Auxiliary Material for
Cold-based debris-covered glaciers: evaluating their potential as climate archives through
studies of ground penetrating radar and surface morphology
Sean L. Mackay1, smackay@bu.edu
David R. Marchant1, marchant@bu.edu
Jennifer L. Lamp1, jenlamp@bu.edu
James Head2, james_head@brown.edu
1
Department of Earth and Environment, Boston University, Boston MA 02215
Department of Geological Sciences, Brown University, Providence RI 02912
2
Journal of Geophysical Research-Earth Surface
INTRODUCTION
The auxiliary material for “Cold-based debris-covered glaciers: evaluating their potential as
climate archives through studies of ground penetrating radar and surface morphology” includes
thirteen figures and two tables. The figures provide additional location information, sample
analysis data, GPR data, and modelling results. The tables provide details of GPR data
collection, and ablation stake measurement results.
Figures:
1. fs01 (Figure S1): Sampling locations along Mullins and Friedman Glaciers. Plotted are the
locations of ice cores, sediment samples, ablation stakes, and meteorological stations.
For clarity, soil excavations are not labelled with respect to excavation number but rather
are plotted to show the areal extent of sample coverage. Likewise, only ice cores MCI08-01 and MCI-09-03, used to help calibrate ground penetrating radar (GPR) returns and
calculate ice temperature at various depths, are highlighted (see text and Figure 15 for
additional details). The background image is a hill-shaded relief map from airborne
LiDAR (2 m resolution [Schenk et al., 2004]); data are not available for left side of
image; dotted lines show the inferred margins for Mullins and Freidman Glaciers (see
Figure 4 for map).
2. fs02 (Figure S2): 400 MHz GPR profiles across a portion of Region 1 on Friedman Glacier,
showing relatively clean glacier ice, superposed ice, and the onset of and FIR-1/ ASD-1.
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Colored profile shows un-migrated radar data; greyscale immediately below displays
migrated data with a Hilbert magnitude transform applied. The base of the superimposed
ice is clearly visible as a horizontal reflector ~1.5 m below the surface between 1580 and
1690 m along the transect. The onset of FIR-1/ IDL-1 occurs immediately down valley
from the superposed ice (see also Fig. 21 for a regional view). Individual parabolas in the
unmigrated data collapse to point reflectors in the migrated profile and are interpreted as
individual rocks within the ice.
3. fs03 (Figure S3): GPR details for the Am – Am’ transect centered across MIR 2 and MIR 3 on
Mullins Glacier (see Figure 7 for transect location). Top panel: un-migrated 80 MHz
radar data. Middle panel: migrated 80 MHz data with a Hilbert magnitude transform
applied. Middle panel: sketch of major radar reflectors and physical interpretation. This
detailed view of the Am – Am’ transect highlights the complex geometry of the internal
reflectors (MIR 2 and MIR 3), as well as hyperbolic reflectors that collapse to point
reflectors in migrated data with the Hilbert magnitude transform applied (middle panel).
The point reflectors are interpreted as individual cobbles or closely spaced clusters of
rocks.
4. fs04 (Figure S4): Transverse radar profile Em - Em’ across Mullins Glacier, collected with the
80 MHz antenna in point mode (see Fig. 5 for transect location). Top panel: un-migrated
radar data. Middle panel: migrated data with a Hilbert magnitude transform applied.
Bottom panel: sketch of major radar reflectors and physical interpretation; also shown are
the locations of corresponding arcuate surface discontinuities (ASD); see text for details.
5. fs05 (Figure S5): Transverse radar profile Fm - Fm’ across Mullins Glacier, collected with the
80 MHz antenna in point mode. Top panel: un-migrated radar data. Middle panel:
migrated data with a Hilbert magnitude transform applied. Bottom panel: sketch of major
radar reflectors and physical interpretation; also shown are the locations of
corresponding arcuate surface discontinuities (ASD); see text for details.
6. fs06 (Figure S6): Transverse radar profile Hm - Hm’ across Mullins Glacier, collected with the
80 MHz antenna in point mode. Top panel: un-migrated radar data. Middle panel:
migrated data with a Hilbert magnitude transform applied. Bottom panel: sketch of major
radar reflectors and physical interpretation.
7. fs07 (Figure S7): Morphometric properties of supraglacial debris on Mullins Glacier; all
samples collected along the glacier centerline (a) Grain size analysis of the < 16 mm
fraction plotted as a function of distance down valley; gravel ≤-1 phi; sand, between 4
and -1 phi), and mud ≥4 phi. Samples were collected 2-5 cm above the buried-ice
surface, regardless of the total debris thickness. Linear trendlines are displayed for the
gravel, sand, and mud fractions. (b) Thickness of supraglacial debris as a function of
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normalized distance along the centerline of Mullins Glacier. Dashed boxes in (a) and (b)
indicate data regions highlighted in Figure 12. (c) Normalized gravel fraction in Region
2 plotted as a function of normalized distance relative to bounding ASDs. The x-axis is
the normalized distance between a given ASD and the next ASD directly down-valley.
The x-coordinate of each data point is calculated as: =
(𝑥𝐻𝑊 − 𝐴𝑆𝐷𝑢𝐻𝑊 )⁄(𝐴𝑆𝐷𝑑𝐻𝑊 − 𝐴𝑆𝐷𝑢𝐻𝑊 ) , where xHW is the distance of the sample
from the headwall datum, and ASDuHW and ASDdHW are the distances of the up valley and
down valley ASD from the headwall datum respectively. The y-axis is the weight
percent fraction of gravel normalized to the total range of fraction values found between
the up-valley and down-valley ASD. The y-coordinate of each data point is calculated
as: = (𝑓𝑠 − 𝑓𝑚𝑖𝑛 )⁄(𝑓𝑚𝑎𝑥 − 𝑓𝑚𝑖𝑛 ) , where fs is the absolute weight percent gravel fraction
of the sample (panel (A)), fmin and fmax are the minimum and maximum weight percent
gravel fractions, respectively, found for the total region within the up-valley and downvalley ASD of the sample location. (d) Normalized sand fraction in Region 2 plotted as
a function of normalized distance relative to bounding ASDs. The axes are defined and
the data normalized following the same procedure as for (c). (e) Normalized debris
thickness as a function of normalized distance relative to bounding ASDs. The x-axis
and values are defined as for (c). The y-axis is the depth of the supraglacial till
normalized to the total range of depths found between the up-valley and down-valley
ASD. The y-coordinate of each data point is calculated as: =
(𝑑𝑠 − 𝑑𝑚𝑖𝑛 )⁄(𝑑𝑚𝑎𝑥 − 𝑑𝑚𝑖𝑛 ) , where ds is the measured depth of the supraglacial till
(panel (b)), dmin and dmax are the minimum and maximum depths, respectively, found
across the total region within the up-valley and down-valley ASD bounding the sample
location.
8. fs08 (Figure S8): Detail of Friedman 80 MHz longitudinal transect centered across IDL-1 and
IDL-2 (See Fig. 5 for location). Top panel: un-migrated 80 MHz radar data. Middle
panel: migrated 80 MHz data with a Hilbert magnitude transform applied. Bottom panel:
sketch of major radar reflectors and physical interpretation; see text for details.
9. fs09 (Figure S9): Transverse radar profile Gf - Gf’ collected with the 80 MHz antenna in point
mode (see Fig. 5 for location). Top panel: un-migrated radar data. Middle panel:
migrated data with a Hilbert magnitude transform applied. Bottom panel: sketch of major
radar reflectors and physical interpretation; see text for details.
10. fs10 (Figure S10): Grain size analysis of supraglacial debris on Friedman Glacier; approach
follows procedures outlined in Fig. 17, panel (a).
11. fs11 (Figure S11): Diagrammatic illustration showing the basic geometry of inclined debris
layers (IDL) and arcuate surface discontinuities (ASD) for Mullins and Friedman
Glaciers. As noted in the text, the GPR data from Mullins and Friedman Glaciers show a
uniform structure consisting of relatively clean glacier ice (containing <1% scattered
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englacial rocks/cobbles) bisected at semi-regular intervals by inclined layers of
concentrated englacial debris (IDL; rock content 20-45% by volume). Most IDL take the
form of eparabolic englacial layers, 1-3 m thick, that extend from near the base of the
glacier, stretch across the entire width of the glacier, and intersect the surface at the
location of arcuate surface discontinuities (ASD); see text for details.
12. fs12 (Figure S12): Measured and modeled ice thickness values for Mullins and Friedman
Glaciers. The measured thickness values (blue line and blue shading) are derived from
GPR. The estimated 5% depth conversion error (blue shading) is equivalent to assigning
a range of average travel velocity from 0.168 m ns-1 (e.g., relatively clean ice) and 0.160
m ns-1 (e.g., relatively debris-rich ice). The modeled thickness values (red line and red
shading) result from the simple steady-state analytical model (section 5.1) that assumes
no basal slip. The spatial extent of the modeled ice thickness is limited in the up-valley
direction by a lack of horizontal-surface flow velocity data in this region [Rignot et al.,
2002]. In the down-valley portion of the transect, the model becomes unstable due to
nearly zero measured ice-surface velocities [Rignot et al., 2002] and small surface
slopes. We minimize the influence of local topography in the model by applying a
smoothing function to the local surface slopes (derived from LiDAR topography [Schenk
et al., 2004]) with a 500 m moving window equivalent to 5 to 10 times the measured
GPR ice thicknesses, and apply a 300 m smoothing function to the measured surface
velocities. The ability of the model to reproduce the observed ice thickness over much of
the lengths of each glacier strengthens confidence in the physical validity of several
critical model assumptions. These assumptions include the lack of active basal slip,
which implies the glaciers are frozen to their beds throughout, and the lack of a subglacial basal deformation component, which implies that basal debris, if present, does not
play a significant role in glacial motion.
13. fs13 (Figure S13): Modeled ice temperatures for Mullins Glacier. To determine the potential
effect of strain heating on elevating basal-ice temperatures, we utilized the thermomechanically coupled ice-flow model contained within the publically available
community Ice Sheet Systems Model (ISSM) [Larour et al., 2012]. Direct coupling
between ice temperature and ice hardness was accomplished via the ice hardnesstemperature relationship discussed in Cuffey and Paterson [2010] or an Arrhenius law
following Payne et al. [2000].
(a) 2-D slice along the central flowline of the ISSM thermal model. Ice core locations
with measured borehole temperatures, and the location of the maximum ice depth are
indicated via the vertical grey bars. Model ice-surface topography were derived from
LiDAR DEM [Schenk et al., 2004] and stereo imagery, interpolated to 1 m resolution.
We used GPR longitudinal transect, Am- Am’ , and all transverse transects to estimate
local ice depths / sub-surface topography (assumed radar travel velocity of 0.168m ns-1).
The full 3-D valley sub-surface topography was then estimated by interpolating between
known GPR depths along the glacier and assuming a parabolic valley cross section. On
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the headwall, where GPR-derived ice depth information is missing, we applied a linear
taper from an ice depth of 1 m at the beginning of the accumulation area to 60 m at the
first know GPR ice-depth point 600m down valley. The model domain was represented
as an unstructured isotropic triangular mesh [Shewchuk, 1996; 2002] of 30 m average
element resolution extruded into 13 vertical layers biased towards increasing resolution
near the valley bed, resulting in 12142 vertices and 20112 model elements. Mechanical
boundary conditions include a free surface boundary at the glacier surface and, assuming
frozen conditions at the bed, a no-slip Dirichlet boundary at the ice-bedrock interface.
We imposed a Dirichlet thermal boundary condition at the surface, setting the model
surface temperatures equal to the measured mean annual temperatures at Mullins met
station locations (Table 1) and interpolating between stations where necessary. For the
headwall region, where measured temperatures were unavailable, we estimated the mean
annual temperature by applying the dry adiabatic lapse rate of -9.868 °C/km, starting
from the measured mean annual ice temperature of -24°C at M_Met_01 (Table 1). At the
basal thermal boundary, we imposed a constant geothermal flux, G. The initial estimate
for G was derived by temporarily ignoring strain heating and extracting the slope from
the resulting linear 2D diffusion model tuned to measured temperature values at 10 m and
30m depth from borehole (MCI-08-01) (Figure 6)(Section 5.2). Surface mass balance
values were estimated in the clean-ice ablation area (Region 1) from ablation stake
measurements (Table S2) and in the debris-covered regions from modeling results of
[Kowalewski et al., 2011] correlated to measured surface debris thicknesses.
(b) Modeled ice temperature depth profiles. Dashed lines show temperature profiles and
geothermal flux estimates derived from applying a simple 1-D diffusion calculation (see
text section 5.2) tuned to measured data points from boreholes MCI-08-01 and MCI-0903. Solid lines show modeled temperature profiles from the ISSM higher order thermomechanically coupled model at the locations of the boreholes and the location of the
maximum ice thickness using an estimated G = 105 mW/m2. All modelling results, even
with unrealistically large values of G, result in sub-freezing basal thermal conditions.
Tables:
14. ts01 (Table S1): Configuration parameters and collection details used for GPR surveys. Data
were collected in one of two possible modes: In distance mode, antennae were fixed at a
common offset and triggered at regular intervals via a terrain-calibrated survey wheel. In
point mode, common offset antennae were manually triggered for a desired number of
stacked scans at a single location. The antennae were then repositioned at the desired
step-size and the process repeated. 80 Mhz, 200MHz, and 400MHz surveys were
conducted in distance mode. Only 80 MHz surveys were conducted in point mode. This
table contains all survey and configuration parameters for each of the two modes and all
antenna frequencies.
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14.1. Column 1: Survey Parameter
14.2. Column 2: Parameter value for 80MHz surveys in point mode
14.2. Column 3: Parameter value for 80MHz surveys in distance mode
14.2. Column 2: Parameter value for 200MHz surveys in distance mode
14.2. Column 2: Parameter value for 400MHz surveys in distance mode
15. ts02 (Table S2): Ablation stake relative surface elevation change. This table contains the
change in the glacier surface relative to ablation stakes over a ~2 year and ~1 year
baseline respectively for Mullins and Friedman Glaciers. It should be noted that Mullins
stake 01 was located in the center of the secondary frozen meltwater pond and does not
represent the ablation dynamics of the glacier ice.
15.1
Column 1 (Stake ID): The ID of the ablation stake. Reference Figure 04 for stake
locations.
15.2
Column 2 (Baseline): The time (in days) between measurements
15.3
Column 3 (Surface elevation Δ): The change in the surface elevation in cm
15.4
Column 4 (Abl. rate): The calculated ablation rate in cm/year
REFERENCES
Cuffey, K., and W. S. B. Paterson (2010), The Physics of Glaciers, 4 ed., Elsevier, Burlington, MA.
Kowalewski, D., D. R. Marchant, K. M. Swanger, and J. W. Head (2011), Modeling vapor diffusion
within cold and dry supraglacial tills of Antarctica: Implications for the preservation of ancient ice,
Geomorphology, 126(1), 159-173, doi:10.1016/j.geomorph.2010.11.001.
Larour, E., H. Seroussi, M. Morlighem, and E. Rignot (2012), Continental scale, high order, high spatial
resolution, ice sheet modeling using the Ice Sheet System Model (ISSM), Journal of Geophysical
Research: Earth Surface 117(F1), F01022, doi:10.1029/2011JF002140.
Payne, A., P. Huybrechts, A. Abe-Ouchi, R. Calov, J. Fastook, R. Greve, S. Marshall, I. Marsiat, C. Ritz,
and L. Tarasov (2000), Results from the EISMINT model intercomparison: the effects of
thermomechanical coupling, Journal of Glaciology, 46(153), 227-238,
doi:10.3189/172756500781832891.
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Rignot, E., B. Hallet, and A. Fountain (2002), Rock glacier surface motion in Beacon Valley, Antarctica,
from synthetic-aperture radar interferometry, Geophysical Research Letters, 29(12), 48-41,
doi:10.1029/2001GL013494.
Schenk, T., B. Csatho, Y. Ahn, T. Yoon, S. W. Shin, and K. I. Huh (2004), DEM generation from the
Antarctic LiDAR data: Site report, http://usarc.usgs.gov/lidar/lidar_pdfs/Site_reports_v5.pdf (September
2012)
Shewchuk, J. R. (1996), Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, in
Applied computational geometry towards geometric engineering, edited, pp. 203-222, Springer,
doi:10.1007/BFb0014497.
Shewchuk, J. R. (2002), Delaunay refinement algorithms for triangular mesh generation, Computational
geometry, 22(1), 21-74, doi:10.1016/S0925-7721(01)00047-5.
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