## The Impact of Different Aerosol Models
### Components of XCO\({}_{2}\) Retrieval Errors  
To assess the impact of different aerosol combination groups while maintaining a constant number of parameters, all components of the XCO\({}_{2}\) retrieval error are compared in Figure 8; the number of aerosol parameters to be retrieved varied from four to seven, which was in accordance with the findings above. Each subfigure illustrates the distribution of the errors for all retrieved aerosol parameter combination groups. Both the forward model parameter error and the interference error are assumed to be aerosol-related only. Figure 7: XCO\({}_{2}\) DFS for four types of aerosols when the number of retrieved aerosol parameters ranges from 1 to 16. The SZA is 20\({}^{\circ}\) and the surface type is vegetation. For each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25 th (q1) and 75 th (q3) percentiles, respectively. The whiskers extend from q3+4\(\times\)(q3\(-\)q1) to q1\(-\)4\(\times\)(q3\(-\)q1), and the remaining data extending this range are plotted as outliers using the ‘+’ symbol. Figure 8: The histograms of the smoothing errors (**a**–**d**), measurement errors (**e**–**h**), forward model parameter errors (**i**–**l**) and interference errors (**m**–**p**) for four to seven retrieved aerosol parameters (columns from left to right), as well as the comparison of the interference error and forward model parameter error in corresponding cases (**q**–**l**). When a different number of retrieved aerosol parameters is selected, the three parameters of AOD, the peak height and width of aerosol profile (**H\({}_{\rm{P}}\)** and **H\({}_{\rm{W}}\)**) are always included. Different colorful bars and circles represent the four aerosol types. The dashed lines in (**q**–**l**) illustrate the interference errors equal to the forward model parameter errors. Generally, the smoothing, measurement, and interference errors fall within a similar range that is smaller than the forward model parameter error. Although the total number of possible aerosol combination groups (shown in Figure 8) increases as the number of retrieved aerosol parameters changes from four to seven, there is a greater fraction of groups with larger smoothing, measurement and interference errors. In contrast, the number of groups increases similarly in all error bins in terms of the forward model parameter error, due to the larger error range. When the number of retrieved aerosol parameters is held constant among the different aerosol parameter combination groups, most show smaller errors, particularly in the case of MA. In contrast, in the DD case, more group errors are close to the median, especially for the forward model parameter error (Figure 8i-l). On average, all error types are smaller for MA than for other aerosol types, owing to the low AOD. For UI and BB aerosols, the errors are slightly larger, while in the DD case, more groups have larger forward model parameter errors. That is, the distribution of the CO\({}_{2}\) forward model parameter error for DD is more uniform. The distinction of the forward model parameter errors between different aerosol parameter combination groups is more pronounced than other error components (Figure 8i-l). Additionally, the interference errors exhibit significantly more differences in response to changes in the retrieved aerosol parameters than other errors, especially when more parameters are retrieved (Figure 8p). Overall, the distribution of the interference error changes the most when the number of retrieved aerosol parameters increases. We also identified errors related to aerosol parameter uncertainties, i.e., the forward model parameter and interference errors, and compared these errors among the parameter combination groups (Figure 8q-t). The interference error was always lower than 2 ppm, whereas the forward model parameter error ranged from less than 1 ppm to more than 12 ppm.