We use the ICESat-2 ATL10 freeboard product (currently at Release 005, rel005), which is disseminated through the National Snow and Ice Data Center (NSIDC) (Kwok et al., 2021a). ATL10 is the end result of a series of algorithms that convert the primary geolocated photon product (ATL03, Neumann et al., 2019) to sea ice height and type (ATL07, Kwok et al., 2021a) and then sea surface height and freeboard (ATL10, Kwok et al., 2021b). Briefly, the ATL07 algorithm subtracts a mean sea surface and time-varying ocean tide and inverted barometer corrections from ATL03 and then aggregates and windows 150 photons around this corrected surface along each beam independently. ATL07 then extracts a best-guess Gaussian height distribution convolved with the expected system response to the photon height histogram to determine a single segment height and various metrics summarizing the goodness of fit and radiometry (e.g. photon rate) of each segment. This photon aggregation results in data with variable segment lengths of, on average, ∼ 15 m for the strong beams and ∼ 60 m for the weak beams (Kwok et al., 2019b). The spatial resolution of the individual segments can be estimated by adding the individual laser footprint size of ∼ 11 m (Magruder et al., 2020) to the segment length, i.e. a mean of ∼ 25 m for the strong beams and 70 m for the weak beams. An empirically based decision-tree algorithm is used to discriminate the height segments as either sea ice or sea surface/lead (Kwok et al., 2016). More details of the surface classification scheme are available in Kwok et al. (2021d) and Petty et al. (2021), while the complete processing methodology is available in the Algorithm Theoretical Basis Document (ATBD) for sea ice products (Kwok et al., 2021c).

ATL10 converts adjacent sea surface segments into lead groups to reduce noise in the lead height estimate and then averages these into 10 km along-track sea surface reference height estimates along each beam. Freeboard is calculated as the difference between the individual ice height segments and the local sea surface height, independently for each beam. Negative freeboards are set to zero. The laser returns are expected to track the snow-covered ice surface, so ATL10 is expected to provide a measure of “total” (ice plus snow) freeboard. The ICESat-2 beams are arranged in “strong” and “weak” beam pairs, with each beam pair separated by ∼ 3.3 km in the across-track direction and the strong/weak beams separated by ∼ 90 m across track and ∼ 2.5 km along track. The weak beams are around 4 times lower energy (lower photon rate) than the strong beams. In this study we utilize only the strong beams to ensure the highest possible data quality.

We use snow depth and density estimates from the NASA Eulerian Snow On Sea Ice Model (NESOSIM) (Petty et al., 2018a, P2018), which is publicly available on GitHub (https://github.com/akpetty/NESOSIM, last access: 1 December 2022). NESOSIM was developed primarily in preparation for the launch of ICESat-2 to enable timely production of snow depth and density estimates for sea ice thickness retrievals using a simple snow accumulation model framework. NESOSIM includes two vertical snow layers and several simple parameterizations (accumulation, wind packing, advection–divergence, blowing-snow loss) to represent the expected primary sources and sinks of snow on Arctic sea ice during the accumulation season. Summer melt processes are currently neglected, so the model is typically run between September and the end of April. NESOSIM v1.0 was first presented in P2018, and the output using this v1.0 framework was used in P2020 to produce snow loading needed to convert ATL10 freeboards (rel002) to sea ice thickness from October 2018 to April 2019. The NESOSIM v1.0 output used in P2020 was forced with snowfall, winds and near-surface air temperature (to scale the initial snow conditions) from ERA-I (Dee et al., 2011), sea ice concentrations from the NASA Climate Data Record (CDR) version 3 (Meier et al., 2017), and ice drifts from the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Ocean and Sea Ice Satellite Application Facility (OSI SAF) (Lavergne et al., 2010), which were all regridded to a 100 km × 100 km Arctic Ocean domain using bilinear interpolation.

We use the same approach as in P2020 to generate estimates of winter Arctic sea ice thickness and an associated uncertainty estimate. Briefly, thickness is calculated assuming hydrostatic equilibrium and input estimates of sea ice density, snow depth and snow density. The coarse-resolution (∼ 100 km) snow depth input estimate, primarily from NESOSIM, is redistributed to the high-resolution (∼ 30 m) ATL10 freeboards using a piecewise functional fit obtained from snow depth and freeboard data collected by NASA's Operation IceBridge mission (Kurtz et al., 2009; Petty et al., 2020). Uncertainties are calculated by propagating errors through the hydrostatic equilibrium equation with contributions from random errors (estimates based on previous studies) and systematic errors (estimates based on the spread in applied input assumptions). Small differences in our thickness processing to that presented in P2020 include a bilinear interpolation scheme instead of nearest neighbour to assign NESOSIM data to the ATL10 freeboard segments. Nearest-neighbour interpolation was originally used to reduce processing time but introduces unphysical step changes. We also fixed some minor bugs in the freeboard uncertainty calculation and have incorporated the new NSIDC regional mask of the Arctic Ocean (Fig. 5). As in P2020 we use daily estimates of ice type from the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Ocean and Sea Ice Satellite Application Facility (OSI SAF, https://osi-saf.eumetsat.int, last access: 1 December 2022) (Breivik et al., 2012) to classify each segment as either first-year ice (FYI) or multiyear ice (MYI). Ice type information is needed in part to derive the modified Warren snow depth estimates (see Sect. 2.2.2. in P2020), so our approach is to assume all ice is MYI unless the OSI SAF product explicitly characterizes the segment as FYI. Thus, in September when OSI SAF does not provide any ice type estimate due to added uncertainties in the end-of-summer retrievals, we assume all our ATL10 and derived thickness data are MYI. The along-track thickness data, both raw segment-scale data and 10 km means, have been made available through the NSIDC (IS2SITDAT4 version 1, https://nsidc.org/data/is2sitdat4/ (last access: 1 December 2022), Petty et al., 2022a). We plan to update this dataset each year as new winter Arctic ATL10 data are generated and released.

In producing the monthly gridded dataset, we use all three strong beams to increase coverage and lower expected uncertainties, compared to the single strong beam used in P2020. The use of all three strong beams was also motivated by the reduction in data coverage in rel003 and onwards ATL10 data processing (described in Sect. 2.1.1 and noted in Fig. 2). Our gridding approach is slightly different from the official gridded ICESat-2 freeboard product (ATL20, https://nsidc.org/data/ATL20, last access: 1 December 2022) as we bin all data within a given month for each grid cell, as opposed to producing daily gridded composites and then monthly gridded composites from the daily gridded data. Our monthly gridded data include ancillary data variables representative of the mean day of the month for each grid cell calculated as the mean date of the input ATL10 data, as well as the number of ATL10 freeboard segments used in the monthly grid cells to enable sampling bias assessments. The monthly gridded data also include monthly NOAA/NSIDC version 4 Climate Data Record (CDR) sea ice concentrations (Meier et al., 2021a), a new NSIDC regional mask of the Arctic Ocean (Meier and Stewart, 2023) and the OSI SAF ice type mask (sub-sampled by ICESat-2 and then gridded monthly). The data are projected onto the NSIDC north polar stereographic grid (EPSG: 3411, https://epsg.io/3411, last access: 1 December 2022) and binned onto a 25 km × 25 km grid.

The initial version of our monthly gridded thickness dataset as described in P2020 was made available through the NSIDC (IS2SITMOGR4 version 1, https://nsidc.org/data/is2sitmogr4/versions/1, last access: 1 December 2022). Our updated dataset presented in this study using rel005 ATL10 data, NESOSIM v1.1, and the updated NSIDC Arctic region mask and CDR sea ice concentrations have been made available as a new version 2 (v2) release of the IS2SITMOGR4 dataset (Petty et al., 2022b). We expect to update this each year along with the along-track product (IS2SITDAT4) as new winter Arctic ATL10 data are made available. We also include in this IS2SITMOGR4 v2 dataset smoothed and interpolated variables of freeboard, snow depth, and thickness in an initial attempt to fill in the pole hole and mitigate the spatial sampling biases. These preliminary variables are not used in the subsequent analysis presented here, but their derivations are described and made available to interested users in the online Jupyter Book discussed below. We expect that future work will explore more sophisticated interpolation procedures and blending with other thickness datasets, which we discuss more in the summary section.

In P2020, monthly gridded ICESat-2 thickness data were compared with thickness estimates generated from the European Space Agency (ESA) CryoSat-2 mission from four different groups: NASA's Goddard Space Flight Center (GSFC, Kurtz and Harbeck, 2017), the Jet Propulsion Laboratory (JPL, Kwok and Cunningham, 2015), the Centre for Polar Observation and Modelling (CPOM, Laxon et al., 2013; Tilling et al., 2018) and the Alfred Wegener Institute (AWI, Hendricks and Ricker, 2016). Large differences were noted on these regional/monthly scales (ICESat-2 generally thinner), so here we repeat the comparison using upgraded monthly gridded thickness data. As the different products make different assumptions regarding snow loading and sea ice, for these comparisons we use the same snow loading assumptions in the ICESat-2 thickness processing to generate direct thickness comparisons to simplify the interpretation of the differences observed (differences should be due to differences in the freeboard retrievals rather than differences in input assumptions). As in P2020, we re-grid the monthly gridded CS-2 estimates to the NSIDC 25 km × 25 km north polar stereographic grid using a simple nearest-neighbour interpolation scheme and compare these with our gridded ICESat-2 sea ice thickness estimates that have been produced using the same snow loading and ice density assumptions as the given CS-2 product, as summarized in Table 2 in P2020. Modified versions of the Warren snow depth climatology (mW99, Warren et al., 1999) were used by all four of these CryoSat-2 thickness products. Differences between mW99 and NESOSIM are discussed in Sect. 2.2.1. To be consistent with the results shown in P2020 we just use strong beam 1 to generate these data. This comparison is not seen as a validation of either product but a way of simply exploring regional/seasonal differences between these products due to the contrasting freeboard retrievals.

As we seek in this study to also track seasonal winter changes in sea ice thickness, we carry out an additional CryoSat-2 comparison of monthly mean Inner Arctic Ocean sea ice thickness between our gridded thickness estimate and various CryoSat-2 thickness estimates. The aim of this comparison is to simply highlight the correspondence (or lack thereof) in the winter seasonal thickness cycles for the years of overlap. In this comparison we compare our best-guess ice thickness (e.g. ICESat-2 thickness using NESOSIM v1.1 snow loading) with the various CryoSat-2 products. We utilize the same CPOM and GSFC products as the earlier comparison, which have been updated through to 2021. We then use an upgraded AWI product that incorporates Soil Moisture and Ocean Salinity (SMOS) estimates of thin sea ice to improve both accuracy and coverage over thinner first-year ice (AWISMOS, Ricker et al., 2017). These data have been used together with our gridded ICESat-2 thickness data to explore recent sea ice thickness/volume changes for the NOAA Arctic Report Card (Meier et al., 2021b). We also utilize a newly released all-season CryoSat-2 thickness product developed by the University of Bristol (UBRIS, Landy et al., 2022) that utilizes snow loading from SnowModel-LG (Liston et al., 2020) and provides data through to summer 2020. Finally, we also show comparisons with thickness data generated from the combination of ICESat-2 and CryoSat-2 data, utilizing the assumption that ICESat-2 profiles total (ice plus snow) freeboard and CryoSat-2 profiles ice freeboard to then derive snow depth and thickness concurrently from the combined altimetry record (KK; Kwok et al., 2020; Kacimi and Kwok, 2022a).

We additionally compare the ICESat-2 and CryoSat-2 monthly mean Inner Arctic Ocean sea ice thickness with those generated from the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS, v2.1; Zhang and Rothrock, 2003). PIOMAS is an ice–ocean model that generates estimates of sea ice thickness, constrained predominantly by the assimilation of sea ice concentration and sea surface temperature. PIOMAS data are commonly used in the sea ice community for assessments of Arctic sea ice thickness variability at regional and basin scales (Tilling et al., 2015; Labe et al., 2018; Petty et al., 2018b; Schweiger et al., 2021; Moore et al., 2018). PIOMAS ice thickness estimates have been shown to exhibit differences on the order of tens of centimetres compared to satellite-derived estimates, although this depends strongly on the season and region analysed (Schweiger et al., 2011; Zygmuntowska et al., 2014; Petty et al., 2018b).

More recently, upward-looking sonar (ULS) draft data from moorings deployed as part of the Beaufort Gyre Exploration Project (BGEP) covering the period after the launch of ICESat-2 have been made publicly available (https://www2.whoi.edu/site/beaufortgyre/data/mooring-data, last access: 1 December 2022). Specifically, data from three separate moorings (A, B and D, locations shown in Fig. 5) are now available from August 2018 through to August/September 2021. Each individual ULS ice draft measurement is assumed to have an uncertainty of < 10 cm (Krishfield et al., 2014). Ice draft measurements benefit from measuring a more significant fraction of the total thickness compared to freeboard, meaning they benefit from providing a reliable indicator of variability in ice thickness and avoid the complexities of snow depth retrievals. BGEP ULS data have been well utilized historically by the CryoSat-2 thickness product developers for validation, and here we offer a first assessments of ICESat-2-derived thickness data using these same data (albeit over a different time period). We follow a similar approach to other studies (Tilling et al., 2018; Landy et al., 2022) and take the mean of ICESat-2 grid cells within a certain radius of a given mooring (we use 50 km in this study; Tilling et al., 2018, use 100 km, while Landy et al., 2022 use 150 km), then we find the nearest grid cell to each mooring for a given month and compare this to a simple monthly average of all ULS data within that month. We provide additional comparisons using different averaging radii also. We convert the gridded ICESat-2 thickness estimates (IS2SITMOGR4 version 2) to ice draft by adding the NESOSIM snow depth and subtracting the total (ATL10) freeboard.

To understand the possible relationships between seasonal/interannual differences in ice thickness and winter Arctic atmospheric conditions, we utilize near-surface (2 m) air temperature and downwelling longwave radiation estimates from the ERA5 reanalysis (Hersbach et al., 2020). A warm bias of 1–4 ∘C in 2 m air temperatures over Arctic sea ice in ERA5 has been noted in comparisons with drifting buoys (Wang et al., 2019; Yu et al., 2021) which has been linked to the basic (fixed thickness) representation of sea ice and its overlying snow cover in reanalyses including ERA5 (Batrak and Müller, 2019). We utilize these data with caution and focus primarily on basin-average/seasonal differences.

In Fig. 6 we show probability distributions of winter Arctic freeboards calculated using rel002 (as used in P2020) through to rel005 ATL10 data. We show distributions from November 2018, January 2019 and April 2019 to assess differences during different regimes of winter Arctic sea ice (early, middle and late winter) for the first season of data collection. The distributions use data collected by beam 1 (strong) within an Inner Arctic Ocean domain (Central Arctic, Beaufort Sea, Chukchi Sea, Laptev Sea, Kara Sea). Note that in these distributions we show only positive values of freeboard and later snow depth and thickness, while in the raw along-track IS2SITDAT4 dataset zero freeboards, typically from open-water lead segments, are included also.

Figure 6 shows that the only notable change in freeboard distribution occurs between rel002 and rel003 – a freeboard decrease of 1.2 cm in November 2018 (26.2 to 25.0 cm), a 1.9 cm increase in January 2019 (27.7 to 29.6 cm) and a 3.4 cm increase in April 2019 (35.9 to 39.3 cm). In contrast, the rel003 to rel005 freeboard distribution differences across these 3 months are small or negligible (< 0.4 cm), with the rel005 freeboards generally the highest from the four releases. As discussed earlier, this was largely expected due to the major algorithm change in rel003 (Kwok et al., 2021d) and the lack of major algorithm changes related to freeboard derivation in rel004 and rel005. The 1.2 cm mean freeboard reduction in November 2018 is due to a stronger primary freeboard peak and a weaker secondary peak in the rel003 to rel005 freeboard distributions, while January 2019 and April 2019 distributions exhibit a clear increase in the unimodal freeboard in rel003 onwards. Kwok et al. (2021d) analysed gridded freeboard distributions in January 2019, June 2019 and October 2019 and found 3, 1 and 2 cm increases, respectively, between rel002 and rel003, broadly in line with the magnitude of the differences observed here. As discussed in Sect. 2.1.1 and demonstrated in Fig. 2, the different releases also include changes in coverage, especially between rel002 and rel003, which may influence these differences along with changes in the freeboard determination algorithm.

Figure 6 (right column) also shows an analysis of the inter-beam differences across the three strong beams for the same time periods and Inner Arctic Ocean region for rel005 data only. The inter-beam differences are small (< 1 cm), similar to the rel003 to rel005 differences. Each strong beam is separated by ∼ 3 km across track, so greater differences are expected at local scales; however, an in-depth analysis of spatial length scales is beyond the scope of this study. We instead note that at basin/monthly scales, the beams provide similar freeboard distributions despite the small differences in coverage (as discussed in Sect. 2.1.1 and highlighted in Fig. S2), increasing our confidence in using all three beams to extend coverage across the Arctic.

Figure 7 shows the impact of ATL10 release changes and the two NESOSIM versions (v1.0 and v1.1) on the redistributed snow depths and resultant sea ice thickness estimates. The piecewise redistribution of the coarse 100 km NESOSIM output to the high-resolution ATL10 data is presented in P2020 and summarized in Sect. 2.3. These assessments were carried out during the period of rel004 availability, so these are the only runs with both NESOSIM versions processed. The difference in mean redistributed snow depth across the 3 months and ATL10/NESOSIM configurations (left column) is < 2.2 cm, with the biggest differences occurring in November 2018, where the Nv1.1 redistributed snow depths are generally thicker than the Nv1.0 snow depths (17.0 cm compared to 15.5 cm when using the same rel004 data) driven primarily by a small positive shift in the tail of the distribution. The rel004/Nv1.0 snow depths are thinner than the rel002/Nv1.0 snow depths (17.7 to 15.5 cm) highlighting the non-negligible role of underlying changes to the freeboard data in the resultant redistributed snow depths. The January and April mean snow depths are similar across the NESOSIM versions and ATL10 releases, although slight differences in the distributions are observed, e.g. a thinner secondary January 2019 snow depth peak in Nv1.1 compared to v1.0 (∼ 22 cm compared to ∼ 26 cm), which holds over the different ATL10 releases.

Figure 7 (right column) shows the impact of ATL10 release and NESOSIM version differences on estimates of sea ice thickness. For the rel004 runs, the impact on thickness from the upgrade from Nv1.0 to Nv1.1 is a decrease of 10 cm in November 2018, no change in January 2019 and a decrease of 2 cm in April 2019. In contrast, the impact on thickness of the upgrade from rel002 to rel004 ATL10 (using Nv1.0) is an increase of 6 cm in November 2018, an increase of 21 cm in January 2019 and an increase of 30 cm in April 2019. The difference between the rel004 and rel005 mean thicknesses (using Nv1.1 snow loading) is < 0 to 3 cm. In summary, the impact on thickness from the choice of NESOSIM version is less significant than the impact from rel002 to rel003 freeboard changes.

In Fig. 8, we show the correlation coefficients, mean bias and standard deviation of differences between monthly gridded ice thicknesses derived from rel002 and rel005 ICESat-2 data and thickness estimates produced from ESA's CryoSat-2. In these thickness comparisons we generate monthly gridded thickness estimates using the same input assumptions, i.e. mW99 for snow loading (see Sect. 2.2.1 and Table 2 in P2020). As in P2020 we only use beam 1 (strong) and mask all data below 0.25 m and outside of an Inner Arctic Ocean domain (Fig. 5) in both datasets before producing these comparisons to simplify interpretation and avoid regions of higher uncertainty within the more peripheral seas of the Arctic. As noted earlier, by using the same input assumptions we maintain focus on the potential impact of freeboard retrieval differences on derived sea ice thickness. The large differences observed in P2020 (ICESat-2 generally much thinner than the CryoSat-2 products despite using the same loading) were noteworthy and motivated this updated comparison.

In general, the agreement between ICESat-2 and CryoSat-2 using rel005 ATL10 freeboards is much improved compared to those based on rel002 ATL10 freeboards (shown in P2020) in terms of the correlation coefficient, mean bias and standard deviation across virtually all months and products. The statistics from all months between November 2018 and April 2019 are shown in Fig. 8. More work is needed to reconcile these datasets and assess sources of bias (as discussed more in the summary), but these results represent an encouraging initial development in terms of reducing the large biases previously noted.

We next focus on development of the version 2 gridded thickness product and comparisons with available data. In Fig. 9 we show an example output of our updated monthly gridded ICESat-2 winter Arctic sea ice thickness product (IS2SITMOGR4 version 2, v2) for April 2021 using the latest default thickness processing configuration (rel005 ATL10 and NESOSIM v1.1 snow loading). Spatial coverage is generally high across all months despite the concerns expressed in Kwok et al. (2021d) and in Figs. 2 and S1, related to reduced lead/sea surface height segments and thus freeboard determination. This was partly mitigated by our use of three strong beams (coverage changes were discussed in Sect. 2.1.1). However, there are still large regions of missing data in our monthly gridded dataset, e.g. the missing data in the Laptev/East Siberian Sea shown in Fig. 9 despite the monthly CDR ice concentrations showing concentrations greater than 50 % in that same region. Data drop-out is often caused by the presence of clouds and the resultant atmospheric scattering impacts on ATLAS retrievals. Our interpolated/smoothed variables of freeboard, snow depth and thickness data (Fig. 9i–k, not used in this study) do not substantially increase coverage in these regions, which was in part by design to avoid over-extrapolation of our thickness estimates. In general, the monthly gridded data gaps are limited but should be considered when using these data to assess regional- and basin-scale thickness variability.

In Fig. 10 we show a comparison of IS2SITMOGR4 v2 converted to ice draft with ice draft estimates obtained by Beaufort Gyre Exploration Project (BGEP) upward-looking sonar moorings (data and methodology described in Sect. 2.6). The comparison statistics are strong, including high correlations (squared Pearson correlation coefficient, r2 = 0.87), relatively low mean bias (11 cm) and low standard deviation of differences (20 cm) when analysing monthly mean data from all three moorings. Mooring A shows higher r2 than mooring B and D (0.93 for A, 0.89 for B and 0.88 for D), but these are all still considered strong. Mooring B shows significantly lower mean bias (1 cm) compared to moorings A (14 cm) and D (20 cm). As noted in Sect. 2.6 all IS2SITMOGR4 data with 50 km are averaged before undertaking these comparisons, following earlier CryoSat-2 studies. In Fig. S5 in the Supplement we also show comparisons using an averaging radius of 25, 50, 100 and 150 km, which all largely show similar results to those presented in Fig. 10 (e.g. some improved correlation but also increased mean differences at 100 km). The BGEP ULS comparisons provide crucial validation of our ICESat-2 thickness data for tracking seasonal/interannual winter Arctic thickness changes.

In Fig. 11 we show a comparison of basin-averaged Inner Arctic Ocean sea ice thickness estimates between IS2SITMOGR4 v2, several CryoSat-2 products and PIOMAS. The goal of this analysis is to provide a basic intercomparison of these commonly used datasets for inferring seasonal/interannual changes in winter Arctic sea ice thickness. Figure 11 includes the raw monthly data (within our Inner Arctic Ocean domain) but also data on a common mask (CM) where data are masked in grid cells missing from the other datasets. These enable a more direct comparison, while differences between the CM and non-CM results are useful indicators of the seasonal impact of spatial sampling biases when assessing basin-scale means. In general, the agreement between IS2SITMOGR4 and the various CryoSat-2 products is strong, albeit significant differences are still observed depending on the product analysed. The AWISMOS comparison shows the highest correlation (r2 = 0.89) and lowest mean bias (-1 cm) and standard deviation of differences (11 cm) of the CryoSat-2 products. The CPOM and UBRIS comparisons are also strong, although the CPOM thicknesses are noticeably higher (20 cm mean bias). The UBRIS comparisons are notable for showing consistently thinner ice compared to IS2SITMOGR4 prior to April, although only two winter seasons are available for this comparison. The combined ICESat-2–CryoSat-2 data (KK) compare the best with IS2SITMOGR4 v2, although as these are generated from ATL10 total freeboards, these are not truly independent (the strong agreement is still encouraging). The GSFC product shows the weakest agreement with IS2SITMOGR4 in terms of the squared correlation coefficient (r2), mean bias and standard deviation of differences. Additional spatial difference plots are generated and provided in the online Jupyter Book.

In general, the PIOMAS results are consistent with the IS2SITMOGR4 v2 and CryoSat-2 products, although they tend to show weaker correlations compared to the CryoSat-2 comparisons and exhibit stronger seasonality than the satellite-derived products, including 20–40 cm thicker ice by the end of the season compared to IS2SITMOGR4. Additional spatial difference plots are generated and provided in the Jupyter Book, which highlight the stronger disagreement at regional scales, e.g. PIOMAS not simulating the thicker ice north of the Greenland and Canadian Arctic Archipelago (CAA) coasts shown in IS2SITMOGR4 data. These results are broadly in line with previous published comparisons between PIOMAS and satellite altimetry-derived thickness data, including comparisons with the original ICESat mission (Schweiger et al., 2011; Petty et al., 2018b; Wang et al., 2016). The strong differences in September/October between the CM and non-CM data highlight the impact of spatial sampling issues earlier in the season (where there is a greater fraction of thin/low-concentration ice in the Inner Arctic Ocean).

In summary, while there is not perfect agreement across the products in terms of the seasonal changes in winter Arctic sea ice thickness, the IS2SITMOGR4 v2 product shows good agreement with existing products and generally lies within the CryoSat-2 product spread (mean biases that were both positive and negative depending on the product analysed). In addition to the BGEP/ULS ice draft validation, this provides us with confidence in undertaking a deeper investigation into winter sea ice changes from this dataset.

In Fig. 12 we show the seasonal evolution of winter freeboard, snow depth/density and sea ice thickness from our IS2SITMOGR4 v2 monthly gridded dataset. The results shown in Fig. 12 are again restricted to our Inner Arctic Ocean domain. The data within this domain in September and October are generally lower concentration (∼ 85 % on average, Fig. 10e) than the preceding months, so changes in early winter are still strongly influenced by the changing coverage of sea ice as the ice pack refreezes. Note that the concentration decline from September to October is due to changes in data coverage as regions with ice concentrations < 50 % are not included in ATL10 and thus our thickness estimates. We therefore mainly focus on analysing November to April changes, the period in which we also have full monthly data available across all three winters. Extended analysis of this data, e.g. utilizing different region masks, is possible through the online Jupyter Book.

Mean monthly Inner Arctic Ocean freeboards from ATL10 show a monotonic increase from 22 cm in November 2018 to 38 cm in April 2019. Mean monthly freeboards in November 2019 are similar to 2018 but consistently lower in subsequent months (lower by ∼ 2–3 cm). Mean freeboards in November 2020 are notably lower than the previous two winters (20 cm mean, lower by ∼ 2–3 cm) and are similar or lower than the 2019–2020 monthly means (lower by ∼ 1–2 cm).

Mean monthly Inner Arctic Ocean snow depths from the redistributed NESOSIM v1.1 output monotonically increase from 14 cm in November 2018 to 24 cm in April 2019, increasing more rapidly between January and April than between November and January. Snow depths in the 2019–2020 winter show a similar seasonal evolution but with snow depths consistently ∼ 2 cm thinner than the 2018–2019 monthly means. The 2020–2021 snow depths are similar to 2019–2020, showing thicker snow in January 2021 compared to January 2020 but thinner snow in April 2021 than April 2020 and 2019. The mean seasonal snow density evolution is similar across the three winters, with the 2020–2021 density lower in November than the previous winters but notably higher than the previous winters between February and April. Due to the crude nature of the NESOSIM density parameterization, we do not view this analysis as a reliable interannual snow density assessment but highlight this more to understand the density variability impact on our ice thickness estimates.

Our mean monthly estimates of Inner Arctic Ocean sea ice thickness show an increase from 1.20 ± 0.30 m in November 2018 to 2.0 ± 0.35 m in April 2019, with the monthly thickness increasing more rapidly between November and February than between February and April. The 2019–2020 monthly mean thickness evolution is similar to 2018–2019 winter but with a lower April 2020 mean thickness of 1.90 ± 0.35 m compared to April 2019. The 2020–2021 mean thicknesses are notably thinner in November through February compared to the previous two winters, ∼ 0.9 ± 0.3 m in November 2020 to 1.90 ± 0.35 m in April 2021. Analysing just these three winters, we observe clear differences in winter Inner Arctic Ocean thickness, with variability in the NESOSIM snow depth, and density to a lesser extent, modulating a significant component of the seasonal freeboard differences observed by ICESat-2. For example, thinner 2019–2020 snow compared to 2018–2019 mitigates the thinner freeboards and results in similar mean thickness across both winters; thinner April 2021 snow compared to 2020 and 2019 April snow mitigates the thinner freeboard and similarly results in a similar mean thickness. It is also worth noting that the fraction of multiyear ice is inversely related to the thickness rankings – i.e. the 2018–2019 winter shows the lowest mean fraction of multiyear ice in this 3-year period but also shows the highest freeboard, snow depths and thickness. Three years is not a long enough record to establish true relationships, but the results highlight the potential pitfalls of inferring thickness from ancillary quantities such as freeboard or multiyear ice fraction if one is interested in tracking interannual changes.

To highlight the spatial distribution of the winter changes discussed above, Fig. 13 shows maps of winter mean (November to April) freeboard, snow depth and thickness from IS2SITMOGR4 v2, while Fig. 14 shows anomalies relative to the three-winter mean. The most notable features of these maps are the positive freeboard and thickness anomalies in 2018–2019 and negative freeboard and thickness anomalies in 2020–2021 north of Greenland and the Canadian Arctic Archipelago (CAA), the region of the Arctic where we generally expect to observe the thickest freeboard, snow depth and thickness. On more regional scales, there are noteworthy examples of the impact of the time-varying NESOSIM snow depths on our thickness retrievals; e.g. the positive snow depth anomalies in the Laptev Sea and the Central Arctic in 2018–2019 modulate the impact of the positive ATL10 freeboard anomalies on our retrieved thickness anomalies. In contrast, the strong negative NESOSIM snow depth anomalies in 2020–2021 modulate the negative ATL10 freeboard anomalies. The low freeboards within the Barents Sea region and the increased potential for surface flooding in this region (Granskog et al., 2017), a process which is not currently simulated by NESOSIM, means those results should also be treated with caution (this region is mostly excluded from our Inner Arctic Ocean domain, Fig. 5).

These results are broadly in line with the analysis of joint ICESat-2–CryoSat-2 sea ice freeboard, snow depth and thickness presented in Kacimi and Kwok (2022a). Their results, analysed within a similar Inner Arctic Ocean region, show encouraging agreement with the results presented here: (i) snow depths increasing from ∼ 10–12 cm in November to ∼ 20–22 cm in April, ∼ 2 cm thinner than our snow depths but with a similar overall decline of ∼ 3 cm over the 3-year period, and (ii) thickness increasing from ∼ 1.0–1.3 m in November to 2.1–2.4 m in April, ∼ 10–40 cm thicker than our snow depths but with a similar overall decline of ∼ 10–30 cm depending on the month analysed, with 2020–2021 notably thinner.

ICESat-2/ATL10. Work is still ongoing to re-introduce dark leads to the sea surface and freeboard algorithm in ATL10, which requires a new filter to skilfully discriminate dark-lead segments (low photon rate) from segments with photon attenuation driven by the presence of clouds. The variable properties of clouds and their impact on photon attenuation, together with the limited availability of coincident imagery for validation (as used in Petty et al., 2021), make this development challenging. An additional near-term goal related to ATL10 is the plan to utilize all six beams, or at least the three strong beams, concurrently to produce two-dimensional interpolated fields of sea surface height, as opposed to the independent beam processing currently utilized. However, residual absolute height biases of several centimetres are still observed between the beams as of Release 005 (updated from the analysis by Bagnardi et al., 2021, not shown), hindering this development. More sophisticated sea surface interpolation methods should also be explored (Landy et al., 2021). Algorithm development efforts related to these issues are ongoing through the ICESat-2 Project Science Office, to be included in future ATL10 data releases.

Snow loading. Work is ongoing to utilize a Markov chain Monte Carlo (MCMC) approach to automate the calibration of NESOSIM and provide a more robust uncertainty estimate of snow depth and density from this simple model framework (Cabaj et al., 2021). This approach benefits from the low computational cost of NESOSIM, allowing thousands of model simulations to be generated across plausible model parameter space. Additional physical upgrades are still desired, e.g. the introduction of a snow melt parameterization to extend NESOSIM through summer. However, additional reliable ground-truth data at regional/basin scales are needed to calibrate and validate such development activities.

Recent studies leveraging newly generated Arctic snow reconstructions and satellite-derived data products, including the joint ICESat-2–CryoSat-2-derived snow depths, are helping collectively provide new insights into snow depth variability and its impacts on sea ice thickness and its contribution to total thickness uncertainty (Zhou et al., 2021; Mallett et al., 2021; Glissenaar et al., 2021; Kacimi and Kwok, 2022a). While these datasets, including NESOSIM, are still generally limited by a lack of contemporary ground-truth data for assessing data accuracy, the creation of new operational, i.e. continuously updated and disseminated, snow products should help enable more comprehensive assessments of systematic snow loading uncertainties. The comprehensive in situ snow observations collected from recent campaigns, including the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition (Wagner et al., 2022), can hopefully aid with the continued refinement of these new snow reconstructions and redistribution methods.

ICESat-2-derived sea ice thickness. Our primary focus of the three-winter thickness assessment was the monthly gridded winter Arctic thickness dataset (IS2SITMOGR4 v2, Petty et al., 2022b). We hope to incorporate a more comprehensive and accurate accounting of the various error contributions where possible, e.g. accounting for the clear representation error associated with grid cell sampling time differences, while also exploring more sophisticated uncertainty quantification methods (e.g. Monte Carlo approaches). Raw (and 10 km smoothed) along-track data at the segment resolution of ATL10 (∼ 20 m) are also available (IS2SITDAT4, Petty et al., 2022a, data shown in Fig. 7), which provide higher-fidelity information regarding the sea ice state than the monthly gridded estimates. Efforts have been recently undertaken to assess the winter Arctic sea ice thickness distribution from these data, including comparisons with model-based estimates (Smith et al., 2022). Continued refinement and/or redevelopment of the snow redistribution scheme is expected. We also hope to combine these data with new ICESat-2-derived floe size estimates (Petty et al., 2021) towards a joint floe-size–thickness distribution in combination with efforts to improve the accuracy of the lead/ice discrimination. The along-track dataset is more computationally demanding, but increasing access to high-performance computing environments (e.g. cloud compute platforms) would help increase its usability. The extension of NESOSIM through summer months will help enable summer preliminary production of summer Arctic thickness estimates, together with improved understanding of the performance of ICESat-2 over the complex summer melt surface for summer freeboard determination (Tilling et al., 2020). A recently completed 2022 ICESat-2 summer airborne calibration/validation (cal/val) campaign should also provide important insights towards this goal.

Sea ice thickness reconciliation. The improved correspondence between our ICESat-2-derived estimates of winter Arctic sea ice thickness and those generated from ESA's CryoSat-2 is encouraging. There are clear advantages (and disadvantages) from estimating sea ice thickness from either radar or laser altimetry, which need to be better considered and utilized for constraining total Arctic, and eventually Antarctic, sea ice volume. Radar altimeters, e.g. CryoSat-2, are highly sensitive to leads and are unaffected by clouds, providing benefits to both the quality and coverage of data collected. In contrast, laser altimeters (e.g. ICESat/ICESat-2) generally provide higher-resolution data and obtain more precise estimates of the snow-covered ice surface height (and thus total freeboard) compared to the arguably less distinct/certain ice–snow interface height (and thus ice freeboard) obtained by typical radar altimeters. The effective radar penetration depth at Ku band is generally considered to come from the ice–snow interface, although recent studies continue to challenge this (Nandan et al., 2017; King et al., 2018). As ICESat-2 profiles the upper snow surface, there is also more constraint on the total snow loading (it cannot be more than the measured freeboard). In both cases, uncertainties in the derived freeboard estimates are combined with uncertainties in the various input assumptions (snow loading, sea ice density) to provide total thickness uncertainty estimates. Constraining the various input uncertainties and residual biases remains challenging, which points to the need for improved exploitation of existing ground-truth data and further field and airborne campaigns considering the fast-changing Arctic. The good agreement between our results and the various CryoSat-2 products on a basin-averaged scale is also encouraging, but significant differences are still observed across specific months and at more regional scales that are worthy of further investigation. Improvements to the underlying freeboard algorithms and input assumptions are urgently needed as we seek to reconcile these datasets and hopefully move towards multi-sensor thickness assessments (increasing coverage and data quality). More work is also needed to agree on standardized methods of uncertainty quantification and propagation of errors for both along-track and gridded datasets, accounting for the different spatial scales involved. Planning is underway for a coordinated intercomparison exercise around new semi-synchronous along-track measurements available since the CRYO2ICE orbit alignment (https://earth.esa.int/eogateway/missions/cryosat/cryo2ice, last access: 1 December 2022).