Passive Microwave Sea Ice Edge Displacement Error over the Eastern Canadian Arctic for the period 2013-2021

Abstract In this study, sea ice edge derived from three passive microwave (PM) algorithms, ARTIST sea ice (ASI), enhanced NASA Team 2 (NT2), and Bootstrap (BT), are compared to those derived from the daily Canadian Ice Service charts over a primarily seasonal ice zone in the eastern Canadian Arctic for 2013–2021. To determine the ice edge error, we introduced an edge-length-based displacement measure called the edge displacement error (EDE), a dimensionless measurement obtained by dividing the weighted average Hausdorff distance by the ice edge length. We found that the ASI algorithm has the highest EDE on average, while the BT algorithm has the lowest one. In October (the beginning of the freeze-up period), the ice edge exhibits significant meandering, and the EDE is less sensitive to changes in the charted area. In the freeze-up period, the PM algorithms have the highest mean EDE value relative to other months due to the appearance of thin ice. A greater range of EDE values was observed in April than in other months. Throughout this region, the wind speed varies the most in April and May, whereas in April, the air temperature fluctuates more than in the other months.


Introduction
Sea ice is a major component of the cryosphere that plays a vital role in the climate system by reflecting most of the incoming solar radiation to space and providing thermal insulation between the ocean and atmosphere (Shokr and Sinha 2015).Although sea ice appears to be a thin blanket covering the ocean surface, it can affect heat, moisture, and momentum fluxes across the ocean-atmosphere interface (Thomas and Dieckmann 2008).Due to this complex interaction between sea ice and critical components of the Earth's climate system, sea ice has become essential in climate research.Remote sensing data are currently a primary source for collecting information about sea ice parameters.Satellite-borne data in the visible and infrared ranges are hampered by clouds, and in this regard, the low-frequency microwave portion of the electromagnetic spectrum is particularly useful.Since late 1978, passive microwave (PM) instruments have been an effective means of monitoring sea ice.They can continuously return information on the Earth's surface, regardless of weather conditions and solar illumination.This benefit is noticeable in polar regions due to harsh climate conditions, limited access, and polar darkness.Moreover, data acquisitions from PM sensors cover a large area, which is beneficial for retrieving sea ice concentration (SIC), given the vast area covered by sea ice.
Sea ice edge identifies the boundary between open water and sea ice.The position of the sea ice edge is a vital sea ice property for ship navigation, as well as delineation of the marginal ice zone (MIZ), an essential habitat for marine mammals and seabirds (LeBlanc et al. 2019).To define the edge contour, a certain SIC threshold (usually 15%) is used.Based on this definition, ice edges are areas (e.g., pixels) with a SIC of 15% or higher.In a previous study by Pang et al. (2018) sea ice edge from passive microwave data derived from the ARTIST sea ice (ASI) and Bootstrap (BT) algorithms with that derived from the pseudoship-observations based on the processing of six moderate-resolution imaging spectroradiometer (MODIS) images over the Arctic was compared.The ASI and BT algorithms' mean SIC at the edge derived from ship observations was 10.5% and 23.6%, respectively.The SIC at the ice edge in summer was similar to that in winter for ASI, whereas there was a significant difference for the BT algorithm.This may indicate that the ASI ice edge location on cloud-free days is less variable than the BT algorithm, possibly indicating the latter is more sensitive to surface emissivity variations.
SIC retrieval algorithms near the ice edge are affected by microwave energy emitted by the atmosphere (Ivanova et al. 2015).The ASI algorithm assumes that atmospheric influence is a smooth function of the ice concentration and selects a third-order polynomial for the sea ice concentration between 0% and 100% ice cover.The BT algorithm uses ice and water tie points that vary seasonally (winter and summer) but are not regionally specific (there is one set of tie points for the northern hemisphere and one set for the southern hemisphere).The NT2 algorithm has a different way of dealing with atmospheric effects than the ASI and BT algorithms.The NT2 algorithm uses a radiative transfer model to account for weather effects that apply over ice and open water based on 12 sets of representative atmospheric conditions.Based on an assessment of the enhanced NASA Team 2 (NT2) SIC using data from a synthetic aperture radar (SAR) sensor on RADARSAT-1 and MODIS images in the Bering Sea (Heinrichs et al. 2006), it was found that the NT2 algorithm and SAR ice edge locations are in reasonable agreement across a range of wind and temperature conditions.This study endorsed the idea of using manually derived ice edges from SAR for comparison with PM data and also pointed out an underestimate of SIC from NT2 for thin ice and an overestimate in frazil ice conditions relative to the SAR.Using the interactive multisensor snow and ice mapping system (IMS), a study on assessing the NT2 sea ice edge over the Arctic also showed that the uncertainty associated with the ice edge location could be higher during the melt season (Liu et al. 2020).
Currently, there is a lack of recent studies regarding the performance of PM sea ice edge estimation relative to ice charts, primarily in seasonal ice zones (SIZs)-which are becoming more prevalent in Arctic regions (Bliss et al. 2019).In light of the importance of PM SIC products in the long-term planning of shipping routes, reanalysis data production, climate monitoring, and forecasting purposes, this study quantifies the extent to which the sea ice edge derived from the ASI (Svendsen et al. 1987), NT2 (Markus and Cavalieri 2000), and BT (Comiso 1995) SIC retrieval algorithms agree with those derived from the daily Canadian Ice Service (CIS) charts in a primarily SIZ over the years 2013-2021.While the ASI algorithm provides finer spatial resolution than many passive microwave sea ice products, the NT2 algorithm addresses the weaknesses of the original NASA Team (NT) algorithm (Cavalieri et al. 1984), especially concerning sensitivity to emissivity variations, which is a key advantage.The BT algorithm has been used to provide a long-term, consistent, and comprehensive sea ice concentration data set (with calibration between sensors) for studying climate change.These characteristics lead us to choose these PM SIC retrieval algorithms to investigate the sea ice edge.
Several studies have assessed the sea ice edge location (Dukhovskoy et al. 2015;Goessling et al. 2016;Goessling and Jung 2018;Melsom et al. 2019), but there is no agreement regarding the best measure for determining the position of the ice edge (Palerme et al. 2019).When comparing products, the ice edges may overlap partially, but they may have different edge lengths, particularly if the region of interest changes from month to month or year to year, which is often the case in regional monitoring for ice operations.To consider both the edge length and edge displacement, in this research, we introduced an edgelength-based displacement measure called edge displacement error (EDE), a dimensionless measurement.This study aims to evaluate the performance of PM SIC products in sea ice edge estimation by using the EDE and the weighted average Hausdorff distance (d wavg H ), a recommended metric by Melsom et al. (2019).This paper is organized as follows.Section Study area and data set introduces the study area and data set.The third section explains the methodology.Afterward, section Results discusses the results, and section Conclusion concludes the paper.

Study area
The study area covers sea ice along Baffin Island and the Davis Strait (Figure 1a).This region has a high species richness of Arctic marine mammals (AMMs), including narwhals, beluga whales, bowhead whales, ringed seals, and bearded seals (Laidre et al. 2015).Pikialasorsuaq, a large polynya in the northern part of Baffin Bay, serves as a critical breeding and feeding habitat for seabirds.In the summer, millions of seabirds visit the western Baffin Bay to feed (Heide-Jørgensen et al. 2013).Thus, this region can play an essential role in polar ecosystems.Local Inuit depend on these AMMs, and the marine environment for their livelihood (Dawson et al. 2020) and use the ice cover as a hunting platform and transportation route.At the same time, shipping traffic in this region is increasing (Dawson et al. 2018), with increasing pressure to lengthen the shipping season due to the Mary River mine (Wilson et al. 2021).Sea ice loss and increased ship traffic may increase noise pollution, and these trends may also threaten AMMs' populations.This region corresponds to the eastern Canadian Arctic charting region for daily ice charts produced by CIS.It is important to note that over the study area, the coverage of the ice chart data set varies, and therefore our study region varies daily, monthly, and annually.An example of how the charted region changes over time is demonstrated in Figure 1b.Each date's coverage is indicated by a polygon with different colors.The study area's size changes daily and month to month due to changes in the area over which CIS is required to provide ice conditions, which depends on shipping and other activities in the region.Notice the largest charted area in Figure 1b is for October, which is when the ice is starting to freeze-up, and there is activity over a large The study area's size changes daily and month to month due to changes in the area over which CIS is required to provide ice conditions, which depends on shipping and other activities in the region.Notice that the largest charted area in (b) is for October when the ice starts to freeze up, and there is still activity over a large region of Baffin Bay.Datum is the world geodetic system 1984 (WGS84), and the projection coordinate system is Lambert conformal conic.
region of Baffin Bay, whereas the smallest charted area is in April when there is little shipping activity in the region.We selected the years 2013-2021 as the study period to focus on recent changes.To evaluate the ice edge in this region, we used the SICs for the months of October to June for sea ice edge calculations.

CIS daily ice chart data
For the SIC reference data set, daily CIS ice charts were obtained from Environment and Climate Change Canada (ECCC).CIS daily ice charts are based on a combination of all available data on ice conditions, including meteorological data, visual ship observations, airborne radar measurements, satellite images, and climatological information.To produce daily ice charts, trained analysts visually inspect all data available to estimate ice conditions.These conditions are used to identify spatial regions that have relatively similar ice attributes, which are indicated by drawing polygons on a map.Similar attributes include total ice concentration (shown as CT), concentrations of the first, second, and third thickest ice (CA, CB, and CC) along with their respective stages of development (SA, SB, and SC), all of which are defined by the world meteorological organization (WMO) ice-observation standards.
These daily ice charts are produced to support operational activities, such as shipping from freeze-up to break-up periods.There is a 2-fold advantage to this time span: firstly, the freeze-up period is when PM SIC retrieval algorithms perform poorly due to the presence of thin ice (e.g., Kwok et al. 2007); secondly, the break-up period is when PM SIC retrieval algorithms do not perform well due to the occurrence of surface melt (e.g., Kern et al. 2020).Daily ice charts (available at a higher temporal frequency than regional/weekly ice charts) are helpful in sea ice edge monitoring during periods when sea ice edge location and length fluctuate frequently (e.g., freeze-up period, a period during which the ice changes quickly in response to changing in air temperature and wind conditions).The daily ice charts can therefore provide insight into these fluctuations.Furthermore, using daily ice charts as reference data set in our study is consistent with our use of daily average PM products.
The accuracy of these products is related to different factors, such as the availability and resolution of source information as well as atmospheric conditions (e.g., cloud coverage or daylight), and surface conditions (e.g., covered with snow or rain) (MANICE 2005).Details of the accuracy of a visually estimated ice concentration from these charts can be found in a recent study by Cheng et al. (2020).It is known that ice charts provide an accurate ice edge location (Heinrichs et al. 2006;Ozsoy-Cicek et al. 2009;Liu et al. 2016).
The CIS daily ice charts are encoded in SIGRID-3 format (one of the WMO standards for archiving digital ice charts).The main component of these files is vector data containing ice information, such as ice polygons and their associated attributes.Vector files must first be converted into raster files.We used the Geospatial Data Abstraction Library (GDAL) in Python to rasterize vector inputs.Using the WGS84 datum and Polar Stereographic projection coordinate system, we created grid cells with a 5 km resolution, allowing comparisons with the rasterized PM data.

ASI algorithm
The ASI algorithm (Svendsen et al. 1987) uses the polarization difference (PD) between ice and water, where TB 89H and TB 89V are the horizontal and vertically polarized brightness temperatures of the 89 GHz frequency channels, respectively.The basis of the algorithm revolves around the fact that the polarization difference of ice is small, whereas the polarization difference of water is large.In the ASI algorithm, intermediate ice concentrations are calculated by interpolating (using a third-order polynomial) between open water and 100% sea ice tie points.While the ASI algorithm provides finer spatial resolution than other comparable PM SIC retrieval algorithms due to the use of the 89 GHz channel, at this frequency (or other high-frequency passive microwave channels), the brightness temperature is more sensitive to atmospheric effects (Shokr and Sinha 2015).The ASI algorithm employs lower-frequency channels as weather filters, a common method for compensating for the sensitivity to atmospheric contamination (Spreen et al. 2008).Since the polarization difference has units of brightness temperature (it is not normalized), this algorithm may be sensitive to ice temperature variability.The ASI algorithm, however, is known to have the least sensitivity to sea ice thickness among 29 SIC algorithms implemented in Heygster et al. (2014), which is a key strength.We obtained the advanced microwave scanning radiometer 2 (AMSR2) daily average ASI SIC with a 6.25 km gridded resolution from the University of Bremen, Germany (Spreen et al. 2008).To ensure calculation consistency, the daily ASI SIC is re-gridded to the charts SIC using bilinear interpolation.

NT2 algorithm
The NT2 algorithm (Markus and Cavalieri 2000) estimates SICs based on lookup tables of calculated rotated gradient ratios (GRs) and polarization ratios (PRs) using the 19, 37, and 85 GHz frequency channels.The PR at a given frequency (f) is defined as where V and H refer to vertical polarization and horizontal polarization, respectively.The GR between two observations from two frequencies (f 1 and f 2 ) at the same polarization (p) is written as For each of 12 representative atmospheric profiles, GRs and PRs are calculated over all possible ranges of sea ice concentration.These calculated GRs and PRs are arranged as look-up tables, with one table for each atmospheric profile.For the Arctic, this process is carried out separately for three different ice types (multiyear ice, first-year ice, and thin ice).These different ice types have different characteristic emissivities, which impact the surface emission portion of the brightness temperatures that are input to the GRs and PRs.The ice concentration of a given pixel is found by choosing the concentration value that best matches the actual and estimated PRs and GRs.This algorithm utilizes the near-90 GHz frequency channel, which makes it easier to distinguish between low ice concentrations and areas with surface effects associated with refreezing (snow layering and glazing).However, surface effects from melt processes have not been addressed in the NT2 algorithm (Meier et al. 2017).This algorithm is susceptible to weather effects not represented by the 12 atmospheres (Scott et al. 2012).We obtained the AMSR2 NT2 SIC with a 12.5 km gridded resolution from the United States National Snow and Ice Data Center (NSIDC, Meier et al. 2018).To ensure calculation consistency, the daily NT2 SIC is re-gridded to the charts SIC using bilinear interpolation.

BT algorithm
The BT algorithm (Comiso 1995) uses the vertically polarized brightness temperatures of the 19 GHz frequency channel and the vertically and horizontally polarized brightness temperatures of the 37 GHz frequency channels to estimate SIC.The algorithm considers two types of surfaces: sea ice (SIC is near 100%) and ice-free (SIC is zero) regions.This technique revolves around the distributions of 100% sea ice multichannel clusters of brightness temperatures since they reveal some unique clustering.Comparing the scatter plot of one passive microwave channel to another channel (among 37V/37H and 37V/19V) shows data points with a SIC of around 100% mainly lie along a cluster, and the open water points primarily lie along another cluster.This algorithm uses the linearity of these data points to identify a suitable tie point for 100% and 0% SIC.The range of these clusters reflects the variability in sea ice emissivity due to different ice-type surfaces with different brightness temperatures; hence, this algorithm is susceptible to temperature variability.This algorithm can be intercalibrated to AMSR-E using varying tie points to account for changes in ice and open water signatures caused by changes in satellite instruments and platforms.We obtained the special sensor microwave imager/sounder (SSMIS) BT SIC with a 25 km gridded resolution from the NSIDC (Comiso 2017).To ensure calculation consistency, the daily BT SIC is re-gridded to the charts SIC using bilinear interpolation.

Wind speed
To investigate the physical condition of the study area, the 10-meter wind speed (m/s) is acquired from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis 5th Generation (ERA5) data at the Copernicus climate data store (Hersbach et al. 2018).The wind speed calculation is based on the meridional and zonal components.ERA5 wind speed provides hourly data over 24 hours with a spatial resolution of 31 km.To ensure calculation consistency, the daily wind speed is re-gridded to the charts SIC using bilinear interpolation.

2-m Air temperature
To investigate the physical condition of the study area, the air temperature at 2 m above the surface (K) is acquired from the ERA5 data at the Copernicus climate data store (Hersbach et al. 2018).ERA5 air temperature provides hourly data over 24 hours with a spatial resolution of 31 km.To ensure calculation consistency, the daily 2-m air temperature is re-gridded to the charts SIC using bilinear interpolation.

Methodology
Chart SIC Following the rasterization process, we updated the total ice concentration based on the code tables for SIGRID-3 variables (Appendix 5 given in Joint 2004).We used SA, SB, SC, CA, CB, and CC to define the ice stage of development and the corresponding partial concentration for each pixel.Consequently, each pixel had three partial ice concentrations associated with three different stages of development in a single day.Lastly, we calculated the daily mean value of each partial ice concentration for each stage of development for the given pixel.
Based on the ice stage of development, we classified the ice type of the ice-covered pixels (where SIC is not zero) into two categories: 1. thin ice: ice with thickness 30 cm (the thickness of more than 30 cm is not considered thin ice (Ivanova et al. 2015), 2. thick ice: ice with thickness >30 cm.
It is noted that the ice thickness range is assigned to each ice type based on the code tables for SIGRID-3 variables (Appendix 5 given in Joint 2004).Table 1 outlines the stage of development associated with each ice category (thin and thick) considered for this study.It should be noted that these categories are less reliable after the ice growth season has been completed (according to our personal communication with CIS).
An illustration of sea ice concentration retrieved from the ASI, NT2, BT algorithms, rasterized ice chart, and CIS daily ice chart on February 3, 2014, over the study area is shown in Figure 2. In panels ad, regions without data are shown in light blue, while the lands are black.

Sea ice edge estimation
Following calculating the daily SIC value for each PM product, we generated the corresponding daily SIC based on the exact geolocation and date indicated on the CIS charts.A common method for estimating the ice edge location (Melsom et al. 2019) for each product is to find pixels with SICs exceeding 15% while their neighbors' SICs are below 15%.For a grid cell at i, j location and concentration of c, we consider it as the edge grid cell or e [i,j] (4) After defining the edge grid cells using Equation (4), we used the density-based spatial clustering of applications with noise (DBSCAN) method (Ester et al. 1996) to find the contour that intersects the MIZ, i.e., obtaining a robust ice edge by removing the isolated ice patches.It is worth noting that the BT algorithm scarcely needed the clustering process, implying that the estimated edge is almost continuous due to its coarse spatial resolution and lack of detail on the SIC and sea ice edge.Figure 3 represents how the DBSCAN clustering method modifies the chart, ASI, NT2, and BT sea ice edges.

Edge displacement error (EDE)
To compare sea ice edge location derived from the PM algorithms (ASI, NT2, BT) with those from the ice charts, we first used a recommended metric (Melsom et al. 2019) where N ch and N PM are the number of edge grid cells derived from the chart and PM product, respectively.d ch and d PM are the distance from the chart edge grid cell to the nearest edge grid cell derived from the PM product and the distance from the PM product edge grid cell to the nearest edge grid cell derived from the chart.A more detailed description, including a detailed comparison with other metrics, can be found in Melsom et al. (2019).Using Equation ( 5), we can determine only the distance between two sea ice edges (Melsom et al. 2019).The sea ice edges, however, may have different edge lengths while overlapping partially.Adapted from the code tables for SIGRID-3 variables (Appendix 5 given in Joint 2004).
Considering that both the location and length of the ice edge can vary over time, we introduced the edge displacement error (EDE), which is a dimensionless measure defined as where L avg is the average ice edge length (in kilometer) and can be expressed as here L ch and L PM are the ice edge length from the chart and PM product, respectively.EDE can be any value equal to or greater than zero, where a zero EDE value indicates the ideal case, i.e., the location and length of the two ice edges are perfectly matched.Ice edge defined in this study is a grid cell set that meets the required condition discussed above (Equation 4).
To find the ice edge length derived from the chart and PM algorithm (L ch and L PM , respectively), we must take into account the position of the ice edge grid cell derived from the chart and PM algorithm (l i, j ch and l i, j PM , respectively) and sum up all grid cells' length (Melsom et al. 2019) PM , where i, j are the position of ice edge grid cell derived from the chart and PM algorithm, respectively.A detailed description of how we computed l i, j ch and l i, j PM can be found in Melsom et al. (2019).The EDE value in the first scenario (Figure 4a) is higher than in the second scenario (Figure 4b), while the d wavg H in the first scenario is smaller than in the second scenario.The discrepancies can be explained by the fact that in the first scenario, the EDE and d wavg H both can capture the edge displacement (regardless of the variation in edge lengths) since the edge lengths are approximately equal.In the second scenario, however, because the sea ice edges meander, the edge lengths are different; thereby, the d wavg H (Equation 5) can capture only the distance between two edges.Here, dividing the d wavg H by the average edge length (Equation 7) provides the normalized edge displacement (Equation 6).The EDE measurement represents edge length and displacement discrepancy in this case.

Results
The annual cycle of sea ice growth and decay from the years 2013 to 2021 over the study area is displayed in Table 2.During these years, CIS daily ice charts cover all months except September 2014 and 2021, shown in Table 2 as blue hatches.It is apparent that ice grows and decays throughout the year.The freezeup period begins in October when thin ice begins to emerge.A peak in the concentration of thin ice occurs at the end of the freeze-up period, just before the beginning of winter in January, and then it gradually develops into thick ice.The thick ice concentration is high from January to March (winter season).From April to June (melt season), total ice concentration decreases (the relative concentration of thick ice may increase).The summer season begins in July and continues until September.
Following the determination of the ice condition over the study area, we calculated the corresponding daily sea ice edge for each PM product based on the exact location and day indicated on the CIS charts for the months of October to June over the years 2013-2021.The chart SIC at the edge is 51.27% on average.These values for winter, melt, and freeze-up seasons are 44.69%,50.65%, and 58.47%, respectively.Since the 15% threshold was used in Equation ( 4) to estimate the sea ice edge, the chart mean SIC at the edge appears high, which is due to the polygonal nature of the ice chart data, where ice chart polygons adjacent to the ice edge can have total ice concentrations that are higher than 15% (see Figure 2).
From the summary in Table 3, we note that the mean value of ASI SIC at the chart ice edge is 10.59%, well below the 15% SIC threshold.This value for the winter season is 7.61% and increases to 16.16% and 8.00% in the melt season and freeze-up period, respectively.The mean value of NT2 SIC at  the chart ice edge is 17.97%, close to the 15% threshold.This value for the winter season is 14.40% and increases to 24.27% and 15.26% in the melt season and freeze-up period, respectively.The mean value of BT SIC at the chart ice edge is 25.07, well above the 15% threshold.These values for winter, melt, and freeze-up seasons are 24.63%,25.28%, and 25.29%, respectively.A possible explanation for these differences is due to the different spatial resolutions of the passive microwave sensors.The SSMIS sensor has footprints of 28-70 km for channels used in the BT algorithm.AMSR2 has a higher spatial resolution than SSMIS (3-26 km sensor footprints for channels used in the ASI and NT2 algorithms).Both sensor footprints are larger than the resolution of the data used to produce ice charts (e.g., primarily SAR).The mean SIC at the ice edge seems to be dependent on PM sensor spatial resolutions, with less variability across seasons for the larger footprint sensor.These statistics indicate that the PM SIC products tend to have a lower SIC at the ice edge than the ice charts.These results are consistent with the polygon nature of the ice charts, as mentioned, as well as the fact that ice charts are operational products that serve a safety purpose.Accordingly, chart SIC values are expected to be higher than PM products at the edge (Wang et al. 2017).The ASI algorithm has the lowest standard deviation (SD) SIC at the chart ice edge (6.48%), indicating consistency of the underestimation.Standard deviation is taken over all data that are first averaged on a monthly basis over the years 2013-2021.The ASI mean SIC value is well below 15%, meaning that a SIC threshold of 10% may lead to the sea ice edge location being in better agreement with the ice charts.While the BT mean SIC value is well above 15%, meaning that a SIC threshold of 20% may lead to a sea ice edge location in better agreement with the ice charts.A potential source of this disagreement is the difference in resolution between PM SIC products and ice charts.A large sensor footprint limits the precision of the ice edge location estimation.For example, due to the mixture of ice and water within a large SSMIS sensor footprint, the observed TB by a PM sensor may tend to smear out the ice edge.In other words, the edge location tends to extend outward.In contrast, the ice edge within a small AMSR2 sensor footprint is likely to result in a concentration below the 15% threshold and consequently underestimate the edge location.In other words, the edge location tends to extend inward.This explanation can be seen in Figure 5, in which the ASI ice edge appears closer to the consolidated ice region (inward); however, the BT ice edge often appears closer to open water (outward) for almost all months of the study period (see Appendix Figure A1).Differences in the algorithms will also play a role, with ASI more sensitive to ice temperature and atmospheric moisture, it has been shown to underestimate the ice edge location in the marginal ice zone (Liu et al. 2016).
A comparison of sea ice edges derived from PM products with those from charts is also summarized in Table 3.We note that the mean values of EDE and d wavg H for the ASI, NT2, and BT algorithms are higher in the melt season and freeze-up period compared to those in winter.The statistics also reveal that the ASI algorithm has the highest EDE and d on average.The lack of spatial resolution, however, makes it difficult to locate the exact location of the ice edge using PM SIC products.For example, the accuracy of the ice edge location is limited by the spatial resolution of the SSMIS SIC product, which is 25 km Â 25 km.The NT2 and BT algorithms also are more consistent with each other in terms of mean d wavg H and value for all three PM algorithms occur in the freeze-up period.The ice edge is diffuse in the freeze-up period due to the emergence of thin ice in this period (see Table 2); small ice floes and filaments, in combination with atmospheric and ocean forcing, lead to an ice edge that is dynamic.Moreover, in the melt season (starting in April), waves and winds can easily break melting rotten ice and diffuse the ice/water boundary, which could lead to an erroneous SIC and sea ice edge, as confirmed Pang et al. (2018).
In Figure 6, box-whisker plots visualization of the d wavg H , L avg , and EDE for the ASI, NT2, and BT algorithms in each month over the whole study period and study area are shown.For each month, the median and average values are indicated by a line with the total length provides an alternative measure for the difference between the ice edge locations that are less sensitive to changes in the charted area.In particular, the long positive whiskers in April indicate significant deviations toward larger values than the mean.This indicates a greater range of EDE values in April, reflecting the edge's highly dynamic nature this month.This is consistent with the fact that in April, the wind speed is relatively high and air temperature fluctuations are greater than for any other month and the temperature is nearing the freezing point (Figure 7).Off-ice winds can propagate ice filaments into the ocean, creating a diffuse ice edge, which could lead to an erroneous SIC and sea ice edge, as also confirmed by Pang et al. (2018).Regarding the different characteristics of April and October, shown in Figure 6, we provided the EDE and d wavg H values for PM products in 2017 April and October in Figure 5.It can be seen that in October (the beginning of the freeze-up period), the ice edge extends further inward, therefore dividing d wavg H by the ice edge length stabilizes the difference and allows the meandering to be captured.

Conclusion
This paper has assessed the performance of three PM SIC products (the ASI, NT2, and BT) in sea ice edge estimation with respect to the operational daily ice charts over the eastern Canadian Arctic for 2013-2021.To analyze the ice edge estimation in this region, the statistics are calculated from October to June, which corresponds to the ice-covered season.According to our findings, the PM algorithms underestimate the chart SIC at the edge.Our results indicate that normalizing the Hausdorff distance, d wavg H , with the average length of the ice edge provides an alternative measure, edge displacement error (EDE), that is less sensitive to changes in the charted area.The ASI algorithm produced the highest EDE on average, while the BT algorithm produced the lowest EDE on average.These discrepancies may be due to differences in the frequencies used, the size of the spatial footprints of the data, and the difference in spatial resolution between the PM SIC products, and ice charts.In the freeze-up period, the ASI, NT2, and BT algorithms have the highest mean EDE value due to the emergence of thin ice.However, the lowest mean EDE value for all these PM algorithms occurs in the winter, when the high concentration of thick ice leads to a well-defined ice edge.A further observation was that the ASI ice edge appears closer to ice than the chart ice edge.The BT ice edge, however, often appears closer to open water than the chart ice edge due to the smear effect caused by the large sensor footprint.Considering the importance of PM SIC products in seasonal ship route planning, reanalysis data production, climate monitoring, and forecasting, this study can assist in selecting an appropriate PM SIC product or bias-correcting a PM product to be fused with ice charts or other SAR-based products.

Figure 1 .
Figure1.The study area.(a) The red outline shows the region of study, which is based on the maximum extent of all available daily ice charts during the study period.(b) An example of the data set coverage over the study area for a given day.Each date's coverage is indicated by a polygon with different colors.The study area's size changes daily and month to month due to changes in the area over which CIS is required to provide ice conditions, which depends on shipping and other activities in the region.Notice that the largest charted area in (b) is for October when the ice starts to freeze up, and there is still activity over a large region of Baffin Bay.Datum is the world geodetic system 1984 (WGS84), and the projection coordinate system is Lambert conformal conic.

Figure 2 .
Figure 2.An illustration of sea ice concentration retrieved from the ASI (a), NT2 (b), BT (c) algorithms, rasterized CIS daily ice chart (d), and CIS daily ice chart (e) on February 03, 2014, over the study area.In panels a-d, regions without data are shown in light blue, while the lands are black.

Figure 4
Figure 4 represents how EDE and d wavg Hcan be different in two scenarios, assuming the grid cell size is 10 km:

Figure 3 .
Figure 3.An example of how the DBSCAN clustering method works for the ASI, NT2, and BT algorithms for the sea ice edge of December 2013 before clustering (panel a, c, e) and after clustering (panel b, d, e).The regions without data are shown in light blue, while the lands are black.

Figure 4 .
Figure 4. Schematic representation of the chart and PM algorithm ice edge lines (represented by green and yellow lines, respectively).Land grid cells are shown in brown.i and j show the position of grid cells.This figure represents how EDE and d wavg H can be different in two scenarios, assuming the grid cell size is 10 km: (a) sea ice edges are in straight lines or with a few turns (EDE ¼ 0.21, d wavg H ¼ 13.87 km), (b) sea ice edges are in meandering patterns with numerous turns (EDE ¼ 0.12, d wavg H ¼ 15.90 km).

Table 2 .
Annual partial concentration for thin (left) and thick (right) ice derived from the CIS ice charts in 2013-2021 over the ice-covered region of the study.The total ice concentration is the sum of the thin and thick ice.The blue hatches indicate no chart available for September 2014 and 2021 over the study area.The colors for seasons appear on the left: light green for melt and dark blue for freeze-up.The colors for seasons appear on the right: light blue for winter and dark orange for summer.
algorithm has the lowest EDE and d wavg H

Figure 5 .
Figure 5.An illustration of the monthly EDE and d wavg H values over the study area for April 2017: (a) ASI, (b) NT2, (c) BT, and October 2017: (d) ASI, (e) NT2, (f) BT.Ice edges determined by the CIS ice chart are in blue color contours, and those from the ASI, NT2, and BT algorithms are in red color contours.Edge determination is based on a 15% SIC threshold, and the ice edges are calculated based on the monthly SIC values.The regions without data are shown in light blue, while the lands are black.

Figure 6 .
Figure 6.A box-whisker plot visualization of the d wavg H : (a) ASI, (b) NT2, (c) BT, L avg : (d) ASI, (e) NT2, (f) BT, and EDE (g) ASI, (h) NT2, (i) BT, in each month over the whole study period and study area.Each measurement's median and average values are indicated by a line across the box and a green triangle, respectively.The box length indicates the corresponding measurement's interquartile range (IQR).The circles outside the box indicate an outlier.

Figure 7 .
Figure 7.A box-whisker plot visualization of the monthly wind speed (m/s) and 2-meter air temperature over the whole study period and study area.Each measurement's median and average value are indicated by a line across the box and a green triangle, respectively.The box length indicates the corresponding measurement's interquartile range (IQR).The circle outside the box indicates an outlier.

Figure
Figure A1.Continued

Table 1 .
Ice categories based on the ice stage of development are included in the CIS ice charts.

Table 3 .
Statistics of sea ice edge derived from the ASI, NT2, and BT algorithms with respect to the CIS ice charts over the study area between 2013 and 2021.SD) is taken over all data that are first averaged on a monthly basis.The Winter season includes January, February, and March.Melt season includes April, May, and June.The freeze-up season includes October, November, and December.Results are statistically significant at a 0.05 level.Ã Sea ice concentration is calculated at the chart ice edge.L avg than the NT2 and ASI algorithms.This suggests that sensor spatial resolution may have played a small role in these statistics.The low EDE and d