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

Problem West Antarcic ice sheet (P 3)
The mass budget equation is obtained by setting the total accumulation equal to the total
flux across the grounding line. This flux equals the ice velocity times the outlet cross
section. Therefore
π a R = 2 π R f * ρ w
ρ i
d 2 = 2 π R f d 2 (P 3.1)
The water depth at the grounding line equals b 0 - s R, so we have
d 2 = b 0
2 + s
2 R
2 - 2 b0 s R (P 3.2)
Combining yields
2 f s 2 R 2 - (4 b 0 f s + a) R + 2 f b 0
2 = 0 (P 3.3)
Special case: b 0 = 0 (a purely marine ice sheet). So the highest point of the continent is
just at sea level. Eq. (P 2.3) reduces to
2 f s 2 R 2 - a R = 0 (P 3.4)
→ R = a
2 f s 2 (P 3.5)
Application to the WAIS (R = 600 km, f = 1 yr -1 , a = 0.25 m yr -1 ):
1/2
→ s = a = 0.25
1/2 = 0.00046 (P 3.6)
2 f R 2 x 1 x 600,000
Sensitivity to changes in accumulation rate:
∂R
∂a = 1
2 f s 2 = 2.37x106 = 23.7 km/% (P 3.7)
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