# Radiometric Cross-Calibration of GF-1 PMS Sensor with a New BRDF Model
## 2 Satellites, Test Sites, and Datasets  
### Satellites  
GF-1 satellite carries six sensors, including four WFV sensors (WFV1, WFV2, WFV3, and WFV4) and two PMS sensors (PMS1 and PMS2). The WFV sensor is a multispectral sensor with four channels, which are blue, green, red, and near infrared (NIR) [25]. The spatial resolution of WFV is 16 m and the swath of each WFV sensor is about 200 km, covering 800 km with four WFV sensors. The PMS sensor has four multi-spectral bands with 7.79 m spatial resolution and a panchromatic band with 1.95 m spatial resolution. The swath of each PMS sensor is about 35 km. Both WFV and PMS sensors are linear CCD detectors. The pixel number of multi-spectral and panchromatic band of PMS sensor are 4548 and 18192, respectively. In this paper, just the PMS1 sensor was cross-calibrated using MODIS and OLI. The MODIS sensor was launched on 18 December 1999 aboard the Terra satellite and has been in operation more than 18 years, providing the global data that are used to monitor long-term changes in the Earth system. The Band 1-4 of MODIS were used to cross-calibrate the PMS1 sensor. The spatial resolutions of MODIS at nadir are 250 m for bands 1 and 2 and 500 m for bands 3 and 4. The reflective solar band (RSB) calibration of MODIS is based on the regular measurements from the solar diffuser (SD) and solar diffuser stability monitor (SDSM), in addition to the monthly scheduled lunar observations. The measurements from SD and SDSM are used for absolute calibration, whereas the lunar measurements along with the SD measurements are used to track the change in on-orbit response vs. scan angle [26; 27]. In addition to its onboard calibration and characterization activities, MODIS has been calibrated vicariously using Earth targets such as Railroad Valley [28]. A 2% uncertainty requirement is specified for the MODIS top-of-atmosphere (TOA) reflectance products, and 5% uncertainty is specified for the MODIS at-sensor spectral radiance products for observations made within \(\pm 45^{\circ}\) viewing angles. Landsat-8, the latest in the Landsat series of satellites, which was launched on 11 February 2013, carries the Operational Land Imager (OLI) as one of its payloads. The OLI is a push broom instrument,whereas all previous recent Landsat instruments are electromechanical (whiskbroom) instruments. The swath of OLI is 185 km and spatial resolution is 30 m for multispectral bands and 15 m for panchromatic band. Two additional multispectral channels were added at 0.445 \(\upmu\)m and 1.372 \(\upmu\)m for coastal aerosol studies and cirrus cloud detection, respectively. The relative spectral response (RSR) of OLI's NIR band is greatly changed compared with ETM+ to avoid the effect of water absorption in 0.825 \(\upmu\)m. MODIS has similar spectral response function compared with OLI. The relative spectral response (RSR) of OLI's panchromatic band is narrower than ETM+ for better distinguishing the vegetation and non-vegetation. The calibration of Landsat 8 OLI is based on inner lamps, solar diffusers, and lunar calibration. The calibration uncertainties of OLI's RSB are about 3% for at-sensor radiance and 2% for at-sensor reflectance [29]. In this paper, the PMS1 sensor is cross-calibrated using both MODIS and OLI. The RSR of these sensors are plotted in Figure 1. The thick black curve is the RSR of PMS, and the red and green thin curves are RSRs of OLI and MODIS, respectively. The RSR of PMS is wider than OLI and MODIS, especially for NIR band. For blue and green bands, the RSR of PMS is more similar with OLI than with MODIS. The RSR of OLI and MODIS in red bands is much closer with each other and narrower than PMS. The center wavelength and solar irradiance of PMS, OLI, and MODIS are summarized in Table 1. The center wavelength is computed by Equation (1). \[\lambda_{\text{sensor,i}}=\frac{\int\lambda*\tau_{sensor,i}(\lambda)\text{d} \lambda}{\int\tau_{sensor,i}(\lambda)\text{d}\lambda} \tag{1}\]  
where \(\tau_{\text{sensor,i}}\) is the RSR of sensor in \(i\)-th band (unit: 1).