Environmental Engineering Reference
In-Depth Information
1.6
1.2
0.50%
1.00%
2.00%
3.00%
4.00%
5.00%
0.8
0.4
0
0
3.9 10.8
Wavelength (micrometer)
12
Fig. 19.22
Distributions of brightness temperature (
BT
) errors due to errors in surface emissivity
from GOES forward simulations
where
T
1
and
T
2
represent the 3.9 and 11
μ
m band uncertainties resulting from the
ε
Δε
uncertainties of the mean emissivity (
), respec-
tively. Using the Sobrino et al. (
1994
) split-window algorithm as an example, these
two components are
) and emissivity difference (
A
4
ε
A
4
ε
δT
1
¼
A
3
δε
and
δT
2
¼
δðΔεÞ
(19.59)
2
Therefore, the maximum LST uncertainty is
s
2
2
A
4
ε
A
4
ε
δT
s
¼
A
3
δε
þ
δðΔεÞ
(19.60)
2
Considering that
ε ¼ ε
11
þ ε
12
ð
Þ=
2 and
Δε ¼ ε
11
ε
12
ð
Þ
, and assuming the
emissivity uncertainties in each band are the same, i.e.,
δε ¼ δε
11
¼ δε
12
,the
maximum uncertainty of the emissivity difference is
.
Thus, the LST uncertainty, Ts, due to the emissivity uncertainty can be calculated
using the above equation.
From the above equations, we can see, in order to reduce the LST algorithm
sensitivity to the emissivity error, the emissivity difference should not be included
in the algorithm formulation.
δðΔεÞ¼ δε
11
j
jþδε
12
j
j¼
2
δε
19.6 Summary and Discussion
In recent years, LST products have been successfully generated from polar-orbiting
instruments, such as MODIS and ASTER. The polar-orbiting system has the
advantage of global coverage. Surface temperature, especially land surface temper-
ature, has a strong diurnal cycle, which cannot be captured by the temporal
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