## 4 Results
### ALH Retrieval Capability for Typical Cases  
In this section, we analyze the ability of MAPMU to detect ALH in the UV band. Four multi-angle observation geometries were used for the forward simulations, and each mean DFS of the observation geometries was calculated under the conditions of AOD = 0.6 (550 nm) and H = 2 km. Figure 5 further illustrates the DFS and posterior errors of ALH retrieval for different aerosol models in the form of histograms, and the error bars correspond to four multi-viewing observation geometries. The gray bottom column represents the prior estimation error for the aerosol layer height, and the visible part of the gray bottom column shows the reduction in the posterior error relative to the prior error in Figure 5c,d (absolute a priori error is 1.5 km). 1. The results show that the multi-angle polarization measurements of ALH retrieval performed well (DFS \(>\) 0.5) in the UV band for the main aerosol models. Previous studies have shown that the surface reflectance on the information content of ALH often has more impact than the optical aerosol properties [29]. It can be seen that the optical properties of aerosols also play crucial roles in ultraviolet ALH retrieval. 2. The determination of ALH for the coarse mode is relatively difficult compared with the fine mode, and the information content of ALH is closely related to the scattering and absorption characteristics of the aerosol model. Combined with the aerosol model SSA presented in Section 3.2.1, the fly ash pollution type (F-BNM) has the strongest scattering characteristics in the five fine modes, as a result of having the lowest DFS result, which is even lower than that found for some coarse modes. Similarly, the difference between the primary dust type (C-UNW) with the highest DFS and background dust with the lowest DFS is 0.07, and the difference grew further to above  
Figure 5: The DFS and posterior error of \(H\) for different aerosol models with AOD = 0.6 for two aerosol types over vegetation surfaces. The error bar are the mean value and standard deviation of different geometries and the aerosol profile H is defined as 2 km. (**a**,**c**) represents fine mode aerosol types and (**b**,**d**) represents coarse mode aerosol types. 0.4 after adding the polarization measurements. The result also indicates a better performance of the MAPMU observations for absorbing aerosol in ALH retrieval. 3. Comparing intensity observation and polarization observation, it can be seen that, regardless of the type of aerosol (except F-ULW), it is difficult to retrieve the scale height parameter using only the intensity observation in the UV band, and the addition of polarization observation information effectively improves ALH retrieval. We supplement and test the information related to ALH retrieval under different aerosol conditions in Section 5.1 and evaluate the improvement produced by adding polarization measurements. 4. As shown in Figure 5c,d, due to the different aerosol models, when only the intensity measurements are included, the posterior error for fine mode is in the range of 1.45 km to 0.92 km; however, once polarization measurements are included, the posterior error can drop to a range of 1.09 km to 0.51 km. For Coarse mode, the posterior error is in the range of 1.46 km to 1.43 km when just intensity measurements are used, while it is in the range of 1.43 km to 0.62 km when polarization measurements are added. In summary, the DFS of the ALH is significantly improved with the addition polarization measurements, and the posterior error is gradually reduced. In addition, we assume that if the wrong aerosol model is chosen, the theoretical error due to the intensity and polarization measurement model choice can be quantitatively assessed by calculating the relative error of the posterior error between different models. As results shown in Figure 6, in extreme cases, the aerosol model used for the actual intensity measurement is the urban pollution type (F-ULW), but we chose the background dust type (C-BHM) for ALH inversion.