Jökull - 01.01.2016, Page 6

Eyjólfur Magnússon et al.
ment between the antenna centres is likely to be bro-
ken at such locations. The 2D migration, which as-
sumes a profile along a straight line, will also generate
less accurate results at profile turns. Finally, to obtain
a record with resolution along profile comparable to
the resolution of the final bed DEM (20 m×20 m cell
size) the elevation of bed traces was filtered along the
length of each profile with 20 m wide triangular fil-
ter (weight of centre value 3 fold that of the edges)
and down sampled to one value each 20 m along the
profile.
The velocity of an electromagnetic wave in snow
and ice is variable, mostly depending on density and
water content. Below we justify our choice of assum-
ing propagation velocity of the radar signal through
the glacier, Cgl, equal 1.70×108 m s−1 (averaged
from glacier bed to surface). The RES data was
compared with a photogrammetric DEM of a glacier
free area in 1994 (Belart, 2013; Magnússon et al.,
2016) buried by glacier during the most recent surge
of Leirufjarðarjökull outlet glacier (Björnsson et al.,
2003; Brynjólfsson et al., 2015). The RMS error
of the bare ground DEM was estimated to be only
1.04 m (estimated from ice free Lidar data; Magn-
ússon et al., 2016). The comparison shows that the
RES bed elevation is on average 2.2 m above the 1994
glacier free DEM with 2.4 m standard deviation (Fig-
ure 4), when using Cgl=1.70×108 m s−1. The de-
rived glacier thickness for this comparison data spans
17–98 m. The difference suggests an average ∼3.5%
underestimate of the glacier thickness indicating that
Cgl=1.75×108 m s−1 would be the appropriate veloc-
ity value. Cgl=1.70×108 m s−1 was however used in
our processing since it results in ∼0 m difference in
the thicker part of the comparison area, with glacier
thickness approaching 100 m. This is more appropri-
ate for the whole data set with average glacier thick-
ness of ∼120 m (thickness at profiles in March 2014).
Both above values of Cgl are unusually high. Clear
dry ice with density of 900–920 kg m−3, has Cice of
1.68–1.70×108 m s−1 (e.g. Evans and Smith, 1969),
while values from wet ice in the ablation area of a tem-
perate glacier typically span 1.55–1.65×108 m s−1
(e.g. Bradford et al., 2009; Murray et al., 2000). Two
physical factors can contribute to the high Cgl in the
range of 1.70–1.75×108 m s−1: Relatively low water
content of the glacier in late winter and a thick win-
ter snow layer (Csnow may exceed 2.00×108 m s−1;
see e.g. Evans, 1965) relative to the glacier thick-
ness. Snow thickness obtained from snow coring dur-
ing the RES survey revealed ∼7 m of snow in the main
area covered by the 1994 comparison DEM. The thick
snow layer could also explain the why the difference
between the 1994 DEM and the RES bed elevations
decreases with increasing glacier thickness.
Underestimates of the glacier thickness may be
caused by the shortcomings of the 2D migration. This
typically occurs when profiles are not driven parallel
to the maximum slope of a steep bed. In such cases the
migrated reflection may be shifted upwards by cross
track bed reflections originating up-slope from the
measurement location. Profiles were generally driven
close to parallel to surface slope, often also reflecting
the bed slope direction, to minimize this effect. De-
spite such effort to avoid erroneous interpretation, mi-
gration error is likely to result in underestimate of the
glacier thickness (assuming a correct value of Cgl).
Using a Cgl value slightly higher than the true Cgl
would compensate for the mean offset caused by the
migration errors. This may to some degree explain
the relatively high Cgl value indicated by the compar-
ison (Figure 4). The comparison data is from pro-
files that are representative of other profiles in terms
of bed topography and how they are aligned relative to
bed slope direction; hence we assume that the possi-
ble overestimation of Cgl, relative to the „true value“,
is likely to reduce the mean offset caused by the mi-
gration errors in other areas as well.
There are 189 crossovers in the RES-profile set.
About half of them have <1 m difference for the trian-
gular filtered bed traces, 92% <4 m difference and all
except 3 have <7.5 m difference. The three outliers,
which have 10, 14 and 20 m difference are all from
sites where the bed slope is very steep (∼45◦ for the
20 m difference). Large difference can be expected at
such location since the 2D migration is very much de-
pendent on whether the profiles were driven approx-
imately parallel to the bed slope direction or not, as
explained above. RMS difference of the traced bed
elevation at the crossing points, with and without the
6 JÖKULL No. 66, 2016