Geoscience Reference
In-Depth Information
The procedure is quite sensitive to the shape factor for air, which appears to depend
on the air content itself. In wet soil (
θ
>
θ
wet
), the air shape factor is given by:
−
−
φθ
φ
(
)
g
a
=
0 333
.
0 333
.
−
0 035
.
(9.19)
where
φ
is soil porosity (m
3
m
-3
). In dry soil (
θ
<
θ
dry
), the air shape factor fol-
lows from:
θ
θ
(
)
g
=
0 013
.
+
g
−
0 013
.
(9.20)
a
a,dry
dry
where
g
a,dry
is the value of Eq. (
9.19
) at
θ
=
θ
dry
. In this way
g
a
varies between 0.013
(
θ
= 0) and 0.333 (
θ
=
φ
).
The thermal conductivity of air-illed pores is considered to be the sum of
λ
da
and
λ
v
, where
λ
da
is the thermal conductivity of dry air (22 J cm
-1
d
-1
K
-1
) and
λ
v
accounts
for heat transfer across the air-illed pores by water vapour. Above the critical water
content
θ
wet
the air-illed pores are assumed to be saturated with water vapour, and
λ
v
is assumed to be 64 J cm
-1
d
-1
K
-1
. Below
θ
wet
we assume that
λ
v
decreases linearly
with water content to a value of zero for oven-dry soil:
θ
θ
λλλ
=+=+
22
64
J cm d K
−− −
1
1
1
(9.21)
a
da
v
wet
In the case that neither water nor air can be considered as the continuous phase (
θ
dry
<
θ
<
θ
wet
),
λ
s
is found by interpolation between values at the wet and dry limits:
()
=
( )
+
( )
−
( )
λθ λθ
θθ
θθ
−
( )
s
et
s
ry
λθ λθ
(9.22)
s
s
dry
dry
−
wet
dry
The values of
θ
dry
and
θ
wet
are commonly taken as 0.02 and 0.05 respectively.
Question 9.8:
Consider a sandy soil with volume fractions
f
q
= 0.55,
f
c
= 0.08, and
f
o
= 0.02. Calculate the soil thermal conductivity
λ
s
for wet (
θ
= 0.25) and dry (
θ
= 0.02)
conditions.
With respect to boundary conditions, in SWAP at the soil surface either the daily
average air temperature
T
avg
or measured soil surface temperatures can be used. At the
bottom of the soil proile either soil temperatures can be speciied or
q
heat
= 0.0 can be
selected. The latter option is valid for large soil columns, with negligible heat luxes
at the bottom.
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