Simultaneous retrieval of temperature and gas abundance

In the absence of independent, direct determinations of planetary prohles such as in situ measurements from an entry probe, it becomes necessary to infer both atmospheric temperature and composition from remotely sensed measurements alone. An example is the determinahon of the helium abundance in the atmospheres of the giant planets. One approach uses a combination of the thermal emission spectrum and the radio signal from the spacecraft occulted by the atmosphere. The radio occultahon measurements can be inverted to obtain an atmospheric refractivity prohle from which a prohle of temperature versus pressure can be calculated if the atmospheric composition is known. An initial atmospheric composition is assumed, and the resulting temperature prohle is used to calculate a theorehcal spectrum that is compared with a measured spectrum acquired near the occultation point. 

While the determination of helium in the atmospheres of the giant planets has been used as an example here, the approach for simultaneously retrieving temperature in combination with other atmospheric parameters by direct inversion of thermal emission spectra can be applied more generally. The basic requirement is that there be multiple points within the spectral range that are redundant in the sense that the atmospheric pressure level of unit optical depth is essentially the same for all points while the sensitivity of the spectrum to various parameters differs from point to point. Each particular application must be studied in order to determine the actual information content of the measurements and the precision of the retrievals. 

We first consider the analysis of solar absorption limb measurements. The geometry of the situation is similar to that illustrated in Fig. 8.2.4 except in this case the Sun serves as a source located at = +oo. Solar radiation transmitted through the atmosphere is measured by a sensor at the spacecraft. As the spacecraft moves, the ray path between the Sun and the sensor passes through different parts of the atmosphere. If it is assumed that thermal emission from the atmosphere is negligible compared with the transmitted solar radiation, the transmittance, f, of the atmosphere along the ray path is given by 

Here /(v, h) is the measured radiance at wavenumber v for the ray path whose closest approach to the planet at the ray tangent point is h, and Io v) is the solar radiance as observed by the sensor in the absence of the intervening atmosphere. 

Usually, measurements are available for a series of ray tangent point heights zq = hi,i = convenient to divide the atmosphere into m discrete 

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