###### Abstract  
Satellite retrievals of the atmospheric dry-air column-average mole fraction of CO\({}_{2}\) (XCO\({}_{2}\)) based on hyperspectral measurements in appropriate near (NIR) and short wave infrared (SWIR) O\({}_{2}\) and CO\({}_{2}\) absorption bands can help to answer important questions about the carbon cycle but the precision and accuracy requirements for XCO\({}_{2}\) data products are demanding. Multiple scattering of light at aerosols and clouds can be a significant error source for XCO\({}_{2}\) retrievals. Therefore, so called full physics retrieval algorithms were developed aiming to minimize scattering related errors by explicitly fitting scattering related properties such as cloud water/ice content, aerosol optical thickness, cloud height, etc. However, the computational costs for multiple scattering radiative transfer (RT) calculations can be immense. Processing all data of the Orbiting Carbon Observatory-2 (OCO-2) can require up to thousands of CPU cores and the next generation of CO\({}_{2}\) monitoring satellites will produce at least an order of magnitude more data. Here we introduce the Fast atmOspheric traCe gAs retrievaL FOCAL including a scalar RT model which approximates multiple scattering effects with an analytic solution of the RT problem of an isotropic scattering layer and a Lambertian surface. The computational performance is similar to an absorption only model and currently determined by the convolution of the simulated spectra with the instrumental line shape function (ILS). We assess FOCAL's quality by confronting it with accurate multiple scattering vector RT simulations using SCIATRAN. The simulated scenarios do not cover all possible geophysical conditions but represent, among others, some typical cloud and aerosol scattering scenarios with optical thicknesses of up to 0.7 which have the potential to survive the pre-processing of a XCO\({}_{2}\) algorithm for real OCO-2 measurements. Systematic errors of XCO\({}_{2}\) range from \(-2.5\,\mathrm{ppm}\) (\(-6.3\%\)) to \(3.0\,\mathrm{ppm}\) (\(7.6\%\)) and are usually smaller than \(\pm 0.3\,\mathrm{ppm}\) (\(0.8\%\)). The stochastic uncertainty of XCO\({}_{2}\) is typically about \(1.0\,\mathrm{ppm}\) (\(2.5\%\)). FOCAL simultaneously retrieves the dry-air column-average mole fraction of H\({}_{2}\)O (XH\({}_{2}\)O) and the solar induced chlorophyll fluorescence at \(760\,\mathrm{nm}\) (SIF). Systematic and stochastic errors of XH\({}_{2}\)O are most times smaller than \(\pm 6\,\mathrm{ppm}\) and \(9\,\mathrm{ppm}\), respectively. The systematic SIF errors are always below \(0.02\,\mathrm{mW}/\mathrm{m}^{2}/\mathrm{sr}/\mathrm{nm}\), i.e., it can be expected that instrumental or forward model effects causing an in-filling of the used Fraunhofer lines will dominate the systematic errors when analyzing actually measured data. The stochastic uncertainty of SIF is usually below \(0.3\,\mathrm{mW}/\mathrm{m}^{2}/\mathrm{sr}/\mathrm{nm}\). Without understating the importance of analyzing synthetic measurements as presented here, the actual retrieval performance can only be assessed by analyzing measured data which is subject to part 2 of this publication.  
**Keywords:** CO\({}_{2}\); satellite remote sensing; OCO-2; radiative transfer