## 7 Discussions  
In this paper, we only consider the mean aerosol loading with constant AOD for each aerosol type, according to the statistical analysis of AERONET inversion products. Would the change in AOD describing different air pollution levels for one aerosol type influence the optimal aerosol model selection for CO\({}_{2}\) retrieval? To address this issue, the information and a posteriori error are compared when AOD ranges from 0.1 to 2.0 at 440 nm (Figure 10). The aerosol DFS becomes larger as the AOD increases, whereas there is a threshold of aerosol DFS. As soon as the aerosol DFS reaches the threshold, increasing the AOD could add little DFS (8.0 DFS in Figure 10f). Generally, the change in the aerosol DFS caused by AOD variation is not more than 1.0 (Figure 10f). Furthermore, comparing the DFSs of different aerosol parameters (Figure 10a-e), each parameter has a larger DFS when the AOD increases, whereas those parameters with larger DFSs change little with AOD. Therefore, although, adding one more retrieved aerosol parameter is more appropriate in those cases with 1.0 more DFS, the optimal aerosol model in this study has already accounted for the most greatest amount of XCO\({}_{2}\) retrieval errors from aerosols. If the AOD is small and shows thin aerosol pollution, the interference of aerosol uncertainties for CO\({}_{2}\) retrieval does not require much focus. Considering the generality of the aerosol model, the variation in AOD would not interfere with the selection of the retrieved aerosol parameters group. Similarly, the aerosol vertical profile mainly affects the total aerosol DFS and the profile parameter information. Given that the height of the aerosol layer changes the absorption of O\({}_{2}\), the measurements in the TanSat O\({}_{2}\)-A band always contain a large amount of information about aerosol profile parameters,  
Figure 10: The DFS of each aerosol parameter (**a–e**) for different AODs over vegetation similar to Figure 6. (**f**) shows the variation in the total aerosol DFS with the change in AOD from 0.1 to 2.0 at 440 nm. no matter where the aerosol is concentrated. Different aerosol profiles have less impact on microphysical parameters information than different aerosol types and their interference errors in XCO\({}_{2}\), meaning that not much attention to the aerosol profile is required when choosing the optimal aerosol model. Considering the limited aerosol information contained in the spectra, an aerosol model with a fixed vertical distribution shape is used instead of retrieving aerosol loading at each layer, and thus, more information would be distributed to the microphysical parameters. In addition, this research focuses on TanSat nadir observations over land, which is assumed to be a combination of both soil and vegetation surfaces. There are still a few areas of land covered by snow or ice with higher reflectances, especially at high latitudes. Based on comparisons of vegetation and soil surfaces, uncertainties in XCO\({}_{2}\) caused by aerosols decrease as surface reflectance increases. Thus, over snow or ice, the interference from aerosols in CO\({}_{2}\) retrieval is so small that this interference would not affect our decision to use the optimal aerosol model. For some water surfaces on land with lower surface reflectance, the radiation reflected by the surface is so small that it is not used to retrieve CO\({}_{2}\). Furthermore, only observations under clear sky are considered in this study, which is a simple assumption for real atmosphere. Based on the cloud contamination model involving cirrus, which has been implemented in the TanSat CO\({}_{2}\) retrieval algorithm, we do not consider complex situations involving thin clouds here. With the methodology used in our study, we analyzed the information content in measured spectra and estimated the retrieval errors directly from the spectrum residual and the status of the measurements and atmosphere, without a practical retrieval process.