442
P. Schliissel
To = ao + a1T3.7 + a2(T3.7 - Tn) + a3(T3.7 - T12 ) + a4(T3.7 - T~.7) + as(T3.7 - T{l) + a6(T3.7 - T{2)
(16.19)
The brightness temperatures at forward view are indicated by primes. The errors achieved with
these retrieval models are lower than for those described above. However, in order to account
for the fact that the pixels at forward view are larger by a factor of about two when compared to
the pixel size at nadir view additional noise has to be expected in areas with strong temperature
gradients. The additional noise of the order 0.1 K propagates into the error of To; the expected
accuracies for (16.18) and (16.19) are 0.34 K and 0.30 K, respectively. Further improvement can
be expected again from including quadratic terms. An analysis of such retrieval schemes shows
that the sixth term in equation (16.19) loses significance. Therefore, the optimized retrieval
schemes read:
(16.20)
To = ao + a1T3.7 + a2(T3.7 - Tn) + a3(T3.7 - Tn)2 + a4(T3.7 - T12 ) + as(T3.7 - T12)2
+a6(T3.7 - T~.7) + a7(T3.7 - T{2) (16.21)
These equations deliver the retrieval schemes with least errors of 0.28 K and 0.24 K, respectively.
However, the complex form of (16.20) and (16.21) might imply weak robustness of the schemes
against undetected clouds in the infrared imagery. The coefficients for equations (16.18) to
(16.21) are listed in table 16.6.
ATSR retrieval model (16.18)
Noise
ao
al
a2
a3
a4
-
-
-
£
wlo 4.70 0.9843 4.7233 3.0148 -2.4542
-
-
-
0.18
with -0.48 1.0020 3.0831
0.8274 -0.6570
-
-
-
0.34
ATSR retrieval model (16.19)
Noise
ao
al
a2
a3
a4
as
a6
-
£
wlo -3.66 0.9883 -3.8879 4.2751 1.4770 0.7687 -1.8872
-
0.15
with
0.40 0.9992 -3.3514 3.0070
0.7148
0.2946 -0.7332
-
0.30
ATSR retrieval model (16.20)
Noise
ao
al
a2
a3
a4
as
-
-
£
wlo 3.12 0.9903 4.1508 0.0762 2.6796 -2.1512
-
-
0.18
with -3.81 1.0153 1.7928
0.2539
0.5476 -0.3314
-
-
0.28
ATSR retrieval model (16.21)
Noise
ao
al
a2
a3
a4
as
a6
a7
£
wlo 0.27 1.0026 -3.1714 -0.ll05 3.5072 0.07055 l.5598 -1.3414 0.12
with -5.84 1.0220 -3.3630 -0.1809 0.1289
2.3494
0.5564 -0.4423 0.24
Table 16.6: Coefficients and errors for retrieval models {16.18} to (16.21).
A prerequisite for the application of the retrieval algorithms is a careful cloud screening. Since
clouds do not transmit enough surface leaving radiation to the satellite that can be analysed
in terms of sea surface temperature any cloud that remains undetected will lead to increased
errors in To. Cloud detection schemes using all spectral channels available have been widely
described in literature (e. g. Olesen and Grassl, 1985; Saunders and Kriebel, 1988; Schliissel
and Grassl, 1990).
P. Schliissel
To = ao + a1T3.7 + a2(T3.7 - Tn) + a3(T3.7 - T12 ) + a4(T3.7 - T~.7) + as(T3.7 - T{l) + a6(T3.7 - T{2)
(16.19)
The brightness temperatures at forward view are indicated by primes. The errors achieved with
these retrieval models are lower than for those described above. However, in order to account
for the fact that the pixels at forward view are larger by a factor of about two when compared to
the pixel size at nadir view additional noise has to be expected in areas with strong temperature
gradients. The additional noise of the order 0.1 K propagates into the error of To; the expected
accuracies for (16.18) and (16.19) are 0.34 K and 0.30 K, respectively. Further improvement can
be expected again from including quadratic terms. An analysis of such retrieval schemes shows
that the sixth term in equation (16.19) loses significance. Therefore, the optimized retrieval
schemes read:
(16.20)
To = ao + a1T3.7 + a2(T3.7 - Tn) + a3(T3.7 - Tn)2 + a4(T3.7 - T12 ) + as(T3.7 - T12)2
+a6(T3.7 - T~.7) + a7(T3.7 - T{2) (16.21)
These equations deliver the retrieval schemes with least errors of 0.28 K and 0.24 K, respectively.
However, the complex form of (16.20) and (16.21) might imply weak robustness of the schemes
against undetected clouds in the infrared imagery. The coefficients for equations (16.18) to
(16.21) are listed in table 16.6.
ATSR retrieval model (16.18)
Noise
ao
al
a2
a3
a4
-
-
-
£
wlo 4.70 0.9843 4.7233 3.0148 -2.4542
-
-
-
0.18
with -0.48 1.0020 3.0831
0.8274 -0.6570
-
-
-
0.34
ATSR retrieval model (16.19)
Noise
ao
al
a2
a3
a4
as
a6
-
£
wlo -3.66 0.9883 -3.8879 4.2751 1.4770 0.7687 -1.8872
-
0.15
with
0.40 0.9992 -3.3514 3.0070
0.7148
0.2946 -0.7332
-
0.30
ATSR retrieval model (16.20)
Noise
ao
al
a2
a3
a4
as
-
-
£
wlo 3.12 0.9903 4.1508 0.0762 2.6796 -2.1512
-
-
0.18
with -3.81 1.0153 1.7928
0.2539
0.5476 -0.3314
-
-
0.28
ATSR retrieval model (16.21)
Noise
ao
al
a2
a3
a4
as
a6
a7
£
wlo 0.27 1.0026 -3.1714 -0.ll05 3.5072 0.07055 l.5598 -1.3414 0.12
with -5.84 1.0220 -3.3630 -0.1809 0.1289
2.3494
0.5564 -0.4423 0.24
Table 16.6: Coefficients and errors for retrieval models {16.18} to (16.21).
A prerequisite for the application of the retrieval algorithms is a careful cloud screening. Since
clouds do not transmit enough surface leaving radiation to the satellite that can be analysed
in terms of sea surface temperature any cloud that remains undetected will lead to increased
errors in To. Cloud detection schemes using all spectral channels available have been widely
described in literature (e. g. Olesen and Grassl, 1985; Saunders and Kriebel, 1988; Schliissel
and Grassl, 1990).