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

5. A volume time scale for valley glaciers
A time scale for the adjustment of glaciers to climate change can be derived from the
requirement of mass continuity (Jóhanesson et al, 1989; Haeberli and Hoelzle, 1995).
We perform a linear perturbation analysis. Conservation of ice volume V can be
expressed as
d V
d t
= d A H m
d t
= H m d A
d t
+ A dH m
d t
. (5.1)
Here A is the glacier area and H m the mean ice thickness. Now we write
V = V 0 + V', A = A 0 +A' and H m = H m,0 + H m ', where the reference state is defined
as (V 0 , A 0 , H m,0 ). By substitution in eq. (5.1) and by neglecting higher-order terms we
then obtain the perturbation equation
d V'
d t
= H m,0 d A'
d t
+ A 0 dH m '
d t
. (5.2)
Next we assume (see Fig. 7.1):
A' = w f L' , (5.3)
Here w f is the characteristic width of the glacier tongue.
Fig. 6.1.
L'
total glacier
area A
w f
flowline
If the mean thickness of the glacier does not change we have for the change of ice volume
with time
17