Figure 2,-Relationship between the logarithm of /? and the water vapor content, W. The line represents the least
squares fitting lnf=-0.621W+5.648.
Then, the operational split-window algorithm proposed for LST is
T = T 4 + [ 1.0+0.58(T4-T 5 )](T4-T 5 ) + 0.51 + 40(1 -e) - pAe (5)
where the coefficient p can be choosen according to the different procedures outlined above. The modified splitwindow
splitwindow equation includes an A coefficient depending on the interchanncl temperature difference, T 4 -T 5 , which
takes into account the atmospheric variability at global scale. For the emissivity correction, the larger source of
error is the knowledge of the effective surface emissivity. Table 1 shows the error in the emissivity correction,
5T e , for various values of the emissivity errors 8 e and 8 Ae. Assuming an error of 0.01 in both e and Ae, the
error associated to B(e) ranges from 0.7 K for moist atmospheres, to 1.4 K for dry atmospheres. The total error
in LST retrieval, 8 T, is the combination of 8 T e and the error due to the atmospheric correction, 8 T a . Table 2
shows the total error of equation (5), considering 6T=[(5T a ) 2 +(5T e ) 2 ] ,/2 . Thus, the current accuracy in LST
retrieval using the split-window technique ranges from 0.7 to 1 .8 °C depending on the errors in the atmospheric
and emissivity corrections, which also depends on the atmospheric water vapor content and on the error in
determining and mapping emissivities. Wc can observe that the error in the emissivity correction is two limes
larger than the error in the atmospheric correction.
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