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

Fig. 1.2
300
200
Surface energy flux (W m -2 )
100
0
-100
ablation
ablation
t e
t e
accumulation
ablation
ablation
-200
accumulation
-300
0 50 100 150 200 250 300 350
Time (days)
We anticipate that the variation of the surface energy flux with altitude is first of all
governed by the parameter A 0 . The upper curve in Fig. 1.2 would correspond to a lower
location on the glacier.
Because the ψ-curve is symmetrical with respect to t = T/2, the total ablation M and
accumulation A can be written as:
M = 2
Lm
0
t e
A 0 + A 1 cos 2π t
T
dt
= 2 A 0 t e
L m
+ A 1 T sin 2π t e
π L m T
(1.3)
A = 2
T/2
P dt
t e
= 2 (T/2 - t e ) P (1.4)
Here P is the precipitation rate, assumed to be constant throughout the year. The mass
balance model can now be formulated as:
(i) A 0 < -A 1 (no ablation): (1.5)
A = T P ,
M = 0 .
(ii) -A 1 < A 0 < A 1 (ablation during part of year): (1.6)
A = 2 (T/2 - t e ) P ,
M = - 2 A 0 t e
L m
- A 1 T sin 2π t e
π L m T
.
4