Jökull - 01.01.2021, Page 39

The 1918 Katla eruption
Figure A1. Sólheimajökull and Kötlujökull. Estimate of the ratio of the actual travel velocity of the layer (Vmax)
and the calculated balance velocity (Vmed). – Mat á hlutfalli reiknaðs jafnvægishraða og raunverulegs hraða
gjóskulagsins niður Sólheimajökul og Kötlujökul.
a.s.l. for Kötlujökull and 1100 m a.s.l. for Sóheima-
jökull. Cross sections through which ice flows were
estimated from the surface map and bedrock maps
(Björnsson et al., 2000; Mackintosh et al., 2000; Páls-
son et al., 2005). When estimating the width of the
section for each glacier, the shallowest part along the
sides was omitted in both outlet glaciers, as well as
very thin ice over major obstacles. The balance values
were adjusted, keeping the equilibrium line fixed, un-
til a net balance of -0.2 to -0.3 m/yr was obtained. The
calculations are presented in Tables A1 and A2. The
numbers obtained indicate that the net mass balance
in the accumulation area of Sólheimajökull is some-
what lower than for Kötlujökull, in broad agreement
with the findings of Ágústsson et al. (2013). More-
over, higher ablation is required for the lower parts
of Sólheimajökull than for Kötlujökull to obtain the
slightly negative mass balance. It is beyond the scope
of this work to elaborate on possible explanations,
but less extensive tephra cover on the lower parts of
Sólheimajökull, coupled with it facing south while
Kötlujökull faces east, are among possible explana-
tions for this difference.
The fact that the tephra layer emerges from the
ice through surface ablation proves that it must have
fallen on the accumulation areas, above the equilib-
rium line. An estimate of the location of fallout for
the tephra exposed at each glacier can therefore be
obtained by finding the approximate travel time be-
low the equilibrium line from the velocity values,
subtracting the result from the time since the erup-
tion (94 years for sampling in 2012), and then use the
velocities above the equilibrium line to estimate the
distance of travel in the accumulation areas. Time of
transfer, ti, along a central flowline between points
defined by a 100 m surface height difference is esti-
mated assuming a linear change in flow velocity with
distance. If the velocity at the up-slope boundary is
vi and at the downslope boundary vi+1 of the longitu-
dinal section of length x, the distance travelled over
time dt is dx, or
dx = (vi + ax ) dt (1)
As the change in velocity is assumed linear the gra-
dient in velocity over distance is defined as a =
(vi+1 − vi)/x, where vi and vi+1 are respectively
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