Aerosols are an important component of the earth's atmospheric system and exert significant effects on radiation forcing, meteorology, environment, quantitative remote sensing, and human health. The demand for high-precision aerosol products in scientific research and social production continues to grow. Multi-spectral, multi-angular, and polarization observations can better achieve global aerosol detection. The directional polarimetric camera (DPC) sensor is currently carried on satellites Gaofen-5A, Gaofen-5B, and the atmospheric environment monitoring satellite to conduct global atmospheric environment monitoring. DPC can obtain observation data from three polarization bands and five non-polarization bands, with a minimum of nine and a maximum of seventeen angles. Currently, there is an urgent need for DPC to provide aerosol products of reliable scientific and application significance. The posterior error analysis in inversion results is an important tool in testing DPC performance.

The entire process of our research includes data matching, aerosol inversion, and analysis of error dependence on wavelength and scattering angle. At the same time, the DPC and polarization and directionality of the earth's reflectance (POLDER) results are compared in the same conditions. First, the satellite transit time over the aerosol robotic network (AERONET) site and the pixel where the AERONET site is located are determined through spatio-temporal matching, and the matching results are trimmed and stored. Second, the generalized retrieval of aerosol and surface properties (GRASP) algorithm is adopted to retrieve the matched DPC and POLDER data. To test the performance of DPC and ensure the comparison in the same conditions, we employ the common band of DPC and POLDER to retrieve both data. Third, the successful order of scattering (SOS) radiation transfer program is leveraged to conduct forward simulation with the inversion results of DPC and POLDER as inputs. Compared with the observed values, the inversion residuals for each band and angle are obtained (RI and RP representing intensity and polarization residuals, respectively), and the distribution of RI and RP in each band is analyzed. Then, the multi-band aerosol optical depth (AOD) observed by AERONET is employed as the real value, and the error distribution differences between DPC and POLDER retrieved AOD relative to AERONET products are compared in the same conditions. Finally, the influence of scattering angles is analyzed. Satellite observation scattering angles are mostly distributed between 100° and 175°. The distribution of RI and RP at 5° intervals is studied, and a comparative analysis of the scattering angle dependence of RI and RP is conducted.

First, the variation of the inversion residual with the wavelength is analyzed. The results show that RI and RP of DPC and POLDER are both at lower levels, which are about 10×10^-3 and 10×10^-4, respectively. The overall distribution of RI and RP from DPC and POLDER is relatively centralized. But for RI@565, RI@865, and RP@865 of DPC, the error bar of them is relatively large (Fig. 1). The inversion results of DPC are generally in good agreement with AERONET, reflecting the DPC ability in aerosol observation. However, AOD@865 is seriously overvalued (Table 2). Second, the variation of inversion residual with scattering angle is also analyzed. We find that the mean values of RI and RP in mountain areas are higher than those in non-mountain areas, with relatively discrete RI and RP. In non-mountain areas, RI and RP are relatively concentrated, but the standard deviation is large when the scattering angle is greater than 160°. The angular characteristics of the DPC and POLDER residuals are relatively consistent, without significant differences (Figs. 2 and 3). Third, after discussing the inversion results of the mountain and non-mountain areas, the inversion ability of DPC in non-mountain areas is proven to be close to POLDER, while in mountain areas it lags behind POLDER (Fig. 4). Fourth, the influence of polarization on AOD inversion is discussed. It is found that polarization information can significantly improve the AOD inversion effect, with correlation increasing from 0.763 to 0.808, RMSE decreasing from 0.373 to 0.213, mean bias decreasing from 0.117 to 0.012, and the proportion of falling into the expected error section R_EE increasing from 44.4% to 55.7% (Fig. 5). Cross comparison between Figs. 4 and 5 shows that deducting large scattering angles in the inversion process can improve the inversion effect, but the effect is not obvious.

First, although the error of AOD@865 from DPC is large, it is excellent at 670 nm band. Due to the common participation of all wavelengths in retrieval, there will be certain constraints between them. AOD@670 still exhibits good results even when there is a large error in the 865 nm band, which indicates that DPC has great potential in aerosol remote sensing. Second, in the case of large scattering angles, the simulation accuracy of the radiation transfer model will decrease, thereby affecting the inversion accuracy. However, due to the small number of large scattering angles and multi-angular constraints, the effect of large scattering angles is reduced. Therefore, in practical multi-angle inversion, large scattering angles do not significantly improve the inversion accuracy. Third, polarization information exerts a significant influence on improving aerosol retrieval accuracy. In multi-angular remote sensing, polarization information can supplement intensity information in estimating surface and aerosol models, thereby improving the retrieval accuracy. Fourth, the DPC inversion in non-mountain areas is similar to that of POLDER, but there is a significant difference in mountain areas. Since the spatial resolution of DPC is higher than that of POLDER, many factors including pixel aggregation, geometric reconstruction, and land surface-atmosphere coupling can affect aerosol retrieval results. This will also be a problem to be addressed in aerosol remote sensing of mountainous areas.