# Radiometric Cross-Calibration of GF-1 PMS Sensor with a New BRDF Model
## 5 Discussion
### Results and Discussion of Time Series Cross-Calibration  
For further study, the PMS1 data on the Dunhuang and Golmud test sites since the launch of GF-1 satellite were collected, and we also obtained the corresponding MODIS and Landsat 8 OLI data. However, as the PMS1 gain was adjusted by the CRESDA after September 2016, the subsequent data are not comparable. Consequently, from the launch date of GF-1 satellite to September 2016, there are another five valid PMS1 data that has been used in research. Among them, there are two scenes at Dunhuang test site and three scenes on Golmud test site. The cross-calibration of PMS1 on the two test sites (Dunhuang, Golmud) is carried out by using the method presented in this paper. The calibration results were shown in Table 10. The relative error between cross-calibration coefficients and CRESDA site calibration coefficients were shown in Table 11. The relative errors are defined as \"1-cross-calibration coefficients/site calibration coefficients\". It can be seen from Tables 10 and 11 that the calibration coefficients obtained by this method were in good agreement, whether at Dunhuang or Golmud sites. Obviously, except for individual bands (NIR band at Golmud test site using MODIS as reference sensor on 12 December 2014), all relative differences were less than 10%, and most of the relative errors were less than 5%. The relative errors of calibration coefficients between the two reference sensors (Landsat 8 OLI and MODIS) were also calculated, as shown in Table 12. The relative error is defined as \"1-cross-calibration coefficient by using Landsat 8 OLI sensor/cross-calibration coefficient by using MODIS sensor\". As can be seen from Table 12, the absolute value of relative error of Golmud calibration test site was less than that of Dunhuang calibration test site. In general, the results obtained from different reference sensors were of obvious consistence. The relative errors at the Golmud test site were less than 5%. While, at the Dunhuang test site, most relative errors were less than 9%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Symbol** & **Blue** & **Green** & **Red** & **NIR** \\ \hline SBAF & 4.85\% & 0.67\% & 1.06\% & 1.59\% \\ BRDF model & \(-0.60\%\) & \(-1.27\%\) & \(-1.16\%\) & 0.97\% \\ Radiative transfer model & 1\% & 1\% & 1\% & 1\% \\ Reference sensor & 2\% & 2\% & 2\% & 2\% \\ Image error & 0.5\% & 0.5\% & 0.5\% & 0.5\% \\ Total uncertainty & 5.40\% & 2.70\% & 2.78\% & 2.95\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Total calibration uncertainty of cross-calibration using MODSI over Golmud test site. In addition, in order to further study the variation of cross-calibration coefficients with time, the variation characteristics of calibration coefficients in the blue band (using MODIS as reference sensor) are drawn, as shown in Figure 8. As can be seen, the GF-1 PMS1 sensor has a certain attenuation, but it is not particularly obvious. The attenuation is \(-3.39\)\(\times\)\(10^{-6}\) per day. However, due to the small amount of valid data to fully explain and discuss the attenuation trend and characteristics of GF-1 PMS1, adequate data needs to be collected from more test sites to complete the issue. The average values of cross-calibration coefficients using two reference sensors were calculated. Moreover, the relative errors between the average cross-calibration coefficients and the laboratory calibration coefficients and the official site calibration coefficients were also compared.