Environmental Engineering Reference
In-Depth Information
Substituting Eqs.
19.10
,
19.11a
,
19.11b
, and
19.12
into Eq.
19.9
, we obtain
Z
l
0
d
l
T
s
T
λ
¼ K
λ
T
s
T
p
(19.13a)
0
Here,
l
0
is the optical depth from the Earth's surface to top of the atmosphere:
Z
1
Z
1
l
0
¼
ρ
d
z
ρ
0
exp
ðz=HÞ
d
z
(19.13b)
0
0
If two close spectral channels are selected to give equal values of
T
p
, such as the
split-window channels 11 and 12
m, we will have two equations with different
absorption coefficient
k
λ
to solve simultaneously:
μ
T
11
T
12
T
s
T
11
T
s
T
12
¼
k
11
k
12
k
11
k
12
k
11
or
T
s
T
11
¼
ð
Þ
(19.14)
Here,
T
11
and
T
12
are brightness temperature of 11- and 12-
μ
m channel;
k
11
and
k
12
are the absorption coefficients of 11- and 12-
m channel. This equation is
frequently used as a basis for split-window SST algorithms (McClain et al.
1985
).
In our case, Eq.
19.14
can be used for any surface type, land or water, as long as the
surface emissivities in the split-window channels are close to unity.
Sun and Pinker (
2003
) introduced a split-window algorithm by using surface
type information instead of traditional surface emissivity:
μ
2
T
s
ðiÞ¼a
0
ðiÞþa
1
ðiÞT
11
þ a
2
ðiÞ T
11
T
12
ð
Þ þ a
3
ðiÞ T
11
T
12
ð
Þ
þ a
4
ðiÞð
Þ
(19.15)
θ
sec
1
where
i
is the surface type index,
is the satellite-viewing angle,
T
11
and
T
12
are the
brightness temperatures at 10.8 and 12.0 mm channels,
a
0
-
a
4
are coefficients, and
T
s
is the derived skin temperature.
θ
19.3.2.2 Some Other Traditional Split-Window-Type LST Algorithms
For GOES 8-11, we can use split-window algorithms. Since several split-window
LST algorithms have been developed in the past, we compared our algorithms with
these split-window-type algorithms in our previous publications (Sun and Pinker
2004
; Pinker et al. 2009). In Sect.
4.3
about simulation analysis, some comparison
will be made for these split-window-type algorithms and their modified forms with
additional path correction term.
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