Geoscience Reference
In-Depth Information
60
50
40
30
Figure 6.4
Calculated soil
temperature at 2 cm (solid
line), 15 cm (dotted line), and
30 cm (broken line) for
damping depth of 0.1 m.
20
0
6
12
18
24
Time (hr)
30
36
42
48
both in seconds are respectively the period of the sinusoidal variation and a time
slip introduced to adjust its phase such that
t
soil
TT
,0
=
when
t
=
t
0
. It can be shown
m
by substitution into (6.10) that the expression:
tt
⎡⎤
−
z
⎡
(
−
)
z
⎤
TTT
D
tz
soil
,
=+
exp
sin 2
p
0
−
(6.12)
⎢⎥
⎣⎦
⎣
⎢
⎥
m
a
P
D
⎦
describes the behavior of soil temperature as a function of time
t
and depth
z
when
Equation (6.11) is the upper boundary condition at the soil surface, with:
0.5
P
a
p
⎛
⎞
D
=
⎜
s
(6.13)
⎟
⎝
⎠
D
has units of distance and is called the
damping depth
. Figure 6.4 shows the daily
variation in soil temperature as a function of soil depth calculated from Equation
(6.12) in response to a sinusoidal cycle of temperature of amplitude 15°C around a
mean temperature of 40°C with a phase delay of 6 hours when the damping depth
is 0.1 m. The variation with depth of the amplitude and phase of calculated soil
temperature can be compared with that measured for a bare sandy loam surface
shown in Fig. 6.2.
The amplitude of the soil temperature wave and its phase relative to the surface
temperature wave changes with depth and are controlled by the thermal diffusivity
of the soil and period of the surface temperature cycle via the value of
D
. Because
damping depth is related to the square root of the period of the surface wave, the
depth of penetration is much greater for the seasonal cycle in surface temperature
than for the daily cycle in temperature. In the case of dry sand (
a
s
= 0.24 × 10
−6
m
2
s
−1
),
D
is about 0.08 m for the daily cycle but about 1.6 m for the yearly cycle. In the case
of wet clay (
a
s
= 0.51 × 10
−6
m
2
s
−1
), the value of
D
is about 0.12 m for the daily cycle
but about 2.24 m for the yearly cycle.
