Environmental Engineering Reference
In-Depth Information
During daytime,
T
3.9
in Eq.
19.37
should be replaced by
T
0
3.9
, therefore, we have
2
LST ¼ a
0
þ a
1
T
11
þ a
2
T
11
T
3
:
9
ð
Þ þ a
3
T
11
T
3
:
9
ð
Þ
þ a
4
T
3
:
9
cos
θ
s
þ a
5
ð
1
εÞþa
6
ð
sec
θ
1
Þ
(19.43)
One-Channel Algorithm
In the atmospheric window channels,
the water vapor absorption is weak.
Therefore,
τ
i
¼
exp
ð
k
i
w
sec
θ
Þ
1
k
i
w
sec
θ
(19.44)
where
i
denotes the channel index,
k
i
is the absorption coefficient at channel
i
,
θ
is
the satellite viewing angle, and
w
is the column water vapor. Hence,
d
τ
i
k
i
sec
θ
d
w
(19.45)
The measured radiance in the thermal window region can be expressed with
respect to channel value from the radiative transfer equation (RTE) as
Z
τ
B
i
T
p
d
R
i
¼ ε
i
B
i
Tð τ
i
þ
τ
0
Z
W
B
i
T
p
d
w
ε
i
B
i
TðÞ
ð
1
k
i
W
sec
θ
Þ þ k
i
sec
θ
ð
19
:
46
Þ
0
where
B
i
is the Planck function weighted for channel
i
,
T
i
is the brightness
temperature (
K
), measured at the satellite level in channel
i
,
T
s
is the surface skin
temperature (
K
),
τ
i
are the surface emissivity and atmospheric transmittance
in channel
i
,
T
p
is the air temperature (
K
) at vertical layer p,
p
is the pressure of the
vertical emitting layer (mb), and
W
represents the total precipitable water (TPW)
(cm). Equation
19.46
is a simplification of Eq.
19.2
, considering channel values
instead of spectral values. Defining an atmospheric mean Planck radiance
ε
i
and
R
W
0
BðT
p
Þ
d
w
B
i
TðÞ¼
(19.47)
R
W
d
w
0
T
a
is the atmospheric mean temperature. Inserting Eq.
19.47
into Eq.
19.46
will
yield
Search WWH ::
Custom Search