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# A comparison of an operational wave-ice model product and drifting wave buoy
observation in the central Arctic Ocean: investigating the effect of sea ice
forcing in thin ice cover

Takehiko Nose1 Jean Rabault2 Takuji Waseda1 Tsubasa Kodaira1
Yasushi Fujiwara1,3 Tomotaka Katsuno1 Naoya Kanna4
Kazutaka Tateyama5 Joey Voermans6 & Tatiana Aleekseva7,8

††footnotetext: 1Department of Ocean Technology, Policy and Environment,
Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa Chiba
Japan ††footnotetext: 2 Norwegian Meteorological Institute, IT Department,
P.O. Box 43, Blindern N – 0313 OSLO ††footnotetext: 3 Now at Kobe University
††footnotetext: 4 The Atmosphere and Ocean, Research Institute, The University
of Tokyo, Kashiwa Chiba Japan ††footnotetext: 5 Kitami Institute of
Technology, Kitami Hokkaido Japan ††footnotetext: 6 The University of
Melbourne, Melbourne Australia ††footnotetext: 7 Arctic and Antarctic Research
Institute, Saint Petersburg Russia ††footnotetext: 8 Space Research Institute,
Moscow, Russia ††footnotetext<EMAIL_ADDRESS>
## Abstract

Two drifting wave buoys were deployed in the central Arctic Ocean, north of
the Laptev Sea, where there are historically no wave observations available.
An experimental wave buoy was deployed alongside a commercial buoy. The inter-
buoy comparison showed that the experimental buoy measured wave heights and
periods accurately; so the buoy data were used to study the predictability of
a wave-ice model in this region. The first event we focused was when both
buoys observed a sudden decrease in significant wave heights $H_{m0}$. The
sudden decrease was caused by the change of wind directions from along the ice
edge to off-ice wind. This event was compared with the ARC MFC wave-ice model
product, which underestimated the $H_{m0}$. The inaccurate model
representation of an ice tongue located upwind of the buoys was found to
constrain the available fetch for wave growth. The second case was when the
buoys entered ice cover as new ice formed; an on-ice wave event was observed
and the buoy downwind measured 1.25 m $H_{m0}$. In this instance, the ARC MFC
wave-ice model product largely underestimated the downwind buoy $H_{m0}$. To
investigate this event, model sea ice conditions were examined by comparing
the ARC MFC sea ice forcing with the neXtSIM sea ice model product. Our
analysis revealed that the thin ice thickness distribution for ice types like
young and grey ice, typically less than 30 cm, were not resolved. The ARC MFC
model’s wave dissipation rate has a sea ice thickness dependence, and
therefore, it overestimates wave dissipation in thin ice cover; sea ice
forcing that can resolve the thin thickness distribution is needed to improve
the predictability. This study provides an observational insight into better
predictions of waves in marginal ice zones when new ice forms.

Keywords drifting wave-ice buoy, ARC MFC wave-ice model, neXtSIM sea ice
model, wave-ice interaction, ice thickness, and Arctic Ocean

## RUNNING HEAD

Investigating the effect of sea ice forcing for a wave-ice model in thin ice
cover

## ABBREVIATIONS

AMSR2 - Advanced Microwave Scanning Radiometer 2
ARC MFC - Arctic Monitoring and Forecast Center
CICE - Community Ice CodE
CMEMS - Copernicus Marin Environment Monitoring Service
HYCOM - Hybrid Coordinate Ocean Model
IMU - inertial measurement unit
MIZ - marginal ice zone
OMB - OpenMetBuoy
SIC- sea ice concentration
SIT - sea ice thickness
WAM - WAve Model

##  1 Introduction

Wave-ice interaction research is attracting renewed attention due to declining
Arctic Ocean sea ice cover and a conjecture that waves in ice have an
influence on the climate system (Squire, 2018, 2020). Despite recent
advancement in model parameterisation since one of the most intensive waves-
in-ice data collection campaign of Thomson et al. (2018), incorporating the
effects of waves in sea ice models and vice versa remains a challenging
problem. In MIZs where sea ice field is heterogeneous and waves most dynamic,
the problem becomes even more challenging as accurate sea ice condition is
difficult to obtain. Uncertainty arising from SIC estimates (from passive
microwave radiometers) used as sea ice forcing for wave-ice models can even
overwhelm the uncertainty of wave-ice interaction parameterisations (Nose et
al., 2020). Due to these challenges, it can be argued that more observations
are needed to better understand wave-ice interaction physics and improve the
predictability of ocean waves in MIZs.

Utilising the recent advances of inexpensive electronics and their open source
philosophy, Rabault et al. (2022) developed and introduced a low-cost, easy to
build wave-ice buoy called OMB. The OMB applies a 6 degrees of freedom IMU to
measure vertical ocean surface motion. The vertical surface oscillation can
then be used to obtain power spectral density, from which integrated wave
statistics like the wave height and periods can be calculated. In September
2021, our research team joined the NABOS campaign (https://uaf-iarc.org/nabos-
cruises/) onboard R/V Akademik Tryoshnikov, and we deployed a prototype of
Rabault et al. (2022)’s OMB alongside a commercial wave buoy in the central
Arctic Ocean where there are historically no wave observations available. In
this study, we evaluated our prototype OMB with a commercial wave buoy; we
then used the buoy dataset to study the wave-ice model predictability in this
region.

To simulate the ice effects on waves, we first need to consider the length
scale between $\lambda$ and $D$ (Linton, 2010) where $D$ could be considered
the diameter of an ice floes and $\lambda$ is the wavelength. For an ice sheet
and grease ice where $\lambda<D$ and $\lambda>>$ SIT, the sea ice can be
modelled as a thin elastic ice layer where waves propagate under ice, and the
ocean-ice interface is where the dissipation occurs. When $\lambda\approx D$,
wave attenuation is understood to be dominated by a conservative process known
as the scattering mechanism, which was first observed by Wadhams (1975). When
$\lambda>D$, waves propagate through smaller sea ice floes and dissipation
occurs in many forms (Squire, 2018); this type of ice cover can be modelled as
a semi-infinite viscous ice layer, in which effective material properties can
be tuned to reproduce the aggregate effect of various sea ice effects on waves
(Squire, 2018).

The $\lambda>D$ regime is primarily observed in the MIZ. This is the length
scale of interest to our wave buoy observation because the ice charts
indicated that the wave buoys were located near and in new and young ice, with
typical thickness less than 30 cm, during the observation period (see Appendix
A.1). For the purpose of a model-observation comparison, we used an
operational model product named ARC MFC+††+CMEMS product name:
ARCTIC_ANALYSIS_FORECAST_WAV_002_014. Data downloaded on 18 Jan 2022..

Because the ARC MFC model’s wave dissipation parameterisation (Sutherland et
al., 2019) is suited for modelling waves in the MIZ thin ice cover, we expect
reasonable model agreement with the observation. Our objective in this study
is to elucidate the predictability of the ARC MFC wave-ice model in the
central Arctic Ocean by applying the drifting wave buoy observations and other
model products ECMWF HRES (wave) and neXtSIM (sea ice). Specifically, we focus
on how sea ice edge and SIT representations in the sea ice forcing affect wave
predictions when new ice is forming.

We describe the buoy observation details including sensor types and platforms
as well as the inter-buoy comparison analysis in Section 2. This is followed
by a description of the numerical models used in this study in Section 3. In
Section 4, we carry out the model-observation comparison using the ARC MFC
wave-ice model. In section 5, we discuss the Section 4 results by exploring
how different sea ice forcing can affect wave-ice models. Conclusions follow
in Section 6.

##  2 Drifting wave buoy observation

###  2.1 Wave buoy sensor and platform description

During the 2021 NABOS campaign, we deployed the first prototype of Rabault et
al. (2022) wave-ice buoy (herein referred to as Zeni-v2021) alongside a SOFAR
Spotter (herein referred to as SPOT-1386). Both Zeni-v2021 and SPOT-1386 buoys
measure ocean surface motion, but using different technology.

Zeni-v2021 was recently introduced in Rabault et al. (2022). The OMB
electronic components for detecting ocean surface motion is a 6 degrees of
freedom accelerometer + gyroscope IMU, ST ISM330DHCX
(https://www.st.com/en/mems-and-sensors/ism330dhcx.html). 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.

Despite the name being a "buoy", the OMB is a sensor unit that is housed in a
waterproof enclosure (see Fig. A1 of Rabault et al. (2022) for example), i.e.,
it is not designed as a floating platform in water. Therefore, the primary
deployment method of OMBs is that the sensor unit be placed on an ice floe,
and the ice floe becomes the sensor’s floating platform (thereby the
terminology "wave-ice buoy"). At the time of the buoy preparation (July 2021),
however, the sea ice extent was following the 2012 record low sea ice
extent+††+although by August, the sea ice extent reduction plateaued,
resulting in a field observation conundrum that there were limited
opportunities for open water deployment. For a quick reference of the sea ice
extent, please visit https://ads.nipr.ac.jp/vishop/#/extent and plot 2012 and
2021 sea ice extents.. Accordingly, an alternative deployment method was
devised by housing the sensor in a floating platform. The ad hoc platform was
a Zenilite GPS tracker enclosure (https://www.zenilite.co.jp/english/prod/new-
chikuden.html), which was conveniently designed to house the OMB electronic
components (see Appendix B of Rabault et al. (2022)). The Zenilite GPS
drifting buoy has a diameter of 340 mm, and is 300 mm in height and weighs ~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 width by 310 mm in
height and weighs 5.3 kg (7.4 kg with a ballast); therefore, SPOT-1386 is an
appropriate benchmark for Zeni-v2021. Spotters are based on a proprietary
firmware that uses a GPS/GNSS receiver to get the device horizontal and
vertical displacements.

###  2.2 Buoy deployment

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 around UTC 05:05 15
September 2021. The deployed location is shown in Fig. 1, and the sea ice
conditions as observed onboard R/V Akademik Tryoshnikov on the day of the buoy
deployment are shown in Fig. 2. SPOT-1386 battery life at high latitudes
without 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 Inset A of Fig. 1, 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
measure analogous wave signal for at least several days. For example, Waseda
et al. (2018); 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 ~13 days when they
measured analogous wave statistics. For our observation, however, Zeni-v2021
and SPOT-1386 wave heights began deviating slightly merely 12 hours after the
buoys were deployed. After 2 days of being deployed, wave heights and periods
varied considerably, which indicates that the measured waves’ evolution did
not occur entirely over open ocean, i.e., sea ice affected how the waves
evolved.

###  2.3 Co-located wave buoy measurements in thin ice field

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 $H_{m0}=4\sqrt{m_{0}}$ where
$m_{0}=\int_{f0}^{f1}S(f)df$ and wave periods (peak period $T_{p}$, which is
the inverse frequency of peak $S(f)$, and $-1$ moment period, also known as
energy mean wave period, $T_{0m1}=\frac{\int_{f0}^{f1}f^{-1}S(f)df}{m_{0}}$).
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 while the
buoy was drifting in open water until around 25 September; the elevated noise
floor is analogous to the Waseda et al. (2017, 2018); Nose et al. (2018)
observation and seems to accompany IMU-based wave sensors housed in a
relatively small floating platform. The same ideal filter method as Waseda et
al. (2017, 2018); Nose et al. (2018) was implemented to derive the wave
statistics. As such, $f0$ was not a constant and depended on the ideal-filter
cut-off frequency. The Zeni-v2021 integration range ($f0$,$f1$) were 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 the Inset A of Fig. 1
seemingly stopped (indicated by the white crosses in Figs. 1 and 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 affects the wave evolution over the effective
fetch.

Although we discuss the possibility that the effective fetch at the buoys’
location after 12 hours of deployment was already affected by the sea ice
lateral boundary in Section 4.1, we aim to consolidate the general inter-buoy
agreement when the buoys were in close proximity. Scatter for $H_{m0}$ and
$T_{0m1}$ are 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, i.e., the effect of
the sea ice field on wave evolution is less for shorter distances. Indeed, the
blue markers, indicating the data when the 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 Rabault et al.
(2022)’s Fig. 7, the spectra agreed well immediately after the buoys were
deployed.

While precise Zeni-v2021 validation with SPOT-1386 were 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, the wave events
observed by the co-located buoy measurements were used to evaluate the
operational ARC MFC wave-ice model predictability in Section 4.

##  3 Numerical models

###  3.1 ARC MFC wave-ice model

The wave-ice interaction parameterisation: The ARC MFC wave-ice model is an
operational wave model product for the Arctic Ocean and includes a wave-ice
interaction parameterisation, i.e., 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 Sutherland et al. (2019); they
modelled wave dissipation with a 2-layer sea ice model: the top layer is
modelled like a thin film that has no horizontal motion with thickness
(1-$\epsilon)h_{i}$ while the bottom layer is modelled as a moving viscous
layer. Here, $h_{i}$ is the ice thickness. Sutherland et al. (2019) describe
that the $\epsilon$ 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 Sutherland et al. (2019) model could be
considered an extension of the Weber (1987) model. In the Weber (1987) model,
the dissipation rate is $\alpha\propto K_{35}f^{3.5}$ where $K_{35}$ is a
constant. The Sutherland et al. (2019) model also has a frequency dependence,
but they also included an ice thickness dependence to the dissipation rate
like $\alpha\propto K_{40}f^{4}$ where $K_{40}$ is a function of ice
thickness. A more thorough discussion on the various dissipation rates in the
literature is provided in Waseda et al. (2022).

The Sutherland et al. (2019) model was developed based on a scaling argument
as they derived that the viscosity scales with SIT, $\nu\propto h_{i}$, which
led to spatial wave dissipation as a function of ice thickness and frequency:
$\alpha\propto h_{i}f^{4}$. The dissipation rate is parameterised in Eq. 16 of
Sutherland et al. (2019) as

$\alpha=\frac{1}{2}\Delta_{0}\epsilon h_{i}k^{2}$ (1)

where $\Delta_{0}\approx 1$. In the CMEMS Quality Information
Document+,††+https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-ARC-
QUID-002-014.pdf accessed 30 Nov 2022. the dissipation rate is denoted
$\alpha=C_{d}h_{i}k^{2}$ where they state that $C_{d}$ is a tuning parameter
and determined by the best fit to observation obtained from the ice covered
fjord, Tempelfjorden, at Svalbard in 2018. Note that when $\epsilon=0$ (or
$C_{d}$), the model may behave like the Weber model (Weber, 1987) if the
boundary layer in the fluid is implemented (not done so in Sutherland et al.
(2019) yet). Lastly, the dissipation rate $\alpha$ is used to estimate the
dissipated wave spectrum like

$S(f)=S_{0}(f)e^{-\alpha x}$ (2)

where $S_{0}$ 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
discretised 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
lon/lat grid at 0.1 deg. 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*††*CMEMS product name: ARCTIC_ANALYSIS_FORECAST_PHYS_002_001_A. The
sea ice model is the CICE and based on the viscous–plastic sea ice rheology.
The sea ice model uses a 1-thickness category sea ice model based on the
thermodynamics described in Drange and Simonsen (1996) (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 is evaluated with the buoy
observations in Section 5.2.

The CICE sea ice model is coupled to the HYCOM. The atmospheric forcing is
obtained from the ECMWF HRES atmospheric forecast. The data assimilation is
performed weekly using the ensemble Kalman filter (Sakov et al., 2012) and for
the following: altimeter sea level, in situ temperature and salinity profiles,
the Operational Sea Surface Temperature and Ice Analysis sea surface
temperature, OSI-SAF sea ice concentration and drift observations, and
CryoSAT2 and Soil Moisture and Ocean Salinity ice thickness (in winter). The
HYCOM has a horizontal resolution of ~12 km, which is more than 3 times the
resolution of the ARC MFC wave-ice model.

###  3.2 ECMWF HRES wave forecast

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 (https://ads.nipr.ac.jp/). We took
a series of 0–24 hour forecasts to produce a time series during the
observation period. The ECMWF 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 lon/lat grid at 0.125 deg. The ECMWF wave model
is useful to evaluate the wave conditions in the open water near the ice edge
based on the following logic:

  1. 1.

When the wave evolution occurs entirely over the open water fetch, the ECMWF
wave and ARC MFC wave-ice models should agree.

  2. 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. 3.

In such cases, the ECMWF wave model that neglects sea ice may produce better
predictions.

###  3.3 neXtSIM sea ice model

The neXtSIM sea ice model+††+CMEMS product name:
ARCTIC_ANALYSISFORECAST_PHY_ICE_002_011. Data downloaded on 19 Jan 2022.
(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 3-category model that includes open water, newly formed ice, and
older ice as described in Rampal et al. (2019). Rampal et al. (2016) shows
their model calculates the ice formation in the newly formed ice category
based on the atmosphere and ocean forcing, whereas a prescribed growth rate is
adopted conventionally in classical models (Rampal et al., 2016). The
thickness range of this newly formed ice category is from 0.05 m to 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, i.e., the OSI-SAF SIC. The
model has a Lagrangian triangular mesh with an equivalent square grid
resolution of ~7 km, for which the data are distributed on the 3 km polar
stereographic projection grid.

##  4 The effects of sea ice on wave evolution as observed by the wave buoys
and models

###  4.1 Sea ice as lateral boundary effects on wave evolution

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 Figs. A2 and A3
of Appendix A.2. In this subsection, we focus on the wave heights between 15
and 19 September immediately after the buoys were deployed in open water (see
Fig. 5).

Following the deployment, Fig. 5 shows that the ECMWF $H_{m0}$ agrees well
with both buoys for up to ~12 hours as denoted by the magenta bars, whereas
the ARC MFC $H_{m0}$ is clearly underestimated. Shortly after, however, the
buoys’ $H_{m0}$ takes a steep decrease at around 14:00 15 September, as
indicated by the green arrows in Fig. 5, and the model-observation trend
reversed, i.e., the ECMWF $H_{m0}$ is overestimated and the ARC MFC $H_{m0}$
agree qualitatively with the observation. It is also noted that this change
coincides with the time when the Zeni-v2021 $H_{m0}$ began deviating slightly
from that of SPOT-1386 (blue dotted line in Fig. 3) as discussed in Section
2.3.

The ARC MFC wave fields immediately after the deployment at 06:00 15 September
are shown in Panel (a) of Fig. 6. The grey vectors are the mean wave
directions scaled by $T_{0m1}$ values. At this time, it can be seen that wave
directions were primarily parallel to the ice edge. Tracing upwind from the
buoys, the ice edge protrude 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, i.e.,
the protruding ice edge may not be an accurate representation of the sea ice
field. For reference, Panel (c) of Fig. A4 in Appendix A.3 shows the buoys are
not sheltered by any protruding ice edge features in the ECMWF sea ice
representation.

Panel (b) of Fig. 6 shows the ARC MFC wave fields at 00:00 16 September after
the models’ trend reversed, i.e., now the ARC MFC $H_{m0}$ has better
agreement than the ECMWF $H_{m0}$. The fetch orientation transitioned from
along the ice edge to off-ice wave conditions. The Panels (b) and (d) of Fig.
A4 in Appendix A.3 show that winds were also blowing from the ice cover. As
indicated by the purple bars in Fig. 6, the ECMWF $H_{m0}$ is clearly
overestimated and the ARC MFC $H_{m0}$ agrees with the observations with a
varying degree of predictability.

The observations here demonstrate the lateral boundary effect that sea ice
imposes on the wave fields. We conjecture that 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 models were
markedly different. This event is described in Appendix A.4 to present further
support to this conjecture.

###  4.2 Wave dissipation due to sea ice on 29 September

South to southeasterly 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. 3).
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. This is depicted in the wave field shown in Fig. 7.

During this event, the ECMWF 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 (see Fig. A2 of Appendix A.2). However, the $H_{m0}$ time series
panel in Fig. 3 depicts that waves were observed at Zeni-v2021 reaching a peak
$H_{m0}$ value over 1.25 m. SPOT-1386 located ~30 km southeast 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.

##  5 Sea ice model representation differences and their effects on wave
evolution

###  5.1 Comparison of ARC MFC and neXtSIM sea ice field representations

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 (shown in Panels (a) and (c)) are effectively limited
to the ARC MFC ocean analysis scale of ~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 sea ice thickness differences. The neXtSIM SIC fields
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, while 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 Section 3.1) whereas the neXtSIM sea ice model
carries out daily data assimilation via the nudging scheme with SIC being the
only control variable (see Section 3.3). The data here suggest that the
difference 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. Appendix A.1 describes the observation-
based ice chart that confirms the ice type near the ice edge and the wave
buoys was 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
$H_{m0}$, i.e., less dissipation because of low SICs and thinner thickness.

###  5.2 Disparate scale between wave dissipation parameterisation and the sea
ice thickness forcing

The SIT disparity between the two models at the regional scale is also shown
in Fig. A6 of Appendix A.5, which indicate the ARC MFC SIT representation up
to 0.5 m is poor. Sea ice thickness is one of the most fundamental sea ice
variables, yet it remains difficult to measure as reliable methods are via ice
core sampling, Electromagnetic–induction instruments, and select satellite
observations (Tateyama et al., 2006; Tilling et al., 2018). In other words,
regional/synoptic scale estimation of a SIT field is typically not readily
available. For wave-ice models, an implication is that ice thickness can often
serve as a wave dissipation tuning parameter. For ocean-ice coupled models,
the essential feedback of sea ice to the ocean is thermodynamics, which is
rather insensitive to thin ice. As such, one of the tuning parameters may be
the minimum thickness parameter; indeed, the ARC MFC thermodynamic model is
based on Drange and Simonsen (1996), which has the minimum thickness of newly
formed ice as 0.5 m.

Another possibility for the poor thin ice representation is the data
assimilation method. The AFC MFC ocean analysis is based on the ensemble
Kalman filter scheme (Sakov et al., 2012) and does not assimilate sea ice
thickness in the summer months. As shown in the previous section, the ice
field beyond the 0.80 SIC contour is practically SIT > 0.3 m in Fig. 8; it is
plausible that ARC MFC ocean analysis data assimilation may assume correlation
between the observed SIC and unobserved SIT, which could be the cause of the
poor thin ice representation.

From the wave-ice interaction viewpoint, however, pancake ice thickness is
typically 10 cm, and new and young ice thickness is less than 30 cm
(http://old.aari.ru/resources/nomen/volume1.php?lang1=0&lang2=1&arrange=0&self=0).
The ARC MFC wave-ice interaction parameterisation is based on the Sutherland
et al. (2019) two layer model, which parameterised the wave dissipation rate
to scale with the sea ice thickness. Accordingly, the poor representation of
MIZ thin ice thickness in the sea ice forcing is a critical issue. Based on
Fig. 8, and Fig. A6 of Appendix A.3, it appears that thin thickness
distribution that is appropriate for the Sutherland et al. (2019) wave
dissipation model is not resolved in the ARC MFC ocean analysis.

According to Sutherland et al. (2019) Eq 16, $\epsilon=1$ determines the
maximum dissipation in the moving viscous ice layer like
$\alpha=\frac{1}{2}h_{i}k^{2}$. The maximum wave dissipation rates along the
approximate wave propagation were plotted in Fig. 9 for the wave period of 7 s
to quantify the effects of SIT differences between the ARC MFC and neXtSIM
models. The SIT was extracted for 200 km along the approximate wave
propagation ray from 121∘E, 82.2∘N on an initial bearing of 150 degrees. For
relevance, $T_{p}=$7 s was roughly the upper limit of the co-located buoy
observation when wave energy was detected (see Fig. 3). For SIT between the
transect distance 25–75 km, Fig. 9 shows that the ARC MFC wave dissipation
rate can exceed 3 times than that of the neXtSIM counterpart. This figure
confirms that the ARC MFC ocean analysis ice thickness is not adequately
resolving the thin ice to apply the dissipation model of Sutherland et al.
(2019); this prohibited a meaningful model-observation comparison to evaluate
the Sutherland et al. (2019) model with our wave buoy observation, e.g., can
their SIT dependent dissipation rate reproduce waves in thin ice-covered MIZs.
For completeness, we conducted an academic experiment to show how
$\frac{dH_{m0}}{dx}$ differ due to poor thin SIT resolution using a Pierson
Moskowitz spectrum with a 7.5 s $T_{p}$ that has a 2.2 m $H_{m0}$. The
dissipated $H_{m0}$ was calculated from the spectrum $S$ using Eq. 2. Assuming
a maximum dissipation rate over a 10 km distance with thickness 0.1 m and 0.5
m, we estimate $H_{m0}=0.1$ and $0.6$ m, respectively. The difference of
$\frac{dH_{m0}}{dx}$ for the 0.5 m thickness results in 2.6 times the
dissipation than the 0.1 m thickness case. However, it is difficult to know
how this is reflected in the ARC MFC wave-ice model as the true SIC field, the
sea ice edge, and the incoming spectra shape are all unknown.

Based on the discussion here, it is clear the ARC MFC wave-ice model during
our buoy observation overestimated the wave dissipation in the thin ice fields
with SIT less than 0.5 m. The ARC MFC wave-ice model in MIZs near the ice edge
needs sea ice thickness forcing that can resolve the thin ice types. It is
worthy to mention that the neXtSIM sea ice model has been experimentally
coupled with the wave model of Boutin et al. (2021), however, with a different
viewpoint: their focus was the effect of waves on ice fragmentation utilising
the brittle rheology of neXtSIM.

##  6 Conclusions

Two drifting wave buoys were deployed in the central Arctic Ocean, north of
the Laptev Sea, where there have not been any wave observations available. The
motivation for the buoy deployments was to validate Zeni-v2021, a prototype of
an experimental wave-ice buoy named OMB (Rabault et al., 2022), with
SPOT-1386, a commercial wave buoy. As such, the buoys were deployed at the
same location in the open water adjacent to an ice edge at a time ocean
surface freezes and new ice forms. We quickly learnt that as the buoy
positions deviated, so did their wave heights, which prevented a full
validation of Zeni-v2021. However, the inter-buoy comparison showed that when
the buoy distances between Zeni-v2021 and SPOT-1386 were close, defined here
with the arbitrary threshold of 5 km, Zeni-v2021 was sufficiently accurate
compared to the commercial SPOT-1386 buoy. As such, the buoy data were used to
study the predictability of waves in the deployment region.

The first event we focused was shortly after the deployment when a sudden
decrease in the buoys’ significant wave heights $H_{m0}$ from ~1.75 m to ~1.50
m was observed. The decrease coincided with the change in wind directions from
along the ice edge to off-ice wind. We compared the observation with an
operational ARC MFC wave-ice model product and found that the model
underestimated $H_{m0}$ before the sudden decrease, but agreed better
afterwards. Tracing upwind of the fetch, we found that the ice tongue
constrained the wave growth over the available fetch. We conjecture the ice
tongue location was inaccurate because the buoy observation agrees well with
the ECMWF HRES wave forecast before the sudden decrease, and there is no ice
tongue upwind of the fetch in the ECMWF sea ice forcing. This shows that the
representation of the ice edge is critically important for accurate
predictions of waves in the nearby open water.

The second case we analysed was when the wave buoys entered ice cover as new
ice formed in the area. An on-ice wave event generated waves that propagated
to the buoys when they were ~30 km apart. Zeni-v2021 was located downwind of
SPOT-1386, but was slightly closer to the ice edge relative to the wind
direction. During this event, Zeni-v2021 measured waves with a peak $H_{m0}$
of 1.25 m, but SPOT-1386 did not detect any waves. To investigate how the wave
energy propagated to Zeni-v2021 but not for SPOT-1386, we compared the buoy
observation with the ARC MFC wave-ice model. Because the ARC MFC model
simulates waves in ice with a wave dissipation model developed for thin ice
covered seas (Sutherland et al., 2019), we expected reasonable model
agreement; however, the ARC MFC wave-ice model $H_{m0}$ was largely
underestimated. With a viewpoint to elucidate the model error, we examined the
model sea ice conditions between the ARC MFC ocean analysis and the neXtSIM
sea ice model product. The analysis showed that the ARC MFC sea ice forcing
does not resolve thin thickness distribution for ice types like new and young
ice with typical thickness less than 30 cm. Since the ARC MFC wave-ice model’s
dissipation rate has a SIT dependence, the ARC MFC model overestimates wave
dissipation in the thin thickness ice field. On the other hand, we found that
another CMEMS sea ice product, neXtSIM, seemed to better resolve the thin
thickness distributions in the MIZ. One of the reason for the difference maybe
that the neXtSIM sea ice model calculates the new ice formation using the
atmosphere and ocean forcing (Rampal et al., 2019) rather than using the
conventional approach of adopting a prescribed growth rate with a minimum
thickness for new ice is configured as 0.5 m (Drange and Simonsen, 1996).
Another factor is the data assimilation; while the ARC MFC data assimilation
is sophisticated with many control variables, it is plausible that its data
assimilation may be assuming correlation between the observed SIC and
unobserved SIT (when SIT is not observed in the summer months) as the ice
covered areas above 0.80 SIC seems to have 0.5 m SIT or higher. Regardless of
the causes, the ARC MFC wave-ice model needs sea ice forcing that reproduces
thin ice thickness cover for better predictions of ocean waves in MIZs when
new ice is forming.

Reliable ocean wave forecasts are crucial for safe navigation in the polar
seas. Our study presented an observational insight into the wave and ice model
coupling for better predictions of waves in MIZ thin ice cover. Observations
and models help us ensure sustainable developments, such as safe navigation,
of the changing Arctic Ocean.

## Acknowledgements

We sincerely thank 2021 NABOS chief scientist Dr Igor Polyakov for supporting
our wave buoy deployment.
We are grateful to Dr Guillaume Boutin and the anonymous reviewer for
providing constructive criticisms during the peer review. Their invaluable
comments led to a much improved manuscript.
The authors are grateful to CMEMS for providing a data distribution platform.
We are also sincerely thankful to the model developers of the ARC MFC wave-ice
model and the neXtSIM sea ice model.

## Funding

Drs N. Kanna and K. Tateyama were supported by the ArCS II Japan-Russia-Canada
International Exchange Program to participate in the 2021 NABOS expedition.
This work was a part of the Arctic Challenge for Sustainability II (ArCS II)
Project (Program Grant Number JPMXD1420318865). A part of this study was also
conducted under JSPS KAKENHI Grant Numbers JP 19H00801, 19H05512, 21K14357,
and 22H00241.

##  7 Figures

Figure 1: A location map of the Arctic Ocean where the co-located wave buoys
were deployed on 15/09/2021. The dashed and solid lines indicate the 0.15 and
0.80 AMSR2 SIC contours on the same day. Inset A shows the Zeni-v2021 (pink)
and SPOT-1386 (green) trajectories between 15 and 29 September, in which the
white circle indicate the deployment location. The white crosses show
approximate location when the visible inertial oscillation stops on
25/09/2021, which could indicate the change in ocean surface conditions. The
0.15 and 0.80 AMSR2 SIC contours for 25/09/2021 are overlaid in Inset A.
Figure 2: Sea ice conditions encountered by R/V Akademik Tryoshnikov on
15/09/2021 after the buoys were deployed. The left image is showing the grey
ice while the right image is showing the grey-white ice; both ice types belong
to the young ice category. Figure 3: An overview of the co-located wave buoy
measurements. Panel (a) is a time series of buoy distances. In Panel (b), the
top panel shows the ECMWF HRES atmosphere forecast wind vector extracted at
the Zeni-v2021 location. The middle panels show the buoy significant wave
height $H_{m0}$ (upper) and energy mean and peak wave periods $T_{0m1}$,
$T_{p}$ (lower). The bottom panel shows the AMSR2 SIC extracted at the buoy
locations. The blue dotted lines indicate when the buoys’ $H_{m0}$ began to
deviate slightly (discussed in Sections 2.3 and 4.1). The white crosses in
this figure corresponds to the approximate times when the inertial
oscillations seemingly stopped as shown in Fig. 1.  Figure 4: Scatter plots of
Zeni-v2021 and SPOT-1386 from 15 to 25 September. The latter date was chosen
to avoid comparing wave periods that were affected by the buoy noise floor
(see the wave periods shown in Fig. 3). Panel (a) shows the $H_{m0}$ (m) and
Panel (b) shows the $T_{m01}$ (s). The marker colours were grouped using an
arbitrary buoy distance threshold where blue and red are less and greater than
5 km apart, respectively. The black dotted lines are the agreement line, and
blue markers tend to cluster to these lines.  Figure 5: Significant wave
height $H_{m0}$ time series comparing the buoy observation (blue) and the
models between 15 and 19 September 2021 when the buoy distances were generally
less than 5 km after the deployment. Both the ARC MFC wave-ice model (red) and
the ECMWF HRES wave forecast (grey) are shown. The missing values in the ECMWF
HRES wave forecast is due to ice masks (grid cells with SIC > 0.30). The top
panel compares the Zeni-v2021 data while the bottom panel compares SPOT-1386.
The magenta bars and text indicate when the buoy observation agreed with the
ECMWF HRES wave forecast. The green arrows show when a sudden reduction in the
wave heights were observed. The purple bars and text indicate when the buoy
observation agreed qualitatively with the ARC MFC wave-ice model. Figure 6:
ARC MFC wave fields showing how the fetch orientation changed from along the
ice edge immediately after the deployment at 06:00 15/09/2021 as shown in
Panel (a) to off-ice by 00:00 16/09/2021 as shown in Panel (b). Both figures
show the $H_{m0}$ via colour while the grey vectors correspond to mean wave
directions with the vector lengths scaled by $T_{0m1}$. Both panels show the
Zeni-v2021 (pink) and SPOT-1386 (green) trajectories and positions, and are
overlaid with the 0.15 (dotted), 0.30 (dashed), and 0.80 (solid) SIC contour
lines. Figure 7: ARC MFC ice and wave fields during the wave event on
29/09/2021 when Zeni-v2021 measured $\sim$1.3 m $H_{m0}$, but the model showed
no waves. Panel (a) indicates the wave conditions in which the colours
indicate $H_{m0}$ while the grey vectors correspond to mean wave directions
with the vector lengths scaled by $T_{0m1}$. Panel (b) is a zoomed view of
Panel (a) near the buoys. Both figures show the Zeni-v2021 (pink) and
SPOT-1386 (green) trajectories and positions, and are overlaid with the 0.15
(dotted), 0.30 (dashed), and 0.80 (solid) SIC contour lines. Figure 8:
Comparison of ice conditions on 29/09/2021 between the ARC MFC (left figures
in Panels (a) and (c)) and neXtSIM models (right figures in Panels (b) and
(d)). The top figures (Panels (a) and (b)) show the SIC and the bottom figures
(Panels (c) and (d)) show the SIT. All figures show the Zeni-v2021 (pink) and
SPOT-1386 (green) trajectories and positions, and are overlaid with the
respective 0.15 (dotted), 0.30 (dashed), and 0.80 (solid) SIC contour lines.
Figure 9: Comparison of Sutherland et al. (2019) wave dissipation rate
$\alpha=\frac{1}{2}\epsilon h_{i}k^{2}$ where $\epsilon=1$ based on the ARC
MFC (red) and neXtSIM (blue) model sea ice thickness $h_{i}$. $\alpha$ is
plotted along a 200 km transect from 121∘E, 82.2∘N at an initial bearing of
150 degrees for waves with 7 s periods. The right axis is the sea ice
thickness.

##  References

  * Boutin et al. (2021) G. Boutin, T. Williams, P. Rampal, E. Olason, and C. Lique.  Wave–sea-ice interactions in a brittle rheological framework.  _The Cryosphere_ , 15(1):431–457, 2021.  https://doi.org/10.5194/tc-15-431-2021.
  * Drange and Simonsen (1996) H. Drange and K. Simonsen.  Formulation of air-sea fluxes in the esop2 version of micom, tech. rep. 125,.  Technical report, Nansen Environmental and Remote Sensing Center, Bergen, Norway, 1996.
  * Hori et al. (2012) M. Hori, H. Yabuki, T. Sugimura, and T. Terui.  AMSR2 Level 3 product of daily polar brightness temperatures and product, 1.00, 2012.  URL https://ads.nipr.ac.jp/dataset/A20170123-003.  [Date accessed 23. Jul. 2019].
  * Linton (2010) C. M. Linton.  Towards a three-dimensional model of wave–ice interaction in the marginal ice zone.  _Journal of Fluid Mechanics_ , 662:1–4, 2010.  10.1017/S0022112010004258.
  * Nose et al. (2018) T. Nose, A. Webb, T. Waseda, J. Inoue, and K. Sato.  Predictability of storm wave heights in the ice-free beaufort sea.  _Ocean Dynamics_ , 68(10):1383–1402, July 2018\.  10.1007/s10236-018-1194-0.  URL https://doi.org/10.1007/s10236-018-1194-0.
  * Nose et al. (2020) T. Nose, T. Waseda, T. Kodaira, and J. Inoue.  Satellite-retrieved sea ice concentration uncertainty and its effect on modelling wave evolution in marginal ice zones.  _The Cryosphere_ , 14(6):2029–2052, June 2020\.  10.5194/tc-14-2029-2020.  URL https://doi.org/10.5194/tc-14-2029-2020.
  * Rabault et al. (2022) J. Rabault, T. Nose, G. Hope, M. Müller, Ø. Breivik, J. Voermans, L. R. Hole, P. Bohlinger, T. Waseda, T. Kodaira, T. Katsuno, M. Johnson, G. Sutherland, M. Johansson, K. H. Christensen, A. Garbo, A. Jensen, O. Gundersen, A. Marchenko, and A. Babanin.  OpenMetBuoy-v2021: An easy-to-build, affordable, customizable, open-source instrument for oceanographic measurements of drift and waves in sea ice and the open ocean.  _Geosciences_ , 12(3):110, Feb. 2022.  10.3390/geosciences12030110.  URL https://doi.org/10.3390/geosciences12030110.
  * Rampal et al. (2016) P. Rampal, S. Bouillon, E. Ólason, and M. Morlighem.  nextsim: a new lagrangian sea ice model.  _The Cryosphere_ , 10(3):1055–1073, 2016.  https://doi.org/10.5194/tc-10-1055-2016.
  * Rampal et al. (2019) P. Rampal, V. Dansereau, E. Olason, S. Bouillon, T. Williams, A. Korosov, and A. Samaké.  On the multi-fractal scaling properties of sea ice deformation.  _The Cryosphere_ , 13(9):2457–2474, 2019.  https://doi.org/10.5194/tc-13-2457-2019.
  * Sakov et al. (2012) P. Sakov, F. Counillon, L. Bertino, K. A. Lisæter, P. R. Oke, and A. Korablev.  Topaz4: an ocean-sea ice data assimilation system for the north atlantic and arctic.  _Ocean Science_ , 8(4):633–656, 2012.  10.5194/os-8-633-2012.  URL https://os.copernicus.org/articles/8/633/2012/.
  * Squire (2018) V. A. Squire.  A fresh look at how ocean waves and sea ice interact.  _Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences_ , 376(2129):20170342, 2018.  10.1098/rsta.2017.0342.
  * Squire (2020) V. A. Squire.  Ocean wave interactions with sea ice: A reappraisal.  _Annual Review of Fluid Mechanics_ , 52(1):37–60, 2020.  10.1146/annurev-fluid-010719-060301.
  * Sutherland et al. (2019) G. Sutherland, J. Rabault, K. H. Christensen, and A. Jensen.  A two layer model for wave dissipation in sea ice.  _Applied Ocean Research_ , 88:111–118, July 2019.  10.1016/j.apor.2019.03.023.  URL https://doi.org/10.1016/j.apor.2019.03.023.
  * Tateyama et al. (2006) K. Tateyama, K. Shirasawa, S. Uto, T. Kawamura, T. Toyota, and H. Enomoto.  Standardization of electromagnetic–induction measurements of sea-ice thickness in polar and subpolar seas.  _Annals of Glaciology_ , 44:240–246, 2006.  10.3189/172756406781811484.
  * The WAMDI Group (1988) The WAMDI Group.  The WAM Model – a third generation ocean wave prediction model.  _Journal of Physical Oceanography_ , 18(12):1775–1810, 1988.  https://doi.org/10.1175/1520-0485(1988)018%3C1775:TWMTGO%3E2.0.CO;2.
  * Thomson et al. (2018) J. Thomson, S. Ackley, F. Girard-Ardhuin, F. Ardhuin, A. Babanin, G. Boutin, J. Brozena, S. Cheng, C. Collins, M. Doble, C. Fairall, P. Guest, C. Gebhardt, J. Gemmrich, H. C. Graber, B. Holt, S. Lehner, B. Lund, M. H. Meylan, T. Maksym, F. Montiel, W. Perrie, O. Persson, L. Rainville, W. Erick Rogers, H. Shen, H. Shen, V. Squire, S. Stammerjohn, J. Stopa, M. M. Smith, P. Sutherland, and P. Wadhams.  Overview of the arctic sea state and boundary layer physics program.  _Journal of Geophysical Research: Oceans_ , 123(12):8674–8687, 2018.  https://doi.org/10.1002/2018JC013766.
  * Tilling et al. (2018) R. L. Tilling, A. Ridout, and A. Shepherd.  Estimating arctic sea ice thickness and volume using cryosat-2 radar altimeter data.  _Advances in Space Research_ , 62(6):1203–1225, 2018.  ISSN 0273-1177.  https://doi.org/10.1016/j.asr.2017.10.051.  The CryoSat Satellite Altimetry Mission: Eight Years of Scientific Exploitation.
  * Wadhams (1975) P. Wadhams.  Airborne laser profiling of swell in an open ice field.  _Journal of Geophysical Research (1896-1977)_ , 80(33):4520–4528, 1975.  https://doi.org/10.1029/JC080i033p04520.
  * Waseda et al. (2017) T. Waseda, A. Webb, K. Sato, and J. Inoue.  Arctic wave observation by drifting type wave buoys in 2016.  In _The 27th International Ocean and Polar Engineering Conference_ , San Francisco, California, USA, 2017. International Society of Offshore and Polar Engineers.
  * Waseda et al. (2018) T. Waseda, A. Webb, K. Sato, J. Inoue, A. Kohout, B. Penrose, and S. Penrose.  Correlated increase of high ocean waves and winds in the ice-free waters of the arctic ocean.  _Scientific Reports_ , 8(1), Mar. 2018.  10.1038/s41598-018-22500-9.  URL https://doi.org/10.1038/s41598-018-22500-9.
  * Waseda et al. (2022) T. Waseda, A. Alberello, T. Nose, T. Toyota, T. Kodaira, and Y. Fujiwara.  Observation of anomalous spectral downshifting of waves in the okhotsk sea marginal ice zone.  _Phil. Trans. R. Soc. A_ , 2022.  10.1098/rsta.2021.0256.  in production.
  * Weber (1987) J. E. Weber.  Wave attenuation and wave drift in the marginal ice zone.  _Journal of Physical Oceanography_ , 17(12):2351–2361, Dec. 1987.  10.1175/1520-0485(1987)017<2351:waawdi>2.0.co;2.  URL https://doi.org/10.1175/1520-0485(1987)017<2351:waawdi>2.0.co;2.
  * Williams et al. (2021) T. Williams, A. Korosov, P. Rampal, and E. Ólason.  Presentation and evaluation of the arctic sea ice forecasting system neXtSIM-f.  _The Cryosphere_ , 15(7):3207–3227, July 2021\.  https://doi.org/10.5194/tc-15-3207-2021.
  * Ólason et al. (2022) E. Ólason, G. Boutin, A. Korosov, P. Rampal, T. Williams, M. Kimmritz, V. Dansereau, and A. Samaké.  A new brittle rheology and numerical framework for large-scale sea-ice models.  _Journal of Advances in Modeling Earth Systems_ , 14(8):e2021MS002685, 2022.  https://doi.org/10.1029/2021MS002685.  URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021MS002685.

##  Appendix Appendix A Appendix

###  Appendix A.1 Ice type near the ice edge

Arctic and Antarctic Research Institute (AARI) ice charts during the 2021
NABOS expedition were available on
http://wdc.aari.ru/datasets/d0040/arctic/png/2021/. The regional ice charts
are updated monthly and available on https://aari.ru/data/realtime (although
only available in the Russian language). The pan-Arctic and regional ice
charts were obtained to estimate the ice type near the buoys during the 29
September event, and these are shown in Fig. A1. The buoys were located around
$\sim$82∘ N, $\sim$122∘ E during the event, and it appears to show that the
ice type near the ice edge is the young ice type. Note that the pan-Arctic ice
chart was obtained from
http://wdc.aari.ru/datasets/d0040/arctic/png/2021/blended_arcice_20210930-20211005_sd_90E.png
and the regional ice chart from
http://old.aari.ru/odata/_d0004.php?mod=0&m=Lap (by selecting year 2021 and
month/day 2021.10.05 on the right side boxes).

Figure A1: AARI ice charts for the stage of development for the pan-Arctic
(left panel) and regional (right panel) waters around the 29 September event
are shown. The buoys were located around $\sim$82∘ N, $\sim$122∘ E during the
29 September event, and it shows that the ice type near the ice edge was young
ice.

###  Appendix A.2 Time series comparison of observed and modelled waves

Significant wave height $H_{m0}$ and wave periods $T_{p}$ and $T_{0m1}$ time
series were extracted from the ARC MFC wave-ice model and the ECMWF HRES wave
forecast at the Zeni-v2021 and SPOT-1386 positions during their co-located
deployment between 15 and 29 September 2021. The time series are plotted in
Figs. A2 and A3, respectively, and supports the Section 4 text. The ECMWF HRES
wave forecast adopts ice masks, which treat grid cells with SIC > 0.30 as
land. From the five $H_{m0}$ peaks captured, as shown in Fig. A2, the models
were not able to reproduce reasonable values at both buoys simultaneously, and
they could only reproduce $H_{m0}$ to a varying degree of accuracy only at one
of the buoys.

Figure A2: Significant wave height $H_{m0}$ time series comparing the buoy
observation (blue) and the models during the co-located measurements between
15 and 29 September 2021. Both the ARC MFC wave-ice model (red) and the ECMWF
HRES wave forecast (grey) are shown. The missing values in the ECMWF HRES wave
forecast is due to ice masks (grid cells with SIC > 0.30). The top panel
compares the Zeni-v2021 data while the bottom panel compares SPOT-1386. Figure
A3: Figure A2 equivalent for wave periods comparing the buoy observation
(blue) with the models. $T_{p}$ is shown as markers and $T_{0m1}$ shown as
lines. Both the ARC MFC wave-ice model (red) and the ECMWF HRES wave forecast
(grey) are shown. The missing values in the ECMWF HRES wave forecast is due to
ice masks (for grid cells with SIC > 0.30). The top panel compares the
Zeni-v2021 data while the bottom panel compares SPOT-1386.

###  Appendix A.3 Lateral boundary effects of sea ice

The wind and sea ice fields for the 15–19 September event are shown in Fig. A4
to support the Section 4.1 text. Comparing the left and right panels, it can
be seen that the fetch orientation changed from along the ice edge (left
panels) to off-ice (right panels). As discussed in Section 4.1, the ARC MFC
representation of the sea ice field has a protruding ice edge that sheltered
the wave buoys from wave evolution along the ice edge immediately after the
buoy deployments. By contract, the ECWMF ice edge representation is smooth,
and the wave evolution towards the buoy appears to not be sheltered by any ice
edge feature.

Figure A4: The figure shows how the fetch orientation changed from along the
ice edge immediately after the deployment at 06:00 15/09/2021 (Panel (a) and
(c)) to off-ice by 00:00 16/09/2021 (Panel (b) and (d)). Both figures show the
SIC via colour while the red vectors correspond to the ECMWF wind field. The
top panels show the ARC MFC sea ice conditions while the bottom panels show
the ECMWF sea ice conditions. All panels show the Zeni-v2021 (pink) and
SPOT-1386 (green) trajectories and positions, and are overlaid with the
respective 0.15 (dotted), 0.30 (dashed), and 0.80 (solid) SIC contour lines.

###  Appendix A.4 Lateral boundary conditions sheltered wave evolution at the
Zeni-v2021 possibly due to misrepresentation of an ice tongue

On 21 September, west to southwest winds generated on-ice waves, i.e., waves
propagating towards the ice edge, that peaked with a $H_{m0}$ value of almost
2 m at Zeni-v2021. At this time, SPOT-1386 was located closer to the ice edge
than Zeni-v2021, and its $H_{m0}$ only peaked at $\sim$1 m.

It can be seen in Fig. A2 that Zeni-v2021 $H_{m0}$ agrees reasonably with the
ECMWF HRES wave forecast whereas the ARC MFC wave-ice model somehow
underestimates the $H_{m0}$. A snapshot of wind, ice, and wave conditions for
the ECMWF and ARC MFC models are provided in Fig. A5. In the ARC MFC wave
field, the Zeni-v2021 position is seaward of the 0.1 SIC contour, so the
underestimation is not caused by anomalous attenuation due to ice. Rather, the
ECMWF and ARC MFC SIC fields as shown in the top panels in Fig. A5 depict the
location of the ice tongue are inconsistent. The ARC MFC SIC field shows the
ice tongue was located near the 110∘ E. Based on the wind and SIC fields, it
can be conjectured that the different representation of the ice tongue
affected the open water fetch; in this particular case, the ARC MFC ice tongue
location was likely inaccurate considering the ECMWF $H_{m0}$ agreement with
that of Zeni-v2021.

Figure A5: The figure shows the different representation of the ice tongue
between the ECMWF and ARC MFC models on 18:00 21/09/2021. The top panels
(Panels (a) and (b)) shows the wind (red vectors) and ice (colours) conditions
and the bottom panels (Panels (c) and (d)) shows the waves. The left panels
(Panels (a) and (c)) correspond to the ECMWF data while the right panels show
the ARC MFC data, although the wind data are the ECMWF HRES atmospheric
forecast for both top panels. All panels show the Zeni-v2021 (pink) and
SPOT-1386 (green) trajectories and positions, and are overlaid with the
respective 0.15 (dotted), 0.30 (dashed), and 0.80 (solid) SIC contour lines.
In the bottom wave figures, the colours correspond to $H_{m0}$ while the grey
vectors indicate the mean wave directions, for which vector lengths are scaled
by the corresponding $T_{0m1}$.

###  Appendix A.5 Disparate sea ice thickness distributions between ARC MFC
and neXtSIM sea ice fields

A comparison of ARC MFC and neXtSIM sea ice fields during the 29 September at
the regional scale is presented in Fig. A6 to support the text in Section 5.2.
It is apparent that ARC MFC sea ice thickness resolution below 0.5 m is
considerably poorer than that of neXtSIM. It is conjectured in the main text
that this may be due to the following. neXtSIM consist of a newly formed ice
category in which the ice formation is calculated from the atmosphere and
ocean forcing, whereas the ARC MFC model uses a 1-thickness category model in
which the minimum thickness of newly formed ice is set as 0.5 m (Drange and
Simonsen, 1996; Sakov et al., 2012). We also discuss another possible
contributing factor, which is the data assimilation method. The poor thin ice
distribution may be caused by the data assimilation method assuming
correlation between observed SIC and unobserved SIT in the ARC MFC ocean
analysis.

Figure A6: A comparison of sea ice thickness (colours) fields for the ARC MFC
wave-ice model sea ice forcing (Panel (a)) and the neXtSIM sea ice model
(Panel (b)) at a regional scale. The figure shows that there is a marked
difference in the thin ice thickness distributions between the two models. The
red vectors are the ECMWF model wind data. Both figures show the Zeni-v2021
(pink) and SPOT-1386 (green) trajectories and positions, and are overlaid with
the respective 0.15 (dotted), 0.30 (dashed), and 0.80 (solid) SIC contour
lines.