58 
Praia, 1993). This last method has been applied, using the TIGR data set including 1761 world-wide 
atmospheric profiles (Scott and Chédin, 1981). Satellite brightness temperatures have been simulated in 
both 11 pm and 12 pm channels for different emissivities and viewing angles. In a first approach a mean 
emissivity for both channels has been taken, ranging from 0.90 to 1. 
Having at our disposal 1761 triplets (T s ,Tbl l,Tbl2). the an, ai2 and c coefficients have been 
obtained from multilinear regression. It has been shown (Becker and Li, 1990, Sobrino et al„ 1993) that 
the Split-Window coefficients actually depend on the atmospheric situations, and especially on the water 
vapor content. In order to achieve a better fit between the surface temperatures and the satellite 
temperatures, the 1761 situations have been splitted into three atmospheric types : Polar, Mid-Latitude 
and Tropical after a statistical data classification performed at LMD (Achard, 1991). All-situations 
coefficients have also been calculated using the 1761 situations. 
The good correlation coefficients obtained (the rms error being lower than 0.1 K) confirmed the 
validity of the method. Fig. 1 shows the variations of the Mid-Latitude coefficients with the surface 
emissivity. 
Mid-Latitude 
coefficients 
a11 
a12 
— cte 
Figure 1 : variation of the Split-Window Mid-Latitude coefficients with the surface emissivity 
The exact symmetry observed between ai i and aj2 illustrates the relation ai i = 1 - ai2 (see Fig. 
2) which has been theorically predicted (Sobrino et al., 1993), although here no such condition was 
prescribed in the regression calculation. On the other hand the third term c does not show any predicted 
behaviour, whereas the order of magnitude is in accordance with the theoretic results of Sobrino et al. 
(1993). 
• a11+a12 
1.5 H ' ■ L 
1 
0.5 
0.9 0.92 0.94 0.96 0.98 1 
Mean spectral emissivity 
Figure 2. Check of the relation al I = / -a!2 for different emissivities