Jökull - 01.12.1975, Qupperneq 8

Subglacial water reseruoirs
and their stability
The geometry of the subglacial water re-
servoirs has been discussed. The stability of the
reservoirs will now be examined.
Fig. 3 a shows a cross-section through a con-
vex glacier surface. A reservoir is situated be-
neath a dome. The flow of water along the
glacier bed depends on the potential cpb in
Equation (1). The potential cpb attains a max-
imum at the centre of the reservoir. If the
glacier is permeable, the water flow in the
cross-section can be described by the potential
distribution cp (x, z, t) = constant. The equi-
potential curve cp = 0 lies above the bed along
tlie entire cross-section. A water divide is locat-
ed beneath the crest of the dome. Meltwater is
continually drained outwards from the dome.
Water flows out from the reservoir at the same
rate as into it. The reservoir remains constant
in size and no jökulhlaups are to be expected.
Oswald and Robin (1973) reported evidence
for reservoirs of this type beneath the Antarctic
Ice Sheet. Detailed mapping of glacier bed topo-
graphy may reveal such reservoirs beneath gla-
ciers in Iceland. Small reservoirs may be situat-
ed in volcanic craters such as Öræfajökull, Eyja-
fjallajökull and Snæfellsjökull, and in calderas
like those observed on ERTS images at Kverk-
fjöll and in Mýrdalsjökull. One might look for
reservoirs in the central parts of Langjökull
and Hofsjökull. The only possible site in the
central part of Vatnajökull appears to be be-
neath the saddle 20—30 km east of Grímsvötn,
see Fig. 1 and a map of surface contours in
Björnsson (1974).
Consider next the growth of a reservoir be-
neath a depression. Fig. 3b shows a cross-section
through a concave glacier surface. The glacier
bed is taken as a plane. The potential qjb at-
tains a minimum beneath the depression and a
maximum at the point C. The maximum for
cpb defines a watershed at the point C. Water
will flow along the bed towards the minimum
of (pb and accumulate beneath the depression.
Water flows towards tliat point. A dome shaped
water reservoir rises like a cupola above the
glacier bed. The overlying glacier is gradually
lifted.
The shape of the water cupola is at any time
6 JÖKULL 25. ÁR
given by the curve qj = 0 or C = 0 in Equation
(8). At a time t0 no water has been accumulated
beneath the depression. The equipotential curve
Cp (x, z, t0) = 0 touches tlie glacier bed in one
point beneath the centre of the depression.
Fig. 3b shows the cupola at time t > tu.
The curve cp = 0 lies beneath the glacier bed
outside the reservoir. The bed attains a posi-
tive potential which indicates that water will
be forced along the bed towards the reservoir.
Thus, the reservoir is sealed by a potential
barrier. The barrier has a width W and a thres-
hold value T, see Fig. 3b. As the cupola grows
the potential barrier is reduced. If the curve
cp = 0 is raised above the glacier bed, a hyd-
raulic connection is introduced between the
reservoir and the subglacial waterways outside.
As water escapes from the cupola the water
pressure at the reservoir starts dropping. The
waterways outside the reservoir will tend to
colse due to the ice overburden pressure, but
the seal will not be restored. Since water is
draining from a voluminous reservoir into a
narrow waterway the pressure head at the re-
servoir will drop very slowly. For some time
after the seal is broken water flows out of the
reservoir at a constant pressure. Frictional heat
from the flowing water will melt ice forming
subglacial tunnels. The tunnels will tend to
close due to the overburden pressure. However,
the rate of enlargement of the tunnels can be
expected to exceed the rate of closure (Liestöl
1956, Nye in press). Therefore, a jökulhlaup
results if any water escapes from the water re-
servoir.
A straight forward argument proves that ac-
cumulation of water beneath a depression must
lead to a jökulhlaup. A surface depression sets
up a potential barrier. The depression is partly
reduced by the rise of a water cupola, partly
by the inflow of ice. As water is denser than
ice, the potential barrier is reduced to nil be-
fore the surface depression is filled up again.
Consider a model in which the glacier thick-
ness is constant. The datum level z0 is trans-
lated upwards at the same rate as the centre of
the water cupola. The roof of the reservoir,
which is given by the curve cp = 0, is translated
upwards at this rate. But outside the cupola
the curve cp = 0 is lifted ten times faster, see
Equation (8). The potential barrier is reducecl
to nil before the depression is filled. — One