Perennial firn aquifers are subsurface meltwater reservoirs
consisting of a meters-thick water-saturated firn layer that can form on
spatial scales as large as tens of kilometers. They have been observed
within the percolation facies of glaciated regions experiencing intense
seasonal surface melting and high snow accumulation. Widespread perennial
firn aquifers have been identified within the Greenland Ice Sheet (GrIS) via
field expeditions, airborne ice-penetrating radar surveys, and satellite
microwave sensors. In contrast, ice slabs are nearly continuous ice layers
that can also form on spatial scales as large as tens of kilometers as a
result of surface and subsurface water-saturated snow and firn layers
sequentially refreezing following multiple melting seasons. They have been
observed within the percolation facies of glaciated regions experiencing
intense seasonal surface melting but in areas where snow accumulation is at
least 25 % lower as compared to perennial firn aquifer areas. Widespread
ice slabs have recently been identified within the GrIS via field
expeditions and airborne ice-penetrating radar surveys, specifically in
areas where perennial firn aquifers typically do not form.
However, ice slabs have yet to be identified from space.
Together, these two ice sheet features
represent distinct, but related, sub-facies within the broader percolation
facies of the GrIS that can be defined primarily by differences in snow
accumulation, which influences the englacial hydrology and thermal
characteristics of firn layers at depth.
Here, for the first time, we use
enhanced-resolution vertically polarized L-band brightness
temperature (TVB)
imagery (2015–2019) generated using observations collected over the GrIS by
NASA's Soil Moisture Active Passive (SMAP) satellite to map perennial firn
aquifer and ice slab areas together as a continuous englacial hydrological
system. We use an empirical algorithm previously developed
to map the extent of Greenland's perennial firn aquifers via fitting
exponentially decreasing temporal L-band signatures to a set of sigmoidal
curves. This algorithm is recalibrated to also map the extent of ice slab
areas using airborne ice-penetrating radar surveys collected by NASA's
Operation IceBridge (OIB) campaigns (2010–2017). Our SMAP-derived maps show
that between 2015 and 2019, perennial firn aquifer areas extended over
64 000 km2, and ice slab areas extended over
76 000 km2. Combined together, these
sub-facies are the equivalent of 24 % of the percolation facies of the
GrIS. As Greenland's climate continues to warm, seasonal surface melting
will increase in extent, intensity, and duration. Quantifying the possible
rapid expansion of these sub-facies using satellite L-band microwave
radiometry has significant implications for understanding ice-sheet-wide
variability in englacial hydrology that may drive meltwater-induced
hydrofracturing and accelerated ice flow as well as high-elevation meltwater
runoff that can impact the mass balance and stability of the GrIS.
Introduction
The recent launches of several satellite L-band microwave radiometry
missions by NASA (Aquarius mission, Le Vine et al., 2007; Soil Moisture
Active Passive (SMAP) mission, Entekhabi et al., 2010) and ESA (Soil
Moisture and Ocean Salinity (SMOS), Kerr et al., 2001) have provided a new
Earth-observation tool capable of detecting meltwater stored tens of meters
to kilometers beneath the ice sheet surface. Jezek et al. (2015) recently
demonstrated that in the high-elevation (3500 m a.s.l.) dry snow facies of
the Antarctic Ice Sheet, meltwater stored in subglacial Lake Vostok can be
detected as deep as 4 km beneath the ice sheet surface. Subglacial lakes
represent radiometrically cold subsurface meltwater reservoirs. Upwelling
L-band emission from the radiometrically warm bedrock underlying the
subglacial lakes is effectively blocked by high reflectivity and attenuation
at the interface between the bedrock and the overlying lake bottom. This
results in a lower observed microwave brightness temperature (TB) at the
ice sheet surface as compared to other dry snow facies areas where bedrock
contributes to L-band emission depth-integrated over the entire ice sheet
thickness.
Similar to subglacial lakes, perennial firn aquifers also represent
radiometrically cold subsurface meltwater reservoirs (Miller et al., 2020)
consisting of a 4–25 m thick water-saturated firn layer (Koenig et al.,
2014; Montgomery et al., 2017; Chu et al., 2018) that can form on spatial
scales as large as tens of kilometers (Forster et al., 2014). Perennial firn
aquifers have been identified via field expeditions (Forster et al., 2014),
airborne ice-penetrating radar surveys (Miège et al., 2016), and
satellite microwave sensors (Brangers et al., 2020; Miller et al., 2020) in
the lower-elevation (<2000 m a.s.l.) percolation facies of the
Greenland Ice Sheet (GrIS) at depths from between 1 and 40 m beneath the
ice sheet surface. They exist in areas that experience intense seasonal
surface melting and rain (>650mmw.e.yr-1) during the
melting season and high snow accumulation (>800mmw.e.yr-1) during the freezing season (Forster et al., 2014). High snow
accumulation in perennial firn aquifer areas thermally insulates
water-saturated firn layers from the cold atmosphere, allowing seasonal
meltwater to be stored in liquid form year-round if the overlying seasonal
snow layer is sufficiently thick (Kuipers Munneke et al., 2014). Koenig et
al. (2014) estimated that the volumetric fraction of meltwater stored within
the pore space of Greenland's perennial firn aquifers just prior to melt
onset ranges from between 10 % and 25 %, which limits the upward
propagation of electromagnetic energy from greater depths within the ice
sheet. Large volumetric fractions of meltwater within the firn pore space
result in high reflectivity and attenuation at the interface between
water-saturated firn layers and the overlying refrozen firn layers as well as
between glacial ice or an impermeable layer and the overlying
water-saturated firn layers. Upwelling L-band emission from deeper glacial
ice and the underlying bedrock is effectively blocked.
While perennial firn aquifers are radiometrically cold, the slow refreezing
of deeper firn layers saturated with large volumetric fractions of meltwater
represents a significant source of latent heat that is continuously released
throughout the freezing season. Refreezing of seasonal meltwater by the
descending winter cold wave (Pfeffer et al., 1991), and the subsequent
formation of embedded ice structures (i.e., horizontally oriented ice layers
and ice lenses as well as vertically oriented ice pipes; Benson et al., 1960;
Humphrey et al., 2012; Harper et al., 2012) within the upper snow and firn
layers, represents a secondary source of latent heat. These heat sources help
maintain meltwater at depth. Perennial firn aquifer areas are
radiometrically warmer than other percolation facies areas where the single
source of latent heat is via refreezing of seasonal meltwater. This results
in a higher observed TB at the ice sheet surface during the freezing
season as compared to other percolation facies areas where seasonal
meltwater is fully refrozen and stored exclusively as embedded ice.
Recently, mapping the extent of Greenland's perennial firn aquifers from
space was demonstrated using satellite L-band microwave radiometry (Miller
et al., 2020). Exponentially decreasing temporal L-band signatures observed
in enhanced-resolution vertically polarized L-band brightness temperature
(TVB) imagery (2015–2016) generated using
observations collected over the GrIS by the microwave radiometer on NASA's
SMAP satellite (Long et al., 2019) were correlated with a single year of
perennial firn aquifer detections (Miège et al., 2016). These detections
were identified via the Center for Remote Sensing of Ice Sheets (CReSIS)
Multi-Channel Coherent Radar Depth Sounder (MCoRDS) flown by NASA's
Operation IceBridge (OIB) campaigns (Rodriguez-Morales et al., 2014). An
empirical algorithm to map extent was developed by fitting temporal L-band
signatures to a set of sigmoidal curves derived from the continuous logistic
model.
The relationship between the radiometric, and thus the physical, temperature
of perennial firn aquifer areas, as compared to other percolation facies
areas, forms the basis of the empirical algorithm. Miller et al. (2020)
hypothesized that the dominant control on the relatively slow exponential
rate of TB decrease over perennial firn aquifer areas is physical
temperature versus depth. L-band emission from the radiometrically warm
upper snow and firn layers decreases during the freezing season as embedded
ice structures slowly refreeze at increased depths below the ice sheet
surface. In the percolation facies, refreezing of seasonal meltwater results
in the formation of an intricate network of embedded ice structures that are
large (10–100 cm long, 10–20 cm wide; Jezek et al., 1994) relative to the
L-band wavelength (21 cm). Embedded ice structures induce strong volume
scattering (Rignot et al., 1993; Rignot, 1995) that decreases
TB (Zwally,
1977; Swift et al., 1985; Jezek et al., 2018).
Ice slabs are 1–16 m thick nearly continuous ice layers that can form
on spatial scales as large as tens of kilometers as a result of surface and
subsurface water-saturated snow and firn layers sequentially refreezing
following multiple melting seasons (Machguth et al., 2016; MacFerrin et al.,
2019). Over time, they become dense low-permeability solid-ice layers
overlying deeper permeable firn layers. Ice slabs have been identified via
field expeditions and airborne ice-penetrating radar surveys in the
lower-elevation (<2000 m a.s.l.) percolation facies of the GrIS at
depths from between 1 and 20 m beneath the ice sheet surface (MacFerrin et
al., 2019). They exist in areas that experience intense seasonal surface
melting and rain (excess melt of 266–573 mmw.e.yr-1; see MacFerrin et al., 2019, for a description) during the melting season and lower snow
accumulation (<572±32mmw.e.yr-1) during the freezing
season as compared to perennial firn aquifer areas (MacFerrin et al., 2019).
Lower snow accumulation in ice slab areas results in a seasonal snow layer
that is insufficiently thick to thermally insulate water-saturated firn
layers and seasonal meltwater is instead stored as embedded ice.
Refreezing of seasonal meltwater by the descending winter cold wave, and the subsequent
formation of ice slabs as well as other embedded ice structures within the
upper snow and firn layers, is the single source of latent heat. While ice
slab areas are radiometrically warmer than other percolation facies areas
with a lower volumetric fraction of embedded ice, they are radiometrically
colder than perennial firn aquifer areas. This results in typically higher
observed TB at the ice sheet surface during the freezing season in ice
slab areas, as compared to other percolation facies areas, but
typically lower observed TB as compared to perennial firn aquifer
areas. Similar to temporal L-band signatures over perennial firn aquifer
areas, temporal L-band signatures over ice slab areas are exponentially
decreasing during the freezing season; however, the rate of TB decrease
is slightly more rapid.
In this study, we exploit the observed sensitivity of L-band emission to
variability in the depth- and time-integrated dielectric and geophysical
properties of the percolation facies of the GrIS to map perennial firn
aquifer and ice slab areas together as a continuous englacial
hydrological system using satellite L-band microwave radiometry.
Methods
We adapt our previously developed empirical algorithm to map the extent of
Greenland's perennial firn aquifers (Miller et al., 2020) using a multi-year
calibration technique. We use enhanced-resolution L-band TVB imagery
(2015–2019) generated using observations collected over the GrIS by the
microwave radiometer on NASA's SMAP satellite (Long et al., 2019) and
airborne ice-penetrating radar surveys collected by NASA's OIB
campaigns (Rodriguez-Morales et al., 2014). First, we correlate (1)
a “firn saturation” parameter derived from a simple two-layer L-band
brightness temperature model; (2) maximum and (3) minimum TVB values;
and (4) exponentially decreasing temporal L-band signatures, with 5 years
of perennial firn aquifer detections (2010–2014) identified via the CReSIS
Accumulation Radar (AR) (Miège et al., 2016) and 3 years of
additional detections (2015–2017) more recently identified via MCoRDS
(Miller et al., 2020). Next, we extend our empirical algorithm to map the
extent of ice slab areas. We correlate the SMAP-derived parameters with 5 years of ice slab detections (2010–2014) recently identified via AR
(MacFerrin et al., 2019). Finally, we recalibrate our empirical model to
map the extent of perennial firn aquifer and ice slab areas over the
percolation facies. Interannual variability in extent is not resolved in
this study; however, it will be explored further in future work.
SMAP enhanced-resolution L-band TB imagery
The key science objectives of NASA's SMAP mission (https://smap.jpl.nasa.gov/, last access: 4 January 2022) are to map terrestrial soil moisture and
freeze/thaw state over Earth's land surfaces from space. However, the global
L-band TB observations collected by the SMAP satellite also have
cryospheric applications. Mapping perennial firn aquifer and ice slab areas
over Earth's polar ice sheets represents an interesting analog and an
innovative extension of the SMAP mission's science objectives. The SMAP
satellite was launched on 31 January 2015 and carries a microwave radiometer
that operates at an L-band frequency of 1.41 GHz (Enkentabi et al., 2010).
It is currently collecting observations of vertically and
horizontally polarized TB over Greenland. The surface incidence angle
is 40∘, and the radiometric accuracy is approximately 1.3 K
(Piepmeier et al., 2017).
The Scatterometer Image Reconstruction (SIR) algorithm was originally
developed to reconstruct coarse-resolution satellite radar scatterometry
imagery on a higher-spatial-resolution grid (Long et al., 1993; Early and
Long, 2001). The SIR algorithm has been adapted for coarse-resolution
satellite microwave radiometry imagery (Long and Daum, 1998; Long and
Brodzik, 2016; Long et al., 2019). The microwave radiometer form of the SIR
algorithm (rSIR) uses the measurement response function (MRF) for each
observation, which is a smeared version of the antenna pattern. Using the
overlapping MRFs, the rSIR algorithm reconstructs TB from the spatially
filtered low-resolution sampling provided by the observations. In effect, it
generates an MRF-deconvolved TB image. Combining multiple orbital passes
increases the sampling density, which improves both the accuracy and
resolution of the SMAP enhanced-resolution TB imagery (Long et al.,
2019).
Over Greenland, the rSIR algorithm combines satellite orbital passes that
occur between 08:00 and 16:00 local time of day to reconstruct SMAP
enhanced-resolution TB imagery twice-daily (i.e., morning and evening
orbital pass interval, respectively). TB imagery is projected on a
Northern Hemisphere (NH) Equal-Area Scalable Earth Grid (EASE-Grid 2.0;
Brodzik et al., 2012) at a 3.125 km rSIR grid cell spacing (e.g., Fig. 1).
The effective resolution for each grid cell is dependent on the number of
observations used in the rSIR reconstruction and is coarser than the rSIR
grid cell spacing. While the effective resolution of conventionally
processed SMAP TB imagery posted on a 25 km grid is approximately 30 km
(e.g., Fig. 1a), the effective resolution of SMAP enhanced-resolution
TB imagery posted on a 3.125 km grid is approximately 18 km (e.g., Fig. 1b), an improvement of 60 % (Long et al., 2019).
(a) Gridded (25 km gridding, 30 km effective resolution) and (b) enhanced-resolution (3.125 km gridding, 18 km effective resolution) L-band TVB imagery generated using observations collected on 15 April 2016 by the microwave radiometer on the SMAP satellite during the evening orbital pass interval over Greenland (Long et al., 2019) overlaid with the 2000 m a.s.l. contour (black line) and the 2500 m a.s.l. contour (dotted black line; Howat et al., 2014), the ice sheet extent (purple line; Howat et al., 2014), and the coastline (black peripheral line; Wessel and Smith, 1996). (c) SMAP enhanced-resolution L-band TVB imagery overlaid with AR- and MCoRDS-derived 2010–2017 perennial firn aquifer (blue shading; Miège et al., 2016), 2010–2014 ice slab (cyan shading; MacFerrin et al., 2019), and 2012 spatially coherent melt layer (white shading; Culberg et al., 2021) detections along OIB flight lines (black interior lines); zoom areas over southeastern Greenland (red box; Fig. 2a) and southwestern Greenland (orange box; Fig. 2b); and AR radargram transect A-B (red line; Fig. 3a) and C-D (orange line; Fig. 3b).
Enhanced-resolution (3.125 km gridding, 30 km effective resolution) L-band TVB imagery generated using observations collected on 15 April 2016 by the microwave radiometer on the SMAP satellite during the evening orbital pass interval over (a) southeastern Greenland (red box; Fig. 1c) and (b) southwestern Greenland (orange box; Fig. 1c,) (Long et al., 2019) overlaid with the ice sheet extent (purple line; Howat et al., 2014); the coastline (black peripheral line; Wessel and Smith, 1996); the AR- and MCoRDS-derived 2010–2017 perennial firn aquifer (blue shading; Miège et al., 2016), 2010–2014 ice slab (cyan shading; MacFerrin et al., 2019), and 2012 spatially coherent melt layer (white shading; Culberg et al., 2021) detections along OIB flight lines (black interior lines); AR radargram transect A-B (red line; Fig. 3a) and C-D (orange line; Fig. 3b); and SMAP Test Site A (blue circle; Fig. 4a), B (cyan circle; Fig. 4b), C (orange diamond; Fig. 4c), D (red triangle; Fig. 4d), and E (yellow circle; Fig. 4e).
As previously noted, for our analysis of the percolation facies we use SMAP
enhanced-resolution TVB imagery over the GrIS. Compared to the
horizontally polarized channel, the vertically polarized channel exhibits
decreased sensitivity to variability in the volumetric fraction of
meltwater, which is attributed to reflection coefficient differences between
channels (Miller et al., 2020). Using the vertically polarized channel also
results in a reduced chi-squared error statistic when fitting TVB
time series to the sigmoid function (Sect. 2.3.4). We construct
TVB imagery that alternates morning and evening orbital pass
observations annually, beginning and ending just prior to melt onset. The
Greenland Ice Mapping Project (GIMP) Land Ice and Ocean Classification Mask
and Digital Elevation Model (Howat et al., 2014) are projected on the NH
EASE-Grid 2.0 at a 3.125 km rSIR grid cell spacing. The derived ice mask
includes the Greenland Ice Sheet and the peripheral ice caps, including
Maniitsoq and Flade Isblink. TVB imagery between 1 April 2015 and 31
March 2019 is ice-masked, and an elevation for each rSIR grid cell is
calculated.
Airborne ice-penetrating radar surveys
AR and MCoRDS (Rodriguez-Morales et al., 2014) were flown over the GrIS on a
P-3 aircraft in April and May between 2010 and 2017. The AR instrument
operates at a center frequency of 750 MHz with a bandwidth of 300 MHz,
resulting in a range resolution in firn of 0.53 m
(Lewis et al., 2015). The collected data have an
along-track resolution of approximately 30 m with 15 m spacing between
traces in the final processed radargrams. At a nominal flight altitude of
500 m above the ice sheet surface, the cross-track resolution varies between
20 m for a smooth surface and 54 m for a rough surface with no appreciable
layover. The MCoRDS instrument operated at three different frequency
configurations: (1) a center frequency of 195 MHz with a bandwidth of 30 MHz
(2010–2014, 2017), (2) a center frequency of 315 MHz with a bandwidth
of 270 MHz (2015), and (3) a center frequency of 300 MHz with a bandwidth of
300 MHz (2016). The vertical range resolution in firn for each of these
frequency configurations is 5.3, 0.59, and 0.53 m, respectively (CReSIS,
2016). The collected data have an along-track resolution of approximately 25 m with 14 m spacing between traces in the final processed radargrams. At the
same nominal flight altitude of 500 m, the cross-track resolution varies
between 40 m for a smooth surface in the highest bandwidth configuration and
175 m for a rough surface with no appreciable layover in the lowest
bandwidth configuration.
The multi-year calibration technique uses perennial firn aquifer detections
previously identified along OIB flight lines via AR (2010–2014) and MCoRDS
(2015–2017) radargram profiles and the methodology described in Miège et
al. (2016). Bright lower reflectors that undulate with the local topographic
gradient underneath which reflectors are absent in the percolation facies
are interpreted as the upper surface of meltwater stored within perennial
firn aquifers (e.g., Fig. 3a). The large dielectric contrast between
refrozen and water-saturated firn layers results in high reflectivity at the
interface. However, the presence of meltwater increases attenuation,
limiting the downward propagation of electromagnetic energy through the
water-saturated firn layer. The total number of AR derived perennial firn
aquifer detections is 325 000, corresponding to a total extent of 98 km2. The analysis assumes a smooth surface, which is typical of much of
the percolation facies, and a grid cell size of 15m×20 m. The total
number of MCoRDS-derived perennial firn aquifer detections is 142 000,
corresponding to a total extent of 80 km2. This analysis also assumes a
smooth surface and a grid cell size of 14m×40 m. The combined total
number of grid cells (467 000) and total extent (178 km2) is
significantly larger than the total number of MCoRDS-derived grid cells
(78 000) and total extent (44 km2) calculated for 2016 (Miller et al.,
2020). Perennial firn aquifer detections are mapped in northwestern,
southern, and south and central eastern Greenland as well as the Maniitsoq
and Flade Isblink ice caps (Figs. 1c and 2a).
We project AR- and MCoRDS-derived
perennial firn aquifer detections on the NH EASE-Grid 2.0 at an rSIR grid
cell spacing of 3.125 km. Each rSIR grid cell has an extent of approximately
10 km2. The total number of rSIR grid cells with at least one perennial
firn aquifer detection is 800, corresponding to a total extent of 8000 km2. However, given the limited AR and MCoRDS grid cell coverage, less
than 1 % of the rSIR grid cell extent has airborne ice-penetrating radar
survey coverage. As compared to the total number of MCoRDS-derived perennial
firn aquifer detections (780) calculated for 2016 (Miller et al., 2020), the
total number of rSIR grid cells with at least one detection is only
increased by 20 for the multi-year calibration technique, corresponding to
an increased total extent of 200 km2.
AR radargram transect (a) A-B (red line; Fig. 2a)
collected on 22 April 2017 and (b) C-D (orange line;
Fig. 2b) collected on 5 May 2017 (Rodriguez-Morales et al.,
2014). (c) AR radargram transect A-B (red line) and C-D
(orange line) elevation profiles. The exceptionally bright upper surface-parallel reflector in panel (a) is a spatially coherent
melt layer. The bright lower reflector in panel (a) is the upper
surface of meltwater stored within a perennial firn aquifer. The
thick dark surface-parallel regions of low reflectivity in
panel (b) are ice slabs. The alternating sequences of bright and
dark surface-parallel reflectors in panel (b) are seasonal snow
accumulation layers.
We also use ice slab detections previously identified along OIB flight lines
via AR (2010–2014) radargram profiles and the methodology described in
MacFerrin et al. (2019) in the multi-year calibration technique. Thick dark
surface-parallel regions of low reflectivity in the percolation facies are
interpreted as ice slabs (e.g., Fig. 3b). The large dielectric contrast
between ice slabs and the overlying and underlying snow and firn layers
results in high reflectivity at the interfaces. However, electromagnetic
energy is not scattered or absorbed within the homogeneous ice slab; it
instead propagates downward through the layer and into the deeper firn
layers. The total number of AR-derived ice slab detections is 505 000,
corresponding to a total extent of 283 km2. Ice slab detections are
mapped in western, central and northeastern, and northern Greenland as well
as the Flade Isblink Ice Cap (Figs. 1c and 2b).
We project the AR-derived ice
slab detections on the NH EASE-Grid 2.0 at an rSIR grid cell spacing of
3.125 km. The total number of rSIR grid cells with at least one ice slab
detection is 2000, corresponding to a total extent of 20 000 km2.
However, less than 2 % of the rSIR grid cell extent has airborne
ice-penetrating radar survey coverage.
An advantage of the multi-year calibration technique as compared to the
single-coincident year calibration technique (Miller et al., 2020) is that
it increases the number of rSIR grid cells that can be assessed. It also
provides repeat targets that can account for variability in the depth- and
time-integrated dielectric and geophysical properties that influence the
radiometric temperature in stable perennial firn aquifer and ice slab areas.
Uncertainty is introduced by correlating the SMAP-derived parameters with
AR- and MCoRDS-derived detections that are not coincident in time. The
multi-year calibration technique assumes the extent of each area remains
stable, which is not necessarily the case as climate extremes (Cullather et
al., 2020) can influence each of these sub-facies. The assumption of
stability neglects boundary transitions in the extent of perennial firn
aquifer areas associated with refreezing of shallow water-saturated firn
layers, englacial drainage of meltwater into crevasses at the periphery
(Poinar et al., 2017, 2019), and transient upslope expansion
(Montgomery et al., 2017). Once formed, ice slabs are essentially permanent
features within the upper snow and firn layers of the percolation facies
until they are compressed into glacial ice. However, they may transition
into superimposed ice at the lower boundary of ice slab areas or rapidly
expand upslope, particularly following extreme melting seasons (MacFerrin et
al., 2019). Thus, we simply consider our mapped extent a high-probability
area for the preferential formation of each of these sub-facies, with
continued presence dependent on seasonal surface melting and snow
accumulation in subsequent years.
Annual perennial firn aquifer and ice slab detections that may introduce
significant uncertainty into the multi-year calibration technique include
those following the 2010 melting season, which was exceptionally long
(Tedesco et al., 2011); the anomalous 2012 melting season, during which
seasonal surface melting extended across 99 % of the GrIS (Nghiem et al.,
2012); and the 2015 melting season, which was especially intense in western
and northern Greenland (Tedesco et al., 2016). Following these extreme
melting seasons, significant changes in the dielectric and geophysical
properties likely occurred across large portions of the GrIS, including
perennial firn aquifer recharging resulting in increases in meltwater volume
and decreases in the depth to the upper surface of stored meltwater. The
upper snow and firn layers of the dry snow facies and percolation facies
were also saturated with relatively large volumetric fractions of meltwater
as compared to the negligible-to-limited volumetric fractions of meltwater
that percolates during more typical seasonal surface melting over the GrIS.
Seasonal meltwater was refrozen into spatially coherent melt layers
following the 2010 and 2012 melting seasons (Culberg et al., 2021) as well
as more recently following the 2015 and 2018 melting seasons identified as
part of the temporal L-band signature analysis in this study (Sect. 2.3.1). As compared to ice slabs, which are dense low-permeability solid-ice
layers, spatially coherent melt layers are a network of embedded ice
structures primarily consisting of discontinuous horizontally oriented ice
layers and ice lenses sparsely connected via vertically oriented ice pipes
(Culberg et al., 2021). Spatially coherent melt layers are relatively thin
(0.2 cm–2 m) and can rapidly form across the high-elevation (up to 3200 m a.s.l.) dry snow facies at depths of less than 1 m beneath the ice sheet
surface following a single extreme melting season. They can further merge
together into thicker solid-ice layers following multiple extreme melting
seasons. Spatially coherent melt layers are exceptionally bright in AR
radargrams (e.g., Fig. 3a). The large dielectric contrast between the
spatially coherent melt layer and the overlying, underlying, and interior
snow and firn layers results in high reflectivity at the interfaces.
However, electromagnetic energy still propagates downward through the high-reflectivity layer into the deeper firn layers. Culberg et al. (2021)
recently demonstrated mapping the extent of spatially coherent melt layers
formed following the 2012 melting season (Nghiem et al., 2012) via AR
(Figs. 1c and 2).
Empirical algorithmTemporal L-band signatures
TB expresses the satellite-observed magnitude of thermal emission and is
influenced by the microwave instrument's observation geometry as well as the
depth- and time-integrated dielectric and geophysical properties of the ice
sheet (Ulaby et al., 2014). The most significant geophysical property
influencing TB is the volumetric fraction of meltwater within the snow
and firn pore space (Mätzler and Hüppi, 1989). During the melting
season, the upper snow and firn layers of the percolation facies are
saturated with large volumetric fractions of meltwater that percolates
vertically into the deeper firn layers (Benson, 1960; Humphrey et al.,
2012). Increases in the volumetric fraction of meltwater result in rapid
relative increases in the imaginary part of the complex dielectric constant
(Tiuiri et al., 1984). This typically increases TB and decreases
volume scattering and penetration depth. The L-band penetration depth can
rapidly decrease from tens to hundreds of meters to less than a meter,
dependent on the local snow and firn conditions. During the freezing season,
surface and subsurface water-saturated snow and firn layers and embedded ice
structures subsequently refreeze. Decreases in the volumetric fraction of
meltwater result in rapid relative decreases in the imaginary part of the
complex dielectric constant. This decreases TB and increases volume
scattering and penetration depth. The L-band penetration depth increases
back to tens to hundreds of meters on variable timescales.
We analyze melting and freezing seasons in temporal L-band signatures
exhibited in TVB time series over and near the AR- and
MCoRDS-derived perennial firn aquifer and ice slab detections projected on
the NH EASE-Grid 2.0 (Fig. 4 and Table 1). We project ice surface temperature
observations calculated using thermal infrared brightness temperature
collected by the Moderate Resolution Imaging Spectroradiometer (MODIS) on
the Terra and Aqua satellites (Hall et al., 2012) on the NH EASE-Grid 2.0 at
a 3.125 km rSIR grid cell spacing. We then derive melt onset and surface
freeze-up dates for each rSIR grid cell using the methodology described in
Miller et al. (2020). We set a threshold of ice surface temperature
>-1∘C for meltwater detection (Nghiem et al.,
2012), consistent with the ±1∘C accuracy of the ice
surface temperature observations. For temperatures that are close to
0 ∘C, ice surface temperatures are closely compatible with
contemporaneous NOAA near-surface air temperature observations (Shuman et
al., 2014). Melt onset and surface freeze-up dates are overlaid on
TVB time series to partition the melting and freezing seasons. Melt
onset dates typically occur between April and July, and surface freeze-up
dates typically occur between July and September. The melting season
increases in duration moving downslope from the dry snow facies and ranges
from a single day in the highest elevations (>2500 m) of the
percolation facies to 150 d in the ablation facies. Similarly, the
freezing season decreases in duration moving downslope and ranges
between 215 and 365 d.
Temporal L-band signatures that alternate morning (white symbols) and
evening (colored symbols) orbital pass interval enhanced-resolution
TVB generated using observations collected over the GrIS by the microwave radiometer on the SMAP satellite (Long et al., 2019) over (a) SMAP Test Site A (blue circles; Fig. 2a), (b) B (cyan circles; Fig. 2b), (c) C (orange diamonds; Fig. 2b), (d) D (red triangles; Fig. 2a), and (e) E (yellow circles; Fig. 2b). Melt onset (red lines) and surface freeze-up (blue lines) dates derived from thermal infrared TB collected by MODIS on the Terra and Aqua satellites (Hall et al., 2012). AR radargram transect A-B (red dashed line; Fig. 3a) collected on 22 April 2017, and C-D (orange dashed line; Fig. 3b) collected on 5 May 2017.
MODIS-derived total number of days in the melting and freezing seasons; SMAP-derived maximum vertically polarized L-band brightness temperature (TV,maxB); minimum vertically polarized L-band brightness temperature (TV,minB); timescales of exponential decrease following the surface freeze-up date for perennial firn aquifer, ice slab, percolation facies, dry snow facies, and wet snow facies areas.
Over perennial firn aquifer areas (e.g., Fig. 4a, SMAP Test Site A:
66.2115∘ N, 39.1795∘ W; 1625 m a.s.l.), maximum
TVB (TV,maxB) values are radiometrically warm during the
melting season. Vertically percolating meltwater and gravity-driven
meltwater drainage seasonally recharges perennial firn aquifers at depth
(Fountain and Walder, 1998). Minimum TVB (TV,minB)
values remain radiometrically warm during the freezing season as a result of
latent heat continuously released by the slow refreezing of the deeper firn
layers that are saturated with large volumetric fractions of meltwater
(Miller et al., 2020). Temporal L-band signatures exhibit slow exponential
decreases and approach, and sometimes achieve, stable TVB values.
TVB can decrease by more than 50 K during the freezing season, which
represents the descent of the upper surface of stored meltwater by depths of
meters to tens of meters beneath the ice sheet surface (Miège et al.,
2016).
Over ice slab areas (e.g., Fig. 4b, SMAP Test Site B: 66.8850∘ N,
42.7765∘ W; 1817 m a.s.l.), TV,maxB values are typically
radiometrically colder than over perennial firn aquifer areas during the
melting season. The presence of dense low-permeability solid-ice layers
reduces the snow and firn pore space available to store seasonal meltwater
at depth. Meltwater may alternatively run off ice slabs downslope towards the
wet snow facies. TV,minB values are also typically radiometrically
colder than over perennial firn aquifer areas during the freezing season as
a result of the absence of meltwater stored at depth. Temporal L-band
signatures exhibit exponential decreases that are slightly more rapid than
over perennial firn aquifer areas and often achieve stable TVB
values.
Over other percolation facies areas (e.g., Fig. 4c, SMAP Test Site C:
66.9024∘ N, 44.7528∘ W; 2350 m a.s.l.), where seasonal
meltwater is fully refrozen and stored exclusively as embedded ice,
TV,maxB values are typically radiometrically colder than over
perennial firn aquifer and ice slab areas during the melting season.
TV,minB values are also typically radiometrically cold during the
freezing season. Temporal L-band signatures exhibit rapid exponential
decreases and achieve stable TVB values. However, over the highest
elevations (>2500 m a.s.l.) of the percolation facies
approaching the dry snow line, where seasonal surface melting and the
formation of embedded ice structures is limited, TV,minB values remain
radiometrically warm during the freezing season. TVB decreases,
often step responses exceeding 10 K, are a result of an increase in volume
scattering from newly formed embedded ice structures within a spatially
coherent melt layer. Temporal L-band signatures that increase several K on
timescales of years indicate the burial of spatially coherent melt layers
formed following the 2010, 2012, 2015, and 2018 melting seasons by snow
accumulation.
Exponentially decreasing temporal L-band signatures transition smoothly
between perennial firn aquifer, ice slab, and other percolation facies areas
– there are no distinct temporal L-band signatures that delineate
boundaries between these sub-facies. Boundary transitions between the dry
snow facies and wet snow facies, however, are delineated above and below
the percolation facies. Over the dry snow facies (e.g., Fig. 4d, SMAP Test
Site D: 66.3649∘ N, 43.2115∘ W; 2497 m a.s.l.),
TV,maxB and TV,minB values are radiometrically warm during
the melting and freezing seasons. Temporal L-band signatures that increase
on timescales of years are observed throughout the dry snow facies at
elevations as high as Summit Station (3200 m a.s.l.) and indicate the burial
of the spatially coherent melt layer formed following the 2012 melting
season (Nghiem et al., 2012) by snow accumulation (Culberg et al., 2021).
Over the wet snow facies (e.g., Fig. 4e, SMAP Test Site E:
67.3454∘ N, 48.4789∘ W; 1469 m a.s.l.), where
seasonal meltwater is fully refrozen and stored as superimposed ice,TV,maxB
values are radiometrically warm during the melting season. As compared to
the percolation facies, where temporal L-band signatures exhibit rapid
increases following melt onset, temporal L-band signatures reverse and
exhibit rapid decreases. These reversals are a result of high reflectivity
and attenuation at the fully water saturated snow layer and/or at the wet
rough superimposed ice–air interface. Meltwater runs off superimposed ice
downslope towards the ablation facies. TV,minB values remain
radiometrically warm during the freezing season. Temporal L-band signatures
exhibit rapid increases and achieve stable TVB values.
Two-layer L-band brightness temperature model
Based on our analysis of TV,maxB and TV,minB in temporal
L-band signatures over the percolation facies (Sect. 2.3.1), we derive a
firn saturation parameter using a simple two-layer L-band brightness
temperature model (Ashcraft and Long, 2006). The firn saturation parameter
is similar to the “melt intensity” parameter derived in Hicks and Long
(2011) that uses enhanced-resolution vertically polarized Ku-band radar
backscatter imagery (2003) collected by the SeaWinds radar scatterometer
that was flown in tandem on NASA's Quick Scatterometer (QuikSCAT) satellite
(Tsai et al., 2000) and JAXA's Advanced Earth Observing Satellite 2
(ADEOS-II) (Freilich et al., 1994). We use the firn saturation parameter to
estimate the maximum seasonal volumetric fraction of meltwater within the
saturated upper snow and firn layers of the percolation facies using
TV,maxB and TV,minB values extracted from TVB time
series. We calculate the firn saturation parameter for each rSIR grid cell
within the ice-masked extent of the GrIS as part of our adapted empirical
algorithm (Sect. 2.3.4).
We assume a base layer underlying a water-saturated firn layer with a given
depth and volumetric fraction of meltwater. Each of the layers is
homogenous. The ice sheet is discretely layered to calculate TVB at an oblique incidence angle (Eq. 1). Emission from the base layer is a
function of both the macroscopic roughness and the dielectric properties of
the layer. It occurs in conjunction with volume scattering at depth and is
locally dependent on embedded ice structures, spatially coherent melt
layers, ice slabs, and perennial firn aquifers. Reflectivity at depth (i.e.,
at the base layer–water-saturated firn layer interface) and at the ice
sheet surface (i.e., at the water-saturated firn layer–air interface) is
neglected. The contribution from each layer is individually calculated.
The two-layer L-band brightness temperature model is represented
analytically by
TV, maxB=T(1-e-κedsecθ)+TV, minBe-κedsecθ,
where TV,maxB is the maximum vertically polarized L-band brightness
temperature at the ice sheet surface and represents emission from the
maximum seasonal volumetric fraction of meltwater stored within the
water-saturated firn layer. TV,minB is the minimum
vertically polarized L-band brightness temperature emitted from the base
layer. T is the physical temperature of the water-saturated firn layer,
θ is the transmission angle, κe is the extinction
coefficient, and d is depth.
We invert Eq. (1) and solve for the firn saturation parameter (ξ)
ξ=lnTV,maxB-TTV,minB-Tcosθ,
where ξ=κed. The maximum vertically polarized L-band
brightness temperature asymptotically approaches the physical temperature of
the water-saturated firn layer as the extinction coefficient and the depth
of the water-saturated firn layer increases. For simplicity, we follow Jezek
et al. (2015) and define the extinction coefficient as the sum of the
Raleigh scattering coefficient (κs) and the absorption
coefficient (κa). This assumes scattering from snow grains, which
are small (millimeter scale) relative to the L-band wavelength (21 cm), and
neglects Mie scattering from large (centimeter scale) embedded ice
structures. However, for water-saturated firn, absorption dominates over
scattering, and increases in the extinction coefficient are controlled by
the volumetric fraction of meltwater (mv).
We assume that thicker water-saturated firn layers with larger volumetric
fractions of meltwater generate higher firn saturation parameter values.
However, the thickness of the water-saturated firn layer is limited by the
L-band penetration depth. Theoretical L-band penetration depths calculated
for a water-saturated firn layer range from between 10 m for small
volumetric fractions of meltwater (mv<1 %) and 1 cm for
large volumetric fractions of meltwater (mv=20 %) (Fig. 5). Large
volumetric fractions of meltwater result in high reflectivity and
attenuation at the water-saturated firn layer–air interface and a
radiometrically cold firn layer.
Theoretical L-band penetration depths for a uniform layer of (a)
refrozen and (b) water-saturated firn. Penetration depths
(1/(κs+κa)) are calculated as a function of the
Raleigh scattering coefficient (κs; Eq. 8) and the
absorption coefficient (κa; Eq. 10). The complex dielectric
constant is calculated using the empirically derived models described
in Tiuri et al. (1984). Refrozen firn penetration depths are
calculated as a function of firn density (ρfirn), and the
curves are plotted for snow grain radii (r) set to r=0.5 mm
(upper curve) and r=4 mm (lower curve). Water-saturated firn
penetration depths are calculated as a function of the volumetric
fraction of meltwater (mv), and the curves are plotted for firn
density set to ρfirn=400kgm-3 (upper curve) and ρfirn=917kgm-3 (lower curve). Given the complexity of modeling embedded ice structures, they are excluded from the penetration depth calculation. Increases in the volumetric fraction of embedded ice within the firn will result in an increase in volume scattering, which will decrease and compress the distance between the penetration depth curves for both refrozen and water-saturated firn.
Continuous logistic model
We adapt our previously developed empirical algorithm to map the extent of
Greenland's perennial firn aquifers (Miller et al., 2020) to also map the
extent of ice slab areas. The empirical algorithm is derived from the
continuous logistic model, which is based on a differential equation that
models the decrease in physical systems as a function of time using a set of
sigmoidal curves. These curves begin at a maximum value with an initial
interval of decrease that is approximately exponential. Then, as the
function approaches its minimum value, the decrease slows to approximately
linear. Finally, as the function asymptotically reaches its minimum value,
the decrease exponentially tails off and achieves stable values. We use the
continuous logistic model to parametrize the refreezing rate within the
water-saturated upper snow and firn layers of the percolation facies using
TVB time series that are partitioned using TV,maxB and
TV,minB values. We calculate the refreezing rate for each rSIR grid
cell within the percolation facies extent as part of our adapted empirical
algorithm (Sect. 2.3.4).
The continuous logistic model is described by a differential equation known
as the logistic equation
dxdt=ζx(1-x)
that has the solution
x(t)=11+(1xo-1)e-ζt,
where xo is the function's initial value, ζ is the function's
exponential rate of decrease, and t is time. The function x(t) is also known as
the sigmoid function. We use the sigmoid function to model the exponentially
decreasing temporal L-band signatures observed over the percolation facies
as a set of decreasing sigmoidal curves.
We first normalize TVB time series for each rSIR grid cell
TV,NB(t)=TVB(t)-TV,minBTV,maxB-TV,minB,
where TV,minB is the minimum vertically polarized L-band brightness
temperature, and TV,maxB is the maximum vertically polarized L-band
brightness temperature. We then apply the sigmoid fit
TV,NBt∈[tmax,tmin]=11+(1TV,NB(tmax)-1)e-ζt.TV,NBt∈tmax,tmin is the normalized vertically polarized L-band brightness temperature
on the time interval t∈[tmax,tmin], where
tmax is the time the function achieves a maximum value, and
tmin is the time the function achieves a minimum value. The initial
normalized vertically polarized L-band brightness temperature
(TV,NB(tmax)) is the function's maximum value. The
final normalized vertically polarized L-band brightness temperature
(TV,NB(tmin)) is the function's minimum value. The function's
exponential rate of decrease represents the refreezing rate parameter
(ζ). An example set of simulated sigmoidal curves is shown in Fig. 6.
Example set of simulated sigmoidal curves that represent our model of the exponentially decreasing temporal L-band signatures predicted over the percolation facies. The initial normalized vertically polarized L-band brightness temperature was fixed at a value of TV,NB(tmax)=0.99, and the time interval was set to a value of t∈[tmax,tmin]=300 observations. The refreezing rate parameter was set to values between ζ=[-1,0] incremented by steps of 0.02. The blue lines correspond to the interval ζ∈[-0.04,-0.02] and produce curves similar to those observed over perennial firn aquifer areas. The cyan lines correspond to the interval ζ∈[-0.06,-0.03] and produce curves similar to those observed over ice slab areas. The black line is the observed lower bound (ζ=-0.09) of the refreezing rate parameter of partitioned TVB time series iteratively fit to the sigmoid function (Sect. 2.3.4).
SMAP-derived extent mapping
Our adapted empirical algorithm is implemented in two steps: (1) mapping the
extent of the percolation facies using the firn saturation parameter derived
from the simple two-layer L-band brightness temperature model (Sect. 2.3.2) and (2) mapping the extent of perennial firn aquifer and ice slab
areas over the percolation facies using the continuous logistic model
(Sect. 2.3.3) we calibrate using airborne ice-penetrating radar surveys
(Sect. 2.2).
Using Eq. (2), we first set a threshold for the firn saturation parameter
(ξT) defined by the relationship
ξT=(κs+κa)d≤ξ.
We calculate the Raleigh scattering coefficient (κs) in Eq. (7) using
κs=Nd83ko4r6εr-1εr+22,
where Nd is the particle density, ko is the wave number of the
background medium of air, r is the snow grain radius set to r=2 mm,
and εr is the complex dielectric constant. The particle density is
defined by
Nd=ρfirnρice143πr3,
where ρfirn is firn density set to ρfirn=400kgm-3,
and ρice is ice density set to ρice=917kgm-3. Our
grain radius and firn density estimates are consistent with measurements
within the upper snow and firn layers of the percolation facies of southeastern Greenland at the Helheim Glacier field site (Fig. 2a, blue circle),
where in situ perennial firn aquifer measurements have recently been
collected (Miller et al., 2017).
We calculate the absorption coefficient (κa) in Eq. (7) using
κa=-2koIεr,
where I{} represents the imaginary part. We calculate the
complex dielectric constant of the water-saturated firn layer in Eqs. (8) and
(10) using the empirically derived models described in Tiuri et al. (1984). We set the volumetric fraction of meltwater to mv=1 %. We
set the depth of the water-saturated firn layer in Eq. (7) to d=1 m. These
values are consistent with typical lower frequency (e.g., 37, 13.4,
19 GHz) passive (e.g., Mote et al., 1995; Abdalati and Steffen, 1997;
Ashcraft and Long, 2006) and active (e.g., Hicks and Long, 2011) microwave
algorithms used to detect seasonal surface melting over the GrIS. Using the
results of Eqs. (7–10), we calculate the firn saturation parameter
threshold to be ξT=0.1.
The first step in our adapted empirical algorithm is to map the extent of
the percolation facies. For each rSIR grid cell within the ice-masked
extent of the GrIS, we smooth the corresponding TVB time series
using a 14-observation (1 week) moving window. We extract the minimum
vertically polarized L-band brightness temperature (TV,minB) and
the maximum vertically polarized L-band brightness temperature
(TV,maxB). We set the physical temperature of the water-saturated
firn layer to T=273.15 K and the transmission angle to θ=40∘. We then calculate the firn saturation parameter (ξ)
using Eq. (2). If the calculated firn saturation parameter exceeds the firn
saturation parameter threshold, the rSIR grid cell is converted to a binary
parameter to map the total extent of the percolation facies.
We note that smoothing TVB time series will mask brief low-intensity
seasonal surface melting that occurs in the high-elevation (>2500 m) percolation facies, where seasonal meltwater is rapidly refrozen
within the colder snow and firn layers (e.g., Fig. 4d). Thus, the calculated
firn saturation parameter will not exceed the firn saturation parameter
threshold, and these rSIR grid cells are excluded from the algorithm. The
exclusion of rSIR grid cells in the high-elevation percolation facies is not
expected to have a significant impact on our results as our algorithm
targets rSIR grid cells in areas that experience intense seasonal surface
melting. The exclusion of rSIR grid cells may slightly underestimate the
mapped percolation facies extent.
The second step in our adapted empirical algorithm is to map the extent of
perennial firn aquifer and ice slab areas over the percolation facies. For
each rSIR grid cell within the mapped percolation facies extent, we
normalize the corresponding TVB time series (TV,NB(t)) using
Eq. (5). We then extract the initial normalized vertically polarized L-band
brightness temperature (TV,NB(tmax)) and the final normalized
vertically polarized L-band brightness temperature
(TV,NB(tmin)) and partition TV,NB(t) on the time
interval t∈[tmax,tmin]. We smooth
TV,NBt∈tmax,tmin using a 56-observation (4 week) moving window. The sigmoid fit is
then iteratively applied using Eq. (6). Smoothing reduces the chi-squared
error statistic when fitting TV,NBt∈tmax,tmin to the sigmoid function. We fix the initial
normalized vertically polarized L-band brightness temperature at
TV,NB(tmax)=0.99, which provides a uniform parameter space in
which the refreezing rate parameter (ζ) can be
analyzed. Variability in TV,NB(tmax) is controlled by the
volumetric fraction of meltwater within the upper snow and firn layers of
the percolation facies and is accounted for in the firn saturation
parameter (ξ), which is analyzed separately.
TV,NBt∈[tmax,tmin] values iteratively fit to the sigmoid function converge quickly (i.e.,
algorithm iterations I∈[5,15]), and observations are a
good fit (i.e., chi-squared error statistic is χ2∈[0,0.1]).
Using the SMAP-derived TV,NB(tmax) and
TV,NB(tmin), rather than the MODIS-derived initial normalized
vertically polarized L-band brightness temperature at the surface freeze-up
date (TV,NB(tsfu)), and final normalized vertically polarized
L-band brightness temperature at the melt onset date
(TV,NB(tmo)) that were used in the empirical algorithm
described in Miller et al. (2020), has several advantages. The key advantage
of this approach is that maps can be generated using TB imagery
collected from a single satellite, which simplifies our adapted empirical
algorithm. Another advantage is that unlike TB collected at
shorter-wavelength thermal infrared frequencies (e.g., MODIS), TB
collected at longer-wavelength microwave frequencies (e.g., SMAP) is not
sensitive to clouds, which eliminates observational gaps and cloud
contamination and provides more accurate time series partitioning and more
robust curve fitting.
We calibrate our adapted empirical algorithm using the AR- and
MCoRDS-derived perennial firn aquifer and ice slab detections projected on
the NH EASE-Grid 2.0. For each rSIR grid cell with at least one detection,
we extract the correlated maximum vertically polarized L-band brightness
temperature (TV,maxB), the minimum vertically polarized L-band
brightness temperature (TV,minB), the firn saturation parameter
(ξ), and the refreezing rate parameter (ζ). For each of the
extracted calibration parameters, we calculate the standard deviation
(σ). Thresholds of ±2σ are set in an attempt to
eliminate peripheral rSIR grid cells near the ice sheet edge and near the
boundaries of each sub-facies, where L-band emission can be influenced by
morphological features, such as crevasses, and superimposed and glacial ice, and
spatially integrated with emission from rock, land, the ocean, and adjacent
percolation facies and wet snow facies areas. The calibration parameter
intervals are given in Table 2. We apply the calibration to each
rSIR grid cell within the percolation facies extent. If the extracted
calibration parameters are within the intervals, the rSIR grid cell is
converted to a binary parameter to map the total extent of each of these
sub-facies.
SMAP-derived calibration parameter intervals used for mapping perennial firn aquifer and ice slab extents.
ξTV,maxBTV,minBζ(K)(K)Perennial firn aquifers0.2–2.8200–275180–250-0.04 to -0.02Ice slabs0.1–2170–260130–240-0.06 to -0.03
Miller et al. (2020) cited significant uncertainty in the SMAP-derived
perennial firn aquifer extent as a result of the lack of a distinct temporal
L-band signature delineating the boundary between perennial firn aquifer
areas and adjacent percolation facies areas. In this study, similar
uncertainty exists in the SMAP-derived perennial firn aquifer and ice slab
extents. This uncertainty could, at least in part, be a result of the rSIR
algorithm. An rSIR grid cell corresponds to the weighted average of TB
over SMAP's antenna footprint (Long et al., 2019). The weighting is the grid
cell's spatial response function (SRF), which is approximately 18 km (i.e.,
the effective resolution) in diameter. The SRF is centered on the rSIR grid
cell. Since the effective resolution (i.e., the size of the 3 dB contour of
the SRF) is greater than the rSIR grid cell spacing, the rSIR grid cell SRF's
overlap and the TB values are not statistically independent.
This uncertainty, however, could also have a geophysical basis, as it is
unlikely that the boundaries between sub-facies as well as between facies
are distinct. The thickness of the water-saturated firn layer or ice slab
may thin and taper off at the periphery, and sub-facies and facies may
become spatially scattered and merge together.
The limited extent (AR, 15m×20 m; MCoRDS, 14m×40 m) of the airborne
ice-penetrating radar surveys as compared to the rSIR grid cell extent
(3.125 km) and the effective resolution of the SMAP enhanced-resolution
TVB imagery is also cited in Miller et al. (2020) as a source of
uncertainty in the empirical algorithm. In this study, similar uncertainty
exists in our adapted empirical algorithm. The total rSIR grid cell extent
with airborne ice-penetrating radar survey coverage is less than 2 %.
Thus, 98 % of the total rSIR grid cell extent from which the SMAP-derived
calibration parameter intervals are extracted is unknown. Calculating the
total rSIR grid cell extent where detections are absent along OIB flight
lines and statistically integrating this calculation into the multi-year
calibration technique may help reduce the uncertainty, particularly the
significant uncertainty in the interannual variability in extent, which we
have yet to resolve. A sensitivity analysis suggests that even small changes
in the SMAP-derived calibration parameter intervals (i.e., several K for TV,minB and TV,maxB, several tenths of a percentage point
for ξ, and several hundredths of a percentage point for ζ) can
result in variability in the mapped extents of hundreds of square
kilometers and boundary transitions between perennial firn aquifer and ice
slab areas. Thus, the mapped extent of each of these sub-facies should
simply be considered an initial result demonstrating the potential of our
adapted empirical algorithm for future work.
Results and discussion
The SMAP-derived maximum vertically polarized L-band brightness temperature
values generated by our adapted empirical algorithm range from between
TV,maxB=150 and 275 K, and the minimum vertically polarized
L-band brightness temperature values range from between
TV,minB=130 and 250 K. These values are consistent with the
range of TV,maxB and TV,minB values given in the temporal
L-band signature analysis (Table 1). Firn saturation parameter values range
from between ξ=0.1 and 4.0. Refreezing rate parameter values range
from between ζ=-0.09 and -0.01. The observed lower bound (ζ=-0.09) of the refreezing rate parameter is significantly higher than the
predicted lower bound (ζ=-1) in our example set of simulated
sigmoidal curves (black line, Fig. 6).
The SMAP-derived perennial firn aquifer, ice slab, and percolation facies
extents are shown in Figs. 7a–9a. The percolation facies extent (5.8×105km2) is mapped at elevations between 500 and 3000 m a.s.l. and extends over 32 % of the GrIS extent (1.8×106km2). The perennial firn aquifer extent (64 000 km2) is mapped at
elevations between 600 and 2600 m a.s.l. and extends over 11 % of
the percolation facies extent and 4 % of the GrIS extent. Predominately
high TV,maxB, TV,minB, ξ, and ζ values
mapped within the perennial firn aquifer extent indicate the widespread
presence of thicker water-saturated firn layers with larger volumetric
fractions of meltwater that are radiometrically warm during both the melting
and freezing seasons and have extended refreezing rates. The ice slab extent
(76 000 km2) is mapped at elevations between 800 and 2700 m a.s.l. and extends over 13 % of the percolation facies extent and 4 % of the GrIS extent. As compared to perennial firn aquifer areas,
decreased TV,maxB, TV,minB, ξ, and ζ values
in ice slab areas indicate the presence of thinner water-saturated firn
layers with lower volumetric fractions of meltwater that are radiometrically
colder and have slightly more rapid refreezing rates. Combined together,
the total extent (140 000 km2) is the equivalent of 24 % of the
percolation facies extent and 10 % of the GrIS extent. The extents of
these sub-facies are generally isolated and somewhat scattered within the
percolation facies. However, in several areas in south, south and central
eastern, and northern Greenland, the sequential formation of sub-facies and facies (dry snow facies–percolation facies–ice slab–perennial firn
aquifer–ablation facies) are mapped.
(a) SMAP-derived perennial firn aquifer (blue shading), ice slab (cyan shading), and percolation facies (purple shading) extents (2015–2019) generated by the adapted empirical algorithm as well as the 2000 m a.s.l. contour (black line) and the 2500 m a.s.l. contour (black dotted line; Howat et al., 2014) overlaid on the 2015 MODIS Mosaic of Greenland (MOG) image map (Haran et al., 2018). (b) SMAP-derived extents are overlaid with AR- and MCoRDS-derived 2010–2017 perennial firn aquifer (blue shading; Miège et al., 2016), 2010–2014 ice slab (cyan shading; MacFerrin et al., 2019), and 2012 spatially coherent melt layer (white shading; Culberg et al., 2021) detections along OIB flight lines (black interior lines); AR radargram transect A-B (red line; Fig. 3a) and C-D (orange line; Fig. 3b).
The SMAP-derived perennial firn aquifer (blue shading), ice slab (cyan shading), and percolation facies (purple shading) extents (2015–2019) generated by the adapted empirical algorithm over southeastern Greenland (red box; Fig. 1c) as well as the 2000 m a.s.l. contour (black line) and the 2500 m a.s.l. contour (black dotted line; Howat et al., 2014) overlaid on the 2015 MODIS MOG image map (Haran et al., 2018). (b) The SMAP-derived percolation facies extent is overlaid with AR- and MCoRDS-derived 2010–2017 perennial firn aquifer (blue shading; Miège et al., 2016), 2010–2014 ice slab (cyan shading; MacFerrin et al., 2019), and 2012 spatially coherent melt layer (white shading; Culberg et al., 2021) detections along OIB flight lines (black lines); AR radargram transect A-B (red line; Fig. 3a); and SMAP Test Site A (blue circle; Fig. 4a) and D (red triangle; Fig. 4d).
(a) SMAP-derived perennial firn aquifer (blue shading), ice slab (cyan shading), and percolation facies (purple shading) extents (2015–2019) generated by the adapted empirical algorithm over southwestern Greenland (orange box; Fig. 1c) as well as the 2000 m a.s.l. contour (black line) and the 2500 m a.s.l. contour (black dotted line; Howat et al., 2014) overlaid on the 2015 MODIS MOG image map (Haran et al., 2018). (b) SMAP-derived percolation facies extent is overlaid with AR- and MCoRDS-derived 2010–2017 perennial firn aquifer (blue shading; Miège et al., 2016), 2010–2014 ice slab (cyan shading; MacFerrin et al., 2019), and 2012 spatially coherent melt layer (white shading; Culberg et al., 2021) detections along OIB flight lines (black interior lines); AR radargram transect C-D (orange line; Fig. 3b); and SMAP Test Site B (cyan circle; Fig. 4b), C (orange diamond; Fig. 4c), and E (yellow circle; Fig. 4e).
Figures 7b–9b show perennial firn aquifers, ice slabs, and spatially coherent
melt layers detected by airborne ice-penetrating radar surveys overlaid on
the SMAP-derived percolation facies extent. The SMAP-derived
perennial firn aquifer extent mapped in southern as well as south and central
eastern Greenland is consistent with the AR- and MCoRDS-derived perennial
firn aquifer detections. Additional smaller perennial firn aquifer areas are
mapped in northern Greenland. The SMAP-derived ice slab extent mapped in
southwestern and central eastern Greenland is generally consistent with
the spatial patterns of the AR-derived ice slab detections but is
significantly expanded upslope in each of these areas. In northern
Greenland, perennial firn aquifers areas are alternatively mapped, and
additional expansive ice slab areas are mapped upslope of perennial firn
aquifer areas. Additional smaller ice slab areas are mapped in south and
southeastern Greenland. We note that the AR- and MCoRDS-derived perennial
firn aquifer and ice slab detections are limited in space and time,
particularly in northern Greenland, with a time interval as large as 9 years between the airborne ice-penetrating radar surveys and the SMAP
enhanced-resolution TVB imagery we use in our adapted empirical
algorithm. In western and northern Greenland, the 2015 melting season was
especially intense (Tedesco et al., 2016). And, in northern Greenland, the
ablation facies have recently (2010–2019) increased in extent (Noël et
al., 2019), and supraglacial lakes have recently (2014–2019) advanced inland
(Turton et al., 2021), indicating a possible geophysical basis for the
observed formation, boundary transitions, and expansion. Neither perennial
firn aquifer nor ice slab areas are mapped on the Maniitsoq and Flade Isblink
ice caps, where spatially integrated L-band emission results in calibration
parameter values outside the defined intervals for each of these sub-facies.
Although the AR-derived spatially coherent melt layer detections are often
observed to be adjacent to perennial firn aquifer and ice slab areas, these
sub-facies were masked in the original airborne ice-penetrating radar survey
analysis by Culberg et al. (2021). Spatially coherent melt layers often
overlay perennial firn aquifers (e.g., Fig. 3a) and merge with ice slabs
(Culberg et al., 2021; Fig. 4).
Shallow buried supraglacial lakes have recently been identified within the
percolation facies of western, northern, and north and central eastern
Greenland using airborne ice-penetrating radar surveys (Koenig et al., 2015)
and satellite synthetic aperture radar imagery (Miles et al., 2017;
Schröder et al., 2020; Dunmire et al., 2021). These buried supraglacial
lakes are within the SMAP-derived perennial firn aquifer and ice slab
extents but are not expected to significantly influence L-band
emission in these areas for two reasons. (1) As compared to SMAP's 18 km
effective resolution, the mean extent of buried supraglacial lakes is limited (less
than 1 km2), and they are sparsely distributed in perennial firn
aquifer and ice slab areas (Dunmire et al., 2021). (2) Supraglacial lakes
form during the melting season as a result of meltwater storage within
topographic depressions at the ice sheet surface (Echelmeyer et al., 1991).
Similar to subglacial lakes (Jezek et al., 2015) and perennial firn aquifers
(Miller et al., 2020), supraglacial lakes represent radiometrically cold
near-surface meltwater reservoirs. Upwelling L-band emission from deeper
firn layers, superimposed and/or glacial ice, and the underlying bedrock are
effectively blocked by high reflectivity and attenuation at the interface
between the lake bottom and the underlying impermeable layer. This results
in low observed TB at the upper surface of meltwater stored within
supraglacial lakes. During the freezing season, the upper surface of
meltwater refreezes and forms a partial or solid-ice cap that is sometimes
buried by snow accumulation (Koenig et al., 2015). Airborne ice-penetrating
radar surveys in April and May between 2009 and 2012 suggest the mean depth
to the upper surface of meltwater stored within buried supraglacial lakes is
approximately 2 m (Koenig et al., 2015). Over buried supraglacial lakes,
L-band emission from the refreezing partial or solid-ice cap, which is
smooth relative to the L-band wavelength (21 cm), likely induces surface
scattering. As a result, TVB decreases over buried supraglacial
lakes are likely negligible. Thus, over SMAP's 18 km effective resolution, we postulate
water-saturated firn layers dominate L-band emission over the percolation
facies of the GrIS.
The SMAP-derived perennial firn aquifer extent (64 000 km2) generated
by our adapted empirical algorithm and the multi-year calibration technique
(2015–2019) is consistent with the extent (66 000 km2) generated by the
previously developed empirical algorithm and the single-coincident year
calibration technique (2016) described in Miller et al. (2020). The
SMAP-derived perennial firn aquifer extent is generally consistent with
previous C-band (5.3 GHz) satellite-radar-scatterometer-derived perennial
firn aquifer extents mapped using the Advanced SCATterometer (ASCAT) on the
European Organization for the Exploitation of Meteorological Satellites
(EUMETSAT) Meteorological Operational A (MetOp-A) satellite (2009–2016, 52 000–153 000 km2; Miller, 2019) and the Active Microwave Instrument in
radar scatterometer mode (ESCAT) on ESA's European Remote Sensing (ERS)
satellite series (1992–2001, 37 000–64 000 km2; Miller, 2019) as well
as the C-band (5.4 GHz) synthetic-aperture-radar-derived extent mapped using
ESA's Sentinel-1 satellite (2014–2019, 54 000 km2; Brangers et al.,
2020). The exception is the ASCAT-derived perennial firn aquifer extent
(2012–2013, 153 000 km2; Miller, 2019) mapped following the 2012
melting season (Nghiem et al., 2012) in which significant changes in the
dielectric and geophysical properties that influence radar backscatter
likely occurred. The unreasonably expansive (i.e., more than twice the mean)
mapped extent is a result of ASCAT's shallow (several meters) C-band
penetration depth (Jezek et al., 1994) and the simple threshold-based
algorithm, which was not calibrated for an extreme melting season that
included saturation of the upper snow and firn layers of the dry snow facies
and percolation facies with relatively large volumetric fractions of
meltwater (Miller et al., 2019). Water-saturated firn layers had extended
refreezing rates; however, seasonal meltwater was not stored at depth.
Widespread spatially coherent melt layers were alternatively formed in many
of the mapped areas (Culberg et al., 2021). The SMAP-derived ice slab extent
(76 000 km2) is also consistent with previous AR-derived ice slab
extents (2010–2014, 64 800–69 400 km2; MacFerrin et al.,
2019).
Although we simply consider our mapped extents a high-probability area for
preferential formation, the maps generated by our adapted empirical
algorithm and the multi-year calibration technique for individual years
suggest there is reasonable interannual variability in perennial firn aquifer
and ice slab extents (Table 3). Our results demonstrate sensitivity to variability in the depth- and time-integrated dielectric and geophysical
properties of the percolation facies that influence the radiometric
temperature, even during the 2015 melting season (Tedesco et al., 2016).
Interannual variability in SMAP-derived perennial firn aquifer and ice slab extents.
Seasonal surface melting over the GrIS has increased in extent, intensity,
and duration since early in the satellite era (Steffen et al., 2004; Tedesco
et al., 2008, 2011, 2016; Nghiem et al., 2012; Tedesco and Fettweis, 2020; Cullather et al., 2020). Consistent with
recent seasonal surface melting trends, meltwater runoff has accelerated to
become the dominant mass loss mechanism over the GrIS (van den Broeke et
al., 2016). Meltwater storage in both solid (i.e., embedded ice structures,
including ice slabs, and spatially coherent melt layers) and liquid (i.e.,
perennial firn aquifers) form can buffer meltwater runoff in the percolation
facies and delay its eventual release into the ocean (Harper et al., 2012).
However, significant uncertainty remains in meltwater runoff estimates as a
result of the lack of knowledge of heterogeneous infiltration and refreezing
processes within the snow and firn layers (Pfeffer and Humphrey, 1996) as well as
the depths to which meltwater can descend beneath the ice sheet surface
(Humphrey et al., 2012).
If the increasing seasonal surface melting trend continues (Franco et al.,
2013; Noël et al., 2021), perennial firn aquifer formation and expansion
may increase the possibility of crevasse deepening via meltwater-induced
hydrofracturing (Alley et al., 2005; van der Veen, 2007), especially if
crevasse fields expand into perennial firn aquifer areas as a result of
accelerated ice flow (Colgan et al., 2016). Meltwater-induced
hydrofracturing is an important component of supraglacial lake drainage
during the melting season (Das et al., 2008; Stevens et al., 2015), leading
to at least temporary localized accelerated ice flow velocities (Zwally et
al., 2002; Joughin et al., 2013; Moon et al., 2014) as well as ice discharge
from outlet glaciers (Chudley et al., 2019) and mass balance changes
(Joughin et al., 2008). Perennial firn aquifers may also support
meltwater-induced hydrofracturing, even during the freezing season (Poinar
et al., 2017, 2019).
The formation and expansion of ice slabs reduces permeability within the
upper snow and firn layers and facilitates lateral meltwater flow with
minimum vertical percolation into the deeper firn layers, thereby enhancing
meltwater runoff and mass loss at the periphery (Machguth et al., 2016;
MacFerrin et al., 2019). Lateral meltwater flow across ice layers overlying
deeper permeable firn layers was first postulated by Müller (1962). The
theory was then further developed by Pfeffer et al. (1991) as an end-member
case for meltwater runoff in the percolation facies, with the other end-member case being lateral meltwater flow across superimposed ice. Lateral
meltwater flow and high-elevation (1850 m a.s.l.) meltwater runoff across ice
slabs in the percolation facies were first observed in visible satellite
imagery collected by the NASA–USGS Landsat 7 mission during the 2012 melting
season (Machguth et al., 2016).
Spatially coherent melt layers represent a recently identified refreezing
mechanism in the dry snow facies (Nghiem et al., 2005; Culberg et al.,
2021). Similar to ice slabs, the formation and expansion of spatially
coherent melt layers reduce the pore space within the upper snow and firn
layers. They can also limit meltwater flow with minimum vertical percolation into
the deeper firn layers, thereby potentially preconditioning the dry snow
facies for the formation of ice slabs and enhanced meltwater runoff from
significantly higher elevations on accelerated timescales. If spatially
coherent melt layers merge with ice slabs upslope of perennial firn aquifers
areas, they may also simultaneously accelerate both meltwater runoff and
meltwater-induced hydrofracturing during extreme melting seasons. The
formation of spatially coherent melt layers overlying deeper perennial firn
aquifers may result in the formation of shallow perched firn aquifers
(Culberg et al., 2021) or may terminate gravity-driven meltwater drainage
and seasonal recharging (Fountain and Walder, 1998), which may eventually
completely refreeze stored meltwater into ice slabs or decameters-thick
solid-ice layers overlying deeper glacial ice.
Summary and future work
In this study, for the first time, we have demonstrated the novel use of the
L-band microwave radiometer on NASA's SMAP satellite for mapping perennial
firn aquifers and ice slabs together as a continuous englacial hydrological system over the
percolation facies of the GrIS. We have adapted our previously developed
empirical algorithm (Miller et al., 2020) by expanding our analysis of
spatiotemporal differences in SMAP enhanced-resolution TVB imagery
and temporal L-band signatures. We have used this analysis to derive a firn
saturation parameter from a simple two-layer L-band brightness temperature
model. And we have used the firn saturation parameter to map the extent of
the percolation facies. We have found that by correlating maximum and
minimum TVB values, the firn saturation parameter, and the
refreezing rate parameter with perennial firn aquifer and ice slab
detections identified via the CReSIS AR and MCoRDS instruments flown by
NASA's OIB campaigns, we can calibrate our previously developed
empirical algorithm (Miller et al., 2020) to map plausible extents.
We note that significant uncertainty exists in the mapped extents as a
result of (1) correlating the SMAP-derived parameters with airborne
ice-penetrating radar detections that are not coincident in time; (2) the
lack of a distinct temporal L-band signature delineating the boundary
between perennial firn aquifer areas, ice slabs areas, and adjacent
percolation facies areas; and (3) the limited extent of the airborne
ice-penetrating radar detections as compared to the rSIR grid cell extent
and the effective resolution of the SMAP enhanced-resolution TVB
imagery.
Miller et al. (2020) normalized SMAP enhanced-resolution TVB time
series and converted the exponential rate of TVB decrease over
perennial firn aquifer areas to a binary parameter to map extent. In this
study, we have converted the SMAP-derived parameters to binary parameters to
map the extent of both perennial firn aquifer and ice slab areas. Moreover,
we have included additional analysis of the spatiotemporal differences in
maximum and minimum TVB values, the firn saturation parameter, and
the refreezing rate parameter. We have shown that spatiotemporal differences
in the SMAP-derived parameters are consistent with our assumption of
spatiotemporal differences in the englacial hydrology and thermal
characteristics of firn layers at depth.
Future work will focus on simulating the temporal L-band signatures observed
over perennial firn aquifer and ice slab areas for a wide range of
geophysical properties. Additionally, we will simulate the
distinct temporal L-band signatures observed over spatially coherent melt
layers and explore mapping the extent. Combining multi-layer
depth-integrated L-band brightness temperature models (e.g., Jezek et al.,
2015) that include embedded ice structure parametrizations (e.g., Jezek et
al., 2018) with models of depth-dependent geophysical parameters can lead to
an improved understanding of the extremely complex and poorly described
physics controlling L-band emission over the percolation facies. The
development of more sophisticated empirical algorithms that incorporate
multi-layer depth-integrated L-band brightness temperature models that are
constrained by in situ measurements can help reduce the significant
uncertainty in the current mapped extents and provide more accurate
boundary delineation that can be used to further quantify interannual
variability.
Data availability
SMAP Radiometer Twice-Daily rSIR-Enhanced EASE-Grid 2.0 Brightness
Temperatures, Version 1, (2015–2019) have been produced as part of the NASA
Science Utilization of SMAP project and are available at
10.5067/QZ3WJNOUZLFK (last access: 1 April 2021; Brodzik et al., 2019). The NASA
MEaSUREs Greenland Ice Mapping Project (GIMP) Land Ice and Ocean
Classification Mask, Version 1, is available at
10.5067/B8X58MQBFUPA (last access: 1 April 2021; Howat, 2017), and the Digital
Elevation Model, Version 1, is available at https://nsidc.org/data/nsidc-0645/versions/1 (last access: 1 April 2021; Howat et al., 2015). The
coastline data are available from GSHHG – A Global Self-consistent,
Hierarchical, High-resolution Geography Database, 10.1029/96JB00104 (last access: 1 April 2021; Wessel and Smith, 1996). Ice surface
temperature imagery (2015–2019) have been produced as part of the Multilayer
Greenland Ice Surface Temperature, Surface Albedo, and Water Vapor from
MODIS V001 and are available at 10.5067/7THUWT9NMPDK (last access: 1 April 2021; Hall and DiGirolamo, 2019). OIB AR-
and MCoRDS-derived perennial firn aquifer detections (2010–2017) are
available at 10.18739/A2985M (last access: 1 April 2021; Miège,
2018). OIB AR-derived ice slab detections (2010–2014) are available at
10.6084/m9.figshare.8309777 (last access: 1 April 2021; MacFerrin,
2019). OIB AR-derived spatially coherent melt layer detections (2017) are
available at 10.18739/A2736M33W (last access: 1 April 2021; Culberg, 2021). OIB AR L1B Geolocated Radar Echo Strength Profiles, Version 2,
are available at 10.5067/0ZY1XYHNIQNY (last access: 1 April 2021; Paden
et al., 2018). The NASA MEaSUREs MODIS Mosaic of Greenland (MOG) 2015 Image Map,
Version 2, is available at https://nsidc.org/data/NSIDC-0547/versions/2 (last access: 1 April 2021; Haran et al., 2018).
SMAP-derived perennial firn aquifer and ice slab extents are available at
10.5281/zenodo.5745983 (last access: last access: 5 January 2022; Miller, 2021).
Author contributions
JZM initiated the study, adapted the empirical model, performed the
analyses, and wrote the manuscript. RC processed and interpreted the airborne ice-penetrating radar surveys. All authors participated in discussions and reviewed
manuscript drafts.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The authors thank Mike MacFerrin and the two anonymous reviewers for their constructive
comments. We acknowledge the use of data
from CReSIS generated with support from the University of Kansas, NASA
Operation IceBridge (grant no. NNX16AH54G), NSF (grant nos. ACI-1443054, OPP-1739003,
IIS-1838230), Lilly Endowment Incorporated, and Indiana METACyt Initiative.
Financial support
Julie Z. Miller, David G. Long, and Mary J. Brodzik are supported by the NASA SMAP Science Team (grant no. 80NSSC20K1806) and by the NASA Cryospheric Science Program (grant nos. 80NSSC18K1055 and 80NSSC21K0749) under grants to the University of
Colorado and Brigham Young University. Riley Culberg is supported by a National Defense
Science and Engineering Graduate Fellowship. Riley Culberg and Dustin
M. Schroeder are supported in part by NASA (grant no. NNX16AJ95G) and the NSF (grant no. 1745137) to Stanford University. Christopher A. Shuman is supported by the NASA
Headquarters Cryospheric Science Program.
Review statement
This paper was edited by Lars Kaleschke and reviewed by Michael MacFerrin and two anonymous referees.
ReferencesAbdalati, W. and Steffen, K.: Snowmelt on the Greenland Ice Sheet as derived from passive microwave satellite data, J. Climate, 10, 165–175, 10.1175/1520-0442(1997)010<0165:SOTGIS>2.0.CO;2, 1997.Alley, R. B., Dupont, T. K., Parizek, B. R., and Anandakrishnan, S.: Access of surface meltwater to beds of sub-freezing glaciers: Preliminary insights, Ann. Glaciol., 40, 8–14, 10.3189/172756405781813483, 2005.Ashcraft, I. and Long, D.: Comparison of methods for melt detection over Greenland using active and passive microwave measurements, Int. J. Remote Sens., 27, 2469–2488, 10.1080/01431160500534465, 2006. Benson, C. S.: Stratigraphic studies in the snow and firn of the Greenland Ice Sheet, PhD thesis, California Institute of Technology, 228 pp., 1960.Brangers, I., Lievens, H., Miège, C., Demuzere, M., Brucker, L., and De Lannoy, G. J. M.: Sentinel-1 detects firn aquifers in the Greenland Ice Sheet, Geophys. Res. Lett., 47, e2019GL085192, 10.1029/2019GL085192, 2020.Brodzik, M. J., Billingsley, B., Haran, T., Raup, B., and Savoie, M. H.: EASE-Grid 2.0: Incremental but significant improvements for Earth-gridded data sets, ISPRS Int. J. Geo-Inf., 1, 32–45, 10.3390/ijgi1010032, 2012.Brodzik, M. J., Long, D. G., and Hardman, M. A.: SMAP Radiometer Twice-Daily rSIR-Enhanced EASE-Grid 2.0 Brightness Temperatures, Version 1, NASA National Snow and Ice Data Center Distributed Active Archive Center [data set], 10.5067/QZ3WJNOUZLFK, 2019.Chu, W., Schroeder, D. M., and Siegfried, M. R.: Retrieval of englacial firn aquifer thickness from ice-penetrating radar sounding in southeastern Greenland, Geophys. Res. Lett., 45, 11770–11778, 10.1029/2018GL079751, 2018.Chudley, T. R., Christoffersen, P., Doyle, S. H., Bougamont, M., Schoonman, C. M., Hubbard, B., and James, M. R.: Supraglacial lake drainage at a fast-flowing Greenlandic outlet glacier, P. Natl. Acad. Sci. USA, 51, 25468–25477, 10.1073/pnas.1913685116, 2019.Colgan, W., Rajaram, H., Abdalati, W., McCutchan, C., Mottram, R., Moussavi, M. S., and Grigsby, S.: Observations, models, and mass balance implications: Glacier crevasses, Rev. Geophys., 54, 119–161, 10.1002/2015RG000504, 2016.CReSIS: CReSIS radar depth sounder data, Digital Media, http://data.cresis.ku.edu/ (last access: 1 April 2021), 2016.Culberg, R.: Refrozen melt layer location, density, and connectivity records from airborne radar sounding, Greenland, NSF Arctic Data Center [data set], 10.18739/A2736M33W, 2021.Culberg, R., Schroeder, D. M., and Chu, W.: Extreme melt season ice layers reduce firn permeability across Greenland, Nat. Commun., 12, 2336, 10.1038/s41467-021-22656-5, 2021.Cullather, R. I., Andrews, L. C., Croteau, M. J., Digirolamo, N. E., Hall, D. K., Lim, Y., Loomis, B. D., Shuman, C. A., and Nowicki, S. M. J.: Anomalous circulation in July 2019 resulting in mass loss on the Greenland Ice Sheet, Geophys. Res. Lett., 47, e2020GL087263, 10.1029/2020GL087263, 2020.Das, S. B., Joughin, I., Behn, M. D., Howat, I. M., King,
M. A., Lizarralde, D., and Bhatia, M. P.: Fracture propagation to the base of the Greenland Ice Sheet during supraglacial lake drainage, Science, 320, 778–781, 10.1126/science.1153360, 2008.Dunmire, D., Banwell, A. F., Wever, N., Lenaerts,
J. T. M., and Datta, R. T.: Contrasting regional variability of
buried meltwater extent over 2 years across the Greenland Ice Sheet,
The Cryosphere, 15, 2983–3005, 10.5194/tc-15-2983-2021, 2021.Early, D. S. and Long, D. G.: Image reconstruction and enhanced-resolution imaging from irregular samples, IEEE T. Geosci. Remote, 39, 291–302, 10.1109/36.905237, 2001.Echelmeyer, K., Clarke, T. S., and Harrison, W. D.: Surficial glaciology of Jakobshavn Isbræ, West Greenland, 1. Surface morphology, J. Glaciol., 37, 368–382, 10.1017/S0022143000005803, 1991.Entekhabi, D., Johnson, J., Kimball, J., Piepmeier, J. R., Koster, R. D., Martin, N., McDonald, K. C., Moghaddam, M., Moran, S., Reichle, R., Shi, J. C., Njoku, E. G., Spencer, M. W., Thurman, S. W., Tsang, L., Van Zyl, J., O'Neill, P. E., Kellogg, K. H., Crow, W. T., Edelstein, W. N., Entin, J. K., Goodman, S. D., and Jackson, T. J.: The Soil Moisture Active Passive (SMAP) Mission, Proc. IEEE, 98, 704–716, 10.1109/JPROC.2010.2043918, 2010.Forster, R. R., Box, J. E., Van Den Broeke, M. R., Miège, C., Burgess, E. W., Van Angelen, J. H., Lenaerts, J. T. M., Koenig, L. S., Paden, J., Lewis, C., Gogineni, S. P., Leuschen, C., and McConnell, J. R.: Extensive liquid meltwater storage in firn within the Greenland Ice Sheet, Nat. Geosci., 7, 95–98, 10.1038/ngeo2043, 2014.Fountain, A. G. and Walder, J. S.: Water flow through temperate glaciers, Rev. Geophys., 36, 299–328, 10.1029/97RG03579, 1998.Freilich, M. H., Long, D. G., and Spencer, M. W.: SeaWinds: A scanning scatterometer for ADEOS-II science overview, Proc. IEEE, 1994, 960–963, 10.1109/IGARSS.1994.399313, 1994.Franco, B., Fettweis, X., and Erpicum, M.: Future projections of the Greenland ice sheet energy balance driving the surface melt, The Cryosphere, 7, 1–18, 10.5194/tc-7-1-2013, 2013.Hall, D. K. and DiGirolamo, N.: Multilayer Greenland Ice Surface Temperature, Surface Albedo, and Water Vapor from MODIS, Version 1, NASA National Snow and Ice Data Center Distributed Active Archive Center [data set], 10.5067/7THUWT9NMPDK, 2019.Hall, D. K., Comiso, J. C., Digirolamo, N. E., Shuman, C. A., Key, J. R., and Koenig, L. S.: A satellite-derived climate-quality data record of the clear-sky surface temperature of the Greenland Ice Sheet, J. Climate, 25, 4785–4798, 10.1175/JCLI-D-11-00365.1, 2012.Haran, T., Bohlander J., Scambos T., Painter, T., and Fahnestock, M.: MEaSUREs MODIS Boulder, Colorado, USA, NASA National Snow and Ice Data Center Distributed Active Archive Center, 10.5067/9ZO79PHOTYE5, 2018.Harper, J., Humphrey, N., Pfeffer, W. T., Brown, J., and Fettweis, X.: Greenland ice-sheet contribution to sea-level rise buffered by meltwater storage in firn, Nature, 491, 240–243, 10.1038/nature11566, 2012.Hicks, B. R. and Long, D. G.: Inferring Greenland melt and refreeze severity from SeaWinds scatterometer data, Int. J. Remote Sens., 32, 8053–8080, 10.1080/01431161.2010.532174, 2011.Howat, I.: MEaSUREs Greenland Ice Mapping Project (GIMP) Land Ice and Ocean Classification Mask, Version 1, NASA National Snow and Ice Data Center Distributed Active Archive Center [data set], 10.5067/B8X58MQBFUPA, 2017.Howat, I. M., Negrete, A., and Smith, B. E.: The Greenland Ice Mapping Project (GIMP) land classification and surface elevation data sets, The Cryosphere, 8, 1509–1518, 10.5194/tc-8-1509-2014, 2014.Howat, I., Negrete, A., and Smith, B.: MEaSUREs Greenland Ice Mapping Project (GIMP) Digital Elevation Model, Version 1, NASA National Snow and Ice Data Center Distributed Active Archive Center, 10.5067/NV34YUIXLP9W, 2015.Humphrey, N. F., Harper, J. T., and Pfeffer, W. T.: Thermal tracking of meltwater retention in Greenland's accumulation area, J. Geophys. Res.-Earth Surf., 117, 10.1029/2011JF002083, 2012.Jezek, K. C., Gogineni, P., and Shanableh, M.: Radar measurements of melt zones on the Greenland Ice Sheet, Geophys. Res. Lett., 21, 33–36, 10.1029/93GL03377, 1994.Jezek, K. C., Johnson, J. T., Drinkwater, M. R., Macelloni, G., Tsang, L., Aksoy, M., and Durand M.: Radiometric approach for estimating relative changes in intraglacier average temperature, IEEE T. Geosci. Remote, 53, 134–143, 10.1109/TGRS.2014.2319265, 2015.Jezek, K. C., Johnson, J. T., Tan, S., Tsang, L., Andrews, M. J., Brogioni, M., Macelloni, G., Durand, M., Chen, C. C., Belgiovane, D. J., Duan, Y., Yardim, C., Li, H., Bringer, A., Leuski, V., and Aksoy, M.: 500–2000 MHz brightness temperature spectra of the northwestern Greenland Ice Sheet, IEEE T. Geosci. Remote, 56, 1485–1496, 10.1109/TGRS.2017.2764381, 2018.Joughin, I., Das, S. B., King, M. A., Smith, B. E., Howat, I. M., and Moon, T.: Seasonal speedup along the western flank of the Greenland Ice Sheet, Science, 320, 781–783, 10.1126/science.1153288, 2008.Joughin, I., Das, S. B., Flowers, G. E., Behn, M. D., Alley, R. B., King, M. A., Smith, B. E., Bamber, J. L., van den Broeke, M. R., and van Angelen, J. H.: Influence of ice-sheet geometry and supraglacial lakes on seasonal ice-flow variability, The Cryosphere, 7, 1185–1192, 10.5194/tc-7-1185-2013, 2013.Kerr, Y. H., Waldteufel, P., Wigneron, J., Martinuzzi, J., Font, J., and Berger, M.: Soil moisture retrieval from space: The Soil Moisture and Ocean Salinity (SMOS) mission, IEEE T. Geosci. Remote, 39, 1729–1735, 10.1109/36.942551, 2001.Koenig, L. S., Miège, C., Forster, R. R., and Brucker, L.: Initial in situ measurements of perennial meltwater storage in the Greenland firn aquifer, Geophys. Res. Lett., 41, 81–85, 10.1002/2013GL058083, 2014.Koenig, L. S., Lampkin, D. J., Montgomery, L. N., Hamilton, S. L., Turrin, J. B., Joseph, C. A., Moutsafa, S. E., Panzer, B., Casey, K. A., Paden, J. D., Leuschen, C., and Gogineni, P.: Wintertime storage of water in buried supraglacial lakes across the Greenland Ice Sheet, The Cryosphere, 9, 1333–1342, 10.5194/tc-9-1333-2015, 2015.Kuipers Munneke, P. K., Ligtenberg, S. R. M., Van Den Broeke, M. R., Van Angelen, J. H., and Forster, R. R.: Explaining the presence of perennial liquid water bodies in the firn of the Greenland Ice Sheet, Geophys. Res. Lett., 41, 476–483, 10.1002/2013GL058389, 2014.Le Vine, D. M., Lagerloef, G. S. E., Colomb, F. R., Yueh, S. H., and Pellerano, F. A.: Aquarius: An instrument to monitor sea surface salinity from space, IEEE T. Geosci. Remote, 45, 2040–2050, 10.1109/TGRS.2007.898092, 2007.Lewis, C., Gogineni, S., Rodriguez-Morales, F., Panzer, B., Stumpf, T., Paden, J., and Leuschen, C.: Airborne fine-resolution UHF radar: An approach to the study of englacial reflections, firn compaction and ice attenuation rates, J. Glaciol., 61, 89–100, 10.3189/2015JoG14J089, 2015.Long, D. G. and Brodzik, M. J.: Optimum image formation for spaceborne microwave radiometer products, IEEE T. Geosci. Remote, 54, 2763–2779, 10.1109/TGRS.2015.2505677, 2016.Long, D. G. and Daum, D. L.: Spatial resolution enhancement of SSM/I data, IEEE T. Geosci. Remote, 36, 407–417, 10.1109/36.662726, 1998.Long, D. G., Hardin, P. J., and Whiting, P. T.: Resolution enhancement of spaceborne scatterometer data, IEEE T. Geosci. Remote, 31, 700–715, 10.1109/36.225536, 1993.Long, D. G., Brodzik, M. J., and Hardman M. A.: Enhanced-resolution SMAP brightness temperature image products, IEEE T. Geosci. Remote, 57, 4151–4163, 10.1109/TGRS.2018.2889427, 2019.MacFerrin, M.: Greenland Ice Slabs Data, figshare [data set], 10.6084/m9.figshare.8309777.v1, 2019.MacFerrin, M., Machguth, H., van As, D., Charalampidis, C., Stevens, C. M., Heilig, A., Vandecrux, B., Langen, P. L., Mottram, R., Fettweis, X., van den Broeke, M. R., Pfeffer, W. T., Moussavi, M. S., and Abdalati, W.: Rapid expansion of Greenland's low-permeability ice slabs, Nature, 573, 403–407, 10.1038/s41586-019-1550-3, 2019.Machguth, H. MacFerrin, M., van As, D., Box, J. E., Charalampidis, C., Colgan., W., Fausto, R. S., Harro, A. J., Mosley-Thompson, E., and van de Wal, R. S. W.: Greenland meltwater storage in firn limited by near-surface ice formation, Nat. Clim. Change, 6, 390–393, 10.1038/nclimate2899, 2016.Mätzler, C. and Hüppi, R.: Review of signature studies for microwave remote sensing of snowpacks, Adv. Space Res., 9, 253–265, 10.1016/0273-1177(89)90493-6, 1989.Miège, C.: Spatial extent of Greenland firn aquifer detected by airborne radars, 2010–2014, Arctic Data Center [data set], 10.18739/A2985M, 2018.Miège, C., Forster, R. R., Brucker, L., Koenig, L. S., Solomon, D. K., Paden, J. D., Box, J. E., Burgess, E. W., Miller, J. Z., McNerney, L., Brautigam, N., Fausto, R. S., and Gogineni, S.: Spatial extent and temporal variability of Greenland firn aquifers detected by ground and airborne radars, J. Geophys. Res.-Earth, 121, 2381–2398, 10.1002/2016JF003869, 2016.Miles, K. E., Willis, I. C., Benedek, C. L., Williamson, A. G., and Tedesco, M.: Toward monitoring surface and subsurface lakes on the Greenland Ice Sheet Using Sentinel-1 SAR and Landsat-8 OLI imagery, Front. Earth Sci., 5, 58, 10.3389/feart.2017.00058, 2017. Miller, J. Z.: Mapping Greenland's firn aquifers from space using active and passive satellite microwave remote sensing, PhD thesis, Department of Geography, University of Utah, 135 pp., 2019.Miller, J. Z.: SMAP-derived Perennial Firn Aquifer and Ice Slab Extents 2015–2019 Version 0, Zenodo [data set], 10.5281/zenodo.5745983, 2021.Miller, J. Z., Long, D. G., Jezek, K. C., Johnson, J. T., Brodzik, M. J., Shuman, C. A., Koenig, L. S., and Scambos, T. A.: Brief communication: Mapping Greenland's perennial firn aquifers using enhanced-resolution L-band brightness temperature image time series, The Cryosphere, 14, 2809–2817, 10.5194/tc-14-2809-2020, 2020.Miller, O. L., Solomon, D. K., Miège, C., Koenig, L. S., Forster, R. R., Montgomery, L. N., Schmerr, N., Ligtenberg, S. R. M., Legchenko, A., and Brucker, L.: Hydraulic conductivity of a firn aquifer in southeast Greenland, Front. Earth Sci., 5, 10.3389/feart.2017.00038, 2017.Montgomery, L. N., Schmerr, N., Burdick, S., Forster, R. R., Koenig, L., Legchenko, A., Ligtenberg, S., Miège, C., Miller, O. L., and Solomon, D. K.: Investigation of firn aquifer structure in southeastern Greenland using active source seismology, Front. Earth Sci., 5, 10.3389/feart.2017.00010, 2017.Moon, T., Joughin, I., Smith, B., Broeke, M. R., Berg, W. J., Noël, B., and Usher, M.: Distinct patterns of seasonal Greenland glacier velocity, Geophys. Res. Lett., 41, 7209–7216, 10.1002/2014GL061836, 2014.Mote, T. L. and Andersen, M. R.: Variations in snowpack melt on the Greenland Ice Sheet based on passive microwave measurements, J. Glaciol., 41, 51–60, 10.1017/S0022143000017755, 1995. Müller, F.: Zonation in the Accumulation Area of the Glaciers of Axel Heiberg Island, N. W. T., Canada, J. Glaciol., 4, 302–311, 1962.Nghiem, S. V., Steffen, K., Neumann, G. A., and Huff, R: Mapping of ice layer extent and snow accumulation in the percolation zone of the Greenland ice sheet, J. Geophys. Res., 110, F02017, 10.1029/2004JF000234, 2005.Nghiem, S. V., Hall, D. K., Mote, T. L., Tedesco, M., Albert, M. R., Keegan, K., Shuman, C. A., DiGirolamo, N. E., and Neumann, G.: The extreme melt across the Greenland Ice Sheet in 2012, Geophys. Res. Lett., 39, L20502, 10.1029/2012GL053611, 2012.Noël, B., van de Berg, W. J., Lhermitte, S. L. M., and van den Broeke, M. R.: Rapid ablation zone expansion amplifies north Greenland mass loss, Sci. Adv., 5, eaaw0123, 10.1126/sciadv.aaw0123, 2019.Noël, B., van Kampenhout, L., Lenaerts, J. T. M., van de Berg, W. J., and van den Broeke, M. R.: A 21st century warming threshold for sustained Greenland Ice Sheet mass loss, Geophys. Res. Lett., 48, 10.1029/2020GL090471, 2021.Paden, J., Li, J., Leuschen, C., Rodriguez-Morales, F., and Hale, R.: IceBridge Accumulation Radar L1B Geolocated Radar Echo Strength Profiles, Version 2, NASA National Snow and Ice Data Center Distributed Active Archive Center [data set], 10.5067/0ZY1XYHNIQNY, 2014 (updated 2018).Pfeffer, W. T., Meier, M. F., and Illangasekare, T. H.: Retention of Greenland runoff by refreezing: Implications for projected future sea level change, J. Geophys. Res.-Oceans, 96, 22117–22124, 10.1029/91JC02502, 1991.Pfeffer, W. T. and Humphrey, N. F.: Determination of timing and location of water movement and ice-layer formation by temperature measurements in sub-freezing snow, J. Glaciol., 42, 292–304, 10.1017/S0022143000004159, 1996.Piepmeier, J. R., Focardi, P., Horgan, K. A., Knuble, J., Ehsan, N., Lucey, J., Brambora, C., Brown, P. R., Hoffman, P. J., French, R. T., Mikhaylov, R. L., Kwack, E., Slimko, E. M., Dawson, D. E., Hudson, D., Peng, J., Mohammed, P. N., De Amici, G., Freedman, A. P., Medeiros, J., Sacks, F., Estep, R., Spencer, M. W., Chen, C. W., Wheeler, K. B., Edelstein, W. N., O'Neill, P. E., and Njoku, E. G.: SMAP L-band microwave radiometer: Instrument design and first year on orbit, IEEE T. Geosci. Remote, 55, 1954–1966, 10.1109/TGRS.2016.2631978, 2017.Poinar, K., Joughin, I., Lilien, D., Brucker, L., Kehrl, L., and Nowicki, S.: Drainage of southeast Greenland firn aquifer water through crevasses to the bed, Front. Earth Sci., 10.3389/feart.2017.00005, 2017.Poinar, K., Dow, C. F., and Andrews, L. C.: Long-term support of an active subglacial hydrologic system in southeast Greenland by firn aquifers, Geophys. Res. Lett., 46, 4772–4781, 10.1029/2019GL082786, 2019.Rignot, E.: Backscatter model for the unusual radar properties of the Greenland Ice Sheet, J. Geophys. Res.-Planet., 100, 9389–9400, 10.1029/95JE00485, 1995.Rignot, E. J., Ostro, S. J., Van Zyl, J., and Jezek, K. C.: Unusual radar echoes from the Greenland Ice Sheet, Science, 261, 1710–1713, 10.1126/science.261.5129.1710, 1993.Rodriguez-Morales, F., Byers, K., Crowe, R., Player, K., Hale, R. D., Arnold, E. J., Smith, L., Gifford, C. M., Braaten, D., Panton, C., Gogineni, S., Leuschen, C. J., Paden, J. D., Li, J., Lewis, C. C., Panzer, B., Gomez-Garcia Alvestegui, D., and Patel, A.: Advanced multi-frequency radar instrumentation for polar research, IEEE T. Geosci. Remote, 52, 2824–2842, 10.1109/TGRS.2013.2266415, 2014.Schröder, L., Neckel, N., Zindler, R., and Humbert, A.: Perennial supraglacial lakes in northeast Greenland observed by polarimetric SAR, Remote Sens., 12, 2798, 10.3390/rs12172798, 2020.Shuman, C. A., Hall, D. K., DiGirolamo, N. E., Mefford, T. K., and Schnaubelt, M. J.: Comparison of near-surface air temperatures and MODIS ice-surface temperatures at Summit, Greenland (2008–2013), J. Appl. Meteorol. Clim., 53, 2171–2180, 10.1175/JAMC-D-14-0023.1, 2014.Steffen, K., Nghiem, S. V., Huff, R., and Neumann, G.: The melt anomaly of 2002 on the Greenland Ice Sheet from active and passive microwave satellite observations, Geophys. Res. Lett., 31, L2040, 10.1029/2004GL020444, 2004.Stevens, L. A., Behn, M. D., McGuire, J. J., Das, S. B., Joughin, I., Herring, T., Shean, D. E., and King, M. A.: Greenland supraglacial lake drainages triggered by hydrologically induced basal slip, Nature, 522, 73–76, 10.1038/nature14480, 2015.Swift, C. T., Hayes, P. S., Herd, J. S., Jones, W. L., and Delnore, V. E.: Airborne microwave measurements of the southern Greenland Ice Sheet, J. Geophys. Res.-Sol. Ea., 90, 1983–1994, 10.1029/JB090iB02p01983, 1985.Tedesco, M. and Fettweis, X.: Unprecedented atmospheric conditions (1948–2019) drive the 2019 exceptional melting season over the Greenland ice sheet, The Cryosphere, 14, 1209–1223, 10.5194/tc-14-1209-2020, 2020.Tedesco, M., Serreze, M., and Fettweis, X.: Diagnosing the extreme surface melt event over southwestern Greenland in 2007, The Cryosphere, 2, 159–166, 10.5194/tc-2-159-2008, 2008.Tedesco, M., Fettweis, X., van den Broeke, M. R., van de Wal, R. S. W., Smeets, C. J. P. P., van de Berg, W. J., Serreze, M. C., and Box, J. E.: The role of albedo and accumulation in the 2010 melting record in Greenland, Environ. Res. Lett, 6, 014005, 10.1088/1748-9326/6/1/014005, 2011.Tedesco, M., Mote, T., Fettweis, X., Hanna, E.,
Jeyaratnam, J., Booth, J. F., Datta, R., and Briggs, K.: Arctic
cut-off high drives the poleward shift of a new Greenland melting
record, Nat. Commun., 7, 11723–11723, 10.1038/ncomms11723, 2016.Tiuri, M. E., Sihvola, A. H., Nyfors, E. G., and Hallikaiken, M. T.: The complex dielectric constant of snow at microwave frequencies, IEEE J. Oceanic Eng., 9, 377–382, 10.1109/JOE.1984.1145645, 1984.
Tsai, W., Nghiem, S. V., and Van Zyl, J. J.: SeaWinds scatterometer on QuikSCAT mission and the emerging land and ocean applications, Proc. SPIE, 4152, 89–99, 10.1117/12.410586, 2000.Turton, J. V., Hochreuther, P., Reimann, N., and Blau,
M. T.: The distribution and evolution of supraglacial lakes on
79∘ N Glacier (north-eastern Greenland) and interannual climatic
controls, The Cryosphere, 15, 3877–3896,
10.5194/tc-15-3877-2021, 2021. Ulaby, F. T., Long, D. G., Blackwell, W. J., Elachi, C., Fung, A. K., Ruf, C., Sarabandi, C., Zebker, H. A., and Van Zyl, J.: Microwave radar and radiometric remote sensing, University of Michigan Press, Ann Arbor, 2014.van den Broeke, M. R., Enderlin, E. M., Howat, I. M., Kuipers Munneke, P., Noël, B. P. Y., van de Berg, W. J., van Meijgaard, E., and Wouters, B.: On the recent contribution of the Greenland ice sheet to sea level change, The Cryosphere, 10, 1933–1946, 10.5194/tc-10-1933-2016, 2016.van der Veen, C. J.: Fracture propagation as means of rapidly transferring surface meltwater to the base of glaciers, Geophys. Res. Lett., 34, L01501, 10.1029/2006GL028385, 2007.Wessel, P. and Smith, W. H. F.: A global, self-consistent, hierarchical, high-resolution shoreline database, J. Geophys. Res., 101, 8741–8743, 10.1029/96JB00104, 1996.Zwally, H. J., Abdalati, W., Herring, T., Larson, K., Saba, J., and Steffen, K.: Surface melt-induced acceleration of Greenland Ice Sheet flow, Science, 297, 218–222, 10.1126/science.1072708, 2002.Zwally, J. H.: Microwave emissivity and accumulation rate of polar firn, J. Glaciol., 18, 195–215, 10.1017/S0022143000021304, 1977.