# Retrieval of High Spatial Resolution Aerosol Optical Depth from HJ-1 A/B CCD Data
## 2 Data and Methods
### Interband Regression Coefficient Lookup Table  
Based on a statistical analysis of the USGS spectral library, the visible bands of the HJ-1 A/B CCD data were well correlated. A linear regression relationship between the blue and green bands was established, as shown in Equation (1):  
\[\rho_{green}=a(\theta_{s},\theta_{v},\varphi;\omega)\cdot\rho_{blue}+b(\theta_ {s},\theta_{v},\varphi;\omega) \tag{1}\]  
where \(\rho_{blue}\) and \(\rho_{green}\) are the reflectance of the blue and green bands (band 1 and 2 of HJ-1 A/B CCD data); and \(a\) and \(b\) denote the slope and intercept of the regression coefficients that vary with solar/view angle and land cover type (\(\omega\)), respectively. Figure 1: Flow chart of aerosol optical depth (AOD) retrieval algorithm. To evaluate the applicability of the regression coefficients for different solar/view angles and land cover types, we analyzed the difference between the true and predicted value by the regression model:  
\[Diff=\rho_{green}-(a(\theta_{s},\theta_{v},\varphi;\omega)\cdot p_{blue}+b( \theta_{s},\theta_{v},\varphi;\omega)) \tag{2}\]  
where \(Diff\) is the difference between the true and predicted value, which can be used for evaluating the variations in interband regression coefficients from the solar/view angle and land cover type. To determine the influence of solar/view angle and land cover type on the regression coefficient, we used the POLDER 3 BRDF dataset for analysis. The POLDER BRDF dataset is the latest multiangular satellite remote sensing data currently available. Featuring rich information in angle, spectrum, and polarization, it is one of the ideal datasets for evaluating land surface anisotropy effects. The POLDER sensor is able to collect observations from up to 16 viewing angles for each orbit, with a maximum view zenith angle of 60\({}^{\circ}\). Hence, a monthly composite dataset can contain hundreds of observations from multiple orbits and viewing angles. The surface reflectance observed during all of the orbits was obtained through processing steps such as cloud removal and atmospheric correction [20]. The POLDER BRDF data files are in ASCII format, which provides the latitude and longitude of the pixels, land cover type (the global land cover of the year 2000, coordinated by the European Commission's Joint Research Center), orbit number, effective times of observation (16 observations at most for each orbit), and the homogeneity of the pixel [21; 22]. The HJ-1A/B BRDF dataset can be obtained from the POLDER BRDF dataset by a band conversion method. The band conversions from POLDER to HJ-1 A/B CCD can be expressed as  
\[\rho_{HJ}(\lambda_{i})=\sum_{i=1}^{n}c_{i}\rho_{POLDER}(\lambda_{i})+offset, \tag{3}\]  
where \(\rho_{HJ}(\lambda_{i})\) is the reflectance of the HJ-1 A/B CCD at a wavelength of \(\lambda_{i}\), \(\rho_{POLDER}(\lambda_{i})\) is the reflectance of POLDER-3 at a wavelength of \(\lambda_{i}\), \(c_{i}\) stands for the conversion coefficients for band \(i\), and \(offset\) stands for the offset coefficient (the conversion coefficients were provided by [PERSON] et al. [23] (Table 2)). Then, the blue and green bands of the HJ-1A/B CCD sensor were linearly regressed for different solar/view angles so as to establish an interband regression coefficient lookup table. In this lookup table, the solar zenith angle of 0-70\({}^{\circ}\) was separated into different angular bins with an interval of 2\({}^{\circ}\), the view zenith angle of 0-40\({}^{\circ}\) was separated into angular bins with an interval of 2\({}^{\circ}\), and the relative azimuth angle was separated into angular bins with an interval of 5\({}^{\circ}\). The regression coefficients (\(a\) and \(b\)) for different solar/view angles were stored in a three-dimensional (solar zenith angle, view zenith angle, and relative azimuth angle) lookup table.