence more closely
resembling the predicted dB range for bed materials .
A quantification and discussion of crossover statistics for σ[R]
is given in Appendix A.
Dielectric and reflective properties of subglacial materials based
on a compilation of past values by
, and . The bulk values take into
account typical ranges of saturation and porosity for the dielectric mixing
of water and ice with the background material. The relative dielectric
permittivity of ice is 3.15, which means that dry (just the background
dielectric) or frozen material (a mixture of the background dielectric with ice)
produces a similar range for [R].
Bed material
Permittivity ϵ
Reflectivity [R] (dB)
Groundwater
80
-2
Wet till
10 to 30
-11 to -6
Wet sandstone
5 to 10
-19 to -11
Dry/frozen granite
5
-19
Dry/frozen limestone
4 to 7
-26 to -14
Dry/frozen till
2 to 6
negligible to -19
Dry/frozen sandstone
2 to 3
-37 to -16
Interpretation of reflectivity variability as a sufficient diagnostic for basal water
Radar bed-echo reflectivity depends on the dielectric
contrast between glacier ice and bed material. For a specular, nadir
reflection, the Fresnel power reflection coefficient is given by
[R]=10log10ϵbed∼-ϵice∼ϵbed∼+ϵice∼2,
where ϵice∼ and ϵbed∼ are the complex
dielectric permittivity of the glacier ice and bed material respectively. The
relative (real) part of the permittivity, ϵbed, is the primary
control on [R]. A summary of dielectric and reflective properties of
glacier bed materials at typical ice-penetrating radar frequencies is given
in Table 1 and is collated from
, and . The permittivity and
reflectivity range for each material arises due to sub-wavelength dielectric
mixing between either ice or water and the bed material, and takes into
account typical saturation and porosity values
. In general, lower values of ϵbed
and [R] occur for dry or frozen bed materials (approximately
ϵbed<7 and [R]<-14 dB), whilst higher values occur for wet
bed materials (approximately ϵbed>7 and [R]>-14 dB).
Dielectric mixing between bed materials can also occur at the length scale of
the Fresnel zone (∼100 m), which results in further averaging of the
observed reflectivity .
Interpretation of bed-echo reflectivity variability,
σ[R], as a diagnostic for basal water. (a, b) Schematics of
the two-state dielectric model for single and multiple along-track
transitions in dry to wet bed material. Both scenarios are identically
parameterised by the wet/dry mixing ratio f (visually, the fraction
of blue to yellow) and wet–dry reflectivity difference, Δ[R]=[Rwet]-[Rdry].
(c) Phase-space plot for σ[R] as a function of f and Δ[R].
σ[R]>6 dB is used as a threshold for positive discrimination
of basal water (corresponding to green, red and yellow regions).
Due to the range of possible bed materials at the ice-sheet scale it is not
possible to formulate a unique dielectric model for diagnosing water from
σ[R]. A simple two-state dielectric model, does, however, enable
us to physically motivate the water diagnostic in terms of dielectric
properties (Fig. ). The model assumes that the along-track
sample window is comprised of two different bed materials: the dry
background bed material with permittivity ϵdry and reflectivity
[Rdry], and the wet material with permittivity ϵwet and
reflectivity [Rwet]. For simplicity, it is assumed that each along-track
measurement is in one of the wet or dry states, with the wet–dry mixing ratio
parameterised by f. In this formulation, a single body of wet material or
multiple smaller bodies of wet material have the same formula for the
reflectivity variability given by
σ[R]=Δ[R]f2(1-f)+(1-f)2f,
where Δ[R]=[Rwet]-[Rdry] is the reflectivity difference
between wet and dry beds. Equation () is derived by considering
the weighted variance for two discrete random variables and does not account
for non-linear variations due to variable scattering coherence. A phase-space
plot for σ[R](f,Δ[R]) is shown in Fig. c,
and shows that, for fixed Δ[R], σ[R] is maximised when f=0.5 (i.e. an even mixing of wet and dry materials).
Past diagnosis of basal water typically associates the upper tail of the
reflectivity distribution with water, prescribing a threshold above which the
bed is interpreted as wet (e.g. ). In this study,
a similar thresholding approach is applied to the distribution of
σ[R] (Fig. b). The threshold choice for basal water
(σ[R]>6 dB) corresponds to the region greater than the
σ[R]=6 dB contour in Fig. c and requires a
minimum wet–dry reflectivity difference of Δ[R]>12 dB. In general,
Δ[R]>12 dB is only possible for a mixture of wet and dry (or
frozen) bed materials (Table 1). For example, an even mixing of groundwater
and dry granite (f=0.5, Δ[R]=17 dB) has σ[R]=8.5 dB.
The contours in Fig. c demonstrate that small
perturbations to even mixing (f≠0.5) produce similar σ[R],
and hence that water detection is insensitive to the discretisation of the
along-track sample window (Sect. ). Overall, the threshold
choice (σ[R]>6 dB) is fairly conservative and is deliberately
intended to reduce false-positive detection of basal water (at the expense of
reduced overall detection). Finally, as discussed in Sect. ,
the 6 dB variability threshold applies to the distribution of log-transformed
reflectivity.
The bed-echo power aggregation in Sect. partially mitigates for
roughness-induced scattering loss and the along-track power variability
associated with this. Supporting evidence is that the crossover analysis for
σ[R] (see Appendix A) demonstrates there to be no significant bias
for the 150 MHz radar systems (ACORDS and MCRDS) versus MCORDS v2 (the
195 MHz radar system used as a benchmark). Additionally, whilst small-scale
roughness transitions (transitions from specular to diffuse scattering) will
often correlate with wet–dry transitions, this scenario will act to amplify
the useful signal component with the σ[R] value increasing.
Table 1 also indicates that, in exceptional circumstances, Δ[R]>12 dB
could be generated in frozen/dry regions that partially contain sandstone
or till that is close to matching the permittivity of ice. However, if
present, these regions are likely to have indistinct bed echoes and will not
be included in the effective coverage in Fig. b.
Basal water distribution and robustness to perturbations in the
attenuation rate estimate, <N>. The original predictions (σ[R]>6 dB)
are represented by all three colours. Persistent water predictions
(σ[R]>6 dB for ±20 % and ±50 % perturbations
to <N>) are indicated by the subset of green and red points, and the
subset of red points respectively. The subset of red and green points is
used in the rest of the paper.
Basal water distribution and robustness to attenuation model bias
The initial basal water predictions (σ[R]>6 dB, pre-
sensitivity analysis) are shown in Fig. (red, blue
and green data), and correspond to ∼3.5 % of bins containing
predominantly good-quality bed echoes (Fig. b). A full
geographic analysis of the spatial distribution is performed in
Sect. . To demonstrate the robustness of the predictions, we performed a
sensitivity analysis with respect to the modelled attenuation correction
<N> (Sect. ) The analysis considered a series of increasingly
large (uniform, multiplicative) perturbations to <N> and then tested
whether σ[R]>6 dB also held for the perturbed model. Examples of
persistent water predictions for ±20 % (red and green data) and
±50 % (red data) perturbations to <N> are indicated. As the
perturbation size increases this results in a slight decrease in the overall
percentage of water predictions (corresponding to ∼2.6 % and
2.1 % of the along-track bins for ±20 % and ±50 %
respectively).
The sensitivity analysis tests the robustness of the water predictions to a
number of different physical scenarios. Firstly, there is inherent bias in the
Arrhenius equation parameters. For example, an empirical correction similar
to the uniform perturbation considered in Fig. was
proposed by to model unaccounted frequency dependence
in the electrical conductivity. Secondly, there is bias in the model temperature field
(<N> is approximately equivalent to depth-averaged temperature). Thirdly,
the bias is due to assumed ionic concentration values. It is hard to formally
quantify the possible range of these uncertainties but, based on solution
variability for <N> using ice-sheet model temperature fields
, ±20 % is a reasonable estimate for temperature-related uncertainty. Subsequently, in the comparison with other data sets in
Sect. the subset of red and green points in
Fig. is used. Inherent bias in the Arrhenius equation
parameters could be significantly higher than temperature uncertainty
. However, since the spatial structure for the basal
water distribution under the ±50 % perturbation is largely preserved,
this is unlikely to significantly alter the conclusions that are drawn.
Additionally, whilst σ[R]>6 dB is used as the threshold,
Fig. c
demonstrates that a less conservative threshold
(σ[R]>4 dB) retains the majority of contiguous regions with no
water predicted (e.g. the interior of southern Greenland).
It is important to emphasise the robustness of σ[R] with respect to
uncertainty and model bias in <N> (particularly compared with bed-echo
reflectivity, [R]). An analogous sensitivity analysis by
demonstrated that systematic over- and underestimates in <N> lead to
pronounced ice-thickness-correlated biases in the distribution for [R] in
northern Greenland (Fig. B1 in ).
Results
The basal water distribution is now compared with existing
analyses for the basal thermal state
(Sect. ), geothermal heat flux (GHF)
(Sect. ), bed topography
and subglacial flow paths (Sect. ) and
ice surface speed (Sect. ). The
basal water predictions in the results are always indicated by red circles
and correspond to the set of red and green points in the sensitivity
analysis, Fig. . In regional zoomed-in panels the circles
are fixed to be 5 km in diameter (a true representation of the along-track
window size and the effective resolution of the radar method). In ice-sheet-scale plots the buffer size of the water predictions are increased for
visualisation purposes. The radar flight tracks represent where there are
good bed echoes (Fig. b) and hence indicate the effective
coverage.
In interpreting the maps it is important to emphasise that the basal water
predictions in this study correspond to a subset of flight-track data where
basal water is present. Specifically, they correspond to where there are
rapid spatial transitions and gradients in the bed dielectric (i.e. small,
finite, water bodies or the boundaries of larger water bodies). The
predictions therefore act as a sufficient constraint on the distribution of
basal water rather than being a fully comprehensive flight-track map for the
water extent. Additionally, since the vast majority of the radar measurements
were collected before the onset of summer surface melt, to a first
approximation the basal water predictions correspond to the winter storage
configuration.
Comparison between basal water distribution and basal thermal
state synthesis by . (a) Ice-sheet scale. Major
regions of disagreement (water in likely frozen regions) are highlighted
in the zoomed-in panels. (b) Camp Century. (c) Far north. (d) North-central
ice sheet. (e) East of GRIP. (f) Around Kangerlussuaq. The zoomed-in panels
all have the same scale (×5 the resolution of a).
Comparison between basal water distribution and geothermal
heat flux (GHF) models. (a) Seismic GHF model by .
(b) Magnetic GHF model by using satellite data. (c)
Magnetic GHF model by derived from spectral methods
using airborne data. The colour bar scale is the same in all panels and
is truncated to emphasise the spatial variation in panel (c).
Comparison between basal water distribution and basal thermal state synthesis
In Fig. a the basal water predictions are
underlain by the basal thermal state synthesis (frozen/thawed likelihood) map
by . The synthesis employed four independent methods:
(i) assessment of thermomechanical model temperature fields, (ii) basal
melting inferred from radiostratigraphy, (iii) basal motion inferred from
surface velocity, and (iv) basal motion inferred from surface texture. The four
methods were then equally weighted, leading to a likelihood map for frozen
beds, thawed beds and uncertain regions. Importantly, the prediction did not
utilise radar bed-echo data and is therefore independent of our basal water
predictions.
The reflectivity variability water diagnostic enables a positive
discrimination of basal thaw, since σ[R]>6 dB is deemed a
sufficient (but not necessary) criteria for basal water. Positive
discrimination of frozen regions is not, however, possible. This is because
low-reflectivity variability (σ[R]<6 dB) could correspond to many
different scenarios: a frozen region, a drier region at or above the PMP or
a wet region that is smoothly varying in bed-echo reflectivity. Since basal
water enables a positive discrimination of thaw, red circles in likely thawed
(pink) regions indicate agreement and red circles in likely frozen (blue)
regions indicate disagreement with the basal thermal state synthesis. Absence
of basal water in likely frozen regions is an indicator of general
consistency between the two methods.
Comparison between basal water distribution, bed topography
and major subglacial flow paths (blue lines). (a)
Ice-sheet scale. (b) Petermann catchment. (c) North-western margins. (d)
North-central ice sheet. To improve clarity the radar flight tracks are
removed from (a) and a hillshade is applied to the bed topography. The
zoomed-in panels are all have the same scale (×4 the resolution of a).
There is general agreement (water in predicted thawed regions) for the beds
of major outlet glaciers and their upstream regions. This includes Helheim,
Kangerlussuaq, Jakobshavn and the other fast-flowing regions identified in
Fig. c. There is also general agreement between basal water
and the extent of predicted thaw in the NEGIS drainage basin. Major regions
of disagreement (water in predicted frozen regions) are highlighted in the
zoomed-in panels, Fig. b–f. The most obvious disagreement is the
quasilinear “corridor” of basal water in the north-central ice sheet
(Fig. d). This feature tracks close to the central ice divides and
extends from the NorthGRIP region in the south toward Petermann Glacier in
the north. There are also noticeable areas of disagreement to the north and
east of the Camp Century borehole (Fig. b), in the far north
(Fig. c), to the east of GRIP (Fig. e), and around
Kangerlussuaq (Fig. f). There is also an absence of water in many
predicted frozen regions, indicating consistency. This includes parts of the
southern interior, north of the NEGIS drainage basin, and the majority of the
interior region between the Camp Century and NEEM boreholes.
Comparison between basal water distribution and ice surface
speed (logarithmic-scale). (a) Ice-sheet
scale. (b) Humboldt, Petermann and Ryder. (c) Kangerlussuaq and region to
south. (d) Helheim (north of panel) and Ikertivaq (south-west of panel).
The zoomed-in panels are all have the same scale (×4 the resolution of
a).
Comparison between basal water distribution and geothermal heat flux models
The basal temperature of glacier ice is governed by surface temperature, GHF,
strain heating from internal deformation, frictional heating, and diffusive
and advective heat transport (e.g. ). In the interior
of the ice sheet, close to the ice divides, GHF, vertical advection, and
diffusion are the dominant processes which influence basal temperature. In
this scenario, the thermodynamic (temperature) equation can be approximated
by the classical Robin model which predicts that basal melting occurs when
GHF is above a certain threshold. For typical values of ice thickness and
surface accumulation rate, which control the rate of vertical heat
advection, the minimum GHF forcing for melt is anticipated to be ∼55–70 mW m-2
in the interior of the ice sheet
. In the water–GHF comparison
we therefore define elevated GHF (i.e. likely to produce basal melt) as >60 mW m-2. This definition is also informed by the lower range of
values (37–50 mW m-2) that are typically associated with non-altered
ancient continental crust .
In Fig. the basal water predictions are underlain by three
different GHF models: the seismic model by and two
models derived from magnetic anomalies by and
. The GHF model by is based on the
correlation between a 3-D tomographic model of the crust and mantle
temperature. The GHF models by and are
based on a thermal model of the lithosphere with the lower boundary defined
by the Curie depth, which is determined from magnetic anomalies.
further describes this approach and the additional
spectral processing method used to produce Fig. c. An older
tectonic GHF model by is not considered and a spatial
plot for the GrIS can be found in along with a
discussion of the caveats of the different types of model. A summary of local
GHF estimates using borehole temperature profiles and thermomechanical model
inversions
are provided by , and demonstrate
general consistency between Fig. c and local estimates at GRIP,
NEEM, NorthGRIP and Camp Century. Local estimates of GHF at Dye 3 (∼20–25 mW m-2) are significantly lower than all three GHF models.
In interpreting Fig. , we limit the comparison to the ice sheet
interior where the spatial correlation between GHF and basal water should be
strongest. The model by , Fig. a, predicts
low GHF (<60 mW m-2) over the vast majority of the central and
northern interior. There is therefore no correlation between elevated GHF and
basal water. The model by , Fig. b,
predicts elevated GHF around GRIP and the southern and eastern boundaries of
the NEGIS basin, and basal water is also present in this region. There is,
however, no correlation between elevated GHF and basal water along the ice
divides north of NorthGRIP. The model by , Fig. c,
exhibits strong overall spatial correlation between basal
water and elevated GHF in the interior of the northern ice sheet. Notably,
there is a striking correlation between elevated GHF and the quasilinear
corridor of basal water that extends from NorthGRIP toward Petermann Glacier. All three models predict regions of elevated GHF in the southern
interior including the Dye 3 region. However, there is only isolated radar
evidence for basal water.
In the comparison between the flight-track water predictions and GHF
distributions in Fig. it is important to bear in mind that the
GHF distributions are evaluated at a lower spatial resolution. For example,
the resolution of the GHF distribution by is a consequence
of the spectral method (window size and overlap), which has an effective
resolution of ∼75 km.
Comparison between basal water distribution, bed topography and subglacial flow paths
In Fig. the basal water predictions are underlain by the
most recent Greenland bed topography digital elevation model (DEM)
. To motivate further discussion about water storage
locations and hydrological connectivity, a predicted subglacial flow path
network is also included. The network structure is governed by gradients in
the hydraulic pressure potential , which was calculated
using the bed elevation and ice thickness surfaces at a grid cell resolution
of 600 m (derived from ). The flow-routing algorithm was
implemented in ArcGIS using the inbuilt flow accumulation tool on a hydraulic
potential surface that had been processed for sink removal using the method
of . Likely hydrological flow paths were identified by
excluding flow paths where 50 or fewer neighbouring cells cumulatively
contribute to a given location.
Figure demonstrates that the vast majority of the basal
water predictions are well aligned with predicted subglacial flow paths. This
alignment is most visually pronounced toward the margins and zoomed-in panels are
shown for the Petermann catchment in Fig. b and
north-western margins in Fig. c. Figure b
also demonstrates that basal water is present along
sections of the “mega-canyon” feature identified by – for
example, north-west of the intersection (80∘ N, 50∘ W). In
the interior of the ice sheet, where the horizontal gradients in ice
thickness are small, local minima in the hydraulic potential surface should
correlate with topographic depressions. The water storage locations in the
interior generally conform to this behaviour (Fig. d).
Comparison between basal water distribution and ice surface speed
In Fig. the basal water predictions are underlain by ice
surface speed , which is based on a temporal average from
1 December 1995 to 31 October 2015. The ice surface speed is determined
using interferometric synthetic aperture radar (InSAR) as described in
. Whilst there is a complex overall relationship between
basal water and ice velocity, there are some clear spatial patterns. Notably,
in the topographically less constrained northern and western outlet glaciers,
basal water is often concentrated in the fast-flow onset regions and
tributaries whilst it is absent from the main trunks. This behaviour is
particularly evident for the Petermann Glacier catchment
(Fig. b). In the topographically more constrained south-eastern
outlet glaciers, there is widespread evidence for basal water storage in both
the fast-flowing glacial troughs and upstream regions. This includes both the
Kangerlussuaq catchment and the tight network of subglacial troughs to the
south (Fig. c), and the Helheim catchment (Fig. d).
In the interior of the ice sheet basal water is predicted near to the head of
the NEGIS ice stream. However, basal water is also predicted in some of the
slowest-flowing regions of the ice sheet interior, notably, close to the
central ice divides between NorthGRIP and Petermann and north-east of GRIP.
Discussion
Basal water, basal thermal state and temperature
The basal water distribution in this study and the basal thermal state
synthesis by represent two independent approaches to
predict where the bed beneath the GrIS is thawed. There is greatest agreement
(basal water in likely thawed regions identified by )
toward the ice margins where ice surface speed is generally higher. The most
noticeable regions of disagreement (basal water in likely frozen regions
identified by ) all occur where the ice surface speed is
low. This includes the north-central ice divide (Fig. d), the
region east of GRIP (Fig. e), and the region west of Kangerlussuaq
(Fig. f). The regions of agreement and disagreement are, perhaps,
unsurprising, since three of the four methods employed by
– ice velocity, surface texture and radiostratigraphy –
associate basal thaw with present (or past) ice sheet motion. In general, a
thawed bed is a necessary (but not sufficient) condition for appreciable
basal motion, and there is likely to be a subset of thawed regions where
basal motion is negligible. This subset naturally incorporates water/thaw
near the ice divides (since driving stress is low) and in the eastern ice
sheet (since ice flow is topographically constrained).
Another key difference between the water predictions in this study and the
thaw predictions by is that their study employed
techniques better tuned to identify continuous regions of basal thaw, whereas
the basal water predictions are localised. This provides another means to
reconcile regions of disagreement, since in some instances the basal water
predictions may correspond to localised patches above the PMP in an otherwise
frozen region. A final explanation for the discrepancies is that the model
temperature fields included in the basal thermal state synthesis were often
tuned around knowledge of GHF at the time (i.e.
).
There is no evidence for basal water at the location of the temperature
boreholes, which, based on the resolution of our method, corresponds to
within 5 km. Since high-reflectivity variability is not necessary for thaw,
this is consistent with both frozen and thawed borehole temperatures. Water
is, however, observed fairly close to two frozen boreholes: ∼10 km
south of GRIP and ∼7 km north-east of Camp Century (Fig. ). At
GRIP this is less surprising, since the basal temperature is 6 degrees below
the PMP and GHF is likely to be
elevated in this region (Fig. ). The basal water predictions near
Camp Century are more surprising, since in the late 1960s basal temperatures
were measured to be 11.8 degrees below the PMP
. One possible explanation, which was
recently invoked to explain the presence of a lake less than 10 km from the South
Pole (where the bed is frozen), is that the basal water is yet to reach
thermal equilibrium . Another possible explanation is that
the presence of hypersaline water could result in a depression of the PMP.
This situation arises at Lake Vida in East Antarctica (where liquid water
exists at -13 ∘C) and at the Devon Ice Cap in the
Canadian Arctic .
Basal water and geothermal heat flux
The comparison between basal water and the different GHF models in
Fig. demonstrates
greatest consistency with the distribution by . Notably
there is a pronounced spatial correlation between elevated GHF and the new
predictions of basal thaw in the northern ice sheet. A recent machine-learning-derived map for GHF beneath Greenland by
is also consistent with there being extensive basal thaw in this region.
However, establishing definitive attribution of regions of the basal melt to
GHF forcing (rather than frictional and strain heating, low advection from
colder ice above, and surface meltwater storage) will require integration
with thermomechanical ice-sheet models. The basal water predictions could
also be used as a constraint in a wide variety of other numerical modelling
contexts. For example, experiments with 3-D models to reconstruct the full ice
temperature history over the last glacial cycle(s) can constrain the minimum
GHF required to produce basal melting at the predicted basal water locations
. Other studies include investigating the sensitivity
of ice-sheet dynamics to the thermal boundary condition
or basal lubrication , and thermal models of the
underlying lithosphere .
Recent analyses imply that much of the spatial variation in GHF beneath the
northern GrIS can be explained by Greenland's passage over the Iceland
mantle plume between roughly 35 and 80 million years ago
. The magnetic GHF map in Fig. c,
alongside gravity data (Bouger anomalies), was recently used
by to infer the most likely passage of the hotspot
track. The most likely predicted path (corresponding to going forwards in
geological time) follows the quasilinear region of elevated GHF in
Fig. c from Petermann Glacier to NorthGRIP and follows a path
previously anticipated by . The spatial correlation
between elevated GHF and the quasilinear basal water corridor provides an
additional source of evidence for the predicted path.
Basal water, bed topography and subglacial flow paths
There is growing evidence that much of the present day subglacial flow path
network beneath the GrIS is palaeofluvial in origin. This includes the
dendritic flow path networks in the Jakobshavn and
Humboldt catchments , along with the prominent
mega-canyon feature which extends from the NorthGRIP region in the south to
the Petermann Glacier in the north . The comparison between
the predicted flow paths and basal water in Fig. enables
a revised assessment of the hydrological flow paths that are likely to be
utilised in the contemporary ice sheet. For example, the flow routing analysis
demonstrates that basal water originating in the Petermann catchment is
likely to route through sections of the canyon toward the ice-sheet margins.
Fig. b supports this hypothesis, since the there is
evidence for basal water along the majority of the canyon. However, it is
important to stress that more rigorously assessing hydrological connectivity
will require incorporation of DEM uncertainty when performing the flow
routing (e.g. ) and use of a coupled hydrological ice
flow model (e.g. ).
Basal water and ice-sheet motion
Both observational (e.g. ) and theoretical
studies (e.g. ) point toward a complex
spatio-temporal relationship between basal water and ice surface speed in
fast-flowing regions of the ice sheet. This ultimately depends on the
details of how the subglacial drainage system responds to surface meltwater.
It is therefore essential to re-emphasise that the basal water predictions
generally correspond to the winter storage (pre-surface melt) configuration
and may, therefore, be of limited utility in understanding spatio-temporal
patterns related to ice dynamics.
In addition to basal water and temperature, spatial variation in the
underlying geology and lithology of the GrIS (notably, presence or absence of
deformable sediment) will also influence ice-sheet motion. It is widely
anticipated that much of the interior of the ice sheet is underlain by hard
pre-Cambrian rocks, with more limited sedimentary deposits toward the margins
and in the NEGIS drainage basin
. It is therefore entirely plausible that much of the
basal water predicted in the interior lies on a hard undeformable bed
(particularly in the context of the igneous rock that would be associated
with the geological remnants of the Iceland hotspot track) and therefore
experiences little motion due to bed deformation.
Comparison with past RES analyses of basal water and disrupted radiostratigraphy in Greenland
Despite acknowledged calibration issues due to both variable radar system
performance and spatial variation in attenuation, the bed-echo reflectivity
analysis of 1990s PARCA RES data by anticipated some of
the water predictions in this study. This includes prior basal water
predictions in the NEGIS onset region and the upstream areas of the
Kangerlussuaq, Petermann and Humboldt glaciers.
There is mixed agreement between the basal water predictions in this study
and those from , who performed joint bed-echo
reflectivity and scattering analysis of the 1990s PARCA data. In general,
better agreement with our results occurs in smoother topographic regions in
the ice-sheet interior, such as close to the NorthGRIP borehole. Since the
effects of spatial bias due to attenuation uncertainty are lower in the
interior of the ice sheet, this is where bed-echo reflectivity as a water
diagnostic should be more robust. Additionally, the water detection method
proposed by will generally not be able to
discriminate water in many outlet glaciers and tributaries including
Petermann and the north-western margins . This is because
these regions tend to exhibit a diffuse scattering signature (associated with
fine-scale roughness), whereas the method proposed by
is specifically tuned to detect water bodies
that exhibit a spatially continuous (near-) specular scattering signature.
By contrast, comparison between the water predictions in this study and the
radar-derived bed roughness maps in and
demonstrate a lack of modulation by bed roughness, with basal water present
in rougher marginal regions and a generally smoother ice-sheet interior.
Basal units of disrupted radiostratigraphy are widely present in Greenland
RES data sets . The features
have been attributed to a supercooling freeze-on process ,
stick-slip mechanisms, and the rheological
anisotropy of ice . In the fast-flow initiation regions
of some outlet glaciers (e.g. Petermann and the northern tributaries of
NEGIS), these basal units are closely aligned with the basal water
predictions.
Limitations of bed-echo reflectivity variability as a RES technique to detect basal water
Bed-echo reflectivity variability provides a practical way to
automate the detection of a subset of basal water with high confidence at the
ice-sheet scale. In particular, as a form of edge detector, the technique is
well-tuned to detect finite water bodies with sharp horizontal gradients in
water content. These attributes are thought likely to be common to basal
water in the (likely hard-bedded) interior of the ice sheet. It is, however,
important to note that the approach will fail to identify basal water with a
homogeneous dielectric and reflective character. This includes the centre of
large subglacial lakes (based on the resolution of our method lakes greater
than 5 km in horizontal extent) and regions of more uniformly saturated
subglacial till. Since all identified subglacial lakes in Greenland are <5 km
in horizontal extent we
believe that the former scenario is likely to be rare. However, extensive
regions of saturated till that evade detection are likely to be present,
particularly beneath larger outlet glaciers. This interpretation is supported
by comparison with the bed-echo reflectivity and basal water maps of the
Petermann catchment in . Specifically, there is a good
agreement between the two water maps in the interior and fast-flow initiation
region, but this study fails to predict the basal water (likely to be wet
sediment) in the main trunk of the outlet glacier. Therefore, if we are focusing on
the catchment-scale subglacial hydrology of Greenland outlet glaciers or
other glaciologically similar regions of Antarctica, a suite of existing RES
techniques to detect and characterise basal water (e.g.
) is better suited.
Finally, it is important to add that part of the subglacial water budget is
likely to comprise groundwater , which would be
practically undetectable by RES.
As is generally the case in RES analysis, certain simplifications were made
in this study when interpreting bed-returned power. Notably, we did not
account for (i) power modulation due to birefringent propagation (ice fabric
anisotropy, e.g. ), (ii) rough surface transmission
(e.g. ) or (iii) scattering by near-surface
water. The first of these mechanisms could potentially influence power
variability near the ice divides, since abrupt fabric transitions can be
present in these regions . However, the zoomed-in panels in these regions (e.g. Figs. b, d, d)
indicate that the water predictions occur over a multiple range of
flight-track orientations relative to the ice divide (which should correlate
with orientation of the principle dielectric axes). We therefore can discount
ice fabric having a dominant influence on the results. The second and third
of these mechanisms will influence power variability primarily in faster-flowing
regions toward the margins, as these regions have higher surface
roughness (e.g. ) and surface melt (e.g.
). The degree of surface-induced power variability
depends on both the surface permittivity and the roughness regime (relative
to the radar wavelength) . It is, however, important to
note that we are likely to get the majority of false positives (elevated
power variability due to surface modulation) in regions where the bed is
predicted to be thawed with high certainty by . In turn,
the central results in this study – the new regions of basal water and thaw
identified in Fig. – are likely to be largely unaffected by surface
modulation.
Summary and conclusions
This study placed a spatially comprehensive observational constraint on the
basal water distribution beneath the GrIS and, hence, regions of the bed at
or above the PMP of ice. The distribution of basal water is influenced by,
and has influence on, multiple ice sheet and subglacial properties and
processes. Subsequently, with a focus on ice-sheet-scale behaviour, we
performed an exploratory comparison with related data sets for the GrIS. This
included an up-to-date synthesis for the basal thermal state
, three different GHF model distributions
, bed topography
and predicted subglacial flow paths and ice surface
speed .
Central to the methods in the study was the use of bed-echo reflectivity
variability (rather than bed-echo reflectivity) as a RES diagnostic for basal
water. Our use of this diagnostic (a form of edge detector) was motivated by
its insensitivity to radar attenuation at the ice-sheet scale, and the
pragmatic advantages when performing data combination for multiple RES field
campaigns. The reflectivity variability diagnostic is, however, only able to
detect wet to dry (or wet to frozen) transitions in bed material and is a
sufficient (but not necessary) condition for basal water. It will therefore
need to be combined with other information to fully map the extent of basal water
and classify basal water bodies.
There was much agreement between the basal water distribution and the thawed
marginal regions predicted by . However, we identified
regions of basal water and thaw in the interior of the ice sheet that were
previously classified as likely to be frozen. The most extensive new region
of predicted thaw is a quasilinear corridor feature which extends from
NorthGRIP in the south to Petermann in the north. This feature, and the
majority of basal water in the northern interior, spatially correlate with
elevated GHF inferred from magnetic data by .
The comparison with bed topography and predicted flow
paths demonstrated good overall agreement between the basal water storage
locations and the geometric constraints imposed by the hydrological pressure
potential. However, many of the basal water predictions in the ice-sheet
interior occur where ice surface speed (and hence basal motion) is
negligible. One plausible explanation is that much of the interior lies on
a hard and undeformable bed. Future investigation of basal control on GrIS
dynamics should integrate information about basal water and the basal
thermal state with better constraints on bed lithology and geology.