Radiation is a key process in the atmosphere. Numerous radiative transfer codes have been developed spanning a large range of wavelengths, complexities, speeds, and accuracies. In the infrared and microwave, line-by-line codes are crucial esp. for modeling and analyzing high-resolution spectroscopic observations. Here we present Py4CAtS—PYthon scripts for Computational ATmospheric Spectroscopy, a Python re-implemen-tation of the Fortran Generic Atmospheric Radiation Line-by-line Code GARLIC, where computationally-intensive code sections use the Numeric/Scientific Python modules for highly optimized array processing. The individual steps of an infrared or microwave radiative transfer computation are implemented in separate scripts (and corresponding functions) to extract lines of relevant molecules in the spectral range of interest, to compute line-by-line cross sections for given pressure(s) and temperature(s), to combine cross sections to absorption coefficients and optical depths, and to integrate along the line-of-sight to transmission and radiance/intensity. Py4CAtS can be used in three ways: in the (Unix/Windows/Mac) console/terminal, inside the (I)Python interpreter, or Jupyter notebook. The basic design of the package, numerical and computational aspects relevant for optimization, and a sketch of the typical workflow are presented. In conclusion, Py4CAtS provides a versatile environment for “interactive” (and batch) line-by-line radiative transfer modeling.

The objective was to validate the carbon monoxide (CO) total column product inferred from Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) full-mission (2003–2011) short-wave infrared (SWIR) nadir observations using the Beer InfraRed Retrieval Algorithm (BIRRA). Globally distributed Network for the Detection of Atmospheric Composition Change (NDACC) and Total Carbon Column Observing Network (TCCON) ground-based (g-b) measurements were used as a true reference. Weighted averages of SCIAMACHY CO observations within a circle around the g-b observing system were utilized to minimize effects due to spatial mismatch of space-based (s-b) and g-b observations, i.e., disagreements due to representation errors rather than instrument and/or algorithm deficiencies. In addition, temporal weighted averages were examined and then the unweighted (classical) approach was compared to the weighted (non-classical) method. The delivered distance-based filtered SCIAMACHY data were in better agreement with respect to CO averages as compared to square-shaped sampling areas throughout the year. Errors in individual SCIAMACHY retrievals have increased substantially since 2005. The global bias was determined to be in the order of $-10$ parts per billion in volume (ppbv) depending on the reference network and validation strategy used. The largest negative bias was found to occur in the northern mid-latitudes in Europe and North America, and was partly caused by insufficient a priori estimates of CO and cloud shielding. Furthermore, no significant trend was identified in the global bias throughout the mission. The global analysis of the CO columns retrieved by the BIRRA shows results that are largely consistent with similar investigations in previous works.

High-quality observations have indicated the need for improved molecular spectroscopy for accurate atmospheric characterization. Line data provided by the new SEOM-IAS (Scientific Exploitation of Operational Missions—Improved Atmospheric Spectroscopy) database in the shortwave infrared (SWIR) region were used to retrieve $\mathrm{CO}$ total vertical columns from a selected set of nadir SCIAMACHY (SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY) observations. In order to assess the quality of the retrieval results, differences in the spectral fitting residuals with respect to the HITRAN 2016 (High-resolution TRANsmission molecular absorption) and GEISA 2015 (Gestion et Etude des Informations Spectroscopiques Atmosphériques) line lists were quantified and column-averaged dry-air $\mathrm{CO}$ mole fractions were compared to NDACC (Network for the Detection of Atmospheric Composition Change) and TCCON (Total Carbon Column Observing Network) ground-based measurements. In general, it was found that using SEOM-IAS line data with corresponding line models improve the spectral quality of the retrieval (smaller residuals) and increase the fitted $\mathrm{CO}$ columns, thereby reducing the bias to both ground-based networks.

The impact of SEOM–IAS (Scientific Exploitation of Operational Missions–Improved Atmospheric Spectroscopy) spectroscopic information on $\mathrm{CO}$ columns from TROPOMI (Tropospheric Monitoring Instrument) shortwave infrared (SWIR) observations was examined. HITRAN 2016 (High Resolution Transmission) and GEISA 2015 (Gestion et Etude des Informations Spectroscopiques Atmosphériques 2015) were used as a reference upon which the spectral fitting residuals, retrieval errors and inferred quantities were assessed. It was found that SEOM–IAS significantly improves the quality of the $\mathrm{CO}$ retrieval by reducing the residuals to TROPOMI observations. The magnitude of the impact is dependent on the climatological region and spectroscopic reference used. The difference in the $\mathrm{CO}$ columns was found to be rather small, although discrepancies reveal, for selected scenes, in particular, for observations with elevated molecular concentrations. A brief comparison to Total Column Carbon Observing Network (TCCON) and Network for the Detection of Atmospheric Composition Change (NDACC) also demonstrated that both spectroscopies cause similar columns; however, the smaller retrieval errors in the SEOM with Speed-Dependent Rautian and line-Mixing (SDRM) inferred $\mathrm{CO}$ turned out to be beneficial in the comparison of post-processed mole fractions with ground-based references.

Monitoring anthropogenic emissions is a crucial aspect in understanding the methane budget. Moreover, a reduction of methane emissions could help to mitigate global warming on a short timescale. This study compares various retrieval schemes for estimating localized methane enhancements around ventilation shafts in the Upper Silesian Coal Basin in Poland using nadir observations in the shortwave infrared acquired from the airborne imaging spectrometer HySpex. Linear and nonlinear solvers are examined and compared, with special emphasis put on strategies that tackle degeneracies between the surface reflectivity and broad-band molecular absorption features – a challenge arising from the instrument's low spectral resolution. Results reveal that the generalized nonlinear least squares fit, employed within the Beer InfraRed Retrieval Algorithm (BIRRA), can measure enhanced methane levels with notable accuracy and precision. This is accomplished by allowing the scene's background covariance structure to account for surface reflectivity statistics. Linear estimators such as matched filter (MF) and singular value decomposition (SVD) are able to detect and, under favorable conditions, quantify enhanced levels of methane quickly. Using k-means clustering as a preprocessing step can further enhance the performance of the two linear solvers. The linearized BIRRA fit (LLS) underestimates methane but agrees on the enhancement pattern. The non-quantitative spectral signature detection (SSD) method does not require any forward modeling and can be useful in the detection of relevant scenes. In conclusion, the BIRRA code, originally designed for the retrieval of atmospheric constituents from spaceborne high-resolution spectra, turned out to be applicable to hyperspectral airborne imaging data for the quantification of methane plumes from point-like sources. Moreover, it is able to outperform well-established linear schemes such as the MF or SVD at the expense of high(er) computing time.

This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the nonlinear parameters remain consistent across all datasets. A well-established approach for solving such problems is the variable projection algorithm introduced by Golub and LeVeque, which effectively reduces a separable problem to its nonlinear component. However, this algorithm assumes that the datasets have equal sizes and identical auxiliary model parameters. This article is motivated by a real-world remote sensing application where these assumptions do not apply. Consequently, we propose a generalized algorithm that extends the original theory to overcome these limitations. The new algorithm has been implemented and tested using both synthetic and real satellite data for atmospheric carbon dioxide retrievals. It has also been compared to conventional state-of-the-art solvers, and its advantages are thoroughly discussed. The experimental results demonstrate that the proposed algorithm significantly outperforms all other methods in terms of computation time, while maintaining comparable accuracy and stability. Hence, this novel method can have a positive impact on future applications in remote sensing and could be valuable for other scientific fitting problems with similar properties.