# SNR-Based GNSS-R for Coastal Sea-Level Altimetry
## 5 GNSS-R Sea Level Altimetry  
The 1-min OTT RLS records from 9 October 2020 are used to assess the performance of the 15-min GNSS-R sea level altimetry. The GNSS-R retrievals are interpolated at the tide gauge epochs; in order to minimize the interpolation errors, missing sea level periods are discarded in either OTT RLS or GNSS-R. The mean difference between tide gauge and GNSS-R is disregarded in this section to compare the two sensors. Figure 5 compares the OTT RLS records to the retrieved GNSS-R sea levels over 199 days. On one hand, the RMSE of the residuals between GNSS-R sea level retrievals and the OTT RLS records at the Port-au-Prince tide gauge station is 3.43 cm. On the other hand, the RMSE between OTT RLS and S12C SDI-12 records over 2014, when both sensors were operational at the Haiti Coast Guard Base in Port-au-Prince is 3.67 cm, with a correlation coefficient exceeding 0.98. Therefore, geodetic GNSS-R sea levels are comparable with those of conventional tide gauge records. A scatterplot of sea levels shows an excellent agreement between tide gauge records and GNSS-R sea level retrievals, with a correlation coefficient exceeding 0.96 (Figure 6). A Van de Casteele diagram (\(y\)-axis presents the sea level error between the OTT RLS records and GNSS-R sea level retrievals and \(x\)-axis represents the OTT RLS records) shows there is no scale error between the two sensors (Figure 6). Carrying out a regression between the two sensors, the slope deviation of \(-0.01\)m/m \(\pm\) 0.02m/m is not statistically significant vis-a-vis its 95% confidence interval. To highlight the importance of the vertical velocity and vertical acceleration corrections for such a small tidal range, the uncorrected GNSS-R sea levels, assuming a static state for the sea surface, are compared with the OTT RLS records. The RMSE between uncorrected GNSS-R retrievals and tide gauge records is 6.73 cm, and the regression slope of \(-0.31\)m/m \(\pm\) 0.27m/m indicates a scale error between the two sea levels. Therefore, the dynamic state of sea level correction, even for the small tidal range's stations, should be applied when sub-hourly products are needed. Figure 5: OTT RLS records and GNSS-R sea level retrievals at Port-au-Prince tide gauge station. The DTT RLS records and GNSS-R sea levels are band-pass filtered, employing a 3-h, 4-h, 6 h, 12-h, and 24-h window. The results of each band are summarized in Table 1. On one hand, the slope deviation and correlation are worse for the highest frequency region (3-h). On the other hand, the performance of GNSS-R in periods greater than 6-h is good, and tidal variations are well captured by geodetic GNSS-R (Figure 7). This is due to the temporal resolution of the geodetic GNSS-R retrievals and can be improved either by using other GNSS constellations such as GALILEO or increasing the reflector height above the mean sea level. Based on the length of the sea level time series, the amplitudes and phases of a set of harmonic tide components are determined based on [34] (Table 2). The complex differences between the DTT RLS records and GNSS-R sea levels for all the eight major tidal constituents are in mm-level agreement. Systematic biases for GNSS-R-derived luni-solar diurnal, principal solar, and luni-solar semidiurnal components were correlated with the GPS orbital period [9, 11]. Here, the systematic effect is cancelled out using GLONASS, with an 11.25 h orbital period. \begin{table}
\begin{tabular}{c c c c c} \hline  & **3-h** & **4-h** & **6-h** & **12-h** & **24-h** \\ \hline
**Correlation** & 0.43 & 0.66 & 0.94 & 0.97 & 0.97 \\
**RMSE (cm)** & 1.81 & 2.28 & 2.74 & 3.10 & 3.17 \\
**Slope deviation (m/m)** & \(-0.66\pm\) 0.03 & \(-0.36\pm\) 0.04 & \(-0.08\pm\) 0.02 & \(-0.03\pm\) 0.02 & \(-0.02\pm\) 0.02 \\ \hline \end{tabular}
\end{table} 
Table 1: Statistics of DTT RLS records and GNSS-R sea level retrievals for each band. Figure 6: Scatterplot of sea levels shows an excellent agreement between DTT RLS records and GNSS-R sea level retrievals (left panel).