# Retrieval of High Spatial Resolution Aerosol Optical Depth from HJ-1 A/B CCD Data
## 2 Data and Methods
### Retrieval of AOD with Constraints  
Based on the interband regression coefficients and the aerosol lookup table, AOD can be retrieved from the apparent reflectance of the HJ-1 A/B CCD. For a specific pixel, the atmospheric parameters \(\rho_{a}\), \(T\), and \(S\) at a prescribed solar/view geometry and different AOD conditions can be obtained from the aerosol lookup table. Thus, atmospheric correction procedures were performed assuming the AOD level. The optimal AOD estimation can be obtained by searching the minimum value of the following object function:  
\[\delta=\left|\widehat{\rho}_{green}(\tau)-(a\widehat{\rho}_{blue}(\tau)+b) \right|, \tag{12}\]  
where \(\delta\) stands for the object function, and \(\hat{\rho}_{green}(\tau)\) and \(\hat{\rho}_{blue}(\tau)\) are the atmospheric-corrected reflectance of green and blue bands for an assumed AOD level \(\tau\), respectively. The interband regression coefficients (\(a\) and \(b\)) can be obtained by the lookup table of regression coefficients. However, we found it difficult to get the optimal AOD estimation due to the systematic errors of the imageries, such as calibration issues with the HJ-1 A/B CCD data. Since the regression intercept \(b\) was not robust due to the systematic error, a correction for the intercept \(b\) was requested by this study. The results of the sensitivity analysis showed that a change of 0.05 in the regression intercept (\(b\)) could lead to a change of about 0.2-0.3 in the retrieved AOD (Figure 3). Therefore, an offset step \(i\) for an entire image was added to each regression intercept \(b\) (with 0.005 as the interval, \(bi=b+(i\times 0.005-0.10)\), mboxemphi = 0-41) (Figure 4). The above-mentioned object function can be adopted as follows:  
\[\delta=\left|\widehat{\rho}_{green}(\tau)-(a\widehat{\rho}_{blue}(\tau)+b+i \times 0.005-0.10)\right|. \tag{13}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Variables** & **Input Parameters** \\ \hline Solar zenith angle & \(0^{\circ}\), \(6^{\circ}\), \(12^{\circ}\), \(18^{\circ}\), \(24^{\circ}\), \(30^{\circ}\), \(36^{\circ}\), \(42^{\circ}\), \(48^{\circ}\), \(54^{\circ}\), \(60^{\circ}\), \(66^{\circ}\) \\ View zenith angle & \(0^{\circ}\), \(3^{\circ}\), \(6^{\circ}\), \(9^{\circ}\), \(12^{\circ}\), \(15^{\circ}\), \(18^{\circ}\), \(21^{\circ}\), \(24^{\circ}\), \(27^{\circ}\), \(30^{\circ}\), \(33^{\circ}\), \(36^{\circ}\), \(39^{\circ}\) \\ Relative azimuth angle & \(0^{\circ}\), \(12^{\circ}\), \(24^{\circ}\), \(36^{\circ}\), \(48^{\circ}\), \(60^{\circ}\), \(72^{\circ}\), \(84^{\circ}\), \(96^{\circ}\), \(108^{\circ}\), \(120^{\circ}\), \(132^{\circ}\), \(144^{\circ}\), \(156^{\circ}\), \(168^{\circ}\), \(180^{\circ}\) \\ Atmospheric model & Mid-latitude summer \\ Aerosol Type & Continental \\  & 0.0001, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.55, 0.6, 0.65, 0.7, 0.75, \\ AOD & 0.8, 0.85, 0.9, 0.95, 1.0, 1.05, 1.1, 1.15, 1.2, 1.25, 1.3, 1.35, 1.4, 1.45, 1.5, 1.55, 1.6, \\  & 1.65, 1.7, 1.75, 1.8, 1.85, 1.9, 1.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Input parameters of 6S model. There are two approaches for determining the offset step \(i\): (1) If the AOD measurements can be used as prior knowledge, the offset step \(i\) for an entire image can be determined directly by Equation (13); (2) if there are no available AOD measurements, optimal estimations of AOD and offset step (\(i\)) can be retrieved with the constraints of the ACI and seasonal variations of the NDVI. With this approach, the ACI was first used for narrowing the searching range of \(i\), and then the seasonal variations of the NDVI were used as references for getting the optimal AOD estimations.