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GSA Data Repository 2017176 1
Palaeofluvial and subglacial channel networks beneath 2
Humboldt Glacier, Greenland 3
Stephen J. Livingstone1, Winnie Chu2, Jeremy C. Ely1, Jonathan Kingslake2 4
1 Department of Geography, University of Sheffield, Sheffield, UK. 5
2 Lamont‐Doherty Earth Observatory, Columbia University, Palisades, New York, USA. 6
E‐mail: [email protected] 7
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The supplementary information provided here adds detail to the methodology involved in the 9
investigation of basal properties from the radio echo sounding data and in the derivation of subglacial 10
and preglacial drainage pathways. 11
IceBridge radar sounding data 12
Here we used the airborne ice‐penetrating L1B radar products collected by the NASA Operation 13
IceBridge campaigns in May 5, 2012 and May 1 to 5 in 2014. These data were obtained using the same, 14
195 MHz radar system, the Multi‐Channel Coherent Radar Depth Sounder 2 (MCoRDS2), operated on a 15
NASA P3 aircraft for both years. The MCoRDS system has a frequency range of 180 – 210 MHz and a 16
transmit power of 1050 W. The along‐track resolution depends on the processing, undertaken by Center 17
for Remote Sensing of Ice Sheet (CReSIS) from the University of Kansas. The standard processing steps 18
for the L1B products involve pulse compression with time and frequency domain windows (usually 19
boxcar or hanning) and correction for aircraft motion, followed by coherent stacking and focused 20
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synthetic aperture radar processing (Gogineni et al., 2001). More details about both the MCoRDS system 21
and the processing can be found at http://data.cresis.ku.edu. 22
The L1B product has a theoretical range resolution of <1 m and an along‐track resolution of around 25 23
m. The cross track resolution varies depending on the roughness of the ice surface. Assuming a rough 24
ice surface (but with no significant layover), an aircraft height of 500 m above the surface and an ice 25
thickness of 1000 m (typical for the data we consider here), the cross track resolution is around 255 m. 26
The bed was picked by CReSIS with a combination of automatic and manual picking techniques. 27
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Basal properties from radar bed power 29
Radar power returned from the ice‐bed interface is a powerful tool for characterizing the subglacial 30
environment of ice sheets. The bed reflectivity, in particular, has been used to identify the distribution 31
of subglacial water in both the Antarctic and Greenland Ice Sheets (Oswald and Gogineni, 2008; Jacobel 32
et al., 2009; Matsuoka et al., 2012; Macgregor et al., 2013; Wolovick et al., 2013; Schroeder et al., 2016). 33
The relationship between basal reflectivity and subglacial hydrology is not simple and relating the two 34
must take account of important caveats that we discuss below. We calculate bed reflectivity, , from 35
the bed returned power, , using the radar equation, which, following the notation of Matsuoka et al. 36
(2011), is 37
, (1) 38
Where is the instrumental factor, is the two‐way englacial attenuation loss, is the geometric 39
spreading loss, and the square bracket notation denote that these quantities are expressed in decibels 40
( 10 ). The geometric spreading loss is a function of ice thickness, , the elevation of the 41
aircraft from the ice surface, , and the index of refraction of ice, (assumed to be 1.78), 42
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2 , (2) 43
The geometrically corrected returned power, , is related to variations to englacial attenuation 44
and bed reflectivity as follows, 45
, (3) 46
With an accurate estimation of , equation (3) provides a way of computing spatial variations in . 47
[S] is an instrumental factor term including transmitted power, system gain and surface transmission. 48
We assume that these settings were constant throughout the campaign, and since the 2012 and 2014 49
campaigns use the same MCoRDS radar system, the influence of the instrumental factors on the 50
reflectivity pattern should also be relatively constant between the two years. We estimate depth‐51
averaged englacial attenuation losses based on the proportionality between the geometrically‐corrected 52
returned power and the ice thickness separately for each year (Winebrenner et al., 2003; Jacobel et al., 53
2009). Estimation from a linear fit to a plot . gives regional englacial attenuation rates of 19 54
and 21 dB/km for the measurements collected in 2012 and 2014 respectively (Fig. DR1). For 2012, the r2 55
value of the fit is 0.72 with a RMSE of 3.9. For 2014, the r2 is 0.66 and 5.4 for the RMSE. The relatively 56
high (>0.6) r2 coefficient indicates that the thickness dependence of the returned power provides a 57
reasonable estimate of englacial attenuation rates if the basal reflectivity is independent of ice thickness 58
(Raymond et al., 2006; Matsuoka et al., 2012). 59
We are interested in examining if we can detect areas of the bed that, due to the presence of subglacial 60
water or a very smooth ice‐bed interface are anomalously bright. We take the simple approach of 61
extracting locations of the bed with a positive reflectivity anomaly exceeding 15 dB (Fig. DR2). This 62
threshold (15 dB) exceeds both the RMS residuals of our depth/bed‐power fit (Fig. DR1) and previously 63
used thresholds used to characterise hydrological properties of the bed (nominally 10 dB) (Peters, 2005; 64
Matsuoka, 2011; MacGregor et al., 2012). In these previous studies, areas where basal reflectivity 65
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exceeds around 10 dB above the mean have been have been interpreted as areas with more subglacial 66
water than other areas. 67
We interpret the alignment of positive bed power anomalies with subglacial channels as supporting 68
evidence that the channels route subglacial water (main text). This is consistent with theoretical flow 69
routing (see below), but a number of caveats related to this radar interpretation need to be 70
considered. An alternative explanation for high reflectivity is a smooth ice‐bed interface. This could be 71
due to a layer of glacial till in contact with the ice base, which is possible in the channels. However, 72
recent analysis of radar data over Humboldt Glacier, considering a different aspect of the bed return (its 73
“peakiness”) by Jordan et al. (2017), suggests that basal roughness is approximately uniform across the 74
part of the bed we consider here. 75
We assume that englacial attenuation is uniform across each year’s survey. However, attenuation rates 76
can vary on a regional scale due to variations in ice temperature and impurity content. It may be 77
reasonable to speculate that the attenuation rate could be higher over the channels, where ice is thicker 78
and driving stresses are higher, but a full solution to this problem would require a 3D thermomechanical 79
ice‐flow model (e.g. Chu et al., 2016) and consideration of the impact of variable internal layer dip (e.g. 80
Holschuh et al., 2014). For this work, we are motivated to make the simple uniform‐attenuation 81
assumption due the reasonable fits between bed power and ice thickness (Fig. DR1). The along‐track 82
resolution of the radar (25‐255 m, along and across track) is much smaller than the spatial extent of the 83
channels, so focussing effects over concave‐up features (such as channels) will be small. 84
We cannot quantify surface conditions and the impact this could have on the apparent bed power. We 85
have no evidence for systematic differences between surface conditions over the channels and 86
elsewhere, but mass balance is known to vary with sometimes‐subtle variations in surface topography 87
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so we cannot rule this out. Future work could use radar systems designed to observe near surface 88
englacial structure to search for such a systematic difference, but this is beyond the scope of this work. 89
Subglacial and preglacial drainage analysis 90
To assess the origin of the channels, we calculated hydrological potential pathways for a number of 91
different scenarios, following the approach of Shreve (1972). The hydraulic potential is given by 92
, (4) 93
where, is the density of water (1000 kg/m3), is acceleration due to gravity, is the bed elevation 94
and is water pressure. In order to calculate the large‐scale drainage pattern, and in the absence of 95
direct data on water pressure, we can make the assumption that the water pressure is equal to the ice 96
overburden pressure. Equation (4) can therefore be re‐written as 97
, (5) 98
where is the density of ice (917 kg/m3) and is the ice thickness. Equation (5) allows us to evaluate 99
the hydraulic potential in a Geographic Information System from bed elevation and ice thickness data. 100
Water is then routed across the hydraulic potential surface using a flow algorithm in ArcMap 10.2. This 101
single‐flow algorithm calculates the hydraulic potential gradient using the D‐infinity flow model, and 102
routes water down the steepest gradient (Tarboton, 1997). Prior to routing, sinks were filled in to 103
produce a freely draining network. 104
First, drainage was calculated beneath the present‐day ice sheet (Fig. 3d) using the mass conservation 105
bed and ice‐surface DEMs (Morlighem et al., 2014). Secondly, following Bamber et al. (2013), we 106
calculated fluvial drainage over a preglacial topography by isostatically correcting the mass conservation 107
DEM to account for the modern ice load (Fig. 3b). As the water pressure in the preglacial experiments 108
are not influenced by an overlying ice mass, they could be calculated in ArcMap without Equation (5). In 109
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addition, to allow comparison of drainage routeways with and without the influence of the channelized 110
topography the mass conservation bed DEM was also smoothed to remove the channels in both the 111
preglacial (Fig. 3a) and present‐day scenarios (Fig. 3c). The smoothing was done in ArcMap 10.2 using 112
focal statistics, which calculates the mean of values within a 15 x 15‐km moving window. 113
SUPPLEMENTARY FIGURES 114
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Figure DR1: Geometrically corrected bed power versus ice thickness for 2012 (A) and 2014 (B). The 116
quality of the fit was estimating using the root mean square error (RMSE) (units: dB) and the coefficient 117
of determination (r2). 118
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Figure DR2: All potential water locations (>15 dB) calculated from the 2012 and 2014 radar lines (grey 121
lines). The high bed reflectivity patches towards the SW of the image, where the bed is more elevated, 122
coincide with an area of smooth terrain determined by Jordan et al. (2017) from the abruptness (pulse 123
peakiness) of the radar return. Thus, the high reflectivity in this region is probably a result of the bed 124
roughness. Conversely, the abruptness values are relatively consistent within the main Humboldt Basin, 125
which supports our interpretation that the bed reflectivity here is most likely a hydrological signature 126
rather than due to variations in roughness. 127
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