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Deriving Specific Humidity from Relative Humidity
We
have shown that the remotely
sensed brightness temperature for GOES channel 3 can be approximated as the
equivalent brightness temperature from a reference level temperature and three
independent terms, one a function of the layer-average water vapor mixing ratio
(or specific humidity), one a function of the layer-average temperature, and one
a function of the satellite viewing angle.
This implies
that when each of these contributing functions is equal to zero (at nadir, and
240K at 400 hPa, with a water vapor mixing ratio of 0.29 g/kg) the remotely
sensed radiative temperature is equal to To.
As the satellite viewing angle increases, the atmospheric path length
increases, and equivalent brightness temperature decreases.
As the layer average temperature of the upper troposphere warms (cools),
the equivalent brightness temperature increases (decreases).
Figure 1 illustrates the relative contribution of each of these terms by
displaying them as variations about the reference level, To.
For convenience we can think of each term as an independent
contribution to the equivalent brightness temperature, T6.7. This clearly demonstrates that GOES equivalent brightness
temperatures are influenced by variations in the layer-average temperature of
the mid-to-upper troposphere. It
also suggests that these remotely sensed brightness temperatures are relatively
sensitive to small changes in water vapor mixing ratio at low absolute water
vapor content.
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