Regularization techniques for inverse problems in Earth's surface radiation: Gauss-Newton meets Bayes-Tikhonov.

FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) is a satellite mission selected in 2019 as the ninth ESA (European Space Agency) Earth Explorer mission. FORUM will provide interfer- ometric measurements in the spectral interval encompassing the Far-InfraRed (FIR) part of the spectrum, responsible for about 50% of the outgoing longwave ux lost by our planet into space. While more accurate measurements of the Top Of the Atmosphere (TOA) resolved spectrum in the FIR are necessary for reduc- ing uncertainty in climate models, existing instruments are insucient. The observations will also improve the knowledge of several atmospheric variables, such as tropospheric water vapor, ice cloud properties and especially surface emissivity in the FIR, the focus of this seminar. In the early stages of the mission development, an End-to-End Simulator (E2ES) has been devised to demonstrate proof-of-concept and to evaluate the impact of instrument characteristics and scene conditions on the accuracy of the reconstructed atmospheric properties. The retrieval is obtained through inversion of the radiative transfer equation. In the retrieval step, performed in the E2ES by the CLAIM (CLouds and Atmosphere Inversion Module) code, the atmospheric state that best reconstructs the simulated measured spectrum is determined. The inversion is a severely ill-conditioned problem, and is solved using a Gauss-Newton (GN) method com- bined with the Optimal Estimation (OE) approach, a Tikhonov regularization scheme based on a standard Bayesian approach. The retrieved proles may present unphysical oscillations, requiring the application of the Iterative Variable Strength regularization (IVS) after the convergence of the GN method. In the rst part of this seminar, I will focus on the retrieval of the surface emissivity, in particular on the choice of the retrieval grid step and the IVS parameters, using the FORUM simulated measurements in dierent latitude bands. Moreover, I will present procedures for the assimilation of observed data and Bayesian techniques for deriving surface emissivity a-priori estimates. Finally, I will conclude by discussing FORUM sensitivity in measuring surface emissivity in both clear and cloudy sky conditions, focusing on different aspects of the computational pipeline.