Jökull - 01.01.2001, Page 13

Jökulsárlón at Breiðamerkursandur
Figure 10. a) Average annual thinning rate (
)
of the terminus of Breiðamerkurjökull according to
maps from 1903, 1945, 1965, 1991 and 1998. Solid
line shows mean values over the intervals between
maps and the dashed line denotes a more likely varia-
tion. b) Winter precipitation and c) Summer tempera-
ture at Fagurhólsmýri, 20 km SW of Jökulsárlón. – a)
Meðalþynning sporðs Breiðamerkurjökuls (m á ári).
Vetrarúrkoma (b) og sumarhiti (c) á Fagurhólsmýri.
Profiles of ice thickness along the central flow line
down Breiðamerkurjökull at various times, 

 ,
were calculated given the basal geometry (Figure 12a)
and the initial ice thickness 

 . Parameters  
and   were derived for every 100 m along the
flow line. The shape factor,   , was calculated for
each cross section as the ratio between and the to-
tal length of the cross section along the bed. Longitu-
dinal velocity was calculated from glacier flow mod-
els (equations 2–5) along several flowlines through
the present day cross sections. The average veloc-
ity through each section  
 was calculated as a
function of surface velocity, ! " 
 , along the central
flow line, i.e. # 

$&% ' ( 

 , where % 
is a constant for each cross section. Temporal varia-
tions in %  are neglected. Calving rate was calcu-
lated at the central flow line from equation (7). The
surface net mass balance along the flow line )( 
* 
is assumed to vary with elevation ( * ) and distance (  )
as the measured average for the years 1997 to 2000
(Figure 7b; Björnsson and Pálsson, 1998; Björnsson
et al., 1998; Pálsson and Björnsson, 1998, 1999; Páls-
son et al., 2001). In this respect, variations in time
are included for each iteration. We use a 100 m grid
and a triangular filter for the surface slope and surface
changes with a base line of 10 to 15 and 30 times the
glacier thickness, respectively.
Figure 11. Sketch describing the parameters in
equation (8); +,$-/.0 of both cross sections is
the same;  is thickness of the glacier along a central
flow line. – Skýringarmynd um reiknistuðla.
The surface profile of 1998 was simulated using
the 1991 observed surface as an input. Agreement
with the 1998 observed surface is good (Figure 12a).
Surface profiles and retreat rate were then predicted at
10 year intervals from 1998 to 2068 (70 years, Figure
12b) and at 50 years intervals from 1998 to 2398 (400
years, Figure 12c). Calving is expected to increase
rapidly as the glacier retreats 2 km inland where the
bed slopes from 200 m to 300 m below sea level (Fig-
ure 12).
The model predicts a similar retreat rate of the
calving front position for the next 1 70 years (Fig-
ure 13), which implies an average lake growth rate
of 0.5 km 2 yr 3!4 . If the presently observed negative
mass balance (1997 to 2000) continues, Breiðamerk-
urjökull will recede from the proglacial lake after
1 200 years and almost vanish in 1 400 years. How-
ever, these calculations assume a constant mass bal-
ance as a function of altitude, while future variation
in mass balance are expected to strongly influence the
glacier geometry and extent.
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