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We describe the approach for the estimation of the atmospheric state, e.g., temperature, water, ozone, from calibrated, spectral radiances measured from the Tropospheric Emission Spectrometer (TES) onboard the Aura spacecraft. The methodology is based on the maximum a posteriori estimate, which mathematically requires the minimization of the difference between observed spectral radiances and a nonlinear model of radiative transfer of the atmospheric state subject to the constraint that the estimated state must be consistent with an a priori probability distribution for that state. The minimization techniques employed here are based on the trust-region Levenberg-Marquardt algorithm. An analysis of the errors for this estimate include smoothing, random, spectroscopic, "cross-state", representation, and systematic errors. In addition, several metrics and diagnostics are introduced that assess the resolution, quality, and statistical significance of the retrievals. We illustrate this methodology for the retrieval of atmospheric and surface temperature, water vapor, and ozone over the Gulf of Mexico on November 3, 2004.
Bowman et al. (2006) studied this question.