# Development of a GNSS Buoy for Monitoring Water Surface elevations in Estuaries and Coastal Areas
## 3 Instrumentation, Results and Discussion
### Field Tests
#### 3.3.3 Wave Data  
For analyzing the wave data, the water surface elevations obtained at two time periods were used. The first period in 2013 was from 21 August, at 02:00 to 22 August, at 17:00, and the second period in 2013 was from 29 August, at 07:00 to 31 August, at 12:00. The data collected during these two periods were selected because the percentages of good altitude data obtained by the GNSS receiver exceeded 95%. During the first period, Typhoon Trami passed through the northern waters of Taiwan, and from 02:00 to 12:00 on 21 August, the typhoon was close to the GNSS buoy. The percentage of good altitude data was 96% at 09:00 on 21 August 2013, and the significant wave height was 2.38 m. Figure 7 compares the water surface elevations obtained at that time from the GNSS receiver with those from the ATC sensor. The black solid line with circles and red dashed line with squares represent the water surface elevations of the ATC sensor and GNSS receiver, respectively. The water surface elevations obtained from the ATC sensor fit well with those from the GNSS receiver, which indicates that the procedures used to obtain water surface elevations from the acceleration measured by the ATC sensor are correct and that both sensors could obtain fairly consistent water surface elevations. Figure 6: Comparison of tide data obtained from the GNSS buoy and tide gauge (20–22 August 2013). Figure 7: Water surface elevations obtained from the ATC sensor and GNSS receiver at 09:00 on 21 August 2013. A comparison of the one-dimensional wave spectra obtained from the ATC sensor and the GNSS buoy is shown in Figure 8. The vertical axis in Figure 8 is the PSD of the water surface elevations. The one-dimensional wave spectrum and the directional wave spectrum discussed in this section were determined based on the theory presented in Appendixs A and B, respectively. Note that the wave spectra obtained from both sensors are consistent. The small deviations shown in Figures 7 and 8 may have been caused by the following reasons. Both the water surface elevation and its PSD obtained from the ATC sensor were transformed from the acceleration raw data based on the procedures described in Section 2.2 and Appendix A. The noise filtering and spectral smoothing techniques are empirical. On the other side, the pitch and roll motions of the GNSS buoy may have also caused uncertainty in the measurement of the water surface elevations. In the future, further improvements should be made to account for the effect of the pitch and roll motions of the buoy. Figure 9a,b shows the directional wave spectra obtained at 09:00 on 21 August 2013 from the ATC sensor and the GNSS receiver, respectively. The peak frequency of the directional wave spectra obtained from both sensors was 0.1055 Hz, and the dominant wave direction from the ATC sensor was 78.75\({}^{\circ}\), and from the GNSS buoy was 67.5\({}^{\circ}\). The peak frequencies were identical, and few differences were observed between the dominant wave directions. Figures 10-12 display the scatter plots and regression lines for the significant wave heights, \(H_{\mathrm{S}}\), zero-crossing periods, \(T_{\mathrm{Z}}\), and dominant (peak) wave directions, _DWD_, respectively. The data in these figures represent 23 hourly data, which were chosen from the field test based on the criterion that the percentages of good altitude data exceeded 95% hourly. The numbers of symbols in certain  
Figure 8: PSD obtained from the ATC sensor and GNSS receiver at 09:00 on 21 August 2013. Figure 9: Directional wave spectra obtained at 09:00 on 21 August 2013 from the (**a**) ATC sensor and (**b**) GNSS receiver. figures were less than 23 because certain data overlapped perfectly. The regressions in Figures 10-12 are reasonable because the residuals from the regression lines were random.