During the 2021 NABOS campaign, we deployed the first prototype of the OMB developed by Rabault et al. (2022), to which we refer herein as the Zeni-v2021, alongside a Sofar Spotter, herein referred to as SPOT-1386. Both Zeni-v2021 and SPOT-1386 buoys measure ocean surface motion, but they use different technology.

The Zeni-v2021 was recently introduced by Rabault et al. (2022). The OMB electronic components for detecting ocean surface motion are a 6 degrees of freedom accelerometer and gyroscopic IMU manufactured by ST (model ISM330DHCX). The attitude heading reference system correction via sensor fusion of three-axis accelerations and angular rates produces true vertical acceleration (Rabault et al. 2022), which is integrated twice to estimate the surface elevation.

The OMB ‘buoy’ is a sensor unit that is housed in a waterproof enclosure (e.g., figure A1 by Rabault et al. 2022); it is not designed as a floating platform in water. The primary deployment method of OMBs is that the sensor unit is placed on an ice floe, and the ice floe becomes the sensor’s floating platform (hence, the term “wave–ice buoy”). At the time of the buoy preparation, in July 2021, the sea-ice extent was low, nearly as reduced as the 2012 record low sea-ice extent. (However, by August, the sea-ice extent had plateaued, resulting in limited opportunities for open-water deployment. See Arctic Data Archive System [2023] for sea-ice extent images.) An alternative deployment method was devised by housing the sensor in a floating platform. The ad hoc platform was a Zenilite GPS tracker enclosure, whose design allowed it to house the OMB electronic components (see Appendix B, Rabault et al. 2022). The Zenilite GPS drifting buoy has a diameter of 340 mm, is 300 mm in height and weighs about 6 kg.

SPOT-1386 is a commercially sold drifting wave buoy; it is a proven technology with thousands of them currently deployed in the world oceans. The dimensions are similar to the Zenilite GPS drifter, which are 420 mm wide by 310 mm high and weigh 5.3 kg (7.4 kg with a ballast); therefore, SPOT-1386 is an appropriate benchmark for Zeni-v2021. Spotters’ proprietary firmware uses a GPS/GNSS receiver to get the device horizontal and vertical displacements.

The wave buoys were deployed adjacent to an ice edge in the central Arctic Ocean, north of the Laptev Sea (81.915°N, 118.763°E) at about UTC 05:05 on 15 September 2021. The deployment location is shown in Fig. 1, and the sea-ice conditions as observed onboard the ship on the day of the buoy deployment are shown in Fig. 2. The SPOT-1386 battery life at high latitudes without a solar charge is approximately 10 days; as such, the co-located deployment duration only lasted between 15 and 29 September. The buoy tracks for this period are shown in Fig. 1a, which is overlaid with the AMSR2 SIC (Hori et al. 2012) contours.

The primary motive for the buoys being deployed at the same location was to validate Zeni-v2021 against SPOT-1386, and we anticipated that the buoys would measure analogous wave signal for at least several days. For example, Waseda et al. (2018) and Nose et al. (2018) describe the trajectories and wave statistics of two buoys deployed at the same location in the ice-free Beaufort Sea in 2016; the buoys drifted along similar tracks for about 13 days, during which time, they measured analogous wave statistics. However, we observed that the Zeni-v2021 and SPOT-1386 wave heights began deviating slightly merely 12 hours after the buoys were deployed. Two days after deployment, wave heights and periods varied considerably between the two buoys, which indicates that the measured waves’ evolution did not occur entirely over open ocean, that is, sea ice affected how the waves evolved.

Overview of the wave data. Figure 3 presents an overview of the co-located buoy observation: the buoy distances, and wind, wave and SIC conditions. Here, wave statistics derived from the vertical surface elevation are significant wave height Hm0=4m0, where m0=∫f0f1S(f)df and wave periods (peak period T_p^ˊ, which is the inverse frequency of peak S(f) and −1 moment period, also known as energy mean wave period, T0m1=∫f0f1f−1S(f) dfm0)⋅ The notations are frequency spectrum S and frequency f. The integration range was (f0, f1) for n th spectral moments m_n, where f1 = 0.308 Hz. Zeni-v2021 data were affected by the noise floor that was elevated whilst the buoy was drifting in open water until about 25 September; the elevated noise floor is analogous to the observation by Waseda et al. (2017), Waseda et al. (2018) and Nose et al. (2018) and seems to accompany IMU-based wave sensors housed in a relatively small floating platform. The same ideal filter method as used by Waseda et al. (2017), Waseda et al. (2018) and Nose et al. (2018) was implemented to derive the wave statistics. As such, f 0 was not a constant and depended on the ideal-filter cut-off frequency. The Zeni-v2021 integration range (f 0, f 1) was matched in the SPOT-1386 wave statistics calculation. It is noteworthy that the elevated noise floor was observed until 25 September, which roughly coincides with the time when the inertial oscillation visible in Fig. 1a seemingly stopped (Figs. 1, 3).

Inter-buoy comparison. It is apparent in the H_m0 panel of Fig. 3 that, despite the buoys having similar drifting trajectories for the first half of the deployment, H_m0 began to vary slightly between them after half a day and considerably after just two days. As we will show throughout the paper, the variability likely indicates that the wave evolution was modified by the sea-ice fields via one of the following effects: (1) waves are attenuated as they propagate into the ice-cover medium; (2) lateral boundary conditions are imposed by the ice fields and affect the wave evolution over the effective fetch.

Although we discuss (below) the possibility that the effective fetch at the buoys’ location after 12 hours of deployment was already affected by the sea-ice lateral boundary, we aim to consolidate the general inter-buoy agreement when the buoys were in close proximity. Scatter for H_m0 and T_0m1 is plotted in Fig. 4. The markers were grouped by an arbitrary buoy distance threshold of 5 km to demonstrate that the buoys’ wave statistics agreed better when the distance between them was shorter, that is, the effect of the sea-ice field on wave evolution is less for shorter distances. Indeed, the blue markers, indicating the data when the between-buoy distance was <5 km, in both panels are clustered closer to the black dotted agreement line than the red markers. Furthermore, as was shown in the left panel of Fig. 7 by Rabault et al. (2022), the spectra agreed well immediately after the buoys were deployed.

Whilst precise Zeni-v2021 validation with SPOT-1386 was impeded by the growing sea-ice fields, we showed that the Zeni-v2021 measurement quality seems sufficiently adequate when the wave evolution was less altered by the sea-ice field (when the distances between them were short). As such, we used the wave events observed by the co-located buoy measurements to evaluate the operational ARC MFC wave–ice model predictability.

The wave–ice interaction parameterization. The ARC MFC wave–ice model is an operational wave model product for the Arctic Ocean and includes a wave–ice interaction parameterization, that is, the model can simulate wave propagation in sea-ice cover. Medium-range forecast and analysis are distributed via the CMEMS platform.

The ARC MFC wave–ice interaction is based on the work of Sutherland et al. (2019). They modelled wave dissipation with a two-layer sea-ice model: the top layer is modelled like a thin film that has no horizontal motion with thickness (1-ε)h_i, whilst the bottom layer is modelled as a moving viscous layer. Here, h_i is the ice thickness. Sutherland et al. (2019) describe that the ε coefficient is related to ice permeability at the microscopic scale and is a function of ice temperature, salinity and ice volume fraction. The assumption of a highly viscous top layer is similar to Weber (1987), who derived a well-known wave dissipation solution by modelling the thin ice cover as an inextensible layer that halts the horizontal motion of the fluid layer underneath. The model by Sutherland et al. (2019) could be considered an extension of the Weber (1987) model. In the latter, the dissipation rate is α ∝ K₃₅ f ^3.5 where K₃₅ is a constant. The model by Sutherland et al. (2019) also has a frequency dependence, but they also included an ice thickness dependence to the dissipation rate: α ∝ K₄₀ f ⁴, where K₄₀ is a function of ice thickness. A more thorough discussion on the various dissipation rates in the literature is provided by Waseda et al. (2022).

Sutherland et al. (2019) developed their model on the basis of a scaling argument as they derived that the viscosity scales with SIT, v ∝ h_i, which led to spatial wave dissipation as a function of ice thickness and frequency: α ∝ h_if⁴. The dissipation rate is parameterized in equation 16 by Sutherland et al. (2019) as:

where ∆₀ ≈ 1. In the CMEMS Quality Information Document (Bohlinger et al. 2022), the dissipation rate is denoted as, α = C_dh_ik ²,where they state that C_d is a tuning parameter and is determined by the best fit to the observation obtained from the ice-covered fjord, Tempelfjorden, in Svalbard, in 2018. Note that when ε = 0 (or C_d), the model may behave like the Weber (1987) model if the boundary layer in the fluid is implemented (not done so in the model by Sutherland et al. [2019], yet). Lastly, the dissipation rate α is used to estimate the dissipated wave spectrum as follows:

where S₀ is the incoming wave spectrum and ^x is a distance between the two points.

The wave part of the ARC MFC wave–ice model is based on Met Norway’s version of WAM (The WAMDI Group 1988). WAM is a spectral wave model that is discretized in frequency and direction and solves the numerical evolution of ocean waves as energy budgets based on the action density balance equation. The surface wind boundary conditions are forced using the ECMWF HRES atmospheric forecast. At the ocean boundary along 53°N latitude, wave lateral boundary conditions are directional wave spectra from the ECMWF HRES wave forecast, also based on WAM. The ECMWF HRES atmospheric forecast has a regular longitude/latitude grid at 0.1 degrees. The ARC MFC wave–ice model has a spatial resolution of 3 km on the polar stereographic projection.

The sea-ice part of the ARC MFC wave–ice model is taken from the ARC MFC ocean analysis (the specific product name is ARCTIC_ANALYSIS_FORECAST_PHYS_002_001_A). The sea-ice model is the Community Ice Code and based on the viscous–plastic sea-ice rheology. The sea-ice model uses a one-thickness category sea-ice model based on the thermodynamics described by Drange & Simonsen (1996) and Sakov et al. (2012). There, the minimum thickness for the newly formed ice is given as 0.5 m. Implications of the minimum thickness value are evaluated with the buoy observations in a later section.

The Community Ice Code sea-ice model was coupled to the HYCOM. The atmospheric forcing is obtained from the ECMWF HRES atmospheric forecast. The data assimilation was performed weekly, using the ensemble Kalman filter (Sakov et al. 2012), for the following: altimeter sea level, in situ temperature and salinity profiles, the OSTIA sea surface temperature, OSI SAF SIC and drift observations, and the (winter) SIT from the CryoSat-2 and Soil Moisture and Ocean Salinity satellites. The HYCOM has a horizontal resolution of approximately 12 km, which is more than three times the resolution of the ARC MFC wave–ice model.

Wave heights and periods from the ECMWF HRES wave forecast were used in this study as a tool to analyse the ARC MFC wave–ice model and the buoy observation comparison. The ECMWF HRES wave forecast was obtained for our research activity by the Arctic Data Archive System, Tokyo, Japan. We took a series of 0–24-hour forecasts to produce a time series during the observation period. The ECMWF HRES wave model accounts for sea ice using ice masks where grid cells with SIC > 0.30 are treated as land. The ECMWF HRES wave forecast model has a regular longitude/latitude grid at 0.125 degrees. The ECMWF HRES wave model is useful to evaluate the wave conditions in the open water near the ice edge based on the following premises. (1) When the wave evolution occurs entirely over the open water fetch, the ECMWF HRES wave and ARC MFC wave–ice models should agree. (2) Near the ice edge, where satellite-derived sea-ice data are uncertain, inaccurate sea-ice representation can cause erroneous wave predictions (Nose et al. 2020). (3) In such cases, the ECMWF HRES wave model that neglects sea ice may produce better predictions.

The neXtSIM sea-ice model (specific product name ARCTIC_ANALYSISFORECAST_PHY_ICE_002_011; Rampal et al. [2016]; Ólason et al. [2022]) is a sea-ice product distributed by the CMEMS and based on the Brittle-Bingham-Maxwell rheology. Rampal et al. (2016) introduced this model describing that fracturing and faulting of sea ice should be expressed as an assembly of plates >O(1 km) and floes O(100 m), rather than an intact solid plate. The neXtSIM thermodynamical component is based on a three-category model that includes open water, newly formed ice and older ice, as described by Rampal et al. (2019). Rampal et al. (2016) show that their model calculates ice formation in the category of newly formed ice on the basis of the atmosphere and ocean forcing, whereas a prescribed growth rate is conventionally adopted in classical models (Rampal et al. 2016). The thickness range of this newly formed ice category is 0.05–0.275 m, which is considerably thinner than that of the ARC MFC ocean analysis.

Unlike the ARC MFC ocean model, neXtSIM is not coupled to an ocean circulation model but is coupled with a mixed-layer model that is relaxed to an ocean circulation model. The ocean part is represented by a single level “slab ocean” model of the mixed layer (Rampal et al. 2016) and uses the following daily averaged forcing from the TOPAZ4 ocean data assimilation model system: sea surface (0–3 m) ocean velocity, temperature and salinity, and the mixed layer depth (Williams et al. 2021). The atmospheric forcing is the ECMWF HRES atmospheric forecast, and the neXtSIM model assimilates OSI SAF SIC via the nudging scheme on a daily basis. Since the control variable is only the SIC, neXtSIM is strongly constrained to the observation, that is, the OSI SAF SIC. The model has a Lagrangian triangular mesh with an equivalent square grid resolution of ca. 7 km, for which the data are distributed on the 3 km polar stereographic projection grid.

Significant wave height H_m0 and period time series were extracted from the ARC MFC wave–ice model and the ECMWF HRES forecast at the Zeni-v2021 and SPOT-1386 positions during their deployment between 15 and 29 September 2021. The full time series for wave heights and periods are shown in Supplementary Figs. S2 and S3. In this subsection, we focus on the wave heights between 15 and 19 September immediately after the buoys were deployed in open water.

Following the deployment, the ECMWF HRES H_m0 agrees well with both buoys for up to ca. 12 hours, whereas the ARC MFC H_m0 is clearly underestimated (Fig. 5). Shortly after, however, the buoys’ H_m0 takes a steep decrease at about 14:00 on 15 September (Fig. 5), and the ECMWF HRES H_m0 is overestimated, whilst the ARC MFC H_m0 agrees qualitatively with the observation. This change coincides with the time when the Zeni-v2021 H_m0 began deviating slightly from that of SPOT-1386 (Fig. 3).

Immediately after the deployment at 06:00 on 15 September, the ARC MFC wave directions were primarily parallel to the ice edge (Fig. 6a). Tracing upwind from the buoys, the ice edge protrudes and shelters the buoys’ effective fetch on which waves can grow. Considering the ARC MFC H_m0 is underestimated, the ice edge sheltering of the buoys may be the cause of the underestimation, that is, the protruding ice edge may not be an accurate representation of the sea-ice field. For comparison, Supplementary Fig. S4c shows the buoys are not sheltered by any protruding ice edge features in the ECMWF HRES sea-ice representation.

The fetch orientation transitioned from along the ice edge to off-ice wave conditions (Fig. 6b) after the models’ trend reversed. (Winds were also blowing from the ice cover [Supplementary Fig. S4b, d].) The ECMWF HRES H_m0 is clearly overestimated (Fig. 6), and the ARC MFC H_m0 agrees with the observations with a varying degree of predictability.

These observations demonstrate the lateral boundary effect that sea ice imposes on the wave fields. We conjecture that the inaccurate representation of the ARC MFC ice tongue imposed a lateral boundary condition that prohibited reproducing the true wave evolution when the fetch was orientated parallel to the ice edge. A similar scenario was also observed on 21 September 2021, in which the ice tongue representations between the ARC MFC and ECMWF HRES models were markedly different. This event is described in the Supplementary material to present further support to this conjecture.

South to south-easterly winds over the Laptev Sea generated on-ice waves on 29 September 2021. The model wave fields are shown in Fig. 7. By this time, both Zeni-v2021 and SPOT-1386 were in dense ice cover with SIC > 0.8 (see Fig. 3e). The ice edge geometry and wave orientation were not straightforward; the Zeni-v2021 location was downwind compared to the SPOT-1386, but the Zeni-v2021 distance to the ice edge relative to the wind direction was closer than that of SPOT-1386 (Fig. 7).

During this event, the ECMWF HRES wave model has no values at both buoys as they are covered by the ice mask. The ARC MFC wave–ice model simulates no waves at both buoys (Supplementary Fig. S2). However, the H_m0 time series panel in Fig. 3c depicts that waves were observed at Zeni-v2021, reaching a peak H_m0 value over 1.25 m. SPOT-1386 located ca. 30 km south-east of Zeni-v2021 did not observe any waves. To investigate how the wave energy propagated to the downwind Zeni-v2021, but not for SPOT-1386, we analysed the model representations of the sea-ice field of the ARC MFC ocean analysis and the neXtSIM sea-ice model product.

Sea-ice fields between ARC MFC and neXtSIM are compared at the buoys’ location on 29 September 2021 in Fig. 8. It is apparent that the horizontal scale of ARC MFC sea-ice features (Fig. 8a, c) is effectively limited to the ARC MFC ocean analysis scale of ca. 12 km. This may be expected as interpolation to a high-resolution grid is unlikely to reveal features less than the original scale; the implication here is that there is an inconsistent scale between the wave–ice model geographical configuration and the model physics resolution. The scale of sea-ice features in the neXtSIM sea-ice model appears to be much finer; the reason for this may be speculated that the Lagrangian nature of the model can influence the thermodynamics as well as the mechanical properties.

Notwithstanding this, the striking differences between the two models pertaining to the buoys’ wave observation are the ice edge location, the 0.80 SIC contour and the SIT differences. The neXtSIM SIC field shows that the distance from Zeni-v2021 to the sea-ice edge is much closer than shown in the ARC MFC field. Moreover, if we take the wave propagation as roughly 150 degrees, then 0.80 SIC ice-covered sea that the waves need to propagate to reach Zeni-v2021 is much shorter than that of the ARC MFC wave–ice model, whilst for SPOT-1386, this distance remains relatively similar. Regarding the sea-ice edge and 0.80 SIC contour differences between the ARC MFC ocean analysis and the neXtSIM sea-ice model, we revisit the data assimilation intervals and scheme differences: the ARC MFC ocean analysis assimilates data at weekly intervals and uses the ensemble Kalman filter with many control variables (see the earlier subsection about the ARC MFC wave–ice model), whereas the neXtSIM sea-ice model carries out daily data assimilation via the nudging scheme with SIC being the only control variable (see the earlier subsection about the neXtSIM sea-ice model). The data here suggest that the differences in the data assimilation intervals and schemes produce diverging sea-ice field representations.

The representation of SIT in the ARC MFC model for thin ice appears to be poor: the ice field beyond the 0.80 SIC contour is practically SIT > 0.3 m. By contrast, the neXtSIM SIT field clearly has a thickness distribution between 0 m and 0.3 m within the plot domain. The Supplementary material describes the observation-based ice chart that confirms the ice type near the ice edge, and the wave buoys were young ice. Although it is beyond the scope of this paper to examine whether coupling a wave model with the neXtSIM sea-ice forcing reproduces the co-located buoy data, there is sufficient evidence to suggest that the neXtSIM sea-ice representation appears to be in accord for reproducing the Zeni-v2021 H_m0, that is, less dissipation because of low SICs and thinner thickness.