# Spaceborne GNSS-R Observation of Global Lake Level: First Results from the TechDemoSat-1 Mission
## 3 Results and Discussions
### Spatial and Temporal Analyses  
We use data from two lakes, i.e., the Caspian Sea and the Poyang Lake, to further show spatial and temporal comparisons among TDS-1, Cryostat-2, and in situ measurements. Caspian Sea (14.85\({}^{\circ}\) N, 50.36\({}^{\circ}\) E) is the largest lake of the world with an area of 386,400 km\({}^{2}\), thus it is a good example to show the spatial variations of water levels with respect to WGS84 ellipsoid over different areas of the lake. Poyang Lake (29.25\({}^{\circ}\) N, 116.06\({}^{\circ}\) E) is the largest lake in China with an area of 4125 km\({}^{2}\). Given the limitation of acquiring in situ data from operational hydrologic stations, we chose this lake to compare the temporal variations of water levels observed by TDS-1 and other approaches. The in situ water levels observed from the hydrologic station are from April to November in 2015 and 2017.  
Figure 4a shows maps of three TDS-1 tracks for the Caspian Sea on 06/07/2015, 08/08/2016, and 06/11/2017. The background map of Figure 4a shows the spatial variations of water levels observed by all the available CryoSat-2 tracks in 2015. Figure 4b-d show the spatial variations of water levels with respect to the WGS84 ellipsoid observed by the corresponding TDS-1 tracks in Figure 4a, with CryoSat-2 derived water levels of the same year as a contrast. Each value of CryoSat-2 data (black point) in Figure 4b-d is determined as the mean value of points within a 0.03\({}^{\circ}\) spatial window around the corresponding TDS-1 specular point. For each year, an overall bias (i.e., \(-\)16.73 m, \(-\)10.68 m, and \(-\)30.1 m for 2015, 2016, and 2017, respectively) is removed which forces the mean lake level estimated from TDS-1 to equal the mean CryoSat-2. The only purpose of doing this removal is to show the possibility of measurements using TDS-1 data. Precise calibration is left to future work or possibly future spacecraft dedicated for altimetry measuring purposes. It shows an overall agreement of spatial  
Figure 3: Correlations of TDS-derived lake level with that from CryoSat-2 and Hydroweb data during the summers of 2015 and 2016. (**a1**) TDS-1 vs CryoSat-2 in 2015; (**a2**) TDS-1 vs Hydroweb in 2015; (**b1**) TDS-1 vs CryoSat-2 in 2016; (**b2**) TDS-1 vs Hydroweb in 2016.  
variations of water level derived from TDS-1 and CryoSat-2. The final RMSE of 2015, 2016, and 2017 is 6.88 m, 7.18 m, and 5.7 m, respectively, which is of the same order as that from previous studies measuring ocean surface (8.1 m and 7.4 m in [3], and 6.4 m in [24]).  
Figure 5 shows water level changes of the Poyang Lake observed by TDS-1, CryoSat-2, Hydroweb, and the hydrologic station in 2015 and 2017. Note that TDS-1 only has one-day lake level due to the strict data filter method (Figure 5a,b). To make the comparison more complete, we additionally involve CYGNSS data from 2017 in Figure 5b to further evaluate the performance of lake level retrieval using the spaceborne GNSS-R technique, since the GNSS-R payloads onboard of CYGNSS and TDS-1 have similar technical parameters. The error bars of TDS-1 in 5(a) and 5(b) show the standard deviations (1.72 m and 3.58 m) of water level values derived from all the specular points located on the lake. The TDS-1/CYGNSS-derived lake level is generally consistent with that derived from other data sources, e.g., the differences between TDS-1 and in situ data are 1.74 m in 2015 and 1.7 m in 2017, and the RMSE of CYGNSS is 2.24 m in 2017 which is of the same order as that of Cryosat-2 (1.39 m). More in situ data should be involved to further evaluate the performance of TDS-1 data for time series analyses.