dT, where Ky(z) = -l is known as the transmission weighting function, and
Cy(z) = By (z)Ky (z) is commonly known as the contribution function. The transmission weighting function for nadir viewing (for which the zenith angle d = o) is a smoothly varying function as can be seen from Figure 6.8, which shows the calculated weighting function at 6oo cm_i and i,3oo cm_i for Jupiter's atmosphere. Also shown in Figure 6.8 is the variation of transmission with height and it can be seen that the weighting function peaks roughly where the optical depth is unity, or equivalently where the transmission to space is o.368. Since transmission of the atmospheric gases varies with wavelength, as was shown in Figures 6.5 and 6.6, the altitude of the peak of the weighting function varies correspondingly. Hence, in spectral regions of high absorption (such as at i,3oo cm_i in Figure 6.8), the weighting function peaks high in the atmosphere and thus most of the radiation observed is emitted from high levels, whereas in spectral regions of low absorption (such as at 6oocm_i), the weighting functions peak at low altitudes and thus most of the radiation comes from deep levels. Figure 6.9 shows how the altitude of the peak of the calculated weighting function varies with wavelength for the Jovian atmosphere, assuming no clouds. At 2,ooo cm_i (or 5 ^m) gas absorption is particularly low and thus radiation is mostly emitted from the deep troposphere. At i,3oo cm_i, in the middle of a strong CH4 absorption, most of the radiation is emitted from the stratosphere. Similar variation of the peak of the weighting function with wavelength is found for the other giant planets. Clearly if we have good models for the absorption spectra of gases we may use the observed thermal emission spectra to infer the variation of both temperature and composition with height in the giant planet atmospheres.
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