## 3 TanSat Simulations and Retrieval Assumptions
### Simulation Input
Considering the AOD range for each aerosol type, we assumed 1.0 AOD\({}_{440}\) for UI and BB aerosols, 0.7 AOD\({}_{1020}\) for DD, and 0.15 AOD\({}_{1020}\) for MA in our simulations, and we input the corresponding microphysical parameters using the relationships presented in Table 3. Aside from the microphysical properties, an aerosol extinction profile with a 2-km peak height was assumed for all aerosol types, indicating aerosol concentrations at the top of the boundary layer. The model primarily simulates TanSat nadir viewing observations with a 0\({}^{\circ}\) relative azimuth angle. To compare the dependence on the scattering angle, cases with SZAs from 20\({}^{\circ}\) to 65\({}^{\circ}\) were simulated. The corresponding Jacobians with respect to all parameters in the bimodal aerosol model were also output and presented in Figure 3. The distinct patterns of the various aerosol parameters illustrate the sensitivities of the ACGS measurements to the aerosol properties, which indicated that some aerosol properties are independent and their information may be obtained through observations. The correlation coefficient matrix of these aerosol parameters is calculated from the posteriori error covariance matrix, as shown in Figure S5 in the Supplement. The high correlations between several parameters lead to their similar information content. The Jacobians of surface BRDF coefficients are also shown in the Supplement and not analyzed here. Figure 1: The scatter plot of aerosol column volume concentration (V\({}^{\mathrm{f}}\) and V\({}^{\mathrm{c}}\)), effective radius (r\({}_{\mathrm{eff}}\) and r\({}_{\mathrm{eff}}\)\({}^{\mathrm{c}}\)) and effective variance (v\({}_{\mathrm{eff}}\)\({}^{\mathrm{f}}\) and v\({}_{\mathrm{eff}}\)\({}^{\mathrm{c}}\)) for fine and coarse particles. The x-axis represents aerosol optical depth (AOD) at 440 nm for urban–industrial (UI) and biomass burning (BB) aerosols and AOD at 1020 nm for desert dust (DD) and marine aerosols (MA) aerosols. The red, black, light blue and blue points (lines, equations) are data for UI, BB, DD and MA, respectively. The straight lines are the results of linear fitting described by the equations in the plots. Figure 2: The histograms of \(m_{t}\) (**a**,**c**,**e**) and \(m_{t}\) (**b**,**d**,**f**) in three ACGS bands fitted by Equations (12) and (13). The \(m_{t}\) and \(m_{t}\) are assumed do not change with the wavelength in each band. Four colorful bars represent four aerosol types as in Figure 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Aerosol Type** & **Urban-Industrial** & **Biomass Burning** & **Desent Dust** & **Maine Aerosol** \\ \hline AERONET site & Beijing, RADI (China) & Alta Brosets (Brazil) & Cape Verde (Capo Verde) & Lani (Hawaii, USA) \\ Time and number of & 2012-2017 (Jun-Sep) & 2011-2016 (Aug-Oct) & 2012-2017 & 1998-2004 \\ measurements (total) & 306 (1119) 1  & 163 (Yq ) & 1012 (1012) 2  \\ Number of measurements & 168 & 156 & 401 & 1156 \\ (chosen) 3  & 0.4 \(\circ\) AOD40 \(\circ\) \(\circ\) \(\circ\) \(\circ\) \(\circ\) \(\circ\) \(\circ\) \\ AO ramp & 0.4 \(\circ\) AOD40 \(\circ\) \(\circ\Figure 3: The simulated weighting functions of each aerosol parameter at three ACGS bands. The rows from top to bottom represent different aerosol parameters: AOD, peak height of aerosol profile (H\({}_{\rm p}\)), width of aerosol profile (H\({}_{\rm w}\)), effective radius for fine particles (\(t_{\rm eff}\)), effective variance for fine particles (\(v_{\rm eff}\)), effective radius for coarse particles (\(t_{\rm eff}\)), effective variance for coarse particles (\(v_{\rm eff}\)), fine mode fraction (fmf), real part of refractive index for fine particles (m\({}_{\rm m}\)), imaginary part of refractive index for fine particles (m\({}_{\rm i}\)), real part of refractive index for coarse particles (m\({}_{\rm i}\)), and imaginary part of refractive index for coarse particles (m\({}_{\rm i}\)).