Environmental Engineering Reference
In-Depth Information
Table 19.1
Spectral characters of GOES-12 through GOES-15 imager
Channels
Central wavelength (
μ
m)
Resolution (km)
1 (visible)
0.65
1
2 (infrared)
3.9
4
3 (infrared)
6.48
4
4 (infrared)
10.7
4
6 (infrared)
13.3
8 (GOES-12/13)
4 (GOES-14/15)
Shaded channels are used for LST retrieval
19.3.1 Physical Description
Under clear sky conditions, the outgoing spectral radiance at the top of the atmo-
sphere can be represented as
Rðλ; μÞ¼ε
0
ðλ; μÞB λ; T
s
ð
Þ τ
0
ðλ; μÞþR
a
ðλ; μÞþR
s
ð
λ; μ; μ
0
; φ
0
Þ
þ R
d
ð
λ; μ; μ
0
; φ
0
Þ þ R
r
ðλ; μÞ
ð
19
:
2
Þ
where
τ
0
is the
transmittance from the Earth's surface to the top of atmosphere,
R
a
is the thermal
path radiance,
R
s
is the path radiance resulting from scattering of solar radiation,
R
d
is the solar diffuse radiance, and
R
r
is the atmospheric thermal radiation reflected by
the surface.
T
s
is the skin temperature,
ε
0
is the surface spectral emissivity,
B
is the Planck function,
λ
is the wavelength,
μ ¼
cos(
θ
), and
μ
0
¼
cos (
ψ
), where
θ
is the satellite zenith angle,
ψ
is the solar zenith angle, and
φ
0
is the
azimuth angle.
The wavelength
is actually the wavelength center of a narrow interval because
there is no way to measure the exact monochromatic signal as a continuous function
of wavelength by satellite sensors. For the far-IR bands, solar contributions can be
negligible, so the outgoing infrared spectral radiance at the top of atmosphere can
be represented by
λ
Rðλ; μÞ¼ε
0
ðλ; μÞB λ; T
s
ð
Þ τ
0
ðλ; μÞþR
a
ðλ; μÞ
(19.3)
The purpose of the LST algorithm is to retrieve the land surface skin temperature
T
s
from the satellite sensor measured radiance
R
(
). Physically, in this problem,
the surface temperature is basically coupled with two other factors: surface emis-
sivity and the atmospheric absorptions. Developing an LST algorithm means to find
a solution of decoupling the emissivity and the atmospheric absorption effects from
satellite received radiance.
As shown from Fig.
19.3
, in order to retrieve surface information from satellite
observations, we need to select window channels with no or less atmospheric
absorption. Some bands, such as 3-4, 8-9, and 10-12
λ
,
μ
μ
m, are some typical
atmospheric windows.
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