# Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR
## 3 Experiment and Analysis of Results
### Results Analysis  
Figure 6 shows the sea level changes over the 31-day period from 1-31 January 2015, determined from the SNR_L1, SNR_L2, L4_d, L4_model and SNR_L2_model. Note that the horizontal axis is in units of \"days of year\" for 2015, and the vertical axis represents the local sea level in meters. It is evident from Figure 6 that the derived results show good agreement with TG observations. Figures 7 and 8 show the correlations of L4 and the SNR method with TG observations, and all the methods used in this paper have a correlation coefficient with TG in excess of 0.97.  
Figure 6: Sea level changes over a 31-day period, as determined from GPS L1 and L2 SNR via double-frequency combination calculated from Equation (8) and the linear model for elevation range 5-15\({}^{\circ}\). Tide gauge (TG) data are also shown (black curves) for the same 31-day period, for comparison.  
Figure 9 shows the sea surface height differences between GPS-derived solutions and TG measurements for the five strategies used from 1-31 January 2015, in which gross errors have not been removed. In the process of statistical evaluation in this paper, gross errors were removed when the residuals were larger than three times their RMSE.  
Figure 8: Correlation of GPS dual-frequency phase combination and SNR estimations for the elevation range 5–15\({}^{\circ}\), using Equation (8) with tide gauge (TG) observations.  
Figure 7: Correlation of GPS dual-frequency phase combination and SNR estimations for the elevation range 5–15\({}^{\circ}\) using a linear regression model with tide gauge (TG) observations.  
Statistical results from the comparison between the GPS-derived sea level data and TG measurements for different elevation ranges are summarized in Table 1. The values of RMSE for different methods fluctuate around 20 cm, which is acceptable when using the multipath effect in GNSS-R altimetry.  
In addition, Table 1 lists the statistical results of five data processing strategies for the elevation ranges, 5\({}^{\circ}\)-12\({}^{\circ}\) and 5\({}^{\circ}\)-15\({}^{\circ}\). We can see that the RMSs of solutions for the elevation angle range, 5\({}^{\circ}\)-15\({}^{\circ}\), are better than those for the elevation angle range, 5\({}^{\circ}\)-12\({}^{\circ}\). The reason for this is that the one pass period of the available SNR data is longer for the 5\({}^{\circ}\)-15\({}^{\circ}\) range than that for the 5\({}^{\circ}\)-12\({}^{\circ}\) range. This makes the SNR oscillations clearer, and, as a result, the retrieved reflector heights have higher precision.  
In the L4_d method, it was found that the remaining result was \(d\)L4 after partial removal of ionospheric delays using high-order polynomial fitting, which consists of two series with different frequencies. Then, Equation (8) was used to calculate the reflector heights from L2 peak frequencies based on the combined dual-frequency carrier phase measurements. However, because the L1 and L2 coexist in \(d\)L4, using Equation (8) to calculate the reflector height from the L2 peak frequency ignores the effect of the L1 term. As a result, the accuracy of data results using this method is still very good. Analysis of the data shows that this might be caused by the frequency difference between L1 and L2, which makes it possible to distinguish between L2 and L1 terms in \(d\)L4. It is also evident that L1 has an impact on L2 because of the slight difference in accuracy of the L4_d method.