## 3 Instrument and Simulation Assumptions
### Simulation Assumptions
#### 3.2.1 Aerosol Model
 \tag{9}\]  
where \(\text{P}_{12}=\text{P}_{2}\) and \(\text{P}_{34}=\text{P}_{43}\). \(\text{P}_{11}\) is the normalized phase function that describes the scalar component of particle scattering, whereas \(-\text{P}_{12}/\text{P}_{11}\) is the polarized scattering that corresponds to DoLP. The single scattering albedo (SSA) in the UV and VIS bands for ten typical aerosol models is also shown in Table 5. SSA represents the ratio of the scattering efficiency to the total extinction efficiency. Compared with the VIS band (443 nm), the SSA in the UV band is higher for the fine mode, while the SSA of the coarse mode is lower. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & & & & \\ \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{\(r_{eff}\)} & \multirow{2}{*}{\(r_{eff}^{sm}\)} & \multirow{2}{*}{\(v_{eff}\)} & \multirow{2}{*}{\(v_{eff}^{sm}\)} & \multicolumn{2}{c}{**Refractive**} & \multirow{2}{*}{\(V_{0}\)} & \multirow{2}{*}{\(V_{0}^{sm}\)} & \multirow{2}{*}{**Refractivity**} & \multirow{2}{*}{**Absorptivity**} \\  & & & & & & & & & \\ \hline F-ULW & 0.175 & \(\backslash\) & 0.300 & \(\backslash\) & 1.414-0.007i & 0.136 & \(\backslash\) & Low & Weak \\ F-UHS & 0.126 & \(\backslash\) & 0.334 & \(\backslash\) & 1.515-0.014i & 0.063 & \(\backslash\) & High & Strong \\ F-BLW & 0.132 & 0.283 & 0.152 & 0.257 & 1.392-0.007i & 0.087 & 0.069 & Low & Weak \\ F-BNS & 0.103 & 0.204 & 0.089 & 0.334 & 1.459-0.016i & 0.046 & 0.089 & Normal & Strong \\ F-BNM & 0.124 & 0.387 & 0.189 & 1.766 & 1.477-0.011i & 0.073 & 0.058 & Normal & Moderate \\ \hline \multicolumn{8}{c}{**Coarse Modes**} & & & & & \\ \hline C-ULW & 2.208 & \(\backslash\) & 0.522 & \(\backslash\) & 1.437-0.006i & 0.089 & \(\backslash\) & Low & Weak \\ C-UHS & 2.558 & \(\backslash\) & 0.500 & \(\backslash\) & 1.522-0.015i & 0.090 & \(\backslash\) & High & Strong \\ C-UNW & 1.970 & \(\backslash\) & 0.305 & \(\backslash\) & 1.495-0.003i & 0.482 & \(\backslash\) & Normal & Weak \\ C-BNM & 1.211 & 2.973 & 0.345 & 0.552 & 1.492-0.009i & 0.059 & 0.105 & Normal & Moderate \\ C-BHM & 1.626 & 4.481 & 0.552 & 0.142 & 1.518-0.008i & 0.121 & 0.076 & High & Moderate \\ \hline \multicolumn{8}{c}{**Particle size distrubution**} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Microphysical parameters of ten typical aerosol models in China. Figure 2: The aerosol volume size distributions for the ten aerosol types defined in Table 4.  
Table 5 indicates stronger absorption for F-ULW, F-BNS, and F-BNS compared to F-BLW and F-BNM. Similarly, weaker absorption is shown for C-BNM and C-BHM compared to C-ULW, C-UHS, and C-UNW for the wavelength at 388 nm. The wavelength-dependent P\({}_{11}\) and \(-\)P\({}_{12}\)/P\({}_{11}\) of various aerosol types vary with different scattering angles, as shown in Figure 3a-d resulting in diverse scattering properties that impact TOA measurements. Figure 3c,d additionally show four multi-viewing observation geometries with varying sensitivities to TOA radiance and DoLP with respect to ALH. As an example, when the scattering angle gradually moves closer to 180\({}^{\circ}\), the aerosol DoLP (\(-\)P\({}_{12}\)/P\({}_{11}\)) with scattering angles for C-BHM and C-BNM is obviously different from the other three coarse aerosol models, and the overall value is negative. This bimodal aerosol model has the characteristics of Asia dust and transport dust. Due to the high aerosol layer and special optical characteristics of the UV band, the absorption is weak. From the perspective of passive remote sensing, we assume that only one aerosol layer is present in the atmosphere, and the definition of the aerosol height depends on how the profile is represented. Meanwhile, the suitable choice of representation often depends on the actual applications. It also depends on whether the measurement can meet the profile model parameters which are in the state vectors to solve at the same time.