## 6 Optimization of the Aerosol Model  
Considering the large amounts of AOD, H\({}_{\text{p}}\), and H\({}_{\text{w}}\) information in all cases (Section 4.2), these three parameters were retrieved, and the other parameters remained to be determined. To derive the aerosol model with the most appropriate seven parameters for retrieval (five for MA), the forward model parameter and interference errors for the different aerosol parameter combination groups including AOD, H\({}_{\text{p}}\), and H\({}_{\text{w}}\) were compared (Figure 9). Given the small range of CO\({}_{2}\) DFS in these groups (Figure 7), the XCO\({}_{2}\) retrieval error is used as the selection criteria. We sought to select those aerosol parameter groups with the lowest XCO\({}_{2}\) errors; thus, only the XCO\({}_{2}\) aerosol-induced errors under 4 ppm are presented in Figure 9.  
In Figure 9, for vegetation, it can be seen that although the forward model parameter errors of most of the aerosol parameter combination groups exceed the corresponding interference errors (Figure 8q-t), there are still some groups with errors that are close to the interference errors, particularly in the cases of UI and BB aerosols. However, with regard to DD and MA, the total XCO\({}_{2}\) errors are dominated by the forward model parameter error in nearly all groups (Figure 9c,d). The number of aerosol parameter combination groups showing lower total XCO\({}_{2}\) aerosol-induced errors for DD is 207, which is significantly less than for the UI (n = 537) and BB (n = 515) aerosols. The total number of combination groups for MA is only 78, which is less than that for the other three aerosol types, due to only five aerosol parameters being retrieved. In other words, the aerosol-induced XCO\({}_{2}\) errors of all MA groups are smaller than 4 ppm, and most of the errors are under 2 ppm. Additionally, the lowest error of DD combination groups is under 2 ppm, and those for UI and BB aerosols are close to 2 ppm. Comparing two surface types, the aerosol-induced XCO\({}_{2}\) errors over soil are apparently lower than those over vegetation for the BB, DD and MA aerosols at only half. Additionally, regarding the value of the total error, a greater number of groups with low errors is found over soil than over vegetation. However, for UI aerosol, most groups have similar XCO\({}_{2}\) errors over soil as those over vegetation, which is approximately 1.5 to 3.5 ppm. Furthermore, for the soil surface, the number of groups with errors that are lower than 4 ppm is also less at only 407. Notably, the lowest XCO\({}_{2}\) error over soil is lower than that over vegetation at only approximately 0.5 ppm (Figure 9a,b). This finding means that for the UI aerosol over soil, the choice of the aerosol parameter combination group is more important for reducing the XCO\({}_{2}\) error. For the other three aerosol types, the XCO\({}_{2}\) errors over vegetation still serve as the main criteria for selecting aerosol groups that are suitable for all land surfaces. Figure 9: Comparison of interference and forward model parameter errors for different aerosol parameter groups in Figure 8 when the number of retrieved aerosol parameters is maintained at seven for UI, BB and DD aerosol, and five for MA, with the total errors from aerosol parameters being smaller than 4 ppm. The left column is for vegetation (**a,c,e,g**) and the right column is for soil (**b,d,f,h**). The four rows represent the four types of aerosols. The x-axis represents the index of different aerosol parameter groups and the numbers at the end of the x-axis are the total number of groups. As Figure 9 illustrates, we sought to select the aerosol parameter combination group with the lowest number of XCO\({}_{2}\) aerosol-induced errors for all aerosol types and all surface types. All of the aerosol parameter combination groups shown in Figure 9 were sorted from low to high by the total number of XCO\({}_{2}\) aerosol-induced errors for each aerosol type.