## 4 Aerosol Parameters in CO2 Retrieval
### Aerosol-Induced XCO2 Retrieval Errors  
The interference errors in XCO2 for each aerosol parameter of the four aerosol types (calculated by Equation (8)) are presented in Figure 5a. These errors from different aerosol parameters range from less than 0.1 to 0.8 ppm. Overall, the interference errors due to \(\mathrm{r_{eff}}\) and \(\mathrm{v_{eff}}\) for both fine and coarse modes, as well as fmf and \(\mathrm{a_{r}}\) for fine mode, exceed those for the other parameters, reaching 0.2 ppm or more at 20\({}^{\circ}\) SZA. Because of the dominance of large particles, the coarse mode PSD parameters of DD result in larger uncertainties than the fine particle parameters, while the opposite is the case for UI and BB aerosols, where smaller particles predominate. Regarding the refractive index coefficients, their interference errors were less than 0.2 ppm at 20\({}^{\circ}\) SZA, and even less than 0.1 ppm for MA. These refractive index-related errors ranged from 0.1 to 0.2 ppm for DD aerosols, which was slightly more than for the other aerosol types. When the interference errors at different SZAs were compared, it was observed that at a smaller SZA, the errors from most aerosol parameters were larger. The reason for this is that more information is allocated to the CO2 profile than to the aerosol properties for longer light paths at larger SZAs, so there is a reduction in the impact of the aerosol parameter uncertainties on XCO2 retrieval (Equation (8)).  
When the interference errors (\(\sigma_{i}\)) from all aerosol parameters are summed (\(\sigma_{i}^{2}=h^{T}\hat{\mathbf{S}}_{i}h\)), the aerosols will induce a 0.2 to 1.0 ppm error in the XCO2 retrievals, depending on the aerosol type and the observation geometry (Figure 5b). Comparison of the four aerosol types reveals that the UI, DD and BB aerosols have greater effects on XCO2 retrieval due to their larger AODs, with an interference error of greater than 0.3 ppm. The MA only cause interference errors of 0.2 to 0.3 ppm, as MA has the lowest aerosol loading. When the SZA is increased, the interference of the aerosols with XCO2 is weakened, except for MA, owing to the longer light paths. For DD, this pattern changes when the SZA is 65\({}^{\circ}\), which is related to the scattering phase matrix. Furthermore, for a soil surface with a larger reflectance, the interference errors in XCO2 caused by aerosol parameters are slightly smaller (Figure S2 in the Supplement), indicating that aerosol scattering has a larger impact due to a lower reflected radiation signal from the satellite.  
In summary, the aerosol parameter uncertainties constitute a significant component of XCO\({}_{2}\) retrieval uncertainty, depending on the aerosol type and observation geometry, or the scattering phase matrix in different scattering angles. This finding presents a challenge that must be overcome before XCO\({}_{2}\) retrieval precision can be improved.  
Figure 5: The interference errors in XCO\({}_{2}\) from the aerosol parameters. (**a**) Interference error from each aerosol parameter for four aerosol types (different colors) at 20\({}^{\circ}\) (star lines) and 50\({}^{\circ}\) solar zenith anlge (SZA) (dot lines) over vegetation. The x-axis is the interference error and the y-axis represents 16 aerosol parameters. (**b**) Total interference error from all aerosol parameters at four SZAs for different aerosol types over vegetation.