# FY3E GNOS II GNSS Reflectometry: Mission Review and First Results
## 3 L1 Calibration and Level 2 Wind Speed Retrieval  
The main Level 1 products are the 122 \(\times\) 20 DDM as a bistatic radar cross-section (BRCS) and observables for the wind speed retrieval. The main Level 2 products are the retrieved wind speeds and mean square slope (MSS). In the Level 1 calibration, the DDM in raw counts are first converted to DDM power using the total receiver instrument gain \(G\):  
\[Y(\tau,f)=G(T)C(\tau,f) \tag{1}\]  
where \(C(\tau,f)\) is the observed 1 s DDM in raw counts after the incoherent average, \(Y(\tau,f)\) is the converted DDM power, \(\tau\) is the time delay and \(f\) is the Doppler frequency. The instrument gain \(G\) is related to the temperature of the instrument, \(T\). The relationship between the instrument gain and the instrument temperature was measured by a pre-launch thermal cycling test and saved as a look-up table. The instrument gain of the in-orbit data can then be computed by the pre-launch look-up table and the instrument temperature measured by a temperature sensor in the receiver.  
The DDM BRCS is computed from the DDM power using a bistatic radar equation [20]:  
\[\sigma(\tau,f)=\sigma_{0}(\tau,f)A_{eff}(\tau,f)=Y(\tau,f)\bigg{(}\frac{ \lambda^{2}P_{t}G_{t}G_{r}}{(4\pi)^{3}R_{t}^{2}R_{r}^{2}}\bigg{)}^{-1} \tag{2}\]  
where \(Y(\tau,f)\) is the observed DDM power, \(\sigma(\tau,f)\) is the DDM BRCS, \(A_{eff}(\tau,f)\) is the effective scattering area and \(\sigma_{0}(\tau,f)\) is the normalized BRCS (NBRCS). \(R_{t}\) and \(R_{r}\) are geometry terms that can be referenced in [20]. \(G_{r}\) is the receiver antenna gain at the specular point. \(P_{t}G_{t}\) is the GNSS EIRP. The EIRPs of GPS and BDS satellites are estimated by look-up tables built from data collected by two power monitors at Beijing using a similar method described in [17]. Figure 8 shows the calibrated DDM power and DDM BRCS converted from the DDM raw counts in Figure 4.  
The observables for the wind speed retrieval are the delay-Doppler map average (DDMA) and leading edge slope (LES). They are computed from a 5 delay \(\times\) 3 Doppler box of the DDM NBRCS near the specular point. The algorithms used are similar to the ones in [2]. The wind speed retrieval geophysical model function (GMF) v1.0 was developed by the simulated data generated by an upgraded GNSS-R simulator [21] in the wind speed range of 0-35 m/s. In the GMF, the retrieved wind speed is a function of the observable and incidence angle at the specular point. The GMFs for GPS and BDS were trained separately. The wind speeds retrieved from the two observables are then combined using the minimum variance estimator [22]. After the wind speed is retrieved by each DDM, a time average is applied to average the wind speed retrieved from a number of consecutive DDMs. The  
Figure 7: Hot points (red asterisk) for the collection of raw sampling data.  
number of DDMs for the time average is less or equal to five, limited by the 25 km spatial resolution. The MSS is computed by the NBRCS \(\sigma_{0}\) and Fresnel reflection coefficient \(\Re\) as in the equation below.  
\[mss=\frac{|\Re(\theta)|^{2}}{\sigma_{0}(\theta)}. \tag{3}\]  
The Level 2 wind speed product can cover the Earth between the latitude \(\pm 85^{\circ}\). Figures 9 and 10 show the Level 2 wind speeds in one day (21 July 2021) and 5 days (21-25 July 2021). The observations of high wind speeds from Typhoon \"IN-FA\" in the west Pacific Ocean can be observed in Figure 10. Figure 11 shows the Level 2 MSS product over 5 days.  
Figure 8: Calibrated DDM power (**a**) and DDM BRCS (**b**) converted from the DDM raw counts in Figure 4.  
Figure 9: GNOS II Level 2 wind speeds in 1 day (21 July 2021). The color grading represents the Level 2 wind speed.