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Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our “Generic Atmospheric Radiation Line-by-line Infrared Code”, utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using “exact” AD Jacobians as a reference. The results indicate that the “standard” two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy. [ABSTRACT FROM AUTHOR]

Abstract: A suite of programs for high resolution infrared-microwave atmospheric radiative transfer modeling has been developed with emphasis on efficient and reliable numerical algorithms and a modular approach appropriate for simulation and/or retrieval in a variety of applications. The Generic Atmospheric Radiation Line-by-line Infrared Code — GARLIC — is suitable for arbitrary observation geometry, instrumental field-of-view, and line shape. The core of GARLIC's subroutines constitutes the basis of forward models used to implement inversion codes to retrieve atmospheric state parameters from limb and nadir sounding instruments. This paper briefly introduces the physical and mathematical basics of GARLIC and its descendants and continues with an in-depth presentation of various implementation aspects: An optimized Voigt function algorithm combined with a two-grid approach is used to accelerate the line-by-line modeling of molecular cross sections; various quadrature methods are implemented to evaluate the Schwarzschild and Beer integrals; and Jacobians, i.e. derivatives with respect to the unknowns of the atmospheric inverse problem, are implemented by means of automatic differentiation. For an assessment of GARLIC's performance, a comparison of the quadrature methods for solution of the path integral is provided. Verification and validation are demonstrated using intercomparisons with other line-by-line codes and comparisons of synthetic spectra with spectra observed on Earth and from Venus. [Copyright &y& Elsevier]

In this paper, we present the Hefei EMI Cloud Retrieval Algorithm (HECORA), which uses information from the O2-O2 absorption band around 477 nm to retrieve effective cloud fraction and effective cloud pressure from satellite observations. The retrieved cloud information intends to improve the atmospheric trace gas products based on the Environment Monitoring Instrument (EMI) spectrometer. The HECORA method builds on OMCLDO2 and presents some evolutions. The Vector Linearized Discrete Ordinate Radiative Transfer (VLIDORT) model has been used to produce the Top of the Atmosphere (TOA) reflectance Look-up Tables (LUT) as a function of the cloud fraction and cloud pressure. Applying the Differential Optical Absorption Spectroscopy (DOAS) technique to the synthetic reflectance LUT, the reflectance spectra can be associated with O2-O2 geometrical vertical column densities (VCDgeo) and continuum reflectance. This is the core of the retrieval method, since there is a one-to-one relationship between O2-O2 VCDgeo and continuum reflectance, on the one hand, and effective cloud fraction and effective cloud pressure, on the other hand, for a given illumination and observing geometry and given surface height and surface albedo. We first used the VLIDORT synthetic spectra to verify the HECORA algorithm and obtained good results in both the Lambertian cloud model and the scattering cloud model. Secondly, HECORA is applied to OMI and TROPOMI and compared with OMCLDO2, FRESCO+, and OCRA/ROCINN cloud products. Later, the cloud pressure results from TROPOMI observations obtained using HECORA and FRESCO+ are compared with the CALIOP Cloud Layer product. HECORA is closer to the CALIOP results under low cloud conditions, while FRESCO+ is closer to high clouds due to the higher sensitivity of the O2 A-band to cloud vertical information. Finally, HECORA is applied to the TROPOMI NO2 retrieval. Validation of the tropospheric NO2 VCD with ground-based MAX-DOAS measurements shows that choosing HECORA cloud products to correct for photon path variations on the TROPOMI tropospheric NO2 VCD retrievals has better performance than using FRESCO+ under low cloud conditions. In conclusion, this paper shows that the HECORA cloud products are in good agreement with the well-established cloud products and that they are suitable for correcting the effect of cloud in trace gas retrievals. Therefore, HECORA has the potential to be applied to EMI. [ABSTRACT FROM AUTHOR]

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained. [ABSTRACT FROM AUTHOR]