Environmental Engineering Reference
In-Depth Information
Table 19.3
Parameter
n
i
for approximate Planck function (power function) for GOES window
channels
Channel (
μ
m)
n
i
(
T
i
<
285 K)
n
i
(
T
i
>
285 K)
3.9
13.88
12.90
10.8
4.99
4.57
12.0
4.51
4.15
Table 19.4
Atmospheric transmittance for standard atmosphere profiles
Atmosphere
Precipitable water (g/cm-2)
τ
10.8
τ
12
US standard
1.13
0.8552
0.8014
Tropical
3.32
0.5574
0.4159
Midlatitude summer
2.36
0.6915
0.5786
Midlatitude winter
0.69
0.8993
0.8646
Subarctic summer
1.65
0.7847
0.7011
Subarctic winter
0.33
0.9336
0.9147
Suppose that surface emissivity and the atmospheric transmittance are known,
and
n
i
is a constant that depends on the spectral channel. Now we have the three
unknown parameters:
T
s
,
T
a
"
, and
T
a
#
, and we can use the information of the three
channels to obtain the surface temperature. In order to take advantage of all the
available information, we choose three channels to solve the equations. Assuming
the channel indexes are
i
1
,
i
2
, and
i
3
, we get
T
s
¼C
1
i
1
T
i
1
C
2
i
1
T
a
"
C
3
i
1
T
a
#
T
s
¼C
1
i
2
T
i
2
C
2
i
2
T
a
"
C
3
i
2
T
a
#
T
s
¼C
1
i
3
T
i
3
C
2
i
3
T
a
"
C
3
i
3
T
a
#
(19.26)
ð
C
3
i
3
C
3
i
2
Þ C
1
i
3
T
i
3
C
1
i
2
T
i
2
ð
Þ C
3
i
2
C
3
i
1
ð
Þ C
1
i
2
T
i
2
C
1
i
1
T
i
1
ð
Þ
T
a
"
¼
ð
C
2
i
3
C
2
i
2
Þ C
3
i
3
C
3
i
2
ð
Þ C
3
i
2
C
3
i
1
ð
Þ C
2
i
2
C
2
i
1
ð
Þ
T
s
¼C
1
i
T
i
C
2
i
T
a
"
C
3
i
T
a
#
For standard MODTRAN atmospheric profiles, we can calculate their atmo-
spheric transmittance, as shown in Table
19.4
.
In the event that the atmospheric transmittance is not available, we can use
regression methods to find the appropriate coefficients for each term in Eqs.
19.25
and
19.26
.
T
s
can then be written as
ð
Þ
ð
Þ
ð
Þ
1
ε
i
1
1
ε
i
2
1
ε
i
3
T
s
¼ a
0
þ a
1
T
i
1
þ a
2
T
i
2
þ a
3
T
i
3
þ a
4
T
i
1
þ a
5
T
i
2
þ a
6
T
i
3
ε
i
1
ε
i
2
ε
i
3
ð
1
ε
i
Þ
C
ji
¼ a
0
ðjÞþa
1
ðjÞ
;
j ¼ i
1
;
i
2
;
i
3
ε
i
(19.27)
Search WWH ::
Custom Search