## 5 Discussion on Potential Applications of the Data Products
### Demonstration of GNSS-R Altimetry
* The second step is to compute the modeled bistatic delay by considering the different propagation delay corrections by \[\rho^{\rm dr}_{\rm model,*}=\rho^{\rm dr}_{\rm geo}+\Delta\rho^{\rm dr}_{ \rm tropo}+\Delta\rho^{\rm dr}_{\rm iono,*}+\Delta\rho^{\rm dr}_{\rm ots}\] (13) in which \(\rho^{\rm dr}_{\rm model,*}\) is the modeled bistatic delay, the subscript (\(*\)) indicates the dependence of the delay on different types of measurements (i.e., group delay or phase delay) and carrier frequency (e.g., GPS L1, L2, L5 or their combinations), \(\rho^{\rm dr}_{\rm geo}\) is the geometric delay between the direct and reflected signal, \(\Delta\rho^{\rm dr}_{\rm tropo}\) is the troposphere delay, \(\Delta\rho^{\rm dr}_{\rm iono,*}\) is the ionosphere delay, and \(\Delta\rho^{\rm dr}_{\rm ots}\) includes the other delay correction terms, e.g., the antenna baseline correction. The last step is to retrieve the surface height using the measured and modeled bistatic delay by \[H_{\text{obs},*}=-\frac{\rho_{\text{obs},*}^{\text{dr}}-\rho_{\text{model},*}^{ \text{dr}}}{2\cdot\cos i}\] (14) in which \(i\) is the incidence angle, and \(H_{\text{obs},*}\) is the relative surface height above the reference surface. Note that the reference surface is the one used in the computation of the modeled bistatic delay. An example of GNSS-R altimetry results using the complex waveform product is shown in Figure 8. The complex waveform is generated from the raw IF data collected by TDS-1 on 27 February 2016, when the sea surface is still frozen along the specular point track of GPS PRN 24. Strong coherent reflection has been detected along the first half of the track (red segment in Figure 8 Left). The delay of the reflected signal can be derived from both the group delay and the carrier phase observations, from which the corresponding surface height measurements can be obtained. As shown in Figure 8 (Right), the sea surface height measurements from both group delay and carrier phase follow the evolution of the DTU18 mean sea surface (MSS) model. In addition, the group delay altimetry results show much larger error comparing to the carrier phase ones (0.88 m vs. 0.04 m), which is mainly due to the longer wavelength of the GPS L1 C/A ranging code (\(\sim\)300 m). It is important to note that due to the receiver orbit error, the carrier phase integer ambiguity in (14) and the residuals of the ionosphere and troposphere corrections, a linear trend has to been removed from the bistatic delay measurements, so that the retrieved sea surface height can better fit the MSS model. In fact, such correction is required for the most of the tracks in the complex waveform products, which should be considered by the users in altimetry exercises. In addition, to demonstrate the surface altimetry application using both the group delay and carrier phase measurements, it is suggested to use the complex waveform tracks over the polar regions from the TDS-1 mission or these over the high altitude lakes, e.g., Lake Qinghai, from the CYGNSS mission. Figure 8: An example of GNSS-R altimetry results over sea ice. The complex waveform is generated from the raw IF data collected by the TDS-1 satellite on 27 February 2016. The GNSS transmitter is GPS PRN 24. **Left**: Sea ice thickness and specular point track. The black line is the ground track of the speuclar point, with the red segment indicating the region with coherent reflections. **Right**: Comparison between the altimetry results and the DTU18 mean sea surface model.