Linear simultaneous solution for temperature and absorbing constituent profiles from radiance spectra

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Abstract
A linear form of the radiative transfer equation (RTE) is formulated for the direct and simultaneous estimation of temperature and absorbing constituent profiles (e.g., water vapor, ozone, methane) from observations of spectral radiances. This unique linear form of the RTE results from a definition for the deviation of the true gas concentration profiles from an initial specification in terms of the deviation of their effective temperature profiles from the true atmospheric temperature profile. The effective temperature profile for any absorbing constituent is that temperature profile which satisfies the observed radiance spectra under the assumption that the initial absorber concentration profile is correct. Differences between the effective temperature, derived for each absorbing constituent, and the true atmospheric temperature are proportional to the error of the initial specification of the gas concentration profiles. The gas concentration profiles are thus specified after inversion of the linearized RTE from the retrieved effective temperature profiles assuming that one of the assumed concentration profiles is known (e.g., CO2). Because the solution is linear and simultaneous, the solution is computationally efficient. This efficiency is important for dealing with radiance spectra containing several thousand radiance observations as obtained from current airborne and planned future spaceborne interferometer spectrometer sounders. Here the solution is applied to spectral radiance observations simulated for current filter radiometers and planned spectrometers to demonstrate the anticipated improvement in future satellite sounding performance as a result of improved instrumentation and associated sounding retrieval methodology.