Jökull - 01.01.2021, Page 30

Gudmundsson et al.
(http://earthice.hi.is/node/900) indicate a net negative
balance close to -10 m a−1 at 200–300 m a.s.l. No
other mass balance measurements have been carried
out for the ablation of the two glaciers. However,
comparison with mass balance measurements on e.g.
Breiðamerkurjökull (Pálsson et al., 2020) provides
helpful constraints, as it covers the elevation range
seen in the ablation areas of Kötlujökull and Sól-
heimajökull. The details of the cross sections, net bal-
ance values, balance velocities and travel times down
both glaciers are given in Appendix A. The results for
ice-flow velocity are presented in Figure 4 (b and c).
Two velocity values are used: (1) The average veloc-
ity that assumes the same, constant velocity over each
cross section, and (2) a maximum velocity. As ice
flow will be slower near the glacier bed and its mar-
gins on both sides (e.g. Cuffey and Paterson, 2010),
the average is an underestimate of the velocity trans-
porting the tephra on and near the central flow-line of
the glacier. To account for this we use a maximum ve-
locity of 1.25 times the mean (Figure 4b and c). This
value is based on the analysis of the actual transfer of
the layer down the outlet glaciers and its comparison
with the calculated balance velocities (Appendix A).
Changes to tephra layer thickness caused by ice-
flow are to a first order expected to be mainly due to
pure shear (vertical compression and horizontal elon-
gation) above the equilibrium line. In contrast, simple
shear (deformation due to gradients in velocity per-
pendicular to flow resulting in differential movement
of parallel planes in the ice) is expected to be impor-
tant near the edges and the bottom (Hudleston, 2015)
but should be relatively minor elsewhere. We there-
fore expect that stretching and thinning of a tephra
layer mainly occurs during its flow through the accu-
mulation area. Thus, the total thinning during trans-
port from the point of deposition of tephra to the point
of maximum velocity will be the same as the ratio of
the maximum velocity and the velocity at the location
of fallout. The total amount of lateral transport in the
direction of ice flow since the eruption can be esti-
mated from the balance velocity of these two glaciers
and this is summarized in Appendix A.
Kötlujökull: The 1918 tephra layer is presently ex-
posed about 10 km below the equilibrium line (Fig-
ure 4a and 4b). The constraints described above put
the most likely point of tephra fall 5–5.5 km above
the equilibrium line, at an elevation of about 1300 m
a.s.l. We put the most likely point slightly to the north
of the present day flowline (Figure 4a), as ice flow
for some years after the eruption would have been de-
flected southwards, towards the centre of the depres-
sion formed around the eruption site and described
by the observers in 1919 (G. Sveinsson, 1919 and P.
Sveinsson, 1930). The total lateral displacement is
estimated to be about 15 km. A calculated maximum
velocity of 470 m/yr occurs just below the equilibrium
line while the velocity at the suspected place of fallout
is approximately 65–70 m/yr, resulting in an estimate
of total stretching and thinning of the tephra layer by a
factor of 6.5, with the 35 cm thick layer exposed now
translating to an original fallout thickness of∼230 cm.
Sólheimajökull: Using the same approach as for
Kötlujökull, with the layer exposed at 8–9 km below
the equilibrium line, the estimated location of fall-
out lies 2–3 km above the equilibrium line and total
transport down-glacier is estimated as about 11 km.
The calculated maximum velocity of 250 m/yr occurs
close to the equilibrium line while velocity at the loca-
tion of fallout is about 70 m/yr, stretching by a factor
of ∼3.6, and an initial layer thickness of ∼120 cm.
Sléttjökull: In contrast to the valley-confined outlets,
the broad, lobe-like geometry and much lower balance
velocities at Sléttjökull (15–25 m/year), result in dis-
placements of 1.5–2 km since 1918 and insignificant
thinning.
These results have considerable uncertainty, both
in terms of fallout location and initial thickness. It is
likely that disturbance to ice flow near the eruption
site in 1918 was considerable, possibly resulting in
lower flow velocities in Kötlujökull in the first years
after the eruption, similar to what was observed within
the depression formed in the Gjálp eruption in Vatna-
jökull in 1996 (Jarosch et al., 2008). Despite this un-
certainty, we consider the overall results robust, and
that the tephra now exposed on the lower parts of the
outlet glaciers of Kötlujökull and Sólheimajökull fell
inside the caldera and has experienced a large amount
of thinning.
28 JÖKULL No. 71, 2021