62 
A simplified secante method has also been investigated without taking into account the 
emissivity. Eq. 2 reduces then to : 
B(T ttc ) = 
B(T f ) cos 0 f - B(T n ) cos 6„ 
cos 0, - cos 6„ 
(4) 
Tsec2 - Ts 
(simplified method) 
A = 0.09 K 
Tsec - Ts 
(normal method) 
A = -0.83 K 
0 0.5 1 1.5 2 2.5 3 
W 
Figure 7. Differences between double-viewing SST and simulated SST for 1761 atmospheric situations 
(plotted versus W the total water vapor content) 
It may be seen on Fig. 7 that when considering sea pixels this simplification makes up for the 
previous -IK bias. The remaining mean error in this case is actually better, reduced to 0.09 K, and is 
always lower than 0.5 K in absolute value when W remains lower than 3 g/cm 2 . This compensation only 
works for sea points because of the combination of the emissivity values (0.99 and 0.97) with the error 
terms in equation (3). Therefore this simplified secante method has been applied on sea ATSR data. 
33. Applications and results 
3.3.1. Application with an ATSR image on the English Channel. The simplified secante method has 
been used and Fig. 8 shows the histogram of the secante retrieved temperatures compared with the 
Lowtran7 retrieved temperatures. The mean error is 0.3 K (with an rms of 0.1 K). Fig. 7 shows that the 
error is in good agreement with the curve (W is 1.267 g/cm 2 on this zone). 
Differences Tsecante - Tradsond (K) 
Figure 8. Application of the simplified secante method on an ATSR image 
(12000 sea pixels over the English Channel)