y
= X/Xo
where
Ao
= value at thaw commencement
Ae
= equilibrium value
T - Ts′
Xe = f
= new equilibrium permafrost thickness.
kuf G
Equation D15 then has the following solution
a1yf + a2 y - 1 a
y + a4 1 + a5
2
+ 2a1τf = 0
- 2 ln f
f
(D17)
ln
a1 + a2 - 1 a3 yf + a5 1 + a4
where
( Ao - Ae )
qg Xo
a1 =
kf (Tf - Ts′) (1 - ye )
( Ao - Ae )
a2 = Ae - ye
(1 - ye )
a3 = a2 + 4a1
2
a2 - a3
a4 =
2a1
a2 + a3
a5 =
2a1
kf (Tf - Ts′)∆t
τf =
2
LXo
and
Xf
yf =
Xo
is the permafrost thickness after Dt years (Table D5).
Note that these results agree quite well with the values with a constant thawed zone heat flow, i.e., con-
stant value of A(t). For this case, 15,000 years is nearly enough time to thaw back to the new equilibrium
thickness of 601.5 m.
Table D5. Permafrost
thickness after thaw.
Ao =1.1792.
Xf (m)
Ae
yf
1.0
0.9678
606.4
1.170
0.945
592.0
1.179
0.9434
591.0
38
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