Chapter 8 - Soil Temperature - LAWR
Chapter 8 - Soil Temperature - LAWR
Chapter 8 - Soil Temperature - LAWR
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SSC 107, Fall 2001 – <strong>Chapter</strong> 8 Page 8-12<br />
T(z,<br />
t) = T + A<br />
o<br />
e<br />
-z/d<br />
[sin ( ω t -<br />
z<br />
)]<br />
d<br />
d is "damping depth" at which the T amplitude decreases to 1/e of A o<br />
d is usually 20-30 cm for diurnal temperature fluctuations<br />
d =<br />
2K T<br />
ω<br />
¯ Calculate d for the annual wave using t for one year.<br />
Amplitude Equation<br />
amplitude at z=o is A o<br />
amplitude at z=z 1 is A 1 = A o exp (-z 1 /d)<br />
amplitude at z=z 2 is A 2 = A o exp (-z 2 /d)<br />
A1<br />
exp(-z1/d)<br />
= = exp [(z<br />
A2<br />
exp(-z2/d)<br />
z2<br />
- z1<br />
ln( A1<br />
/ A 2)<br />
=<br />
d<br />
z2<br />
- z1<br />
d =<br />
ln( A1<br />
/ A 2)<br />
2<br />
- z<br />
1<br />
)/d]<br />
2K<br />
T ω<br />
z<br />
2<br />
- z1<br />
=<br />
ln( A 1/<br />
A 2)<br />
K<br />
T<br />
ω ⎡ z<br />
2<br />
- z1<br />
⎤<br />
=<br />
2<br />
⎢ ⎥<br />
⎣ln(<br />
A1<br />
/ A 2)<br />
⎦<br />
2
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