Jökull - 01.12.1977, Page 24

Fig. 7. The left part shows approximate curves
correlating tlie function ln (H/y) and observed
age (according to the model, tobs) for different
glacier thickness (H). The inset in the right
half shows the deviation in observed depth from
that calculated, for the best-fit curve (H =
519 m).
spaced. In order to overcome tliis weakness we
can relax the first simplifying assumption and
assume instead that X only remains constant
within eacli time interval. The X-value for a
given interval tj to ti+1, Xj, can then be
calculated as follows:
First the corresponding layer between the
two liorizons dt and d is in effect “brought
to the surface” by multiplying the measured
thickness d i+1 — d( by the ratio H/yt, where
y4 = H — dj. Then we are in a position to make
use of a relation analogous to (a) in order to
estimate X(, the result being that
X,=
H
1 i+l —
ln
P'
V Yi+1
(c)
Once eacli X( has been calculated the mean
balance X for the entire profile can be cal-
culated:
Mynd 7. Ferlarnir til vinstri lýsa sambandi
hœðar yfir jökulbot7i (y) og aldurs (tobs) skv.
likaninu, fyrir mismunandi þykkt jökulsins (H).
Minnst frávik frá beinni linu fcest fyrir H =
519 m, og hœgri hluti myndarinnar sýnir frá-
vik mceldrar dýptar á hin ýmsu lög frá reiknaðri
dýpt þeirra fyrir þessa þykkt.
_ u / u
X = 2 cOiXi / 2c0i (d)
i=l / i = l
where a>i — t i+1 — tj, i.e. a weighting factor pro-
portional to the length of each period. The
“best fit” is obtained varying H by trial and
error to minimize the weightecl variance s2:
(p = 0.9 g/cm3) in the interval to about 100 m
depth. In order to compensate for this we may
imagine that the glacier is compressed so as to
make the density uniform. Measuring all thick-
nesses in meters this compression was approx-
imated by the equation
dj = dj - 12.5 (1 - e _a4 di), i = 1,... M (b)
wliere d( is the depth to a given horizon, start-
ing from the top of thc profile, whereas dj is
the depth in the compressed glacier, M being
the number of data points. Accordingly we
have for the total thickness of the compressed
glacier, H, that H = H — 12.5. Using the cor-
rected data, a best fit similar to tliat in Fig. 7
is obtained for H = 521 m and X = 2.53 m/yr.
An obvious weakness of the above analysis,
apart from having to accept the simplifying
assumptions leading to (a), is that undue em-
phasis is put on the uppermost (younger) part
of the profile, as the points there are better
22 JÖKULL 27. ÁR
M 2 M 2 / 11
2 WiXi - ( 2 WiXi \ / 2aii
„o »=1 ^ i = l / / ' i = l (e)
M
2 i i = l
Using the corrected depths as described above
(eqns. b—e), and all the data points, yielded
the following results
H X s2
600 2.11 0.2945
590 2.14 0.2934
581 2.18 0.2931
580 2.18 0.2931
579 2.18 0.2931
575 2.20 0.2932
560 2.26 0.2956
526 2.43 0.3226
500 2.63 0.3979
420 4.88 13.3714