Jökull - 01.01.2001, Side 10

Helgi Björnsson et al.
face geometry (
and  ) of Breiðamerkurjökull
for those years. The upglacier position of the vertical
cross section remained fixed to the 1998 position (see
Figure 2b). The cross section was limited to the west
by the Esjufjöll medial moraine but extended eastward
with time, to account for all ice drainage toward the
lake. The ice depth at the cross section was obtained
from observed changes in glacier geometry (Björns-
son et al., 1992; Boulton et al., 1982). The distribu-
tion of the surface velocity along the cross section was
assumed to be the same as in 1997–1999 (Figure 6).
Figure 6. Measured mean velocity through a cross
section above Jökulsárlón, 1997 to 1999. a) Location
of stakes for measuring the surface velocity ( 
).
Surface and bedrock contours are shown; see also
Figure 2a. b) Measured and estimated distribution
of the mean annual velocity over a cross section. –
Mældur meðalskriðhraði um snið ofan Jökulsárlóns
1997–1999.
Using this approach the following empirical rela-
tionship was obtained for the calving rate in m yr 

(Figure 8a):
  
  (7)
where


is water depth (in m) of the central flow
line toward the calving front (Figures 2, 4 and 6). Us-
ing average values of


over the entire calving front
we obtain  = 4.9
 + 3.6 (Figure 8b). These es-
timates of calving rate for the saline Jökulsárlón are
higher than those for fresh water lakes, where Funk
and Röthlisberger (1989) suggested  = 1.9
 +
12. The calving rate is, however, much lower than
for glaciers calving into fjords (Meier and Post, 1987)
and for tidewater glaciers in Alaska where Brown et
al. (1982) derived  
 with  = 27.1 2 yr 
.
SIMULATION OF PAST AND FUTURE
ICE FLUXES
Our models, tuned by observations of 1997–1999,
were used to simulate past and present ice fluxes at
the terminus of Breiðamerkurjökull.
Reconstruction of past ice fluxes
Data on the geometry of Breiðamerkurjökull during
the 20th century were used to determine the compo-
nents in equation (1) at the terminus (Figure 9) for
every year, in a similar way as described for 1997 to
1999. Calculated values are given in Figure 9. Both
the ice flux toward the lake ( !#" ) and the calving rate
( !# ) into the lake have increased rapidly during the
last two decades (Figure 9c, g). Calving has increased
as has the depth of the lake at the calving front. The
surface mass balance was assumed to be constant at
b = –10 m yr 
but it was probably lower during the
warm period of 1930-1960 (Figure 10). This is re-
flected in the observed average thinning of the glacier
(Figure 10a).
Prediction of future changes of Breiðamerkur-
jökull and the expansion of Jökulsárlón
Using data on ice flow and calving along with the con-
tinuity equation for ice, we can make predictions for
future area and volume changes of the glacier and the
lake, for given mass balance scenarios.
10 JÖKULL No. 50