Maximizing the Information Content of Ill-Posed Space-Based Measurements Using Deterministic Inverse Method

For several decades, operational retrievals from spaceborne hyperspectral infrared sounders have been dominated by stochastic approaches where many ambiguities are pervasive. One major drawback of such methods is their reliance on treating error as definitive information to the retrieval scheme. To overcome this drawback and obtain consistently unambiguous retrievals, we applied another approach from the class of deterministic inverse methods, namely regularized total least squares (RTLS). As a case study, simultaneous simulated retrieval of ozone (O₃) profile and surface temperature (ST) for two different instruments, Cross-track Infrared Sounder (CrIS) and Tropospheric Emission Spectrometer (TES), are considered. To gain further confidence in our approach for real-world situations, a set of ozonesonde profile data are also used in this study. The role of simulation-based comparative assessment of algorithms before application on remotely sensed measurements is pivotal. Under identical simulation settings, RTLS results are compared to those of stochastic optimal estimation method (OEM), a very popular method for hyperspectral retrievals despite its aforementioned fundamental drawback. Different tweaking of error covariances for improving the OEM results, used commonly in operations, are also investigated under a simulated environment. Although this work is an extension of our previous work for H₂O profile retrievals, several new concepts are introduced in this study: (a) the information content analysis using sub-space analysis to understand ill-posed inversion in depth; (b) comparison of different sensors for same gas profile retrieval under identical conditions; (c) extended capability for simultaneous retrievals using two classes of variables; (d) additional stabilizer of Laplacian second derivative operator; and (e) the representation of results using a new metric called "information gain". Our findings highlight issues with OEM, such as loss of information as compared to a priori knowledge after using measurements. On the other hand, RTLS can produce "information gain" of ~40-50% deterministically from the same set of measurements.