## 5 Tidal Effects on the Local Magnetometers  
### Tidal Wave Complexity Index (TWCI)  
Data representing tidal wave measurements can be retrieved from the University of Hawaii, Sea Level Center website [48]. The data of the tidal waves (hourly sea level measured in millimeters) are collected from stations located at the closest meridians compared to the magnetometers. The data covers the period from 28 February 2015 to 11 March 2015, matching the timeframe of the magnetic field investigation. The selected measurement stations include Easter Island, Chile (\(-27.15000\), \(-109.44800\)); Hanimaadhoo, Maldives (6.76700, 73.17300); Dzaoudzi, France (\(-12.78200\), 45.25800); San Francisco, CA, USA (37.80700, \(-122.46500\)); and Honningsvag, Norway (70.98300, 25.98300) (Table 7). Note that the oceanic water movements do not have a strong impact on the measurement of SRA because all magnetometers of the Global Coherence Monitoring System are located far from the shoreline. An example of the computed results is shown in Figure 12. Note that there is an observable phase difference between the SRCI and TWCI signals in Figure 12. However, we use statistical formulae, not visual comparisons, between plotted signals to derive correlations between signals. The explanation of this phase difference in Figure 12 goes beyond the objectives of this study. As defined in the previous section, magnetic field data are represented by the SRCI index. To maintain consistency in the comparison between magnetic field and tidal wave data, we introduce the Tidal Wave Complexity Index (TWCI). The computation methodology for the TWCI remains the same as that presented for the SRCI in previous sections. The size of the Hankel matrix used to embed the tidal wave data is set to \(24\times 24\) due to the hourly sea level measurements. H-rank computations are performed in overlapping observation windows (the width of the window is set to 48 data points). Computations continue until the last data point in the two-week observation period is reached. Note  
Figure 11: Relation between Pearson’s correlation coefficient and longitude angles where magnetometers are placed (without NZ). that the calibration of \(\varepsilon\) is performed once for the first 48 iterations. The strategy for the calibration of the threshold parameter \(\varepsilon\) remains the same as for the SRCI. The aim is to choose such a value of \(\varepsilon\) that the average TWCI would be exactly equal to 50%. The calibrated threshold parameter \(\varepsilon\) for each location of the tidal wave is presented in Table 8.  
Then, the complexity index characterizing the algebraic complexity of the investigated time series is computed as the arithmetic average of all H-ranks computed on the current day (which automatically eliminates the diel cycle). As previously, the threshold \(\varepsilon\) is not recalibrated for the subsequent days. Those complexity index values are named as the Tidal Wave Complexity Index (TWCI). \begin{table}
\begin{tabular}{l l} \hline \hline
**Location of the Tidal Waves Measurement Station** & **Location of the Magnetometer** \\ \hline Hanimaadhoo, Maldives (6.76700, 73.17300) & New Zealand ( \(-\)38.526368, 175.675718) \\ \hline Dzaoudzí, France ( \(-\)12.78200, 45.25800) & Saudi Arabia (25.383333, 49.583333) \\ \hline Honningsvag, Norway (70.98300, 25.98300) & Lithuania (55.638929, 23.722195) \\ \hline Easter Island, Chile ( \(-\)27.15000, \(-\)109.44800) & Canada (53.364561, \(-\)113.41565) \\ \hline San Francisco, CA, the USA (37.80700, \(-\)122.46500) & California (37.4192, \(-\)122.057) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The nearest tidal waves measurement stations to the magnetometers (in terms of meridian coordinates). Figure 12: SRCIs computed for the magnetometer data located in California in the frequency ranges 0–1 Hz, 0–3.5 Hz, and 3.5–36 Hz are shown in blue. The TWCI computed for the tidal wave measurement station located in California is shown in red.