Geoscience Reference
In-Depth Information
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
Search WWH ::




Custom Search