Jökull - 01.12.1975, Qupperneq 6

Fig. 2. A schemaric sec-
rion of a glacier to illu-
strate symbols.
Mynd 2. Þversnið af jökli
og vatnslóni.
glacier parallel to the bed. The potential (pt)
is given by
(J) Cpb = PwSzb + Pb
The symbol zb represents the elevation of the
glacier bed relative to a horizontal datum level
which is placed at the level of the glacier snout,
pw represents the. density of water, g is the
acceleration of gravity, and pb denotes the
water pressure at the bed-rock.
Ones aim is to find a representative mean
distribution for cpb along the glacier bed. The
pressure pb is taken equal to the overburden
pressure which the ice and water exert on the
glacier bed. For a certain length scale 1 along
the bed the ice overburden pressure can be
taken to be hydrostatic (or glaciostatic, cf. litho-
static) as a result of the glacier creep. On this
scale one can estimate
(2) Pb = Pi g Hj + pw g Hw
in which Hj and Hw are the thicknesses of the
ice and water masses, respectively. The symbols
Pj and pw represent the densities of ice and
water, respectively. This estimate for pb re-
presents mean values for areas of the order of
l2 in which 1 is of the order of, say 10—100 m.
The potential cpb can now be written
(^) cpb = pw g (zb + Hw) + Pi g Hj
By eliminating Hj = zs - zw and Hw = zw - zb
one obtains
(4) cpb = (pw - Pi) g zw + Pi g zs
and the negative pressure gradient
(5) Vcpb = (pw - Pi) g Vzw + p, g Vzs
in which zw represents the elevation of the top
surface of the subglacial water layer, and zs is
the elevation of the glacier surface. Numerical
values for the densities are pw = 1000 kg m-3
for water and pj = 910 kg m~3 for ice.
Equation (5) contains important results. First,
the glacier surface slope is about ten times
more effective than the surface slope of the sub-
glacial water layer in directing the water flow at
the bed-rock of the glacier. In the case of a sheet
flow of water Hw«H^. Then, one can put
Hw sO in Equation (2), and zwíszb. The slope
of the water sheet is then equal to the slope
of the glacier bed. Second, Equation (5) defines
the conditions for the formation of a water re-
servoir at the bed of a glacier, a neccessary condi-
tion for which is that V cpb = ° in the area.
Hence, the equation
defines the relationship between the slopes of
the water/glacier boundary and the glacier sur-
face. The surface of the water reservoir tends
to slope some ten times steeper than the glacier
surface. The slopes of these two surfaces are
opposite in direction. Figs. 3 a and b show two
4 JÖKULL 25. ÁR