Simple analytical models of glacier-climate interactions - by Prof. J ...

d V'
d t
= w f H m,0 d L'
d t
= amount of mass added . (5.4)
In a perturbation analysis we have two contributions to the mass added to or removed
from the glacier:
change of volume = A 0 B' + w f B f L' . (5.5)
B' is the perturbation of the balance rate (constant over the glacier), and B f the
characteristic balance rate at the glacier front. The first term is simply the amount of ice
added or removed by the balance perturbation on the reference glacier area. The second
term is the amount of ice lost or gained because the length of the glacier deviates from that
of the reference state. Combining eqs. (5.4)-(5.6) yields
d L'
d t
=
A 0
w f H m,0
B' +
B f
H m,0
L' . (5.7)
The equilibrium state is obtained by setting the time derivative to zero. This gives:
L' = - A 0
w f B f
B' . (5.8)
The response time for glacier length according to this model is apparently
t L = -
H m,0
B f
. (5.9)
Some examples on response times are given in the table below. The quantities marked
with • are the input data. Eq. (6.1) has been used to calculate H o . The response time is
then obtained from eq. (5.9).
•Ao
•Lo
•s
•β
Ho
•W f
•B f
t L
(km 2 )
(km)
(m 2 yr -1 )
(m)
(m)
(m yr -1 )
(yr)
Nigardsbreen 48.8 10.4 0.13 0.0078 125 500 -10 13
Abramov Glac. 25.9 9.1 0.09 0.0055 136 700 -4 34
Rhonegletscher 18.5 9.8 0.13 0.0066 122 900 -5 24
Franz-Josef Gl. 36 11.4 0.21 0.0125 107 600 -22 5
Aletschgletscher 86.8 24.7 0.1 0.0066 215 1200 -8 27
Ob. Grindelw.gl. 10.1 5.0 0.25 0.0066 65 500 -7 9
18