Geoscience Reference
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A
A
Figure 2.23
Two methods to determine the damping depth from observed soil tem-
peratures at two depths. Top: Ratio of amplitude at two depths yields damping depth
through
Az
=
−−
. Bottom: Phase shift between temperature waves
at two depths gives damping depth through
tt
(
z
z
) /
D
()/( )
Az
e
d
2
d
1
d
2
d
1
.
−=
(/ )(
P
2
π
d
z
−
zD
)/
21
2
d
1
In the diurnal cycle shown in
Figure 2.18
the yearly cycle is superimposed, and as a
result the temperature at larger depth is not in balance with the mean temperature at
the surface.
The model of the soil temperature given by the combination of Eqs. (
2.34
) and
(
2.35
) can be used to estimate the thermal diffusivity from soil temperature observa-
tions at two depths by two methods (see also
Figure 2.23
):
•
If the amplitudes of the temperature wave at two depths (
z
d1
and
z
d2
) are com-
pared,
D
can be derived from the ratio
A
(
z
d2
)
/A
(
z
d1
) in combination with Eq. (
2.36
):
Az
=
−−
. From
D
the diffusivity can be derived, with a known
ω
. In
practice it is usually easier to determine twice the amplitude by taking the difference
( /( )
Az
e
(
z
z
) /
D
d
2
d
1
d
2
d
1
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