Retrieval of atmospheric profiles from satellite sounder measurements by use of the discrepancy principle

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Abstract
It is known that an infrared or a microwave remote-sensing equation is an integral equation of the first kind. As a result, it is ill-posed, the solution is unstable, and difficulties arise in its retrieval. To make the solution stable, either an a priori error covariance matrix or a smoothing factor γ is necessary as a constraint. However, if the error covariance matrix is not known or if it is estimated incorrectly, the solution will be suboptimal. The smoothing factor γ depends greatly on the observations, the observation error, the spectral coverage of channels, and the initial state or the first guess of the atmospheric profile. It is difficult to determine this factor properly during the retrieval procedure, so the factor is usually chosen empirically. We have developed a discrepancy principle (DP) to determine the γ in an objective way. An approach is formulated for achieving an optimal solution for the atmospheric profile together with the γ from satellite sounder observations. The DP method was applied to actual Geostationary Operational Environment Satellite (GOES-8) sounder data at the Southern Great Plains Cloud and Radiation Testbed site. Results show that the DP method yields a 21.7% improvement for low-level temperature and a 23.9% improvement for total precipitable water (TPW) retrievals compared with the traditional minimum-information method. The DP method is also compared with the Marquardt–Levenberg algorithm used in current operational GOES data processing. Results of the comparison show significant improvement, 6.5% for TPW and 11% for low-level water-vapor retrievals, in results obtained with the DP method compared with the Marquardt–Levenberg approach.