Jökull - 01.12.1974, Side 17

Fig. 12. A model of the
Grímsvötn water basin
illustrating terms in the
water and energy bal-
ances.
Mynd 12.
Líkan af vatnasvœði
Grimsvatna.
been carried out in the water basin. However
on the basis of numerous occasional measure-
ments (published in Jökull since 1951 and re-
cently added to by core drillings) one can esti-
mate the glacier surface accumulation rate c =
2200 mm/yr and the surface ablation rate as =
500 mm/yr (not more) as average values for
the water basin. To show the mass balance
variation over the glacier surface, the water
basin is divided into two parts. For the south-
ernmost part of the water basin, an area of
100 km2 south of the 1650 m elevation contour,
values of c = 3000 mm/yr and as = 1000 mm/yr
are estimated. For the northern part of the
water basin (200 km2) values of c = 1800 mm/yr
and as = 400 mm/yr are estimated. The surface
net balance rate is b = 2000 nim/yr in the south
area and b = 1500 mm/yr in the north area.
The known estimates of the jökulhlaup run-
off volumes can be used to test the mass balance
model. For A = 300 km2 and an average of
c = 2200 mm/yr for the entire water basin,
equation (7) yields a total water flow rate into
the lake of q = 0.66 km3/yr. The measured
volumes of jökulhlaups (V) are approximately
3—3.5 km3 for one jökulhlaup every 5 to 6
years and approximately 6—7 km3 for one
jökulhlaup in a decade. The good agreement
between the predicted water accumulation rate
and the estimated volume of jökulhlaups sug-
gests that the steady state assumption (Eq. (7))
ts a valid approximation even though Vatna-
jökull has been shrinking during the whole of
the present century. Likewise, the result cloes
not contradict the assumption of a closed water
basin.
The conservative estimate of as = 500 mm/yr
for the surface ablation rate in the water basin
implies (according to equation (3)) that a water
volume of about (%) q = 0.50 km3/yr must be
melted subglacially by a geothermal area. The
power of this geothermal area, given by equa-
tion (4), is therefore Q = 1.5 • 1017 J/yr or 5000
MW.
The ice flux into the geothermal area
For a steady state glacier, the surface balance
inside the geothermal area, added to the ice
flux into the geothermal area, is equal to the
ice volume melted by the geothermal area. If
the melting capacity of the geothermal area and
the net surface balance are known, equation
(6) can be used to estimate the ice flux into
the geothermal area and to estimate the extent
of the geothermal area.
Data on the surface balance in the water
basin show that the balance (b) decreases from
Grímsvötn towarcl the north. The balance is
therefore higher inside the geothermal area
(Aff) than in the part of the water basin that
is outside the geothermal area. A trial and
error solution of equation (6) yields a geo-
thermal area Ag of approximately 100 km2.
Tlie surface balance terms are given above;
c = 3000 mm/yr and as = 1000 mm/yr in-
side the geothermal area and c = 1800 mm/yr
JÖKULL 24. ÁR 1 5