An Assessment of Sea Ice Motion Products in the Robeson Channel Using Daily Sentinel-1 Images

: Sea ice motion is an essential parameter when determining sea ice deformation, regional advection, and the outﬂow of ice from the Arctic Ocean. The Robeson Channel, which is located between Ellesmere Island and northwest Greenland, is a narrow but crucial channel for ice outﬂow. Only three Eulerian sea ice motion products derived from ocean/sea ice reanalysis are available: GLORYS12V1, PSY4V3, and TOPAZ4. In this study, we used Lagrangian ice motion in the Robeson Channel derived from Sentinel-1 images to assess GLORYS12V1, PSY4V3, and TOPAZ4. The inﬂuence of the presence of ice arches, and wind and tidal forcing on the accuracies of the reanalysis products was also investigated. The results show that the PSY4V3 product performs the best as it underestimates the motion the least, whereas TOPAZ4 grossly underestimates the motion. This is particularly true in regimes of free drift after the formation of the northern arch. In areas with slow ice motion or grounded ice ﬂoes, the GLORYS12V1 and TOPAZ4 products offer a better estimation. The spatial distribution of the deviation between the products and ice ﬂoe drift is also presented and shows a better agreement in the Robeson Channel compared to the packed ice regime north of the Robeson Channel.


Introduction
Sea ice motion, which is primarily driven by wind and oceanic forcing, is an essential parameter for characterizing ice advection and deformation [1,2]. The outflow of sea ice from the Arctic Ocean to the North Atlantic Ocean plays a crucial role for both the annual variation of the Arctic sea ice mass [3,4] and the formation of deep water in the North Atlantic Ocean [5]. The Arctic sea ice motion products are also important for initializing and/or verifying sea ice-ocean coupling model simulations [6].
The Robeson Channel, which is located between Ellesmere Island and northwest Greenland, is a narrow but significant gate for sea ice and freshwater outflow from the Arctic Ocean ( Figure 1). This channel has contributed to the recent loss of multiyear sea ice since the majority of this type of ice in the Arctic is located north of the Robeson Channel [7,8]. The characteristics of the sea ice motion through the channel have strong intermittency and seasonal dependency [9], because of the interruption of the Arctic ice outflow during periods when an ice arch exists either at the entrance of the Robeson Channel or at the southern location of Smith Sound (the locations are shown in Figure 1). From September 2016 to August 2017, the ice influx in the Robeson Channel was blocked by the northern arch for~110 days, while the southern arch failed to form; therefore, the ice floe is free to drift in the channel in the rest of the year. However, the phenomenon that the southern and northern arches exist simultaneously almost never happens. Essentially, the ice motion can become blocked in the channel after the development of the ice arch at Smith Sound, or accelerated after the formation of the northern arch at the entrance of the channel [10]. In addition, a few other factors affect the ice motion in the Robeson Channel. Northerly wind prevails in this region, which is conducive to the outflow of sea ice [7]. The relatively large tidal range in this area, compared with other regions in the Arctic Ocean, is another potential factor causing sea ice breakup and the enhanced oscillation of the ice motion [11]. Furthermore, the outflow of sea ice through the Nares Strait plays a crucial role in a wide range of perspectives, e.g., in the formation and cessation of the North Water Polynya in the northern Baffin Bay [12], as well as the physical and biological processes in the southern Nares Strait [13,14]. A variety of sea ice motion products are available from different sources with various spatial and temporal resolutions. These products are generally estimated from a combination of numerical simulations and observations, including buoy data and satellite observations when using data assimilation techniques (e.g., reanalysis products), or directly estimated from satellite observations, which is the case for the Ocean and Sea Ice Satellite Application Facility (OSI SAF) product and the French Research Institute for Exploitation of the Sea (IFREMER)/CERSAT product. However, only three ocean-sea ice reanalysis products are available to characterize the sea ice motion in the Robeson Channel, because of its narrow width (~30-40 km): (1) GLORYS12V1, which was derived from the Copernicus Marine Environment Monitoring Service (CMEMS) global ocean eddy-resolving reanalysis, providing sea ice motion data with a spatial resolution of 1/12 • for the period of 1993-2019 [15]; (2) PSY4V3R1 (referred to as PSY4V3 here), which was derived from a global ocean analysis and prediction system implemented by CMEMS, with a horizontal resolution of 2 km near the poles for the period of 2016-2021 [16]; and (3) TOPAZ4, which was released by the Arctic-Monitoring Forecasting Centre (ARC MFC), led by the Nansen Environmental and Remote Sensing Center (NERSC), providing sea ice velocities with a spatial resolution of 35 km for the period of 1991-2019 [17]. However, uncertainties in the forcing and initial conditions of the numerical models, incomplete physical parameterization schemes, the limitation in model resolution, and uncertainties in observation data can all induce errors in the reanalysis products [18]. Therefore, these products should be assessed against observations before being applied to ice motion related studies, such as the monitoring of ice advection and ice flux, as well as before being used as the initial fields for sea ice-ocean models.
An assessment of the Arctic sea ice motion products has been conducted in a few studies, but usually either at the large scale of the Arctic Basin or in certain crucial regions, such as the Fram Strait, which is the primary gate of ice outflow to southern latitudes. Hwang and Lavergne [19] assessed the OSI SAF low-and medium-resolution products and the IFREMER/CERSAT products using in situ measurements from ice-tethered profilers. They found that the OSI SAF (medium-resolution) products have relatively low statistical errors when compared with the IFREMER product. Rozman et al. [20] compared the sea ice motion products from IFREMER, OSI SAF, and the Advanced Synthetic Aperture Radar (ASAR) instrument with in situ measurements of ice drift from moored acoustic doppler current profilers in the Laptev Sea in the winter of 2007/08. The results indicated that IFREMER has a relatively high correlation with the measurements and a low standard deviation compared to the other two products. Sumata et al. [18] investigated four coarseresolution remotely sensed ice drift products in the Arctic Ocean, excluding narrow straits. Their results, which were derived from an intercomparison between the products and comparisons with buoy data, indicated that the differences between the products can be related to the differences in the ice conditions, including the sea ice concentration (SIC) and thickness. Ricker et al. [4] investigated the performance of sea ice motion products in the Fram Strait. Their results demonstrated clear uncertainties in the estimations of ice flux obtained using the sea ice motion products from OSI-405-c, IFREMER/CERSAT, and the National Snow and Ice Data Center (NSIDC). The accuracies of the sea ice motion products provided by NSIDC and OSI SAF have been validated using data recorded by ice drifters that were deployed in the western section of the Arctic Ocean [21]. This study concluded that the uncertainties in these products are relatively large during the ice melt season and in the marginal ice zone, compared to during the freezing season and in the pack ice zone.
However, the uncertainties of the sea ice motion products in the Robeson Channel (or any narrow channel for that matter) have not yet been assessed, partly due to a lack of direct observations of sea ice motion. Data measured by ice drifters are extremely scarce in the Robeson Channel compared with the Arctic Basin and the Fram Strait (e.g., Lei et al. [22]). To date, the intercomparison of the sea ice motion products has been a common approach, using the mean value of all the products located in the same grid [4,23,24]. However, this method is only feasible when the uncertainties of each product are well known. Moreover, remote sensing data have also been used to evaluate a few sea ice motion products [25]. Gui et al. [21] revealed that the accuracy of the sea ice motion products can be expected to be relatively low for regions close to the coast, because of shore constraints and the coarse resolution of the products. Therefore, an assessment of ice motion in narrow channels requires validation data acquired at fine spatial and temporal resolutions. Synthetic aperture radar (SAR) images can be suitable for this purpose, if daily (or more frequent) data are available. For example, Kwok et al. [26] tracked sea ice motion using the classic maximum cross-correlation (MCC) technique from sequences of SAR images acquired by the European Remote Sensing (ERS) satellites every 3 days in the Arctic Ocean and daily in the Fram Strait and Baffin Bay. The results were then used to assess the sea ice motion products derived from satellite passive microwave observations. Sumata et al. [25] assessed the errors in low-resolution sea ice motion products in the Arctic Ocean using the high-resolution sea ice motion product from the RADARSAT Geophysical Processor System (RGPS). In general, ice motion information obtained from SAR data is being increasingly used, and can be expected to have high potential for validating sea ice motion products.
The objective of this study is to assess the sea ice motion obtained from three reanalysis products in the Robeson Channel, using the drift of individual ice floes tracked from daily Sentinel-1 images covering two periods, from September 2016 to August 2017, and from January 2018 to March 2018. The influence of free versus constrained motion (i.e., linked to the presence/absence of an ice arch), regional dependence, wind speed, ice speed, as well as tidal forcing on the bias of the sea ice motion products was evaluated. The unique contribution of this study is the assessment of ice motion in a narrow channel exposed to interruption and release of ice flux due to the formation or absence of ice arches, using daily SAR data, which enabled manual Lagrangian tracking of individual ice floes. We believe that this approach of manual tracking of individual ice floes can offer the most accurate data to validate reanalysis-based or satellite-derived Eulerian sea ice motion products.

Study Area
The Robeson Channel, which is located between Ellesmere Island and northwest Greenland, is one of five main gates for Arctic sea ice and freshwater outflow, through which sea ice drifts southward from the Arctic Basin to Baffin Bay ( Figure 1). The Robson Channel is a relatively narrow (~30-40 km), short (~80 km), and deep channel (>400 m along its axis). Local sea ice drift in the Robeson Channel is primarily driven by wind and currents. In particular, the sea ice velocity is significantly affected by meridional wind [27].

Sea Ice Motion Products
In this study, three sea ice motion products(GLORYS12V1, PSY4V3, and TOPAZ4) were assessed. The basic information for each product is summarized in Table 1.

GLORYS12V1
The GLORYS12V1 product was generated from Version 3.1 of the Nucleus for European Modelling of the Ocean (NEMO) model, coupled with a prognostic thermodynamicdynamic sea ice model based on Version 2 of the Louvain-la-Neuve Ice model (LIM2). The assimilated observational data include altimeter data, sea surface temperature (SST) and SIC data from satellite observations, and Coriolis Ocean dataset for Reanalysis (CORA) 4.1 temperature and salinity (T/S) data from CMEMS [15]. The atmospheric forcing for the NEMO/LIM2 model was derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA-Interim). It has been shown that the previous version of this product (GLORYS2V4) can reproduce the seasonal cycles of Arctic sea ice extent and area well [28].
This product includes three datasets and provides daily and monthly mean data for temperature, salinity, sea level, mixed layer depth, and sea ice parameters, e.g., SIC, thickness, and velocity. The daily and monthly sea ice velocity data are available from 1993 to 2019, defined on a standard regular grid of 1/12 • (approximately 9 km (meridional) × 1.5 km (zonal) in our study region).

PSY4V3
The PSY4V3 product was derived from a global ocean analysis and prediction system that was implemented by CMEMS. This product was also produced by the use of a coupled ocean-sea ice model based on NEMO 3.1 and LIM2. The assimilated observational data include CORA 4.1 T/S data, Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) SST data, and OSI-450/430 SIC data. This product provides daily sea ice velocity from 2016 to 2021 on a standard regular grid, also with a resolution of 1/12 • . The effectiveness of PSY4V3 in reproducing the physical variables of Arctic sea ice, e.g., the Lagrangian drift trajectory of sea ice, was assessed in Bertosio et al. [29].

TOPAZ4
The TOPAZ4 product is a subsystem released by ARC MFC that is based on an advanced sequential data assimilation method [30]. This product was produced by the use of the global Hybrid Coordinate Ocean Model (HYCOM) coupled with an elastic-viscousplastic sea ice model. The TOPAZ4 reanalysis dataset includes both three-dimensional variables (such as current, temperature, and salinity) and two-dimensional variables (such as sea surface height, SIC, thickness, and velocity), and is ultimately interpolated onto standard grids and depths. The sea ice drift data used for the assimilation were provided by the IFREMER/CERSAT dataset for 2002-2010 [31], followed by the OSI SAF near real-time (NRT) product from 2011 onwards. Compared to buoy measurements from the basin region of the Arctic Ocean, the bias of the TOPAZ4 ice motion product shows seasonal dependence, i.e., generally overestimation in the winter months and underestimation in the summer months [32]. This dataset provides daily and monthly sea ice velocities from 1991 to 2019, with a spatial resolution of approximately 14 km (meridional) × 2.2 km (zonal) in our study region.

Sentinel-1 Data
Sentinel-1A and -1B are two near-polar sun-synchronous satellites developed as part of the satellite constellation of the European Space Agency's (ESA's) Copernicus program. The Sentinel-1A and -1B satellites were launched on 3 April 2014 and 25 April 2016, respectively. Both instruments operate at the C-band (central frequency of 5.405 GHz) with single or dual polarization. The two satellites have four operational modes: Stripmap, Interferometric Wide swath (IW), Extra-Wide swath (EW), and Wave. The EW mode products, which cover a 400 km swath at a median resolution of 20 m × 40 m, offer near-daily coverage of the Robeson Channel. In addition, the IW mode products, which cover a 250 km swath at a spatial resolution of 5 m × 20 m, have a revisit cycle of 6 days for the Robeson Channel. By combining the EW and IW modes, an approximately one-day repeat cycle can be obtained, which is suitable for monitoring the sea ice motion in the Robeson Channel. Therefore, in this study, the EW and IW mode products were chosen to track the ice floes in this region on a daily basis. Since thin ice cannot be identified in HV polarization [33], the Level-1 Ground Range Detected products of the EW and IW modes acquired in HH polarization were used in this study.
Consequently, 589 sequential Sentinel-1A and -1B images, from 1 September 2016 to 31 August 2017, and 156 sequential Sentinel-1A and -1B images, from 1 January 2018 to 21 March 2018, were used to extract the ice floe-based motion data. All images were calibrated to the backscatter coefficient in decibels and then georeferenced and resampled to 50 m × 50 m to reduce the speckle noise.

Wind Speed and Tide Level Data
The near-surface wind speed (10 m) data used in the assessment were obtained from ERA5 [34], which is the successor to ERA-Interim. The data were generated by combining simulated data and observations at a spatial resolution of 0.25 • × 0.25 • (4.3 km (meridional) × 27.8 km (zonal) for the study area). The higher accuracy of ERA5 for the wind speed has been proven via comparisons with other reanalysis data from the US National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR), the NCEP/Department of Energy (NCEP/DOE) reanalysis, and ERA-Interim in the region of the Robeson Channel [10].
Tidal forcing can regulate the magnitude of sea ice velocity by strengthening the semidiurnal oscillation and promoting the fragmentation of large floes, which, in turn, can be expected to affect the accuracy of sea ice motion products. In this study, the influence of year-round tidal forcing on the accuracy of the sea ice motion products was evaluated using data obtained from tidal gauge measurements, taken between 1 September 2016 and 31 August 2017, at the Wrangel Bay tide station ( Figure 1) in the Robeson Channel [35]. Qualitatively, the daily tidal range was used to assess the influence of tidal forcing on the accuracy of the sea ice motion products.

Estimation of Sea Ice Motion Using Sentinel-1A/-1B Images
As mentioned before, generating ice floe motion using the widely applied MCC technique is not applicable in narrow water passages. Accordingly, we estimated the velocity of individual ice floes during their lifetime within the Robeson Channel. This was performed by tracking selected ice floes in the daily Sentinel-1A/-1B images. A detailed procedure of ice floe tracking method is presented in [10].
In this study, two datasets of Sentinel-1A/-1B images were used to estimate the daily ice floe drift. The first dataset covered a period of one year from 1 September 2016 to 31 August 2017 with 589 Sentinel-1A/-1B images. In this dataset, 129 ice floes were tracked. A total of 1830 samples of ice floe locations were obtained from this dataset, from which the sea ice velocity vectors were estimated, with most being obtained in October and November of 2016 (Table 2). Since the northern ice arch formed on 25 January 2017, the ice floe stopped moving in the Robeson Channel until 11 May 2017. Therefore, the second dataset was used to study ice floe motion covering the period of January to March 2018. In this dataset, 156 Sentinel-1A/-1B images were used, 85 ice floes were tracked, and a total of 582 samples of ice floe locations were obtained. The southern ice arch existed between 28 February and 1 July 2018.

Grouping of the Ice Motion Data
For the purpose of assessing the reanalysis products of sea ice motion, the ice floe speed data obtained from the daily Sentinel-1 images were grouped into three groups: This resulted in the formation of a polynya-like ice field with fewer ice floes (mostly thin), leading to a nearly free drift regime. Under this condition, the impacts of the wind and oceanic forcing on the ice motion were enhanced, resulting in faster ice motion [10,36]. After the formation of the southern arch between 22 February and 1 July 2018, the ice slowed down in the channel until it eventually came to a stop.

Assessment of the Sea Ice Motion Products
The gridded ice motion from the three reanalysis products was generated for 12:00 UTC. To match this, we should emphasize again that the ice floe speed from Sentinel-1 was calculated at the same time, by assuming that the ice floe drift was linear between the two satellite revisit times. The calculated ice floe drift along the trajectory (magnitude and direction) was then compared to the product's drift at the nearest grid point. Since the time span of the two successive Sentinel-1 images used to calculate the ice floe motion was not a fixed value (~24 h), due to the deviation of the satellite revisit time, the orientation of the ice floe drift was not taken into account when evaluating the ice motion speed from the reanalysis products.
In this study, the correlation coefficient (R), mean absolute error (MAE), root-meansquare error (RMSE), and skewness were used to quantify the differences in the magnitudes between the ice drift from each of the examined sea ice motion products and that from Sentinel-1. In addition, histograms of the ice motion, kernel density estimation, and box plots were also provided. Two parameters (the bin width and the end points of the bins) need to be considered in the construction of a histogram. Kernel density estimation, as one of the most commonly used non-parametric estimation methods, can provide useful information about the features in a dataset without the uncertainty of the bin widths and end points [37]. A box plot, which is a way of characterizing a dataset based on an interval scale, can represent the shape of a distribution, and the maximum, minimum, and upper and lower quartiles in a dataset. Figure 2 presents the daily ice floe speed obtained using the sequential Sentinel-1 images, as well as the wind speed. Each red point represents the daily average ice drift from all the identifiable ice floes inside the Robeson Channel. Each green point represents the daily average wind speed from ERA5 for the four grid points closest to the ice floe. The blue areas in the figure mark the periods of presence of the northern or southern ice arch.  Figure 2 shows that the daily average ice floe speed fluctuates significantly within a short period (and even between successive days). However, it should be kept in mind that not all the ice floes in the channel on any given day were tracked and used to calculate the motion in the sequential daily Sentinel-1 images. This can partly explain the fluctuations. However, the main cause is likely the combined actions of the wind and current forcing, given their possible different directions, as well as the interaction between ice floes, which varies according to the variable SIC surrounding the ice floes. In addition, some ice floes used in the calculation may have been slowed down as a result of friction with the coastline or fast ice. Fluctuations of ice floe speed can still be observed during the periods of the northern and southern ice arches. Figure 2a shows the data from September 2016 to August 2017, covering the period of the northern arch, and Figure 2b shows the data from January to March 2018, covering the period of the southern arch. During the period of the northern ice arch (the blue area in Figure 2a), the SIC in the Robeson Channel can be expected to be low, with thin ice dominating. The average ice floe speed during this period was 30.77 km/d, which is slightly higher than the average speed of 26.98 km/d observed outside this period. This is a confirmation of the enhanced ice motion in ice cover with a lower SIC and ice floe thickness. During the period of the southern ice arch (the blue area in Figure 2b     In the open sea, ice typically drifts at a speed of approximately 2% of the wind speed and about 25 • to the right of the wind in the Northern Hemisphere [38]. However, the ice floe speed data from the present dataset shows that this ratio is significantly larger, as it fluctuates between 0 and 60%. In general, the wind has more of an effect on ice drift in narrow channels than in the open sea, particularly when the wind direction coincides with the constrained geographic orientation of the channel. The cohesion of the ice cover is also an important factor when studying the influence of the direction and magnitude of the wind on the movement of ice floes. The cohesion of the ice cover related to ice thickness and concentration; it is relatively low in this study since only individual floes with the relatively low surrounding sea ice concentration and abundant leads or open water were tracked. In addition, the sea ice movement would be affected by current stress, horizontal gradient (sloping sea surface) stress, Coriolis stress, and ice internal stress. In the strait regions, even if the sea ice concentration is low, the ice internal stress can be ignored, and the current stress still can play a strong role due to the gorge effect (e.g., [22,39]). In the study region, the role of the current, especially tidal current [11], cannot be ignored. Therefore, although the ice floes are mainly related to wind force, it can also be affected by other factors, especially current stress. During the time with relative weak wind forcing, the contribution of current stress would be enhanced. The air temperature would play trivial roles on the ice motion through regulating the consolidation of sea ice, and the water temperature is not a factor that affect motion because the water covered by the ice would have a small temperature variation.

Overall Assessment
For an overall assessment of the three sea ice motion products, the data were compared to the Sentinel-1 ice floe speed from the entire datasets for 2016/2017 and 2018. Figure 6 presents scatter plots of the ice floe drift versus the gridded ice motion from each reanalysis product. The frequency distributions of the ice speed derived from the three sea ice motion products, as well as Sentinel-1, are also shown.
The scatter plot obtained using the GLORYS12V1 data shows that this product underestimates the ice drift speed, and most of the speeds from this reanalysis product do not exceed 27 km/d. Uotila et al. [28] also indicated an underestimation of the freshwater exports through the Fram Strait, Barents Sea, Davis Strait, and Bering Strait using the GLORYS2V4 product. The R value from the GLORYS12V1 product is moderate (0.549), compared with the ice floe speed obtained using the Sentinel-1 images, but still significant at a statistical level of 0.01. The scatter plot and the distribution of the PSY4V3 product present the best agreement with the ice floe speed obtained using the Sentinel-1 images. Moreover, a relatively high correlation between the two datasets is shown, with an R value of 0.830 (p < 0.001). Conversely, the TOPAZ4 product performs poorly as it gives extremely low motion values (<5 km/d), with a very low R value of −0.132, and is insignificant at a statistical confidence level of 0.05. This product is a near-complete mismatch with the results derived from the Sentinel-1 imagers. According to Simonsen et al. [17], the TOPAZ4 product assimilates ice drift data from OSI-405-c. This dataset covers most of the central Arctic Ocean, but often has a data gap in the region of the Robeson Channel. The kernel density and the three parameters (MAE, RMSE, and Skewness) representing the deviation of the sea ice motion product from the ice floe drift are presented in Figure 7. Among the three products, PSY4V3 has the lowest MAE and RMSE when compared to the ice floe speed obtained from the Sentinel-1 images, with values of 6.35 km/d and 9.67 km/d, respectively. The probability distribution of the deviation of the PSY4V3 product from the estimated ice floe drift peaks near 0 km/d, with a lowest absolute skewness of −0.27, suggesting a near-normal distribution. The negative skewness from the data of the three products indicates that the ice motion is generally underestimated by these products, especially the TOPAZ4 product. As a result of the deviation between the ice motion data derived from the TOPAZ4 product and that from Sentinel-1 is quite large, the data from the TOPAZ4 product were not used in the assessments described below. The TOPAZ4 product is not deemed suitable for depicting the sea ice motion in the region of the Robeson Channel. The above assessment was conducted without considering the ice motion direction in relation to the wind direction. In the rest of this Section, we discuss the difference between the direction of the ice floe drift obtained from Sentinel-1 and that from the GLORYS12V1 and PSY4V3 products. This is represented using rose diagrams in Figure 8a-c for the data north of the Robeson Channel, and in Figure 8d-f for the data inside the Robeson Channel. The length of each spoke around the circle in the diagram indicates the amount of time that the ice floe drifts in a particular direction. The colors of the spokes indicate the categories of wind speed. From Figure 8a-c, it can be seen that the dominant orientation of the ice floe motion is from south-southeast (SSE) to south or southwest (SW). However, ice drift heading north is observed in the ice floe drift data from Sentinel-1. This is the only difference between the ice motion reanalysis data (GLORYS12V1 and PSY4V3) and the ice floe drift data from Sentinel-1. The PSY4V3 product is slightly superior to the GLORYS12V1 product. In the orientation from SSE to SW, the ice floes from Sentinel-1 and PSY4V3 have similar motion speeds and orientation distributions, whereas GLORYS12V1 clearly underestimates the speed. As for the situation inside the Robeson Channel, due to the limitation of the coastal landform, the ice floe motion is concentrated to the SW and south-southwest (SSW). Similar to the area north of the Robeson Channel, the GLORYS12V1 and PSY4V3 products are unable to simulate the northward ice motion.

Impact of the Ice Arches on the Bias of the Sea Ice Motion Products
As mentioned in Section 2.3.2, the presence or absence of an ice arch impacts the ice types and SIC in the Robeson Channel. The presence of the northern ice arch causes more free ice drift, whereas the southern arch causes the congestion of the channel with thick ice, and eventually leads to stagnation. Figure 9 shows scatter plots of the Sentinel-1 ice floe speed versus the sea ice motion product for three situations of ice in the Robeson Channel: (1) without an ice arch; (2) in the presence of the northern arch; and (3) in the presence of the southern arch. Table 3 lists the correlation coefficient (R) values of the data under the aforementioned conditions.  Under the no arch condition, R is 0.826 and 0.524 for PSY4V3 and GLORYS12V1, respectively. This is not significantly different from the values resulting from the use of the entire dataset. Under the presence of the northern arch, where the surface is covered with sparse and thin ice floes, the R value for GLORYS12V1 increases slightly to 0.563 and decreases slightly to 0.786 for PSY4V3. These are marginal changes, so we do not consider that the behavior of the two products is affected by the presence of the northern arch. When the southern arch forms, the R value decreases remarkably to 0.544 for PSY4V3 and remains at nearly the same value (0.554) for the GLORYS12V1 product. The formation of the southern arch causes the jamming of the ice floes in the channel. The lower R value for the PSY4V3 product means that the product fails to account for the interactions between the floes in a compacted ice regime. On the other hand, the tendency of the GLORYS12V1 product to underestimate the motion makes it insensitive to the motion of a jammed ice field. The results listed in Table 3 show the superiority of the PSY4V3 product over the GLORYS12V1 product under both the conditions of the presence and absence of the northern arch, with no difference between the behavior of either product under the presence of the southern arch. It is worth noting that a period of no ice motion was encountered between 21 March 2018 and 1 July 2018, shortly after the formation of the southern ice arch. During this period, GLORYS12V1 produced an average motion speed of 0.06 km/d, while PSY4V3 produced an average motion of 15.64 km/d. Once again, this does not mean that the GLORYS12V1 product is better overall, but rather that it produces better results in situations of slow or no ice motion. In fact, the TOPAZ4 product reproduces the correct zero motion during the period of stagnation, although it is not reliable when the ice floe starts to drift.

Influence of the Wind Speed on the Accuracy of the Sea Ice Motion Products
Wind is an important factor affecting ice drift, with an increasing influence in regions with a low SIC and thin ice [10]. In this section, the influence of wind on the accuracies of the sea ice motion products is evaluated. The wind speed is grouped into two categories separated by the median value of 9.86 km/h. The accuracies of each product compared to the ice floe speed from Sentinel-1 are then compared for each wind category in Table 4. All of the statistics listed in Table 4 indicate that the PSY4V3 product performs better than the GLORYS12V1 product under the different wind speed regimes. The atmospheric forcing used in the PSY4V3 product is taken from the ECMWF Integrated Forecast System [40], while the forcing in the GLORYS12V1 product is taken from the ERA-Interim Reanalysis in earlier years and the ERA5 Reanalysis in recent years. The relatively high uncertainty of ERA-Interim for the wind fields compared to ERA5 has been demonstrated by Shokr et al. [10]. Assimilating the data of ERA-Interim in the early stage is a potential error source for the GLORYS12V1 product.
Note that the accuracies of the sea ice motion products are slightly better (especially for the GLORYS12V1 product) in the low-speed wind range than in the high-speed range. This is likely because stronger wind forcing can enhance the interactions between the ice floes and weaken the ice motion response to wind forcing [41]. This mechanism is primarily related to high-frequency processes, which are likely to be ignored in the numerical models (e.g., Heil and Hibler [42]). However, the influence of the different wind regimes on the accuracy of the products is moderate because the differences in the accuracies under the two wind regimes are much lower than the accuracies themselves, especially for the PSY4V3 product. For example, the difference in the RMSE values of PSY4V3 corresponding to the two wind regimes is 0.15 km/d (or −4.50%).

Influence of Ice Floe Speed on the Deviation of the Sea Ice Motion Products
Does the sea ice speed itself influence the accuracy of the PSY4V3 and GLORYS12V1 products? Sumata et al. [25] indicated that the uncertainty of several sea ice motion products versus the estimation from RGPS observations in the Arctic Ocean depends on the sea ice speed. To further explore the influence of ice floe speed on the deviation in the sea ice motion products, the speed was grouped into 10 bins ranging from 0 to 100 km/d, as shown in Figure 10. The deviation of the PSY4V3 and GLORYS12V1 products from the ice floe speed (measured in terms of the MAE) is negligible when the ice floe drift does not exceed 10 km/d. The MAE then increases with the increasing ice floe speed. A significant positive relationship (R 2 = 0.984, p < 0.001) between the GLORYS12V1 MAE and the ice floe speed can be identified in Figure 10. When the ice floe speed is between 90 km/d and 100 km/d, the GLORYS12V1 MAE is~73 km/d, which is approximately 15 times larger than the value when the ice floe speed is less than 10 km/d. Conversely, the MAE from the PSY4V3 data is relatively stable when the ice floe speed is greater than 30 km/d. However, the PSY4V3 MAE shows fluctuations when the ice floe speed is between 70 and 100 km/d. This can be partly attributed to the limited samples of ice floe speed records from the Sentinel-1 images, with only 3 and 11 tracked ice floes having ice speeds of 90-100 km/d and 80-90 km/d, respectively. In general, the influence of the ice floe speed on the accuracies of the products is smaller for PSY4V3 than for GLORYS12V1. As previously mentioned, the data used in the assimilation of the GLORYS12V1 product are mainly obtained from reanalysis data, which differ from the satellite image-based ice speed results. Conversely, the PSY4V3 product partly assimilates satellite data (Special Sensor Microwave Imager Sounder (SSMIS) data in recent years), which are more similar to the satellite image-based estimated ice speed.

Influence of Tidal Forcing on the Bias of the Sea Ice Motion Products
The Nares Strait (including the Robeson Channel) has a relatively large tidal range compared with other regions in the Arctic Ocean. Davis et al. [11] indicated that the strongest M 2 and S 2 tides occur in the Kane Basin and to the south. Whether the accuracies of the reanalysis products are influenced by the tides in the Robeson Channel is unknown. Therefore, this study combined the analysis of the deviation of the PSY4V3 and GLORYS12V1 products with that of the tidal range data to investigate the influence of year-round tidal forcing on these products. A significant correlation between the tidal range and the ice floe speed from the Sentinel-1 images is apparent, only in certain months ( Figure 11). For example, the negative R value (−0.771, p < 0.01) in February 2017 indicates that the ice motion was greatly influenced by the strong tidal effect for some ice floes. Around 12 February, the large tidal range induced a low ice floe speed. Davis et al. [11] observed strong tides in the Nares Strait resulting from a standing wave with a semidiurnal tide cycle. Therefore, the horizontal motion of an ice floe can be slowed under the forcing of a standing wave. However, the monthly correlation is not stable, and the correlation is insignificant for 7 months at the statistical level of 0.05. Furthermore, the relationship between the tidal range and the deviation between the sea ice motion products and the ice drift data is insignificant for most months (Figure 12). This is because the tidal frequency in the Robeson Channel is twice per day (M 2 tide). Therefore, it cannot be captured in the daily data from the Sentinel-1 images. Accordingly, further studies need to be conducted using satellite images with a higher temporal resolution.

Spatial Differences in the Accuracy of the Sea Ice Motion Products
As the SIC regulates the interactions between ice floes, it constitutes another factor affecting ice drift [43], and consequently influences the accuracy of the remote sensing based products for sea ice motion [21]. The SIC is different for regions inside and outside the Robeson Channel, with higher values outside ( Figure 13). Therefore, we assessed the performance of each product separately in the two sub-regions.
Violin plots, which combine a box plot and kernel density, are used to represent the probability distributions of the deviation between the sea ice motion products and the ice floe speed obtained from the Sentinel-1 images in Figure 14. Outside the Robeson Channel, the probability distributions of the deviation of the PSY4V3 and GLORYS12V1 products versus the ice floe speed estimated using the Sentinel-1 images are similar, with a single steep peak and a normal distribution. However, the peak of the GLORYS12V1 product is slightly lower than 0 km/d, which indicates that the ice motion is slightly underestimated by the GLORYS12V1 product in this sub-region.  Inside the Robeson Channel, the distributions of the deviation of the PSY4V3 and GLORYS12V1 products also approximate a normal distribution. However, they have a larger standard deviation and a broader peak compared to the distributions found outside the Robeson Channel. The data from GLORYS12V1 also peak at a value that is lower than 0 km/d, and the probability distribution reveals an asymmetric pattern, with the absolute value of the upper quartile being lower than that of the lower quartile. Both statistical patterns indicate that the ice motion is underestimated by the GLORYS12V1 product inside the Robeson Channel, which is generally consistent with the distribution of the kernel density shown in Figure 7a. Table 5 includes a few statistical parameters to summarize the accuracy of each product inside and outside the Robeson Channel. The different SICs between the outer and inner sub-regions result in different mean ice speeds of 7.00 km/d and 28.99 km/d, respectively. To remove the influence of the ice speed itself, the ratios of both MAE and RMSE to the mean speed were calculated. The ratio of MAE to mean speed is called the relative deviation. The PSY4V3 product has lower MAE, RMSE, and relative deviation values than GLORYS12V1 for both sub-regions, which suggests that the PSY4V3 product provides a more accurate representation of the sea ice motion for both regions. The ratios of the MAE/mean speed and RMSE/mean speed present opposite characteristics, when compared to the MAE and RMSE values. That is to say, both ratios are smaller inside than outside the Robeson Channel for both products. Therefore, the differences in the MAE and RMSE values for the two sub-regions are primarily caused by the differences in ice speed, which are in turn related to the differences in the SIC. Outside the Robeson Channel, the ice motion pattern is not free drift, but is impacted by the internal stress, to a high degree, which is not easy to accurately capture in the reanalysis products. This likely leads to greater relative MAE and RMSE values, compared with the sub-region inside the channel. Figure 15 presents the spatial distribution of the relative deviation of each product, compared with the ice floe speed from the Sentinel-1 images. Outside the Robeson Channel, and especially in the region near the entrance from the Lincoln Sea to the Robeson Channel, the negative deviations are larger than the positive relative deviations (Figure 15a), which also indicates that the ice motion is generally underestimated by the GLORYS12V1 product in this sub-region. Conversely, the positive and negative relative deviations are comparable in the sub-region outside the channel for the PSY4V3 product (Figure 15b), which agrees with the near-normal probability distribution of the deviation ( Figure 14). Note that the relative deviation of the PSY4V3 product is also relatively large near the entrance, which can be due to the instability of the SIC in this sub-region.
Inside the Robeson Channel, it is clear that the PSY4V3 product performs better than the GLORYS12V1 product, with a smaller relative deviation error. However, the distributions of the relative deviation are different for the two products. The GLORYS12V1 product performs worse in the region south of Hall Basin, while the PSY4V3 product performs worse within Hall Basin. This can be due to regional differences in the atmospheric forcing or currents, which is difficult to assess quantitatively. More specifically, the relative deviation of the speed is between −0.5 and 0.5 for the PSY4V3 product (in Figure 15b) near the gate inside the Robeson Channel, which indicates that the ice motion is accurately simulated at this gate by the PSY4V3 product. Therefore, PSY4V3 has great potential to be used to estimate the ice flux through the Robeson Channel.

Conclusions
In this study, we validated the ice motion data from the three ocean-sea ice reanalysis products of PSY4V3, GLORYS12V1, and TOPAZ4 in the Robeson Channel. This is a narrow but significant channel for sea ice and freshwater outflow from the Arctic Ocean. The reanalysis ice motion product within this channel is available only from the three aforementioned products. Ice floe speeds (magnitude and direction) were extracted from daily Sentinel-1 images between September 2016 and March 2018, including periods of ice arch formation at the northern entrance of the channel and the northern location of Smith Sound. These satellite-derived ice floe drift data (Lagrangian representation) were used to validate the gridded reanalysis products (Eulerian representation).
The daily average ice floe speed showed a significant fluctuation (Figure 2), which was probably caused by the complex integrated influence of wind, current forcing, and the floe track being surrounded by different ice concentrations or being close to fast ice edges. Anomalies of ice floe speed (e.g., >75 km/d) were also apparent in the data, which were mainly triggered by the prevailing strong northerly wind in areas of free drift.
The validation of the ice motion reanalysis products showed general underestimation by the three products with respect to the ice floe speed from Sentinel-1 images ( Figure 6). The PSY4V3 product showed the least underestimation, with the lowest MAE of 6.35 km/d and RMSE of 9.67 km/d. It also showed the best correlation with the ice floe speed from Sentinel-1 images (R = 0.830, p < 0.001). TOPAZ4 grossly underestimated the ice motion, and it should only be used in areas where the ice motion is negligible. This was likely due to the lack of sea ice data in the process of assimilation of the observations. For this reason, in this study, focus was placed on the evaluation of the PSY4V3 and GLORYS12V1 products.
The ice motion from these two products was evaluated under three situations of ice drift in the Robeson Channel: (1) in the absence of an ice arch; (2) in the presence of the northern arch, where the condition of free drift is more likely; and (3) in the presence of the southern arch, where the condition of compacted ice is likely. While the PSY4V3 product still produced better results in both conditions in terms of deviation and correlation with the ice floe drift data ( Figure 9; Table 3), no difference was found between the behaviors of either product in the presence or absence of the northern arch. In contrast, under the condition of the southern arch, the correlation between the PSY4V3 product and the ice floe speed decreased from 0.830 to 0.544, indicating the sensitivity of this product to ice concentration. No similar decrease was found for the GLORYS12V1 product, which provides superior results but only in situations of slow or no ice drift (i.e., compacted ice).
The impacts of the absolute magnitude of the wind and ice floe speed, and that of tidal forcing, on the accuracies of the sea ice motion products were also explored. The impact of wind was found to be moderate, as the differences in the accuracies of each reanalysis product under two wind regimes are much lower than the accuracies themselves, especially for the PSY4V3 product ( Table 4). The deviation of the two reanalysis products compared with the ice floe speed was negligible when the ice floe speed was lower than 10 km/d ( Figure 10). The deviation then increased linearly at a high rate after 10 km/d for the GLORYS12V1 product and at much less rate for the PSY4V3 product. The impact of tidal forcing on the daily sea ice motion products was not as significant as its influence on the ice floe speed itself, which was primarily related to the relatively coarse temporal resolution of the reanalysis products and the ice floe speed from the Sentinel-1 images ( Figure 12).
Furthermore, a spatial difference in the accuracies of the sea ice motion products was identified. The relative deviation from the ice floe speed inside the channel was better than that obtained outside the channel ( Figure 14; Table 5). This was essentially related to the differences in the SIC, which is higher outside the channel. The spatial differences in the accuracy of the PSY4V3 product were smaller than those of the GLORYS12V1 product for both sub-regions. Moreover, the PSY4V3 product presented a high performance near the gate to the Robeson Channel ( Figure 15), which reveals its high potential for quantifying the ice flux through the Robeson Channel.
Overall, the PSY4V3 product presented better effectiveness, robustness, and accuracy in the Robeson Channel compared to the other two products, and has better potential for characterizing the ice motion and estimating sea ice or freshwater outflow flux through the channel. The quantitative results of this study will provide useful information when choosing products to monitor variations in the ice motion or sea ice flux at various temporal scales in the Robeson Channel or similar narrow channels. Johnson et al. [44] indicated that the assimilation of the sea ice motion can lead to an improvement in the simulation of sea ice thickness in the Arctic Ocean. Therefore, the results of this study can also provide background information when choosing products to simulate sea ice thickness. Furthermore, this study proved the applicability that the ice floe speed from sequential daily Sentinel-1 images can be considered as virtual Lagrangian buoy data, and can be used in a wide variety of studies of sea ice dynamics. However, such data cannot represent all the ice floes drifting in the channel, due to the limitation of manual identification of ice floes from Sentinel-1 images, which are seriously affected by noise.  Data Availability Statement: Sentinel-1A/-1B product (https://scihub.copernicus.eu/, accessed on 5 February 2021); the ERA5 reanalysis products (https://cds.climate.copernicus.eu/cdsapp#!/ dataset/reanalysis-era5-single-levels?tab=overview, accessed on 5 February 2021); GLORYS12V1, PSY4V3, and TOPAZ4 products (https://resources.marine.copernicus.eu/?option=com_csw&task= results, accessed on 5 February 2021); and tide data (https://mobilegeographics.com, accessed on 20 November 2020).