Jökull - 01.01.2021, Page 61

Bedrock and tephra layer topography within the Katla caldera
of the magenta coloured points in Figure 5c, denoting
bed interpreted from the 2D migrated profile, more
than 80 m below the bed derived from the 3D migrated
data; generally the 2D migrated traces are above the
3D migrated DEM due to cross-track reflections. This
was due to wrong interpretation of bed reflection in
the 2D migrated data. The first strong reflection near
the bed in the 2D migrated profiles was considered
to be a reflection from the top of a water chamber di-
rectly beneath the centre of K6. A reflection at greater
depth, considered to be from the bed directly beneath,
was in this case likely a strong cross-track reflection
from a mound 300 m NNE of this location. The actual
bed directly beneath the radar was probably screened
by the water body in spring 2016.
This comparison demonstrates that using 2D mi-
grated RES-data, without any adjustments to compen-
sate for the effects of cross track reflections, will re-
sult in an upward bias of the resulting bed DEM for
steep and rugged bed terrain. The 10 m offset of
2D migrated RES-data for this area is too high to
be explained by other systematic errors. Accurately
repeated surveys, both the 3D migrated surveys pre-
sented here and repeated 2D migrated profiles sur-
veyed on Mýrdalsjökull and Vatnajökull (Magnússon
et al., 2017; 2021) suggest that temporal variations
due to such errors are generally less than 3 m from one
survey to another. A similar experiment comparing
2D and 3D migrated RES-data obtained above steep
bedrock beneath Gulkana Glacier, Alaska, also indi-
cated a similar underestimate in bed elevation from
the 2D migrated data (Moran et al., 2000). The com-
parison presented here also shows that if the effects of
cross track reflections are not considered, measuring
a denser set of profiles than done in 2016 for K6 and
vicinity (∼200 m between profiles) would not have
much increased the accuracy of the interpolated DEM.
The DEM accuracy had already reached the accuracy
of the input data used in the interpolation. This sug-
gests that the interpolation errors were insignificant in
comparison with the errors caused by the limitations
of the 2D migration. The benefit of profiles denser
than 200 m apart for similar radar set-ups in areas of
comparable bed slopes and ice thickness (300–600 m)
are likely small if the effects of cross track reflections
are not considered. For more gentle slopes, denser
profiles can improve the resulting bedrock DEM.
In our study, the difference at the crossing points
of the 2D migrated profiles has been used to adjust the
location of traced bed reflections for the profiles that
are likely to be substantially affected by cross-track
reflections, before carrying out the bedrock interpola-
tion (see Data and Methods and Figure 3). We expect
our simple approach to substantially reduce the errors
caused by cross-track reflections, but we still expect
significant errors of this kind to remain in our bedrock
DEM in steep areas.
Water potential and drainage basins
Using the new bedrock DEM and the surface DEM
from 2019, with 20× 20m cell size, the water divides
between drainage basins (Figure 7b) were updated
from previous work (Björnsson et al., 2000, and more
recent unpublished work of IES-glaciology group)
within the study area. This was done by assuming
that the water flow along the gradient of the static wa-
ter potential, ϕ, at the glacier bed with water pressure
corresponding to the full ice overburden pressure (e.g.
Björnsson, 1975):
ϕ=ρwgzb + ρigH Eq. 1
where ρw=1000 kg m−3 and ρi=900 kg m−3 is the
density of water and ice, g=9.82 m s−2 the accel-
eration due to gravity and zb the bedrock elevation.
H = zs−zb is the ice thickness where zs is the surface
elevation. The procedure of drawing water divides,
as explained in Magnússon et al. (2012), includes fil-
tering of the surface DEM with a circular filter prior
to calculating the water potential. The filter weight
decreases linearly to zero at distances corresponding
to half ice-thickness, hence it is assumed that due to
the strength of the ice, the weight of an ice column
affects the ice overburden pressure over a distance
equal to the ice thickness. The filter smooths out noise
and small scale errors in the DEM as well as actual
small scale features such as crevasses. The revision
of the water divides (Figure 7b) shifts them in some
cases a few hundred metres from the ones presented
by Björnsson et al. (2000). Substantial part of this
change is not related to the improved bedrock DEM
but to difference between surface DEMs; the change
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