## 2 Data and Method
### Albedo Direct Estimation  
The basic principle of albedo direct estimation originated from [PERSON] _et al._[33] by linking surface broadband albedo (\(\alpha\)) with TOA spectral reflectance (\(\rho_{\mathrm{i}}\)):  
\[\alpha=\sum_{i=1}^{n}\rho_{i}\cdot c_{i}+c_{0}\,, \tag{1}\]  
where \(\rho_{\mathrm{i}}\) is the TOA spectral reflectance for band \(\mathrm{i}\in[1,n]\), and \(c_{\mathrm{i}}\) and \(c_{0}\,c_{0}\) are regression coefficients as a function of sun-sensor-target geometries. To establish such statistical relationship, the 6S radiative transfer codes [34] were employed to simulate TOA reflectance under various atmosphere and surface conditions. Configurations of atmospheric conditions and geometries are listed in Table 2.  
To account for the effects of surface BRDF on TOA observations, prior knowledge of the surface BRDF is needed as the input to train the statistical relationship, which however is not yet available for the manner of HJ spectral bands. Employing the legacy from the MODIS surface BRDF product [25] can help solve this problem. However, due to the difference in the band design of HJ CCD and MODIS sensors, directly applying MODIS data to HJ bands may lead to errors. A total of 245 surface albedo spectrum samples collected from the US Geological Survey (USGS) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) spectral libraries, including samples of vegetation, soil, rock, water, snow, and ice, were used to evaluate the impacts band differences of the two types of sensors on spectral albedo [31]. The surface albedo spectrum data and the sensors' spectral response functions were used to calculate the albedo of the spectral bands through convolution integration. Figure 2 shows the difference of surface spectral albedos estimated for the two types of sensors. The results demonstrate that errors originated from the band differences are not negligible with RMSEs ranging from 0.007 to 0.021. The errors will propagate into the broadband albedo estimation. Thus, it is necessary to convert the MODIS data to HJ bands considering the band differences. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Solar zenith angle & 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, and 70 \\ View zenith angle & 0, 5, 10, 15, 20, 25, 30, and 35 \\ Relative azimuth angle & 0, 30, 60, 90, 120, 150, and 180 \\ Aerosol optical depth & 0.05, 0.10, 0.15, 0.20, 0.30, 0.40, and 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Configurations for simulating surface albedo and TOA reflectance data. In order to further mitigate the uncertainty in the band conversion process, the other three MODIS land bands were included, namely Band 5 (1.23-1.25 \(\upmu\)m), Band 6 (1.63-1.65 \(\upmu\)m), and Band 7 (2.11-2.16 \(\upmu\)m). The convoluted integrals of HJ spectral albedos were regressed against those of MODIS spectral albedos. Stepwise regression was used for each of the HJ bands to remove unnecessary MODIS bands in the conversion. Linear regression equations are as follows:  
\[f_{1}^{H}=-0.0087f_{2}^{M}+0.8764f_{3}^{M}+0.1313f_{4}^{M}+0.0050f_{6}^{M} \tag{2}\]  
\[f_{2}^{H}=0.2457f_{1}^{M}-0.0090f_{2}^{M}+0.0555f_{3}^{M}+0.7089f_{4}^{M}-0.002 6f_{6}^{M} \tag{3}\]  
\[f_{3}^{H}=1.0883f_{1}^{M}-0.0930f_{4}^{M}+0.0246f_{6}^{M}-0.0149f_{7}^{M} \tag{4}\]  
\[f_{4}^{H}=-0.0386f_{1}^{M}+1.0190f_{2}^{M}-0.0339f_{3}^{M}+0.0861f_{4}^{M}-0. 0564f_{5}^{M}+0.0225f_{6}^{M} \tag{5}\]  
With the help of linear regression, the uncertainties due to band differences (Figure 2) have been significantly reduced with RMSEs ranging from 0.003 to 0.007 (Figure 3). The reason why the linear  
Figure 2: Comparison of spectral albedo integrated using surface albedo spectrum data and sensors’ spectral response functions: (**a**) HJ band 1 _vs._ MODIS band 3; (**b**) HJ band 2 _vs._ MODIS band 4; (**c**) HJ band 3 _vs._ MODIS band 1; and (**d**) HJ band 4 _vs._ MODIS band 2. All 245 spectrum samples are included in the scatter plots.