## 4 Conclusions
The quality of the spectral fits in the O\({}_{2}\) fit window is usually 2.5 to 4 times better than expected from instrumental noise. In the CO\({}_{2}\) fit windows, the quality of the spectral fits is usually at least 7 times better than expected from instrumental noise and even smaller fit residuals are obtained in the SIF fit window. Systematic errors of XCO\({}_{2}\) range from \(-2.5\,\mathrm{ppm}\) to \(3.0\,\mathrm{ppm}\) and are usually smaller than \(\pm 0.3\,\mathrm{ppm}\) (for the tested scenarios). The stochastic uncertainty of XCO\({}_{2}\) is typically about \(1.0\,\mathrm{ppm}\). Systematic errors of XH\({}_{2}\)O range from \(-243\,\mathrm{ppm}\) to \(0\,\mathrm{ppm}\) and are usually smaller than \(\pm 6\,\mathrm{ppm}\). The stochastic uncertainty of XH\({}_{2}\)O is typically about \(9\,\mathrm{ppm}\). Note, \(1000\,\mathrm{ppm}\)\(\cong 6.44\,\mathrm{kg/m^{2}}\) for the analyzed H\({}_{2}\)O profiles. The degree of freedom for the retrieved five-layered CO\({}_{2}\) and H\({}_{2}\)O profiles is typically 2.2. As SIF is retrieved from Fraunhofer lines in a spectral region with negligible gaseous absorption features, it can be retrieved without significant interferences with the retrieved scattering properties. The systematic SIF errors are always below \(0.02\,\mathrm{mW/m^{2}/sr/nm}\), i.e., it can be expected that instrumental or forward model effects causing an in-filling (a reduction of the line depths) of the used Fraunhofer lines will dominate the systematic errors when analyzing actually measured data. The stochastic uncertainty of SIF is usually below \(0.3\,\mathrm{mW/m^{2}/sr/nm}\). All SCIATRAN and FOCAL RT computations have been performed with an Intel Core i7-3770 CPU with four cores running at 3.4 GHz (released in 2012). On a single core, the SCIATRAN (programmed with FORTRAN) computations of the _Rayleigh+Aerosol BG+Water cloud_ scenario took about 32,000 s. This compares to 0.06 s for FOCAL (programmed with IDL) if only the spectrum and 0.11 s if also the Jacobian is computed. The convolution of spectrum and Jacobian adds 0.22 s and is, therefore, currently the main driver of the total computation time of 0.33 s needed for the forward model of the retrieval. Especially in view of potential future satellite missions similar to CarbonSat easily exceeding one million quality-filtered cloud-free soundings per day [4; 36], a gain in processing speed of this magnitude is urgently needed. Approximating for convenience that on average ten iterations are needed per sounding, results in a need for about 400 CPU cores to process such a data stream ten times faster than acquired which may reduce to 20 up-to-date CPU cores at launch date. FOCAL's computations are simple enough for an adaptation to GPU architecture with reasonable effort which has the potential for a further substantial acceleration. Without understating the importance of analyzing synthetic measurements as presented here, the actual retrieval performance can only be assessed by analyzing measured data including, e.g., pre- and post-filtering, and all kinds of instrumental effects, which is subject to part 2 of this publication [25]. This work was in part funded by ESA/ESRIN (GHG-CCI II project), the European Union (Copernicus Climate Change Service led by ECMWF), and the State and the University of Bremen. The OCO-2 data were produced by the OCO-2 project at the Jet Propulsion Laboratory, California Institute of Technology, and obtained from the OCO-2 data archive maintained at the NASA Goddard Earth Science Data and Information Services Center. Additionally, NASA provided the absorption cross section database ABSCO. We used solar spectra made available by [PERSON] and [PERSON] and a chlorophyll fluorescence spectrum published by [PERSON] made available the CarbonTracker CO\({}_{2}\) fields. ECMWF provided the used meteorological profiles.