To retrieve surface and atmospheric temperature profiles, together with trace species concentrations is a fundamental challenge in numerical weather prediction and Earth monitoring. Over the last 20 years, the development of high-resolution infrared sensors on board Earth observation satellites has opened new remote sensing opportunities, providing an unprecedented source of information. However, infrared sensors cannot probe into thick cloud layers, rendering their observations insensitive to surface under cloudy conditions. This results in spatial fields flagged with missing data, disrupting the continuity of inferred information and hindering accurate modeling of energy fluxes between the surface and the atmosphere. Consequently, advanced interpolation techniques and spatial statistics are essential to process the available (very large) data sets and produce satellite products on a regular grid mesh. This paper reviews and presents the physical modeling of radiative transfer in the atmosphere and the related mathematics of inversion, tailored for high spectral-resolution infrared sensors.

The new σ-IASI/F2N radiative transfer model is an advancement of the σ-IASI model, introduced in 2002. It enables rapid simulations of Earth-emitted radiance and Jacobians under various sky conditions and geometries, covering the spectral range of 3-100 μm. Successfully utilized in δ-IASI, the advanced Optimal Estimation tool tailored for the IASI MetOp interferometer, its extension to the Far Infrared (FIR) holds significance for the ESA Earth Explorer FORUM mission, necessitating precise cloud radiative effect treatment, crucial in regions with dense clouds and temperature gradients. The model's update, incorporating the "linear-in-T" correction, addresses these challenges, complementing the "linear-in-tau" approach. Demonstrations highlight its effectiveness in simulating cloud complexities, with the integration of the "linear-in-T" and Tang correction for the computation of cloud radiative effects. The results presented will show that the updated σ-IASI/F2N can treat the overall complexity of clouds effectively and completely, at the same time minimizing biases.

This paper describes a new fast line-by-line radiative transfer scheme which computes top of the atmosphere spectral radiance and its Jacobians with respect to any set of geophysical parameters both for clear and cloudy sky, and presents the software which implements the procedure. The performance of the code has been evaluated with respect to accuracy and speediness through a comparison with a state-of-art line-by-line radiative transfer model. The new code is well suited for nadir viewing satellite and airplane infrared sensors with a sampling rate in the range 0.1-2 cm-1.