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

3. A simple glacier model
We consider a glacier that has a uniform width, rests on a bed with a constant slope s,
and behaves perfectly plastically in 'a global sense' (Fig. 3.1).
Fig. 3.1
Altitude
h = b + H
b = b
0
- sx
equilibrium line
L
x
The specific balance is written as
b = β (h - E) , (3.1)
where E is the equilibrium-line altitude and β the balance gradient (assumed to be
constant). The glacier is in balance when the total mass budget is zero:
L
b n dx = β
0
0
L
(H + b 0 - s x - E) dx = 0
. (3.2)
Solving for glacier length L yields:
L = 2 (H m + b 0 - E)
s
. (3.3)
In this expression H m is the mean ice thickness. Note that the solution does not depend
on the balance gradient! The next step is to find an equation for H m . We use again the
concept of perfect plasticity:
H m =
τ 0
ρ g s
. (3.4)
Substituting this in eq. (3.3) yields:
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