## 3 Validation of the Instrument v2021
### Autonomy and Satellite Communication Test in the Arctic: February 2021 Deployment
By contrast, by placing the instrument on top of the paddle that is controlled by a closed-loop control system, we ensure that the vertical displacement of the instrument is exactly equal to the one specified in the control system. In this section, we will refer to the displacement prescribed as \"wavemaker signal\", to emphasize that the signal we measure is the vertical displacement of the plunger-type wavemaker on which the instrument sits, rather than the motion of the water. The experiment aims to evaluate the instrument accuracy when it measures centimeter-scale vertical displacement signals at low frequencies corresponding to typical waves in ice conditions. As such, we tested the instrument using both 1 and 2 cm amplitude sinusoidal wavemaker vertical motion for 12, 14, and 16 s periods (as well as an \"extreme\" test with 0.5 cm amplitude and 16 s period, to test the very limit of the instrument sensitivity), which resemble lower-bound wave signals that were previously measured in ice-covered ocean [14]. The spectral analysis setup was slightly modified from that of Section 2.2 so that each test case duration was reduced from 20 min to roughly 7 min in order to be able to perform the tests within the allocated time slot. For this, the segment overlap was  
Figure 4: Illustration of the wavemaker experiment setup in the wave–ice tank of JAMSTEC (Japan Agency for Marine-Earth Science and Technology) at the Kashiwa campus of the University of Tokyo, Japan. The instrument v2021 location is shown by the yellow arrow. reduced to 50% (corresponding to 1024 points), which yields a total number of 3 segments per 7 min measurement interval. All other processing configurations remained the same as Section 2.2. The wavemaker signal experiment results are summarized in Table 4. The frequency of the wavemaker motion was not tuned to the exact frequency bins; nevertheless, the peak of the energy was consistently captured in the nearest frequency bin, as reflected in Table 4. Then, the best estimate of the wave amplitude can be derived as  
\[A_{mono}=\sqrt{df\times(S(i-1)^{2}+S(i)^{2}+S(i+1)^{2})}, \tag{6}\]  
where \(S(i)\) is the spectrum produced by the instrument, taken at the peak of the amplitude spectrum, and we consider also the neighboring frequency bins. The results of the wavemaker signal experiments summarized in Table 4 indicate that the instrument is capable of measuring monochromatic wave amplitudes of 1 to 2 cm with roughly 0.1 cm accuracy. The spectra obtained during these tests, as well as two spectra corresponding to the instruments while at rest, are presented in Figure 5. As visible there, the noise background of the instrument increases slightly when motion is present, which may be explained by a variety of reasons (small vibrations in the wave paddle mechanism when it is undergoing displacement, diffusion of numerical noise in the processing algorithms, inherent properties of the 9-dof sensor). However, the increase in the noise threshold when there is motion remains very limited. The signal-to-noise ratio is superior or equal to a factor of 50 in all experiments, except for the smaller waves (0.5 cm at 16 s period), in which case the signal-to-noise ratio is around 10. This means that, even in this last \"extreme\" test case, the signal-to-noise ratio is still good enough to clearly distinguish the motion from the noise floor, though noise starts to be visible in the integrated statistics, as discussed in the previous paragraph and in Table 4.  
Following this successful laboratory validation, we decided to perform a field validation experiment in the Arctic, which is described in the next subsection.