Jökull - 01.01.2004, Page 31

Glaciological application of InSAR topography data of W-Vatnajökull
0.65 in 1993 and 0.6 in 1994 (Björnsson et al., 1998).
These values are based on the DEM from 1981 and
are probably underestimated as well due the lowering
of the ablation area of Tungnaárjökull from 1981 to
1994. The net balance on Tungnaárjökull was positive
in 1992 and 1993 and around zero in 1994 (Björnsson
et al., 1998). The mass balance on Köldukvíslarjök-
ull was around +1 m in 1992 and around nil in 1994
but has since been negative (Björnsson et al., 1998,
2002). A comparison of the AAR as a function of the
ELA, based on the new DEM and the DEM and in
the 1980s (Figure 9) shows that for the ELA observed
on Tungnaárjökull in the recent years, the accumula-
tion area percentage of the total area, would be close
to 5% lower (0.05 lower AAR) than if no surges had
occurred. The same applies to Sylgjujökull, Skaftár-
jökull and Síðujökull, which all recently surged, while
the two AAR curves represented for Köldukvíslarjök-
ull, where no large surge occurred, are almost identi-
cal.
A depression in Köldukvíslarjökull created by sub-
glacial melting
A depression in the glacier surface of Köldukvíslar-
jökull was discovered in the DEM from 1998 (Figure
10). This depression is also observed in the DMA
maps (Defence Mapping Agency and the Icelandic
Geodetic Survey, edition 1-DMA, series 761) from
mid 1980s and it appears to exist on the surface DEM
made by the Science Institute in 1982 (Björnsson et
al., 1988c). According to the DEM from 1998, the
depression is around 4 km2 and up to 25 m deep.
Due to the absence of large bedrock bumps this de-
pression can hardly be a flow feature. We suggest
that it is formed by geothermal activity. A sulphurous
odour has been observed from river outlets at the mar-
gin of Köldukvíslarjökull (Guðmundur Jónasson pers.
comm., 1978). The depression is also in line with the
Skaftá cauldrons to the east and the geothermal area
in Hágöngulón, west of Köldukvíslarjökull.
We calculated streamlines around the depression
using n=3 and along two cross sections above and be-
low the depression (Figure 11). The continuity equa-
tion for ice flow between these cross sections (e.g. Pa-
terson, 1994) in terms of volume changes over time
∆t can be written as
∆V
∆t
= Qin − Qout + Bs − Bb (5)
where ∆V is the volume change within the area out-
lined by the streamlines and the two cross sections,
Qin is the ice volume flux flowing into the area
through the upper cross section, Qout is ice volume
flux flowing out of the area at the lower cross section,
Bs is the surface balance rate and Bb is the basal melt-
ing rate.
Mass balance measurements have been conducted
at locations K01, K02 and K03 (Figure 10) since 1991
(Björnsson et al., 2002; Pálsson et al., 2001, 2002).
We applied the surveyed mass balance profile to the
depression but shifted the elevation by the elevation
difference of the margin below the two locations. The
elevation is 880 m below the depression and 930 m be-
low the balance profile. By shifting the balance func-
tion down by 50 m we find that balance around the
depression should be around -3 m/year. By compar-
ing the measured elevation of K02 and K03 in 2001
(Pálsson et al., 2002) with the DEM from 1998 and
the DEM from 1982, we find that the glacier has been
lowered by 4 m/year in K02 but been in balance at
K03. By using the same 50 m shift in height and in-
terpolating with height we estimate that the average
surface elevation change for the depression is around
3 m/year.
Repeated DGPS measurements revealed a surface
velocity of ∼10 m/year in K02 and ∼35 m/year in
K03 (Pálsson et al., 2001, 2002). Using the same
shift and interpolation as before, the velocity at the
upper cross section is ∼20 m/year and at the lower
cross section ∼10 m/year. Using these velocities and
the area of the two cross sections of the glacier we de-
rive Qin and Qout and subsequently, using Equation
5, a basal melting of Bb = 4.3 × 106 m3/year. The
thermal power needed for that basal melting rate is
about 40 MW. The velocity at the lower profile might
be affected by the depression. The derived melting
is, however, not sensitive to changes in this velocity.
We obtain 50 MW and 30 MW for velocities 0 m/year
and 20 m/year, respectively. Since the three variables
(Qin, Bs and ∆V ) are just roughly estimated, due
to lack of data, we can only say that the power of
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