## 5 Discussion
### The Influence of Model Errors  
We also needed to quantitatively investigate the influence of predefined model errors on the retrieval results of ALH, because the predefined aerosol model will inevitably introduce model errors into the retrieval of critical aerosol and surface parameters in our inversion framework. Using Equation (15), we used the specified constant measurement errors from the previous section to calculate the DFS results resulting from various model errors. Previous research has shown that the DFS of the aerosol layer height will be affected by the aerosol types and has shown the differences, but the impact of AOD generally appear similar in different aerosol types [7; 29]. Therefore, we concentrated on AOD = 0.6 and scale height = 2 km as a demonstration. Additionally, we have given an example of AOD = 0.2 in Figure A1 as a comparison. It was assumed that all aerosol and surface parameters change from 5% to 100%, as defined in Section 3.2.3 It was found that for both fine mode and coarse aerosol types, the DFS of ALH decreases with an increase in the parameter error, but the influence of each parameter is not the same, as shown in Figures 10 and 11. We obtained the following conclusions:  
1. For aerosol model parameters, the F-ULW and F-UHS aerosol types, the total aerosol volume, and the effective radius have the greatest influences, and decreases in DFS are all above 0.3. For the other three fine particle aerosol types, although the real part of the complex refractive index is an important factor that affects the scattering, the difference in DFS caused by the change of aerosol parameters is controlled within 0.1 (Figure 10). However, for the five coarse mode aerosol types, the influence of the total aerosol volume and the imaginary part of refractive index on the DFS occupies the main role (Figure 11).
2. Similarly, for fine-mode aerosol types, the error of \(k_{1}\) of surface parameters has the greatest influence on the DFS of ALH retrieval. In coarse mode, the DFS is much more affected by the surface BRDF \(\rho_{s}\) error than the other two parameters.
3. When combined, the aerosol model coappearance probability is greater than 5% (F-ULW, F-UHS, F-BLW, C-BHM, C-UHS and C-ULW). For the ten typical aerosol models used in China, an iteration procedure among several predefined typical aerosol models has been designed to further decrease the probability of choosing a very bad value for the actual retrieval, and priority should be given to reducing the retrieval errors of three key parameters: the aerosol volume column concentration, effective variance, and imaginary part of the refractive index in the aerosol model, as well as the surface BRDF \(\rho_{s}\) and \(k_{1}\) parameters will effectively improve the DFS of the aerosol retrieval in the UV band.  
Figure 9: The DFS of \(H\) as a function of the scattering angle with single-angle polarization observations. (**a**) represents fine aerosol model types and (**b**) represents coarse aerosol model types.  
Figure 10: DFS of \(H\) as a function of the fine aerosol model and surface model parameter errors from 5% to 100% in steps of 5% with AOD = 0.6, in which left (**a**,**c**,**c**,**e**,**g**,**i**) and right panel (**b**,**d**,**f**,**h**,**j**) corresponds to the aerosol model and surface model respectively.  
Figure 11: The same as Figure 10, but DFS of \(H\) as a function of the coarse aerosol model and surface model parameter errors from 5% to 100% in steps of 5% with AOD = 0.6, in which left (**a**,**c**,**c**,**e**,**g**,**i**) and right panel (**b**,**d**,**f**,**h**,**j**) corresponds to the aerosol model and surface model respectively.