# Radiometric Calibration of the Near-Infrared Bands of GF-5-02/DPC for Water Vapor Retrieval
## 3 Methods
### Radiometric Calibration of the DPC at the NIR08 Band  
The data of the 865 nm band of the POSP is used for radiometric calibration of the 865 nm band of the DPC. Due to the fact that the SRFs of the bands at 865 nm for the DPC and POSP are not completely consistent, it is necessary to determine the conversion relationship between the observation data of these two bands before radiometric calibration. In this study, we first use spectral data from typical ground objects (such as rocks, vegetation, and bare soil) and the SRFs of POSP and DPC to determine the surface reflectance of these two bands under different conditions. For any spectral curve (referred to as curve X), the surface reflectance of any band of either the DPC or POSP (referred to as band X) can be calculated using Equation (1) [17]. The spectral reflectance data used are illustrated in Figure 3[18].  
\[\rho=\frac{\int_{\lambda_{1}}^{\lambda_{2}}\left(S_{\lambda}\times\rho_{ \lambda}^{\prime}\right)d\lambda}{\int_{\lambda_{1}}^{\lambda_{2}}S_{\lambda}d \lambda}, \tag{1}\]  
where \(\rho\) is the surface reflectance of band X; \(\lambda_{1}\) and \(\lambda_{2}\) represent the starting and ending wavelengths corresponding to the spectral response function of band X; \(S_{\lambda}\) represents the response of band X at the wavelength equal to \(\lambda\); \(\rho_{\lambda}^{\prime}\) denotes the reflectance of curve X at the wavelength equal to \(\lambda\).  
Figure 3: _Cont._Then, we would use RTM to simulate the observations of these two bands under different aerosol contents (range of AOD at 550 nm: 0-1.5, interval: 0.3), relative azimuth angle (range: 0-360\({}^{\circ}\), interval: 20\({}^{\circ}\)), satellite zenith angle (range: 0-70\({}^{\circ}\), interval: 10\({}^{\circ}\)) and solar zenith angle (range: 0-70\({}^{\circ}\), interval: 10\({}^{\circ}\)). After that, a linear transformation relationship between the observations of the 865 nm band of the DPC after radiometric calibration and the observations of the 865 nm band of the POSP can be determined. Subsequently, we can use the actual observations of the 865 nm band of the POSP to simulate the observations without systematic radiometric calibration error of the 865 nm band of the DPC, and finally calculate the radiometric calibration coefficient of the 865 nm band of the DPC (referred to as \(k1\)), according to Equation (2).  
\[k1=\frac{\sum_{i=1}^{N}\left(R_{865\ nm,\ i}^{\prime}/R_{865\ nm,\ i}^{\prime} \right)}{N}, \tag{2}\]  
where \(N\) denotes the count of valid matching results between the observations of DPC and POSP, \(R_{865 nm,i}\) is the i-th observation of the 865 nm band of the DPC simulated using the observation data of POSP, and \(R_{865 nm,i}^{\prime}\) is the actual observation of the 865 nm band of the DPC with systematic calibration error corresponding to \(R_{865 nm,i}\).  
Since the observation times of the DPC and POSP are not equal at all pixels, it is necessary to match DPC and POSP data before calibrating the 865 nm band of the DPC using the observations of the 865 nm band of the POSP. The valid matching results between POSP and DPC data at any given location requires that the following requirements are met: (1) the differences in satellite zenith angle and solar zenith angle between DPC and POSP data are less than 0.005 degrees; (2) the time difference in the observations between DPC and POSP should be less than 5 min. To mitigate the potential negative impact of outliers on the calibration results, we would sort the ratio of \(R_{865\ nm}^{\prime}\) to \(R_{865\ nm}\), and the matching results of \(R_{865\ nm}^{\prime}\) and \(R_{865\ nm}\) corresponding to the top 2% and bottom 2% of the data are not utilized in Equation (2).