Geoscience Reference
In-Depth Information
The explanation and physical description of the features presented in
Figure 2.18
and
Figure 2.19
are given in
Section 2.3.4
, but irst the theory of heat transport in soils
needs to be treated.
2.3.2 Heat Transport in Soils
This section deals with the transfer of heat in a homogeneous soil, that is, the soil
physical properties do not vary in space. Heat transport in the soil mainly takes place
by conduction, that is, it is a function of the local temperature gradient and a thermal
conductivity
λ
s
(in W m
-1
K
-1
). Hence, the soil heat lux density
G
is given by:
=−
∂
∂
T
z
G
λ
s
(2.29)
d
The soil heat lux in turn may change with depth. This implies that heat is stored in the
soil or extracted from the soil: if more heat enters a soil layer at the top than leaves the
layer at the bottom, the layer has to heat up. This is expressed by:
∂
∂
=−
∂
T
t
G
z
ρ
ss
c
∂
(2.30)
d
where
ρ
s
is the density of the soil and
c
s
is the speciic heat capacity (in J kg
-1
K
-1
): a
change of temperature in time is due to the divergence of the lux with depth.
Combination of Eqs. (
2.29
) and (
2.30
) leads to the following diffusion equation:
λ
ρ
2
2
∂
∂
=
T
t
∂
∂
T
z
∂
∂
T
z
s
=
κ
(2.31)
s
c
2
2
ss
d
d
where
κ
s
is the thermal diffusivity of the soil (in m
2
s
-1
). Equation (
2.31
) describes
how the temperature in the soil changes in time depending on the shape of the tem-
perature proile (recall that the second derivative of the temperature proile is the
curvature (non-linearity) of the proile). With the use of the deinition of the thermal
diffusivity (
κλρ
s
= /(
c
) given earlier, Eq. (
2.29
) can then be written in a form that
is more familiar in atmospheric applications:
s
ss
∂
∂
T
z
Gc
=−
ρκ
ss s
(2.32)
d
(see
Chapters 1
and
3
to compare). In the soil the use of volumetric quantities is usu-
ally more convenient. Therefore, the product
ρ
s
c
s
is often replaced by the volumetric
heat capacity
C
s
.
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