## 5 Discussion  
### The Influence of Adding Polarization Measurements  
In Section 4.2, we analyze the ability of MAPMU to detect the aerosol layer height for typical cases and show the impact of uncertainty for aerosol models. However, previous studies have shown that the aerosol vertical distribution is also affected by the aerosol model parameters (AOD, H), while the impact of these parameters generally appears to  
Figure 6: Heat maps of the absolute error corresponding to the posterior error caused by inaccurate aerosol models. (**a**) represents intensity measurements only; (**b**) represents “intensity + polarization” multi-angle measurements. be similar in different aerosol types [7; 29]. Therefore, in this section, we test the changes in ALH information under different aerosol optical depth conditions (AOD is from 0.2 to 1.0) and scale height conditions including near-ground aerosols and transported aerosols above the boundary layer (H is from 1 km to 5 km) for the vegetation surface. At the same time, combined with the corresponding posterior error, the improvements in the information quantity and posterior error after adding polarization measurements under different aerosol conditions are analyzed. Figure 7a,b shows the variation in the DFS for the parameter H for ten typical aerosol models used in China with the aerosol condition (AOD, H) used for the intensity measurements. The figure is presented in the form of a box plot. Figure 7c,d corresponds to the DFS after adding polarization measurements, and the other parameters are the same as those used in Figure 7a,b. When the AOD varies from 0.2 to 1.0, each box in Figure 7a-f depicts the DFS and the uncertainty reduction of ALH. On each box, the median value (solid line in the box), maximum value (whisker top), and minimum value (whisker bottom) correspond to AOD values of 0.6, 1.0, and 0.2, respectively. Figure 7e,f represents to extent to which uncertainty reduction might be improved by including polarization measurements by comparing the reduction in posterior uncertainties of H for intensity measurements with the addition of polarization measurements. The uncertainty reduction is similar to the percentage of prior error assumed in the prior error covariance matrix, which is discussed in Section 3.2.3. In this way, we can evaluate the improvement achieved by adding polarization measurements. For Figure 7, we conclude the following:  
1. Comparing Figure 7a-d, it can be seen that no matter which aerosol model is used, the DFS of ALH increases at larger AOD values. For the intensity measurements, the DFS increases gradually with the increase in H. After adding the polarization measurements, the DFS gradually decreases, but the overall value is much higher than that of the intensity measurements. The polarization especially improves the ALH retrieval when the prior setting of the scale height is less than 3 km. At the same time, the difference between aerosol models has a greater impact on DFS than the changes in AOD and H, which is especially obvious for the coarse modal aerosol types. 2. As shown in Figure 7e,f, the influence of polarization measurements on ALH retrieval gradually decreases. This is because the troposphere contains more height information, and the detection accuracy of the aerosol height is relatively high in this range. As \(H\) increases, the enhancement effect of polarization gradually weakens. Similar to the study presented in [33], DoLP measurements increase the sensitivity to \(H\), and polarization multi-angle observations offer a high potential for ALH detection, but the polarization improvement shows obvious differences between aerosol models. 3. The comparison of different models shows that the difference between the fine-mode aerosol types is small, while the difference is generally higher than that for the coarse mode aerosols. The ALH retrieval uncertainty can be reduced by 10-39% at most through the addition of polarized measurements for F-ULW, but it can only be reduced by 6-24% for F-BNM.