## 4 Simulated CAPI Measurements and Aerosol Sensitivity  
CAPI measurements (radiances at the TOA) are simulated at multiple viewing angles by our forward model, and Jacobians with respect to the state vector are obtained. We select four viewing angles including the nadir (0\({}^{\circ}\)), the largest angle in the FOV (16\({}^{\circ}\)) and two larger angles (30\({}^{\circ}\), 60\({}^{\circ}\) \begin{table}
\begin{tabular}{c c c c} \hline \hline
**State Vector Element** & **Aerosol Types** & **A Priori** & **A Priori Error (1\(\sigma\))** \\ \hline AOD 1  & - 2 & 0.3 & 0.3 \\ \hline \multirow{4}{*}{Real refractive index 1  \\  & Dust & 1.53 & \\  & Soot & 1.75 & \\  & Sea salt & 1.381 & \\  & Sulfate & 1.43 & \\ \hline \multirow{4}{*}{Imaginary refractive index 1  \\  & Dust & 0.008 & 0.02 \\  & Soot & 0.44 & 1.0 \\  & Sea salt & 4.26 \(\times\) 10\({}^{-9}\) & 1.0 \(\times\) 10\({}^{-8}\) \\  & Sulfate & 1.0 \(\times\) 10\({}^{-8}\) & 3.0 \(\times\) 10\({}^{-8}\) \\ \hline \multirow{4}{*}{PSD mode radius} & Dust & 0.39 & 0.4 \\  & Soot & 0.0118 & 0.01 \\  & Sea salt & 0.209 & 0.2 \\  & Sulfate & 0.695 & 0.07 \\ \hline \multirow{4}{*}{PSD variance} & Dust & 2.0 & \\  & Soot & 2.0 & \\ \cline{1-1}  & Sea salt & 2.03 & 2.0 2 \\ \cline{1-1}  & Sulfate & 2.03 & \\ \hline \multicolumn{1}{c}{Vegetation fraction} & - 2 & 0.5 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: State vector elements used in the simulation for each aerosol type. in the target mode. To compare the influence of surface albedo for the different bands and aerosols, the simulation is repeated over two different surfaces (large albedo of \(\alpha(\lambda)\), called the bright surface, and small surface albedo of 0.5 \(\times\)\(\alpha(\lambda)\), called the dark surface). We also simulate observations in both winter and summer to investigate the impact of SZA on retrieval. Table 3 summarizes the simulation scenarios, with the corresponding observation geometries. The Jacobians of radiance and polarization, with respect to various aerosol properties, are calculated by linearization capabilities of the forward model. Figure 1 illustrates the Jacobians of radiance and polarization with respect to AOD. These Jacobians of radiance depend on the wavelengths and aerosol types and show little sensitivity to the surface albedo. Polarization at 670 nm is largely sensitive to the viewing angles and aerosol types. The Jacobian of radiance for soot is always negative due to its absorption of radiation, while the main scattering property of sea salt and sulfate causes their Jacobians to be positive regardless of the surface albedo. Moreover, the effect of surface albedo on the Jacobian of radiance is not consistent for each band. For example, the Jacobians for dust increase at 1640 nm, but decrease at 380 nm when the surface albedo is higher (Figure 1). This is the result of the balance of aerosol scattering and surface reflection in different bands. Figure 1: Jacobians of AOD in all channels of CAPI at four viewing angles (0\({}^{\circ}\), 16\({}^{\circ}\), 30\({}^{\circ}\), 60\({}^{\circ}\)) and 20\({}^{\circ}\) solar zenith angle (SZA) with a bright and a dark surface for four types of aerosols. (**a**–**c**) represent Jacobians at 380 nm, 870 nm and 1375 nm, respectively. (**d**–**f**) and (**g**–**i**) are polarized Jacobians of Stokes vector I, Q and U at 670 nm and 1640 nm, respectively. The black, red, green and blue markers mean radiance or polarization for dust, soot, sea salt and sulfate, respectively. The asterisks represent the bright surface with albedo \(\alpha(\lambda)\), and squares mean the dark surface with 0.5 \(\times\)\(\alpha(\lambda)\) as albedo. The thin blue dashed line represents zero Jacobian.