## 8 Conclusions  
In this study, we have focused on optimizing the aerosol model for the CO\({}_{2}\) retrieval algorithm based on TanSat observations, which was in accordance with information estimation and error analysis. The hyperspectral of TanSat's three NIR bands, and the corresponding weighting functions with respect to the retrieved parameters, were simulated by a forward radiative transfer model, VLIDORT. Our simulations considered four types of aerosols, comprising fine and coarse particles with different microphysical properties over two types of land with different surface reflectance, vegetation and soil. These aerosol microphysical properties were obtained from the most recent five-year AERONET inversion products for several sites, similar to our previous study. The surface reflection was characterized by the Ross-Li BRDF model using MODIS products. The information content of the parameters retrieved from observations was represented by the DFS. The a posteriori error in XCO\({}_{2}\) was composed of four components, including the smoothing error, measurement error, forward model parameter error, and interference error, which could be calculated from the _a priori_ assumptions by applying the optimal estimation theory. To reduce the effects of aerosols on CO\({}_{2}\) retrieval, the aerosol-related components of the XCO\({}_{2}\) retrieval error were given focus. If all 16 aerosol parameters are retrieved synchronously with CO\({}_{2}\) information, two size distribution parameters for fine and coarse particles (r\({}_{\text{eff}}\), v\({}_{\text{eff}}\)), real refractive index coefficient of fine mode (a\({}_{\text{r}}\)and fmf cause the largest interference errors in the XCO\({}_{2}\), reaching 0.2-0.8 ppm. The total interference errors of all aerosol parameters range from 0.2 to 1.0 ppm and increase with smaller SZAs due to the shorter light path. MA parameters cause the fewest interference errors with no more than 0.3 ppm. The lower surface reflectance for vegetation indicates the larger impact of aerosols on XCO\({}_{2}\) retrieval. However, not all aerosol parameters could be retrieved from the TanSat hyperspectral observations, as there were only 4-7 DFSs serving as aerosol parameters over both surface types. When more aerosol parameters in the algorithm were simultaneously retrieved, the CO\({}_{2}\) information decreased with the lower DFS. The principle of optimization is to minimize the aerosol-induced XCO\({}_{2}\) error components while retaining a large amount of CO\({}_{2}\) information. Combined with the estimated aerosol information, retrieval of four to seven aerosol parameters is more reasonable. Of the four XCO\({}_{2}\) retrieval error components, the forward model parameter and interference errors are associated with uncertain aerosol parameters. Overall, aerosol-induced XCO\({}_{2}\) errors are dominated by the forward model parameter error rather than the interference error, due to the larger values of the former. When the number of retrieved aerosol parameters increases from four to seven, more aerosol parameter combination groups have fewer forward model parameter errors, despite hte CO\({}_{2}\) DFS decreasing slightly. Considering a greater reduction in the aerosol-induced XCO\({}_{2}\) error, seven aerosol parameters are deemed the most appropriate for XCO\({}_{2}\) retrieval. For MA, the number of retrieved aerosol parameters should be five because of the low amounts of aerosol information. The XCO\({}_{2}\) errors of different aerosol parameter combination groups vary, even when the number of retrieved aerosol parameters is constant. To minimize aerosol impact, the total aerosol-induced XCO\({}_{2}\) retrieval errors of different groups with seven retrieved aerosol parameters (five for MA) were compared and sorted from low to high. Ultimately, the aerosol parameter combination group with the lowest aerosol-induced XCO\({}_{2}\) errors was selected.