# On-Orbit Calibration Method for Correction Microwave Radiometer of the HY-2 Satellite Constellation
## 4 Calibration in the HY-2 Satellite Constellation  
In the restricted spatio-temporal range, there are crossovers between the HY-2B satellite and the other two satellites in the HY-2 satellite constellation. In theory, the BT deviation is small from different satellites at the intersection of channels of the same frequency, but this is not certain from the above when cross-checking for BT (see Figure 4). On-orbit calibration aims to revise BT data in the HY-2 satellite constellation, minimizing the root mean square error (RMS) to BT data from three different CMRs. In order to obtain enough effective data for on-orbit calibration, this experiment selected the third group data (see Table 2) during 12 months in the HY-2 satellite constellation. A total of 53,664 crossovers between HY-2B and HY-2C and 51,386 crossovers between HY-2B and HY-2D were necessary to calibrate HY-2C and HY-2D to HY-2B, respectively. The distribution of crossovers is shown in Figure 5. It can be seen that, within one year, the distribution map of crossovers between the HY-2B satellite and other two satellites is very similar, with high-density points in high-latitude regions and points distributed uniformly in global mid-low-latitude regions. In terms of distribution or quantity, crossovers can guarantee accuracy for on-orbit calibration equations. In-situ observation is the most accurate method for obtaining atmospheric water vapor data at present [30]. During the on-orbit test, every satellite of the constellation cooperates with the observation ship to produce in-situ data. When the satellite flies over the ship, it releases sounding balloons to obtain the integral amount of atmospheric water vapor, measured to validate observations from the CMR. The in-situ points used to observe are shown in Figure 6. For atmospheric water vapor, the RMS is small between CMR and scene: it is 2.55 mm for HY-2C and 2.45 mm for HY-2D, and the RMS of HY-2B is 2.23 mm, which is less than those of HY-2C or HY-2D. Lower errors may occur because the CMR of HY-2B has three feed sources for three channels, and exclusive waveguides can be more beneficial for measuring radiation. The HY-2B satellite altimeter observes the sea level reasonably well and within its specifications, which shows BT from the HY-2B satellite CMR is also credible [31]. Figure 4: Comparing brightness temperature (BT) differences of three channels in crossovers for two satellites: (**a**) BT differences between HY-2B and HY-2C, concentrated from \(-\)10 K to 20 K, and BT differences between HY-2B and HY-2D, concentrated from \(-\)20 K to 20 K, as obtained from three channels. (**b**) Correlation between any two groups of BT data at crossovers between two satellites. Figure 5: The distribution of crossovers for on-orbit calibration. Comparing the position of yellow lines in (**a**) and red lines in (**b**), more uniform crossovers are distributed between HY-2B and HY-2C on mid-low-latitudes, and crossovers between HY-2B and HY-2D have larger areas than between HY-2B and HY-2C at high latitudes. Figure 6: In-situ observation at sea. The HY-2B satellite is selected as a reference satellite for on-orbit calibration in the HY-2 satellite constellation, and its BT datasets are regarded as a benchmark; on-orbit calibration equations are established by ordinary least squares and one year's worth of datasets [32]. The BT datasets of the HY-2C and HY-2D satellites are calibrated to the HY-2B satellite to minimize BT differences between the same channels of any two satellites. The on-orbit calibration equation for HY-2C and HY-2D can be obtained using the 23.8 GHz channel, as follows:  
\[T_{RC\_238}=0.967\cdot T_{C\_238}+0.7984 \tag{1}\]  
\[T_{RD\_238}=0.9236\cdot T_{D\_238}+7.3746 \tag{2}\]  
The variables are as follows: \(T_{C\_238}\) and \(T_{D\_238}\) are, respectively, the BT of HY-2C and HY-2D for the 23.8 GHz channel of the CMR; \(T_{RC\_238}\) and \(T_{RD\_238}\) are the corrected BT.