Jökull - 01.01.2021, Page 40

Gudmundsson et al.
the ice velocities at the up-slope and down-slope ends
of the longitudinal section. Inserting a into (1), solv-
ing for dt and integrating, the result is
ti = x
vi+1−vi
ln[vi+1
vi
] (2)
Tables A1 and A2 show travel times for each 100 m
height interval between 1300 m and 400 m elevation
on Kötlujökull and 1300 m to 300 m on Sólheimajök-
ull. The results indicate travel times of 88 years for
Kötlujökull and 91 year for Sólheimajökull, slightly
less than the 94 years between eruption and time of
sampling assuming that the velocity was 1.25 times
the calculated average balance velocity. This value of
1.25 is derived by finding the velocity that best fits the
location of the tephra layer in the two outlet glaciers
in 1937 and 2012.
The 1937 position is estimated from aerial photos
taken by the Danish Geodetic Institute. Figure A1a
shows the best fitting estimate for the velocity over
the period 1918–1937. Figure A1a shows the calcu-
lated travel time from the equilibrium line (6.4 km for
Kötlujökull, 3.8 km for Sólheimajökull). Since the
layer emerged from within the ice in 1937 as indi-
cated schematically in Figure 4b, it is assumed that
it must have originated within the accumulation area
and experienced burial for a minimum of 2–4 years.
The travel time within the ice of the ablation area is
therefore estimated to have been 15–17 years (hori-
zontal dashed lines in Figure A1a). This is achieved
with Vmax/Vmed = 1.26.
For the period 1918–2012, figure A1b shows the
calculated total travel time from the 1300 m contour
down to the location of the tephra layer in 2012. As-
suming that the time of transport above the location of
the 1300 m contour was between zero and 10 years,
travel time from the 1300 m contour was 84–94 years
(horizontal dashed lines in Figure A1b). The best fit-
ting estimate is Vmax/Vmed = 1.24. The value of 1.25
is the mean of the values for 1937 and 2012. For
Kötlujökull the calculated time of travel through the
ablation area of the tephra that become exposed in
2012, is about 50 years and just over 70 years at Sól-
heimajökull. Although these values have considerable
uncertainty they constrain the fallout locations to spe-
cific regions in the accumulation areas.
38 JÖKULL No. 71, 2021