## 6 Optimization of the Aerosol Model
The first combination group was chosen as the best aerosol model for the CO\({}_{2}\) retrieval algorithm. Table 5 summarizes the first few combination groups and their total aerosol-induced XCO\({}_{2}\) retrieval errors for all aerosol types and both surfaces. For MA, it would evidently be better to retrieve five aerosol parameters, namely, AOD, H\({}_{\text{P}}\), H\({}_{\text{w}}\), ref\({}^{\text{c}}\), a\({}^{\text{c}}\), for the CO\({}_{2}\) retrieval algorithms with an aerosol-induced XCO\({}_{2}\) error of less than 0.5 ppm. For the other three types of aerosols, three aerosol parameter combination groups with low errors were selected as Groups 1, 2, and 3 (Table 5). In these groups, six of the seven aerosol parameters were identical: AOD, H\({}_{\text{P}}\), H\({}_{\text{w}}\), ref\({}^{\text{c}}\), a\({}^{\text{r}}\) and a\({}^{\text{r}}\)\({}^{\text{c}}\); this finding indicates that in addition to the AOD and the aerosol profile, the size parameter of the coarse aerosol and the real part parameter of the refractive index of both modes should also be retrieved. There was a little difference among the groups in the remaining aerosol parameters, which were fmf, size parameter of fine mode, and the other refractive index coefficient. In a comparison of the total aerosol-induced XCO\({}_{2}\) errors, the differences in UI and DD among Groups 1-3 were less than 0.1 ppm and more than 0.1 ppm for BB. Comparing different surface types, the errors over soil for the three groups are apparently smaller than those over vegetation except for UI. As we demonstrated in Figure 9, the XCO\({}_{2}\) error caused by the UI aerosol over soil shows a larger difference to even more than 0.8 ppm among Groups 1-3 when the aerosol group changes. Despite the lower error of Group 2 for UI and DD over soil than Group 1, BB aerosol leads to greater XCO\({}_{2}\) uncertainty for the vegetation surface, whcih exceeds 2 ppm. Considering the generality, we recommend Group 1 as the optimal aerosol modelto maintain the aerosol-induced XCO\({}_{2}\) error below 1.7 ppm for all three aerosol types and both surface types. If additional information concerning aerosol size or optical properties are obtained prior to retrieval, such as from CAPI measurements or MODIS inversion products, so that DD may be distinguished from UI and BB, Group 4 is recommended. In this group, two different aerosol parameters, including the size and refractive index parameter, are selected for DD and the other two aerosol types, as shown in Table 5. Consequently, the parameters pertaining to fine mode aerosols for UI and BB, such as b\({}_{\text{r}}\)f and v\({}_{\text{eff}}\)f, are replaced by similar parameters but of coarse mode for DD as the optimal model, which is mainly due to the large particle size of the DD aerosol. Accordingly, the total aerosol-induced XCO\({}_{2}\) errors are clearly reduced for DD and UI. Finally, AOD and two aerosol profile parameters (H\({}_{\text{P}}\) and H\({}_{\text{w}}\)), as well as one particle size parameter (r\({}_{\text{eff}}\)f) and one real part coefficient of refractive index (a\({}_{\text{r}}\)f) for coarse particles are recommended for the CO\({}_{2}\) retrieval state vector for all aerosol types to minimize aerosol-induced errors. Owing to a larger amount of aerosol information for the other three aerosol types except MA, two more parameters of fine particles including size and real refractive index parameters (v\({}_{\text{eff}}\)f and a\({}_{\text{r}}\)f) could also be retrieved.