## 3 Results  
### Sea Level Determination Based on the Tidal Fluctuations  
To enable the assessment of tidal-induced sea level oscillations, a total of 12,444 h of observed time series data was used to perform DFT and obtain an amplitude spectrum (Figure 9). Due to the nature of the observed signal, inspection of the amplitude spectrum offers the presence of the trend, visible within the bins corresponding to the lowest frequencies. In total, seven tidal harmonics has been identified as dominant, thus ensuring the tidal-induced sea level oscillation characterization.  
While tidal amplitudes and periods were determined directly from the spectrum shown in Figure 9, phases were determined from the complex component of each of the seven tidal harmonics. All characteristic values for the relevant tidal constituents are shown in Table 1. The quality of the determined harmonic values were checked by the application of the correlation coefficient when applied to both the simulated and observed time series.  
Both the observed and simulated sea level signals, one for each 1000 h of the available time series, are compared by using Pearson correlation coefficient and root mean square error. When simulating the sea level by using Equation (2), the simulated signal discovers the absence of the trend within, which is incorporated in the next step as a response to long-term barometric pressure changes. The residual was determined as a difference between the observed and simulated signals. Both signals are shown relative to the HVRS71 vertical datum, as explained in the Methodology section. The same procedure was repeated for each 1000 h data of the total 12,444 h data representing the total sample. Both Pearson correlation coefficient and root mean square error values are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline
**Constituent** & **Amplitude (m)** & **Period (h)** & **Phase (°)** \\ \hline O1 & 0.02821644 & 25.81743 & \(-\)160.6065 \\ K1 & 0.02339150 & 24.06963 & 105.3624 \\ P1 & 0.08773618 & 23.93077 & 153.1416 \\ N2 & 0.01279412 & 12.65921 & 65.3833 \\ M2 & 0.07688095 & 12.41916 & \(-\)31.55806 \\ S2 & 0.05696792 & 12.00000 & \(-\)126.8397 \\ K2 & 0.01636003 & 11.96538 & 116.0807 \\ \hline \end{tabular}
\end{table}
Table 1: Tidal constituents with corresponding values of amplitude, period and phase.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Data Sets (h)** & **0–** & **1000–** & **2000–** & **3000–** & **4000–** & **5000–** & **6000–** & **7000–** & **8000–** & **10,000–** & **11,000–** & **0–** \\
**1000** & **2000** & **3000** & **4000** & **5000** & **6000** & **7000** & **8000** & **9000** & **11,000** & **12,444** & **12,444** \\ \hline RMSE & 0.198 & 0.141 & 0.083 & 0.082 & 0.075 & 0.071 & 0.147 & 0.241 & 0.091 & 0.159 & 0.095 & 0.136 \\
**Pear. Corr. Coef.** & 0.551 & 0.597 & 0.749 & 0.782 & 0.923 & 0.802 & 0.664 & 0.639 & 0.752 & 0.834 & 0.791 & 0.578 \\ \hline \end{tabular}
\end{table}
Table 2: Pearson coefficient and root mean square values obtained between the measured and simulated sea water elevation by Equation (2).  
Figure 9: Amplitude Spectral Density for observed sea level reduced for the mean value.  
For the entire observed and simulated set of 12,444 h data, the root mean square value equals to 0.136 [m], while Pearson's correlation coefficient equals 0.578 [-]. The high value of RMSE and low value of the correlation coefficient indicate the sea level fluctuations are not only subjected to tidal variations, but also to other factors.