# Radiometric Cross-Calibration of GF-1 PMS Sensor with a New BRDF Model
## 1 Introduction
The sensors with similar spatial resolution are reasonably selected as reference for the radiometric cross-calibration of high-resolution, narrow-width satellites, such as GF-1 PMS and Landsat 8 OLI However, due to the long revisit period and low frequency of satellites passing through the calibration site, it is difficult to obtain reference images with the same imaging time and nadir observation as the satellites to be cross-calibrated. Under these circumstances, there are two ways to accomplish on-orbit cross-calibration for high-resolution and narrow-swath sensors. The first one is to use satellite images with the same imaging date but large view-angle and low spatial resolution as reference. The other is to select the satellite images with different imaging dates but nadir observation as reference sensor, such as Landsat 8 OLI. [PERSON] et al. carried out the research on this issue. Landsat 8 and MODIS were both selected as reference sensors to cross-calibrate the GF-1 PMS sensor at Dunhuang and Golmud test sites, respectively [20]. The results show that the calibration accuracy based on Landsat 8 is better than that based on MODIS calibration, which indicates that, at large observation angles, the error caused by the difference of observation angle is larger than that caused by the difference of imaging date. However, in this paper, both the two test sites were assumed to be Lambertian, without considering the difference caused by the change of surface directional reflection. Some researchers have developed some new cross-calibration methods by BRDF (Bidirectional Reflectance Distribution Function) correction. As to the cross-calibration of GF-1 satellite, [PERSON] et al. has taken Landsat-8 OLI as the reference sensor to cross calibrate the GF-1 satellite WFV sensor [21]. The large observation angle difference between Landsat 8 OLI image and GF-1 WFV images were corrected using TerraMODIS bi-directional reflectance distribution function (BRDF) products. [PERSON] et al. developed a new cross-calibration technique for HJ-1 satellite CCD (Charge-coupled Device) sensor [22]. In this method, the Landsat ETM+ and Advanced Space-borne Thermal Emission and Reflection Radiometer global digital elevation model (ASTER GDEM) product are used to develop a BRDF model of a desert site. [PERSON] et al. updated the method proposed by [PERSON] et al. and used for the GF-1 satellite WFV sensor [23]. The Landsat 8 and the DEM extracted by the three-line camera sensor (TLC) onboard ZiYuan-3 are replaced to develop BRDF model of a desert site. [PERSON] et al. also applied this technique to calibrate the GF-4 satellite PMS sensor [24]. It can be seen that the BRDF models in prior studies are based on ground measured data or existing BRDF products. Moreover, the MODIS BRDF product and ground reflectance BRDF model are based on the given solar angle, which has some drawbacks and limitations. Therefore, as the absence of ground reflectance and without using BRDF products, how to construct a TOA BRDF model of calibration site and correct the TOA reflectance with a large observation angle (such as MODIS images) to verify the accuracy of calibration results is the main purpose of this paper. The structure of this paper is as follows: GF-1 PMS, MODIS, Landsat 8 OLI, the test sites, and datasets are described in Section 2. Section 3 introduces the methods of this paper, including BRDF model construction method and radiometric cross-calibration method. The BRDF model construction results, the radiometric cross-calibration results based on BRDF model and the verification of the accuracy of the method proposed in this paper are illustrated in Section 4. Section 5 discusses the uncertainty caused by ground measured data, BRDF model, etc., and the total uncertainty of cross-calibration using MODIS as reference sensor are given. The conclusions of our research are made in Section 6.