Jökull - 01.12.1975, Page 7

examples which illustrate this geometrical rela-
tionship. Beneath a convex glacier surface the
top of a water reservoir would be in concave
shape. For such a configuration a depression
would have to be present in the glacier bed.
Beneath a concave glacier surface a reservoir
has a convex shape, rising above the bed. The
bed-rock itself may even be convex. Given maps
of a glacier surface and the glacier bed-rock
one can determine whether a reservoir is to be
expected at the glacier bed.
Temperate glaciers are considered to be per-
meable to water (Nye ancL Frank 1973, Nye in
press). The flow of water in a cross-section can
be described by the potential distribution
(7) (p (x, z, t) = pw g (z - z0) + p
in which p is the water pressure in the water
passages, x and z are the horizontal and the
vertical coordinates, respectively, z0 is an arbitr-
ary datum level and t is the time. The water
pressure inside the ice may be estimated equal
to the ice overburden pressure pf = p{ g (zs — z),
in which zs is the elevation of the glacier sur-
face. The family of equipotential curves
Cp (x, z, t) = C = constant illustrates the flow of
water in the cross-section. These curves are
given by
In an isotropic permeable medium the stream-
lines would be perpendicular to the equipo-
tential lines.
Figs. 3 a and b show the potential distribu-
tion in a cross-section. The location of the
datum level needs some explanation. The re-
servoir has a shape which gives an equilibrium
of vertical forces such that the overlying glacier
floats in an isostatic equilibrium (one consequ-
ence of Equation (2)). A horizontal datum line
z0 can be placed above the reservoir. The height
of the datum line may be chosen such that the
equipotential line (surface in three dimensions)
cp = 0; (C = 0) marks the roof of the water
reservoir. This elevation is found by adding the
height (pi/pw) Hj (that is °/io of the ice thick-
ness) to the top of the water reservoir. This
datum level is a convenient reference level for
the overburden pressure at the glacier bed. —
According to Equation (8), the surface of the
water reservoir is the mirror image, magnified
vertically by the factor pi/(pw —Pi); of the
glacier surface about the datum level. The same
result is given in Equation (6). The other equi-
potential curves are drawn by the vertical
translation of the curve cp (x> z, t) = 0. In the
ice above the glacier bed cp > 0. Inside the
water reservoir the water pressure is hydro-
static and cp = 0. Water flows towards the
water reservoir from high to low potentials.
Fig. 3. A schemadc sec-
tion of a glacier to illu-
strate the relationship be-
tween glacier surface and
the shape of subglacial
water reservoirs.
a) Stable reservoir in a
bed-depression
beneath a dome.
b) Water cupola beneath
a surface depression.
Mynd 3. Þversnið af jökli,
sem sýnir samband milli
lögunar yfirborðs og
vatnsgeyma.
a) Geymir i skál undir
jökulbungu.
b) Hvelfdur geymir undir
dœld í jökulyfirborði.
JÖKULL 25. ÁR 5