61 
1 
A = -0.18 K 
e 
:r 
d 
e 
s 
f 
8 
0.8 
0.6 
0.4 
0.2 
K 0 
- 0.2 
-0.4 
- 0.6 
- 0.8 " . 
- 1 1 1 1 1 1 1 i l i I i 
• Delta Tsw - Tsea (using the mid-latitude SW coefficients) 
+ Delta Tsw (vapor) - Tsea (using the total vaper amount when available) 
Figure 6. Application of the Split-Window method on ATSR data over the Coral Sea 
(September to December 1991) 
3 - THE DOUBLE-VIEWING METHOD 
3.1. Methodology 
The double-viewing method, or secante method, relies on the hypothesis that the atmospheric 
transmittance is a function of the secante of the satellite viewing angle. This method, proposed by 
Saunders et al. (1967) and McMillin et al. (1975), was first tested by Chidin et al. (1981) who mixed 
together METEOSAT and AVHRR data in order to dispose of different viewing angles. The difficulty 
was to harmonize the heterogeneous data, the satellite having neither the same pixel size, neither the 
same spectral filter function. This problem does not occur with ATSR which provides us two quasi- 
simultaneous views : the Nadir view and the Forward view. Under some assumptions (the reflected 
radiance by the surface may be neglected,...) the surface temperature may be derived : 
B(T ) = g(r / )cos6 / ~ B(T„)cos0 n (2) 
t f cos Qf - e n cos d n 
B being the Planck's function, T the satellite brightness temperature (the 11 pm channel was used in this 
study), 0 the satellite viewing angle and e the surface emissivity. The subscripts n and f refer respectively 
to nadir and forward views. 
3.2. Preliminary study 
It appears that the secante method does not require prior calculations of coefficients as with the Split- 
Window method, but the necessary knowledge of the Forward and Nadir emissivities is an obvious 
limitation of the method. Furthermore, even with the correct values of the emissivities, for most 
situations, the method underrates the retrieved temperature. The error is given by the following equation : 
^ £„ cos - e / cos 8 f J £„ cos 6„ - e f cos 8 f 
The first term represents the error due to the fact that the reflected surface radiance may not be neglected 
and the second term is the error due to the fact that en and ef are not equal. Fig. 7 shows the variation of 
the error with W for simulated sea points using the TIGR data set (with e n =0.99 and ep=0.97, according 
to Masuda et al., 1988, François and Ottlé, 1992). For a typical situation the error is of the order of -1 K.