## 3 TanSat Simulations and Retrieval Assumptions
### Simulation Input
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Center Wavelength (nm)** & \(f_{iso}\)**(\(\lambda\))1  \\ \hline
768 & 0.8632/0.2525 2  & 0.1747/0.1650 & 0.2569/0.0226 \\
1610 & 0.2107/0.4197 & 0.1100/0.1670 & 0.0286/0.0550 \\
2060 & 0.1052/0.3279 & 0.0305/0.0826 & 0.0236/0.0670 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Bidirectional reflectance distribution function (BRDF) coefficients of three kernels in each ACGS band defined for both soil and vegetation. In the simulations, aerosol particles were assumed to be spherical with a bimodal lognormal particle size distribution (PSD) function, characterized by effective radius \(r_{\text{eff}}\) and effective variance \(v_{\text{eff}}\) for both fine and coarse modes [34; 48; 49]. To describe aerosol composition, the complex refractive indices for both aerosol modes are required in addition to the PSD parameters. A Gaussian shape is assumed for the aerosol extinction profile, which is described by peak height and width at the aerosol extinction half maximum [39; 50]. Because human activities near the surface are the main sources of heavy haze or air pollution and under these circumstances CO\({}_{2}\) retrieval is significantly affected, our focus in this study is on tropospheric aerosols with low peak heights. Although stratospheric aerosols could also result in CO\({}_{2}\) retrieval uncertainties, as OCO-2 studies have shown [19], most are related to less frequent volcanic eruption or smaller AODs. Considering the various emission sources and mixtures of aerosol particles that exist, several typical aerosol types with different microphysical properties were simulated and compared. Based on work by [PERSON] [51], multiyear, global data from the Aerosol Robotic Network (AERONET) of ground-based observations were used to represent distinct aerosol optical properties at key locations. Daily averaged inversion products from the last five years at similar AERONET sites used by [PERSON] [51] were included to obtain the representative properties for four main aerosol types: urban-industrial (UI), biomass burning (BB), desert dust (DD) and marine aerosols (MA). According to the accuracy of individual AERONET retrievals, a decrease in aerosol information content for low aerosol loading could result in significant uncertainties in refractive index retrievals. Therefore, only those products with AOD at 440 nm (AOD\({}_{440}\)) larger than 0.4 for UI and BB aerosols, AOD at 1,020 nm (AOD\({}_{1020}\)) larger than 0.3, and an Angstrom exponent (between 440 and 870 nm) smaller than 0.6 for DD are involved in our analysis, similar to the AERONET products quality document. The variability of the screened aerosol column volume concentration (V\({}^{\text{f}}\) and V\({}^{\text{c}}\)), \(\text{r}_{\text{eff}}\)\({}^{\text{f}}\) and \(\text{r}_{\text{eff}}\)\({}^{\text{c}}\), and \(\text{v}_{\text{eff}}\)\({}^{\text{f}}\) and \(\text{v}_{\text{eff}}\)\({}^{\text{c}}\), for fine and coarse particles at the center wavelength are presented in Figure 1. Figure 2 shows the histograms of fitted \(m_{\text{r}}\) and \(m_{\text{i}}\), assuming little variation in each band. In addition to the V\({}^{\text{f}}\) and V\({}^{\text{c}}\), and \(\text{r}_{\text{eff}}\)\({}^{\text{f}}\) and \(\text{r}_{\text{eff}}\)\({}^{\text{c}}\) of the UI and BB aerosols, other parameters exhibit little relationship with the AOD. Consequently, the statistics of the aerosol properties, expressed as means \(\pm\) standard deviation, or as a linear relationship with AOD, are presented in Table 3, which is similar to Table 1 in the study by [PERSON] [51].