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In this context, the objective of the present paper is to propose another technique that permits 
obtaining, for a cloud free situation, quantitative information on the atmospheric contribution to the radiance 
measured by a satellite borne sensor. This method, which is found insensitive to the values of channels 
emissivities, is practical because it obtains the atmospheric transmittance and the total water vapor content from 
satellite data alone. In this way it is possible to produce a novel extension to the standard split-window 
algorithm for better estimates of surface temperature from the brightness temperatures measured in Channels 4 
and 5 of AVHRR. 
2-PRINCIPLE OF METHOD 
The radiance Ij measured from space in channel i, for a cloud-free atmosphere under local thermodynamic 
equilibrium, may be written with good approximation as, 
Ii = Bj (Tj)= £j Bj (T, ) Tj + R a tiT + (f'Ei )Rati .L^i (1) 
In (1) all quantities refer to a spectral integration over the band width of channel i. Ti is the 
corresponding brightness temperature of I;, and £j is the surface emissivity. Bj (T s ) is the radiance which would 
be measured if the surface were a blackbody with the surface temperature T s , ij is the total transmittance of the 
atmosphere, R a tiT is the upwelling atmospheric radiance, and R a ui is the downwelling atmospheric radiance. 
The first term on the right-hand side is the radiation emitted by the surface that is attenuated by the atmosphere. 
The second term is the upwelling radiation emitted by the atmosphere towards the sensor and the third term is the 
downwelling radiation emitted by the atmosphere that reaches the earth's surface and then is reflected towards the 
sensor. 
Under the condition that the atmosphere is unchanged over the neighboring points where the 
surface temperature changes, and considering adjacent pixels that does not present a large difference in the 
emissivity values; i.e.: sea and sand, (Sobrino et al., 1994), the variation of radiance measured from space in 
channel i due to the change of surface temperature (AT S = T s j * Tso)> can be expressed from Eq. (1) as 
Alj = [BifliO-Bi (T io )] = £j [Bj (T s i)-Bj (T so )]Xj (2) 
where Tj] and T, 0 are the brightness temperatures for the two conditions. If we expand the radiance Bj(T) to first 
order approximation about its mean temperature T 0 , in the form Bj(T) = Bj(T 0 )+(T-T 0 ) . then Eq. (2) 
becomes 
(Til ■ Tio) — Ei (Tsl - T so ) Xi 
(3) 
Similarily, for the measurements in channel j, we have 
(Tji - Tj 0 ) = £j (T sl - Tj 0 ) Xj 
(4) 
Dividing (4) by (3) gives 
(Til - T i0 )*|| = Tji - T j0 
(5) 
If the assumptions made above hold, for instance over N neighbouring pixels, then, by least- 
squares analysis of Eq. (5), the ratio of Xj£j to Xj£j can be obtained as 
N 
X(Tik - T i0 )(T jk - Tj 0 ) 
£ £^_ k=l 
Xj £j" N 
- T i0 ) 2 
k=l 
( 6 ) 
If emissivity in Channel 4 is equal to that in Channel 5 at a scale of an AVHRR pixel (this 
might be a good approximation for most surfaces) and if we define R 54 as