2.1 Sea-ice concentration data sets

For this study, we consider 10 different sea-ice concentration products (Table 2, with more details in Appendices A–F). There are many more algorithms and products available than we are using here; see e.g. Ivanova et al. (2015). The main criteria for our choice of algorithms and products are (1) length of the product time series, (2) grid resolution, and (3) accessibility and sustained production. We exclude products with less than 10-year coverage and/or with a finer grid resolution than 12.5 km. Following Table 2 we comment on several specific issues that are important for the correct interpretation of sea-ice concentration products, namely the grid resolution, the land spillover correction, the weather/open water filter, and the sea-ice concentration distributions around 0 % and 100 %.

We group the products according to their concept for sea-ice concentration retrieval (Table 2, column “Group”). Group I contains the four European Organisation for the Exploitation of Meteorological Satellites-Ocean and Sea Ice Satellite Application Facility – European Space Agency-Climate Change Initiative (EUMETSAT OSI SAF and ESA CCI) products. Group II contains the Comiso bootstrap (CBT) algorithms, which are CBT–SSMI (Special Sensor Microwave/Imager), CBT–AMSR-E (Advanced Microwave Scanning Radiometer aboard Earth Observation Satellite), and National Oceanic and Atmospheric Administration (NOAA) CDR (the third is a combination of CBT–SSMI and NASA Team (NT1)–SSMI but is clearly dominated by CBT–SSMI). NT1–SSMI and Artist Sea Ice (ASI)–SSMI are assigned to group III. These algorithms follow a different concept to retrieve the sea-ice concentration where the sea-ice concentration is mainly based on a brightness temperature polarization difference. Finally, the enhanced NASA Team (NT2)–AMSR-E is assigned to group IV; its concept to derive sea-ice concentrations via a lookup table and modelled atmospheric profiles is fundamentally different from the other nine algorithms.

2.1.3 Weather/open water filter

The two standard weather filters based on brightness temperature gradient ratios at 19, 22, and 37 GHz, which mitigate noise due to atmospheric moisture and wind-induced roughening of the ocean surface (Cavalieri et al., 1995, 1999), are applied in the products NT1–SSMI and NT2–AMSR-E. In the products CBT–SSMI and CBT–AMSR-E, spurious sea-ice concentrations caused by weather effects are filtered using the same frequencies as mentioned above but applying a bootstrap technique (Comiso and Nishio, 2008). For NOAA CDR (Appendix F), the above-mentioned weather filters are applied before the merge (Meier and Windnagel, 2018). In the two National Aeronautics and Space Administration Goddard Space Flight Center (NASA GSFC) (Appendices C, D) sea-ice concentration products, i.e. NT1–SSMI version 1 and CBT–SSMI version 3, weather effects are reduced by screening of input brightness temperatures, application of the above-mentioned weather filters, and some additional manual correction (Meier and Windnagel, 2018; Peng et al., 2013, https://nsidc.org/data/g02202/versions/3, last access: 7 February 2019, https://nsidc.org/data/nsidc-0051, last access: 7 February 2019, and https://nsidc.org/data/nsidc-0079, last access: 7 February 2019). In the ASI–SSMI product no specific weather filter is applied to the ASI algorithm itself. However, ASI algorithm sea-ice concentrations are set to 0 % where NASA Team algorithm sea-ice concentration values are < 30 % (see Appendix B). Because the above-mentioned two weather filters are applied to the NASA Team sea-ice concentration, the ASI–SSMI product implicitly contains a weather filter as well (Ezraty et al., 2007). Note that the 5 d median filter used for the ASI–SSMI product used here (Kern et al., 2010) not only removes remaining spurious sea ice over open ocean but also reduces weather-induced elevated sea-ice concentrations along the ice edge. In the group I products a dynamic open water filter is applied. It is based on the quoted standard weather filters but takes into account changes in filter efficiency due to changes in the frequencies between the different sensors, for instance between SMMR and SSM/I. Also, it does not use the channels close to 22 GHz. All weather filters may in addition to the spurious ice also remove real ice along the ice edge. All 10 products apply a monthly varying climatological sea-ice cover mask to erase spurious sea ice at low latitudes.

We investigate the temporal consistency of the weather filters. For this we focus on the sea-ice concentration interval ]0.0 %, 30.0 %]; i.e. we exclude grid cells set to exactly 0.0 % by the weather filter. Then, for each day of the month, we identify the 5th percentile of all gridded sea-ice concentrations falling into the above-mentioned interval. Subsequently, we average over the month. We look at two aspects. First, it is desirable that these time series are mostly stable across the time period covered by a given data record, indicating that the weather filter cuts the sea-ice edge evenly across inter-annual variability and changes of frequencies. Second, it is also desirable that the weather filter cuts “well below” the 15 % SIC threshold that is commonly used in the computation of the sea-ice extent (SIE) (e.g. Gloersen et al., 1992; Meier et al., 2014; Comiso et al., 2017a). We choose the 5th percentile (and not a minimum value) to obtain less noisy time series. We plot examples of these time series for all 10 products in Figs. 1 and 2 for the Arctic and Antarctic, respectively. For the Arctic we use March (Fig. 1a) and September (Fig. 1g); for the Antarctic we use September (Fig. 2a) and February (Fig. 2g). In addition to the time series, we also plot the cumulative distribution of the daily sea-ice concentrations of the range ]0.0 % to 30.0 %] for the respective month for the year 2004 as an example for CBT–SSMI, OSI-450, NT1–SSMI, ASI–SSMI, and NT2–AMSR-E.

Figure 1Time series of the monthly mean 5th percentile sea-ice concentration of the range ]0.0 % to 30.0 %] for the Arctic in (a) March and (g) September for all 10 products. Panels (b–f) and (h–l) show daily cumulative sea-ice concentration distributions of five selected products in these two months, respectively, in a sample year: 2004. See Table 2 for the time periods with data from the respective products.

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Figure 2Time series of the monthly mean 5th percentile sea-ice concentration of the range ]0.0 % to 30.0 %] for the Antarctic in (a) September and (g) February for all 10 products. Panels (b–f) and (h–l) show daily cumulative sea-ice concentration distributions of five selected products in these two months, respectively, in a sample year: 2004. See Table 2 for the time periods with data from the respective products.

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Figure 3Examples of the sea-ice concentration distribution at near-100 % reference sea-ice concentration locations. Black symbols and lines show values cut off at 100 %; blue lines denote the original distribution (for SICCI-25km and SICCI-50km only); red lines denote the distribution resulting from the Gaussian fit to values of the distribution ≤ 99 %. In each panel, the modal sea-ice concentration (centre of the Gaussian fit: C_modal), the standard deviation of the fit σ_C and fit parameters with respect to the fraction of the distribution ≤ 99 % (F₉₉, ΔF₉₉; see text for more explanation), and the root-mean-squared difference (RMSD) between original and fitted probability are given. (a–c) Arctic; (d–f) Antarctic. See Appendix H for Figs. H1 and H2 containing plots of this kind for all 10 products.

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We find little inter-annual variation in the monthly mean percentile sea-ice concentration over time, particularly for OSI-450 and SICCI-25km (see also Lavergne et al., 2019). Changes as caused due to a switch in sensor remain below 1 %. On average, the 5th percentile sea-ice concentration is < 12 %, which ensures that the enhanced open water filter applied in these two products barely influences computation of SIA and SIE. For group II products, these monthly mean 5th percentile sea-ice concentrations are considerably larger and sometimes exceed 15 %. Additionally, the time series for CBT–SSMI and NOAA CDR reveal larger inter-annual variations than OSI-450, inter-sensor transitions (e.g. in 1987–1988 changing from SMMR to SSM/I, Fig. 1g); and in 2007–2008 changing from SSM/I to SSMIS, Fig. 1a) leading to trends in the percentile time series. Compared to OSI-450 and SICCI-25km, for NOAA CDR we find the following. (1) The sea-ice concentration at which the weather filter applies varies seasonally. For instance, in the year 1996, the mean 5th percentile of sea-ice concentrations within the interval ]0 %, 30 %] is 14 % for the Arctic in March but 17 % in September, and for the Antarctic it is 16 % in September but 18 % in February. OSI-450 cuts at 10 % and SICCI-25km cuts at 11 % in these months, and for both hemispheres. (2) The inter-annual variation in the sea-ice concentration at which the filter applies is larger for NOAA CDR than for OSI-450 and SICCI-25km. The time series for NT1–SSMI, ASI–SSMI, and NT2–AMSR-E, in contrast, have very low (∼ 1 %) monthly mean 5th percentile sea-ice concentration values with little or no inter-annual variation.

In the plots showing the daily cumulative fraction for the year 2004, which exemplifies the typical cumulative fraction, we find a cumulative distribution with a first increasing, later merely constant slope with no sea-ice concentrations below ∼ 10 % and ∼ 8 % for CBT–SSMI and OSI-450, respectively (panels b, c, h and i in Figs. 1 and 2). This agrees with the application of the open water filter presented in Lavergne et al. (2019). For NT1–SSMI and NT2–AMSR-E, in contrast, we find a substantial amount of near-0 % sea-ice concentrations (panels d, f, j and l in Figs. 1 and 2). This suggests that while a weather filter is applied (according to the documentations) there are still concentrations near 0 % left. We checked this by looking at the respective daily sea-ice concentration maps. Both products reveal a considerable number of grid cells with < 5 % sea-ice concentration along the ice edge. All but the group I products (see Table 2) only provide integer sea-ice concentration values. At the near-0 % end of the sea-ice concentration distribution these products have sea-ice concentrations of 0 %, 1 %, 2 %, and so forth. The number of NT2–AMSR-E sea-ice concentration values of 1 % exceeds the 5th percentile most of the time, which is the explanation for why most NT2–AMSR-E values are missing in the time series in plots (a) and (g) of Figs. 1 and 2. We take the results shown in these two figures into account when discussing the results presented in Sect. 3.

2.1.4 Distribution around 100 %

A considerable fraction of this paper focuses on the evaluation near 100 % sea-ice concentration. Sea-ice concentrations are retrieved from satellite microwave brightness temperatures using a geophysical algorithm, usually involving tie points. Tie points are typical signatures, e.g. brightness temperatures, or parameters derived from these, of ice (SIC: 100 %) and open water (SIC: 0 %). Because of the natural variability of the surface properties of 100 % sea ice relevant for its microwave remote sensing, one fixed tie point value for 100 % sea ice, even if retrieved daily, can only be an average representation of these properties. In other words, 10 different kinds of 100 % sea ice can cause 10 different brightness temperatures. As a result, a retrieved sea-ice concentration naturally varies around 100 %. This means even though the actual sea-ice concentration is exactly 100 % the retrieved one could be, for example, 97 % or 100 % or 103 %. While the group I products retain the naturally retrieved sea-ice concentration, the others do not; in all group II to group IV products (see Table 2) sea-ice concentrations are truncated at 0 % and 100 %; i.e. values < 0 % are set to 0 % and values > 100 % are set to 100 %. Figure 3 illustrates the sea-ice concentration distribution at the locations of the near-100 % sea-ice concentration reference data set (see Sect. 2.2) for SICCI-25km, SICCI-50km, and NOAA CDR for the Arctic (panels a–c) and the Antarctic (panels d–f).

We use a Gaussian fit to reconstruct the true distribution of the sea-ice concentration retrieval around 100 % for group II and III products. The methodology is tested on the group I products. This is done by finding that Gaussian curve which provides the lowest root-mean-squared difference (RMSD) to the sea-ice concentration distribution for values ≤ 99 %, i.e. basically the left-hand side of the histograms shown in Fig. 3. For the fitting process, we also take into account the fraction of sea-ice concentrations ≤ 99 % relative to the entire count of valid sea-ice concentrations: F₉₉. The difference between original F₉₉ and F₉₉ resulting from the Gaussian fit, ΔF₉₉, has to be < 0.1. We allow a maximum RMSD value of 0.0125. We first binned SICCI-25km and SICCI-50km sea-ice concentration values to integer values to be consistent with the other products. Figure 3a, b and d, e illustrate that the fits (red) agree well with the originally retrieved SICCI-25km and SICCI-50km sea-ice concentrations (blue) with modal values slightly below 100 %. Figure 3c, f illustrate how well the Gaussian fit matches the original sea-ice concentration distribution for sea-ice concentrations ≤ 99 % for NOAA CDR as an example. Here the modal sea-ice concentrations of the Gaussian fit are larger than 100 %: 103.5 % for Northern Hemisphere (NH, Fig. 3c) and 100.9 % for Southern Hemisphere (SH, Fig. 3f). In addition, the Gaussian curve is broader than for SICCI-25km and SICCI-50km, resulting in larger values for the standard deviation. We also note that F₉₉ is ∼ 0.6 and ∼ 0.5 for SICCI-25km and SICCI-50km, respectively, but only ∼ 0.2 and ∼ 0.4 for NOAA CDR. We take the information from Fig. 3 into account when interpreting the results presented in Sects. 4 and 5. We refer to Appendix H for the full set of sea-ice concentrations and Gaussian fits obtained for all 10 products in both hemispheres.

Figure 4Illustration of the typical distribution of near-100 % SIC reference data by means of the co-located OSI-450 sea-ice concentration for (a, b) the Arctic and (c, d) the Antarctic in a year with good (a, c) and poor (b, d) data coverage.

2.2 The near-100 % sea-ice concentration reference data set

For the evaluation of the 10 products at 100 % sea-ice concentration (see Sect. 4), we use the Round Robin Data Package version 2 (RRDP2) near-100 % reference sea-ice concentration data set developed within the ESA Sea_Ice_cci and European Union “Spaceborne observations for detecting and forecasting sea ice cover extremes” (EU-SPICES) projects (Pedersen et al., 2019). In short, for this reference data set, areas of ∼ 100 % sea-ice concentration are found by identifying areas of interest (AOIs) of approximately 100 km × 100 km with net convergence in the ice drift pattern on two consecutive 1 d periods. Information about convergence is derived from the PolarView/MyOcean/CMEMS ice drift data set derived from Envisat ASAR, RADARSAT-2 SAR, and Sentinel-1 SAR imagery. By choosing AOIs for regions with high concentrations, near-100 % sea-ice concentration can be assured (e.g. Kwok, 2002; Andersen et al., 2007) in winter. Each AOI contains up to a hundred 10 km × 10 km cells for which the SAR ice drift is computed. The number of cells depends on SAR image coverage. Convergence in the ice drift pattern results in a decrease in the total area of these cells. A cell is included in the data set of ∼ 100 % sea-ice concentration if the area reduction between day 1 and day 2 is between 0.4 % and 1.5 % and if more than 40 % of the AOI contains cells with such an area reduction. The RRDP2 near-100 % sea-ice concentration reference data set contains the AOI centre geographic latitude and longitude, time, total sea-ice concentration (100 %), and AOI average area reduction due to net ice convergence. It is available for the years 2007 through 2015 for both hemispheres.

We cannot provide a definite uncertainty for this reference data set but for its production. We combine a suite of measures to ensure high precision and close-to-zero bias (high accuracy). The drift–convergence selection is based on convergence on two consecutive days of 1 d drift. During winter, i.e. November through March (Arctic) and May through September (Antarctic), this is assumed to ensure that all openings existing on day 0 (prior to the two convergence days) are closed by convergence or refrozen. The refreezing assumption is the reason for the product quality to be higher during winter when openings rapidly refreeze than during summer when openings may not freeze up. There is no prior assumption of the initial ice concentration (on day 0), but the ice drift product requires quite high concentrations for the 2-D cross correlation to work. Andersen et al. (2007) reported a sea-ice concentration standard deviation of ∼ 1 % for cold-season high-resolution high-quality SAR image classification and an accuracy of 2 % for ice-water SAR image classification from ice analysts without additional drift–convergence information. Based on our above-mentioned measures and the results of Andersen et al. (2007), we can state estimated values for precision (∼ 1 %) and accuracy (< 0.5 %) for our reference data set.

We co-locate the sea-ice concentrations of the 10 products with the selected AOI grid cells by computing the minimum distance between AOI grid cell centre and grid cell centre of the respective sea-ice concentration product. For this step, we convert the geographic coordinates of all data sets into Cartesian coordinates taking into account the different projections. Figure 4 illustrates the spatial distribution of selected AOIs for both hemispheres for two different years by showing the co-located OSI-450 sea-ice concentration. We give an example of a typical “good distribution” (Fig. 4a, c) and of a typical “poor distribution” (Fig. 4b, d). The RRDP2 near-100 % sea-ice concentration reference data set contains basically no AOIs in the eastern Antarctic because of the lack of SAR image coverage required for the ice drift product used to generate this RRDP2 data set.

We evaluate the products at their native grid resolution without applying any spatial averaging. For each product, we compute the mean difference “product minus 100 %” and its standard deviation as well as the cumulative distribution function of the differences.

2.3 Ship-based visual sea-ice cover observations

According to the Antarctic Sea Ice Processes & Climate (ASPeCt) protocol (http://www.aspect.aq, last access: 18 February 2019; Worby and Allison, 1999; Worby and Dirita, 1999; see also Worby et al., 2008) and the Ice Watch/ASSIST (Arctic Ship-based Sea-Ice Standardization) protocol (http://icewatch.gina.alaska.edu, last access: 5 March 2019), ship-based observations of the sea-ice conditions shall be carried out every hour, at least every second hour, during daylight conditions while the ship is traversing the sea ice. Observations shall be carried out from the ship's bridge for an area of about 1 km around the ship and shall report ice conditions as follows: total ice concentration, type of openings, concentration, thickness, ridge fraction and height, and snow depth and type for up to three ice types. All ship-based visual observations used here result from manual, non-automated observations.

For our evaluation of the 10 products with respect to ship-based visual observations of the sea-ice conditions (see Sect. 5), we use about 15 000 individual observations. About ∼ 7000 of these were carried out in the Antarctic (ASPeCt) and ∼ 8000 in the Arctic (Ice Watch/ASSIST). A substantial fraction of the Antarctic observations (until 2005) is available via http://www.aspect.aq (last access: 18 February 2019, Worby et al., 2008). The more recent observations were collected from various sources (e.g. PANGAEA, ACE-CRC, AWI; see also Beitsch et al., 2015) and merged with the existing ASPeCt data. The majority of the ASSIST data are taken from the data portal http://icewatch.gina.alaska.edu (last access: 5 March 2019). Additional sources for ASSIST data are PANGAEA (for Polarstern cruises before Ice Watch/ASSIST), the Arctic Data Center of the NSF (https://arcticdata.io/catalog/#data, last access: 5 March 2019), and the data archive of the Bering Sea Ecosystem Study (BEST): https://www.eol.ucar.edu/projects/best/ice.shtml (last access: 5 March 2019). All data are standardized; i.e. the ASCII format data files containing the observations use similar formats for all variables and missing data. The data are also manually quality checked for outliers. For the comparison presented in this paper, we use all ASPeCt and Ice Watch/ASSIST observations from the period June 2002 through December 2015 (Kern, 2019).

Figure 5Spatio-temporal distribution of the ship tracks for (a, b) the Arctic and (c, d) the Antarctic from which ship-based visual observations of the sea-ice cover were used. Panels (a, c) illustrate the years, and panels (b, d) distinguish between winter (red) and summer (cyan) months.

Figure 5 summarizes the locations of the ship-based observations used in this paper, separately for the Arctic (Fig. 5a, b) and the Antarctic (Fig. 5c, d). For both hemispheres, just comparably small regions contain such observations. Figure 5a, c illustrate that some regions were visited during several years, while others were visited just once or twice during the 13-year period considered. The seasonal distribution (Fig. 5b, d) illustrates that the more central (Arctic) or southern (Antarctic) regions were only visited during summer months due to harsh winter conditions and missing daylight for these regions.

We co-locate the sea-ice concentrations of the 10 products with the selected ship-based observations by computing the minimum distance between geographic location of the ship-based observation and the grid cell centre of the respective sea-ice concentration product. For this step, we convert the geographic coordinates of all data sets into Cartesian coordinates taking into account the different projections of the sea-ice concentration products. Following the co-location, we average over all ship-based and all satellite-based sea-ice concentration values, including reports of open water, i.e. 0 % concentration, of 1 d following the approach of Beitsch et al. (2015). This results in a comparison of along-ship-track daily average sea-ice conditions. Data pairs with fewer than three ship-based observations per day are discarded. The results of the comparison between ship-based and satellite-based sea-ice concentration are solely based on these daily average sea-ice concentrations. Note that all satellite-based data are used at their native grid resolution.

The ship-based and satellite-based sea-ice concentration data sets are inter-compared (Sect. 5) by means of scatterplots and linear regression analysis and statistics separately for summer data, winter data, and data of the entire year. Summer comprises the months May through September for the Arctic and the months November through March for the Antarctic; winter comprises the remaining months. In the scatterplots, we compare the daily average sea-ice concentrations and additionally compute averages of the satellite-based sea-ice concentration after binning the ship-based data into 5 % wide bins (0 % to 5 % and 95 % to 100 %) and 10 % wide bins (sea-ice concentrations between 5 % and 95 %) and vice versa. We compute the overall average sea-ice concentration difference and its standard deviation and perform a linear regression analysis based on the daily average and the binned data.

Figure 6Arctic sea-ice area (a, b) and extent (c, d) computed in (a, c) winter (March) and (b, d) summer (September) from the sea-ice concentration data sets used. See Table 2 for start and end months of the respective time series.

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3.1 Arctic sea-ice area and extent time series

The SIA and SIE time series for the Arctic reveal a very similar overall development for the products extending back into the 1980s and 1990s (Fig. 6). This applies to (i) the overall negative trend in both quantities; (ii) the inter-annual variability as, for instance, during 1991–1997 and around 2007 and 2012 for SIA and SIE in September (Fig. 6b, d), or in 2011 for the relative minimum in March SIA and SIE (Fig. 6a, c); and (iii) the ranking between the products. NOAA CDR and CBT–SSMI provide the largest SIA and SIE in both March and September. NT1–SSMI provides the lowest SIA and SIE in September, while in March we find SIA and SIE from ASI–SSMI to be even lower. It is obvious that differences between products are smaller for SIE than for SIA as was also shown by Ivanova et al. (2014). For the AMSR-E period, when SIA and SIE of all 10 products are available, the inter-annual variation is similar for all 10 products. We find ESA CCI products, CBT–AMSR-E, and NT2–AMSR-E fall into the ranges of SIA and SIE given by the other products. An exception to this is SICCI-50km, which clearly provides the lowest SIE of all products in March (Fig. 6c). We will discuss this finding in Sect. 3.3.

3.2 Antarctic sea-ice area and extent time series

The SIA and SIE time series for the Antarctic reveal a similar overall development for products extending back into the 1980s and 1990s (Fig. 7). This applies to (i) the overall positive trend until 2015 in both quantities; (ii) the inter-annual variability, for instance, during 2000–2003 for SIA and SIE in February (Fig. 7b, d), or in 2008 for the relative minimum in SIA and SIE in September (Fig. 7a, c); and (iii) the ranking between products. NOAA CDR and CBT–SSMI provide the largest SIA while NT1–SSMI provides the smallest SIA, being ∼ 1.8 million km² and 300 000 km² below the SIA of NOAA CDR and CBT–SSMI in September and February, respectively. OSI-450 and CBT–SSMI provide the largest SIE, exceeding the smallest SIE of NT1–SSMI by ∼ 500 000 km² and ∼ 300 000 km² in September and February, respectively (Fig. 7c, d). Inter-product differences are larger for SIA than SIE in September but not in February. For the AMSR-E period, the inter-annual variation is similar for all 10 products. In September, SIA and SIE of the ESA CCI products mostly fall between ASI–SSMI and OSI-450 (Fig. 7a, c). In February (Fig. 7b, d), SICCI-50km provides the smallest overall SIA and SIE while the SICCI-12km and SICCI-25km products agree closely with OSI-450. In contrast to the Arctic (compare Fig. 6), NT2–AMSR-E clearly provides the largest SIA in September and February (Fig. 7a, b). NT2–AMSR-E provides the largest SIE in February as well (Fig. 7d).

Figure 7c contains an example of discontinuities caused by the application of weather filters not adapted to sensor changes. Wintertime Antarctic OSI-450 and CBT–SSMI SIE agree with each other for the SMMR period. After 1987 the CBT–SSMI SIE is lower than the OSI-450 SIE by ∼ 150 000 km². This corresponds to the area of one-quarter of all 25 km grid cells at a latitude of 60^∘ S, the approximate average location of the Antarctic sea-ice edge in September. This change in SIE is concomitant with a jump in the weather filter sea-ice concentration from 11 % to 14 % (Fig. 2a). It is noteworthy that the 23.0 GHz channels of the SMMR instrument were highly unstable from launch and eventually ceased to function on 11 March 1985 (Njoku et al., 1998). Thus, the water vapour part of the “classic” weather filter is unreliable in the early decade of the satellite data record. This is solved in the OSI-450 product by relying on explicit atmospheric correction of the brightness temperatures using – among others – water vapour fields from atmosphere reanalysis (see Lavergne et al., 2019). Another example of this kind (not shown) is a shift between OSI-450 SIE and NOAA CDR SIE by 50 000 to 100 000 km² between 2007 and 2008. This shift is concomitant with a discontinuity in the weather filter sea-ice concentration for NOAA CDR in March (Arctic, Fig. 1a) and September (Antarctic, Fig. 2a) during the transition from 2007 to 2008. This corresponds to when SSMIS (F17) is processed instead of SSM/I (F15). OSI-450 exhibits no discontinuity here.

Figure 8(a–j) Maps of the difference between the multi-annual average monthly SIC of the individual algorithms and the 10-algorithm ensemble median multi-annual average monthly SIC (k) for the Arctic in winter (March) 2003–2011. Differences are only computed for sea-ice concentration of both data sets > 15 %. Roman numbers I to IV denote the group assigned to the respective algorithm (see text for details).

3.3 Arctic sea-ice concentration distribution differences

In March, the difference between the sea-ice concentration of an individual product and the ensemble median of all 10 products (Fig. 8) remains within ±5 % over most of the Arctic Ocean, except for ASI–SSMI (Fig. 8h) and SICCI-12km (Fig. 8a). The largest differences between individual products and the ensemble median are located in the peripheral seas. Group II and IV (see Table 2) products have more sea ice than the ensemble median (Fig. 8e–g, j); differences can exceed 20 %. NT1–SSMI (Fig. 8i) has less sea ice than the ensemble median with negative differences greater than 10 % or even 15 % in magnitude in all peripheral seas. Differences of OSI-450 or SICCI-25km and the ensemble median are within ±5 % almost everywhere (Fig. 8b, d). SICCI-50km exhibits negative differences greater than 20 % in magnitude along some of the coastlines, e.g. the Labrador Sea, the Irminger Sea, or the coastlines of the Pechora Sea and Barents Sea (Fig. 8c). A careful check of these areas in daily and monthly mean maps of the SICCI-50km sea-ice concentration reveals that for regions with a relatively narrow sea-ice cover stretching along coastlines, the coarse resolution of the 6.9 GHz frequency channel entering the algorithm (see Table 2), in combination with land spillover filter and open water filter, can result in an unwanted complete removal of sea ice from the grid cells of the product. We are confident that this explains the particularly low SICCI-50km SIA and SIE shown in Fig. 6a and c for Arctic SIE in March.

Figure 9Differences (row minus column) between all 10 products of, from left to right, the average sea-ice concentration SIC, average SIA, and average SIE for the Arctic (NH) in winter (a–c) and summer (d–f). The averages are computed from monthly mean values of the respective months (March, September) of the AMSR-E period June 2002 to September 2011. All data are on the EASE-Grid 2.0 with 50 km grid resolution. The land mask of the SICCI-50km product is applied to all products. Roman numbers I to IV denote groups according to Table 2. For matrices of all remaining months, we refer to Figs. G1–G3 in Appendix G.

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Figure 10(a–j) Maps of the difference between the multi-annual average monthly SIC of the individual algorithms and the 10-algorithm ensemble median multi-annual average monthly SIC (k) for the Antarctic in winter (September) 2002–2011. Differences are only computed for sea-ice concentration of both data sets > 15 %. Roman numbers I to IV denote the group assigned to the respective algorithm (see text for details).

For the matrices shown in Fig. 9 (and Fig. 12, Appendix G1–G6), we re-grid the monthly mean sea-ice concentration onto the EASE-Grid version 2.0 with 50 km grid resolution using bilinear interpolation, and we apply a common land mask (that of SICCI-50km) to all products. The differences between SIA and SIE values are computed from these gridded 50 km resolution, common land mask products. Figure 9a agrees with the results shown in Fig. 8. In winter (March), sea-ice concentration differences between members of groups I to III are < 1 %. Group III members NT1–SSMI and ASI–SSMI (see Table 2) exhibit less sea ice than the other groups. Group II and IV members exhibit higher sea-ice concentrations than the other two groups in winter and summer (September). In summer (Fig. 9d), sea-ice concentration differences remain < 2 % between members of groups I and II but not within group III, where differences exceed 10 %. We refer to Appendix G for the respective results of the other months.

3.4 Antarctic sea-ice concentration distribution differences

In September (Fig. 10), most products show more sea ice than the ensemble median over high-concentration ice and less sea ice along the marginal ice zone. NT1–SSMI (Fig. 10i) exhibits considerably less sea ice than the ensemble median almost everywhere (see also Fig. 12a). ASI–SSMI (Fig. 10h) exhibits a distribution of sea-ice concentration differences that is reversed compared to most other products. CBT–AMSR-E and especially NT2–AMSR-E (Fig. 10g, j) show more sea ice than the ensemble median for most regions. This is evident in Fig. 12a as well.

Figure 11As Fig. 10 but in summer (January) 2003–2011.

Figure 12Differences (row minus column) between all 10 products of, from left to right, the average sea-ice concentration SIC, average SIA, and average SIE for the Antarctic (SH) in winter (a–c) and summer (d–f). The averages are computed from monthly mean values of the respective months (September, February) of the AMSR-E period June 2002 to September 2011. All data are on the EASE-Grid 2.0 with 50 km grid resolution. The land mask of the SICCI-50km product is applied to all products. Roman numbers I to IV denote groups according to Table 2. For matrices of all remaining months we refer to Figs. G4–G6 in Appendix G.

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In January (Fig. 11), the few, comparably small, high-concentration areas exhibit sea-ice concentration differences mostly below ±5 %. Over the lower-concentration areas, i.e. mainly in the Weddell Sea and the Ross Sea, most products show less sea ice than the ensemble median with differences between 0 % and −6 %. NT1–SSMI has less sea ice while ASI–SSMI and particularly NT2–AMSR-E have more sea ice (see also Fig. 12d). Important to note are the negative differences of ∼ −10 % along most of the Antarctic coast for SICCI-50km (Fig. 11c). Like for the Arctic, the coarse resolution of the 6.9 GHz frequency channels combined with land spillover and open water filters can result in the unwanted removal of sea ice from grid cells (compare Fig. 8c and discussion of it) with the same influence on SICCI-50km SIA and SIE values (Fig. 7b, d). This is also evident in Fig. 12d where SICCI-50km exhibits the largest inter-product differences within group I.

For the results shown in Figs. 6–12 we used the truncated sea-ice concentration values as far as it concerns group I products. Repeating these computations with the non-truncated values, e.g. in September and March, does not change the results with respect to SIE. SIA increases by ∼ 50 000 km² in winter months and there is almost no impact in summer.

3.5 Summary and discussion of sea-ice area and extent findings

The inter-product mean sea-ice concentration differences (Figs. 8–12) are associated with a notable impact on SIA and SIE (Figs. 9 and 12). For summer SIE, inter-product differences are below ∼ 200 000 km² (Arctic, Fig. 9f) and below ∼ 300 000 km² (Antarctic, Fig. 12f) for most products. NT1–SSMI (Arctic) and SICCI-50km, NT1–SSMI, and NT2–AMSR-E (Antarctic) show the largest differences here. For winter SIE, most inter-product differences are below ∼ 200 000 km² for the Antarctic (Fig. 12c); larger differences are mostly found for NT1–SSMI (see also Fig. 7c). For the Arctic (Fig. 9c), inter-product differences range between 100 000 and 600 000 km² and seem to be associated with the type of algorithm and partly also the sensor.

For Arctic winter SIA (Fig. 9b), group III products provide systematically smaller values (by ∼ 400 000 km²) than the other three groups while group II SSMI products provide systematically larger values (by ∼ 300 000 km²). Group I and CBT–AMSR-E and NT2–AMSR-E exhibit the lowest inter-product SIA differences. For Arctic summer SIA (Fig. 9e), group II and IV products agree with each other within 100 000 km² but exceed group I SIA by ∼ 400 000 km². This is equal to 10 % of the summer minimum Arctic SIA. For Antarctic summer SIA (Fig. 12e), NT2–AMSR-E exceeds SIA of all other products by ∼ 400 000 km². This equals 20 % of the summer minimum Antarctic SIA. SIA differences between the other products are almost all < 200 000 km². For Antarctic winter SIA (Fig. 12b), NT2–AMSR-E and NT1–SSMI stand out with very large systematic differences from all other products.

We summarize our findings from the matrices in Figs. 9 and 12 (see also Appendix G1–G6) as follows: (i) absolute and relative (to the respective minimum or maximum value) inter-product differences are smaller for SIE than for SIA. (ii) SIA and SIE derived from products of different algorithms of the same group (see Table 2) may differ considerably. (iii) Inter-product differences for SIA and SIE for the investigated CDRs are, on average, larger for the Arctic than the Antarctic.

We note that the grid resolution of the products is not necessarily compatible with the true spatial resolution because the footprints of the satellite sensor channels used in some of the algorithms are coarser (Table 2). This applies to NT1–SSMI, CBT–SSMI, NOAA CDR, and OSI-450, i.e. the products at 25 km grid resolution based on SMMR, SSM/I, and SSMIS data. For these products, we expect that gradients in the sea-ice concentration are more smeared than for products with a better match between footprint size and grid resolution such as, for instance, CBT–AMSR-E or SICCI-25km. This is illustrated for OSI-450 and SICCI-25km in Lavergne et al. (2019, Fig. 6). For a typical wintertime Antarctic ice edge at 65^∘ S comprising half a compact and half an open sea-ice cover, this difference in the match of true resolution and grid resolution between SSM/I and AMSR-E products would result in a slightly larger SIE (by ∼ 200 000 km²) derived from the SSM/I product. This is because a compact ice edge is smeared more in the SSM/I product, resulting in more grid cells with a sea-ice concentration > 15 %, the threshold used currently to compute SIE. In fact we find that during winter OSI-450 SIE exceeds SICCI-25km SIE by ∼ 100 000 km² in the Arctic (Fig. 9c) and by ∼ 200 000 km² in the Antarctic (Fig. 12c). Since the algorithms used for the sea-ice concentration retrieval for these two products are almost identical, the difference in SIE can well be attributed to the above-mentioned impact of differences between true and grid resolution. The second pair of almost identical algorithms is CBT–SSMI and CBT–AMSR-E. In the Arctic, in winter, CBT–SSMI SIE exceeds CBT–AMSR-E SIE by ∼ 400 000 km² (Fig. 9c) but in the Antarctic CBT–SSMI SIE is smaller than CBT–AMSR-E SIE by ∼ 100 000 km² (Fig. 12c). Differences in the algorithm itself and/or in the weather filter might be the cause. We refer to the discussion at the end of Sect. 3.2 in this context.

4.1 Arctic

The distribution of the sea-ice concentration near 100 % is shown for the Arctic for each product in Fig. 13a in the form of the cumulative fraction of the deviation (bias) from 100 %. As expected, the cumulative fraction increases towards 1.0 for all products. Considerable differences between the products are evident. Group I products (see Table 2) exhibit a cumulative fraction between ∼ 0.5 and ∼ 0.7 in bin −1.5 % … −0.5 %. Group II products and NT1–SSMI exhibit substantially lower fractions for this bin: between ∼ 0.2 (NOAA CDR; see also F₉₉ in Fig. 3c) and ∼ 0.4 (NT1–SSMI). Consequently, the change in cumulative fraction to the last bin is between 0.6 and 0.8 for group II and NT1–SSMI but only between 0.3 and 0.5 for group I. The respective F₉₉ values in Fig. 3 and Appendix H suggest that a large portion of the cumulative fraction in the last bin is in fact due to sea-ice concentrations > 100 % being set to 100 % (i.e. truncated). For NT2–AMSR-E, the cumulative fraction increases abruptly from < 0.1 in bin −2.5 % … −1.5 % to ∼ 0.8 in bin −1.5 % … −0.5 %. This behaviour is completely different from all other products and confirms the results of Andersen et al. (2007) and Ivanova et al. (2015). For their inter-comparison of sea-ice concentration algorithms in the high Arctic, Andersen et al. (2007) extended the range within which the NT2 algorithm permits the retrieval of the sea-ice concentration to 120 % in order to be able to properly compare all algorithms with respect to their precision close to 100 %. The original implementation of the NT2 algorithm is constrained to sea-ice concentrations up to 100 %. Ivanova et al. (2015) also aimed to compare the precision of several sea-ice concentration algorithms at 100 % by means of computing the standard deviation of the sea-ice concentration at 100 %. They were, however, unable to obtain standard deviations with comparable statistics because of large positive biases for the NT2 and ASI algorithms and because of the truncation of sea-ice concentrations at 100 %. Only by constructing a reference sea-ice concentration of 75 %, were Ivanova et al. (2015) able to carry out a comparison of the sea-ice concentration standard deviation based on non-truncated sea-ice concentrations.

These cumulative distributions suggest that an inter-comparison of the mean difference to 100 %, i.e. the bias, and its standard deviation, i.e. the precision, should be carried out by means of the Gaussian fit proposed in Sect. 2.1.4. Consequently, the mean sea-ice concentrations of the 10 products shown by the black symbols in Fig. 14a for the Arctic near-100 % reference sea-ice concentration locations are the modal values of the Gaussian fits. The error bars denote 1 standard deviation of this fit around the modal value. The blue symbols and error bars denote the respective mean and 1 standard deviation computed from the non-truncated group I sea-ice concentration products. All values shown here are summarized together with the results obtained from the truncated sea-ice concentration products in Table 3.

Table 3Inter-comparison results to near-100 % SIC (RRDP2) for the Arctic (see Fig. 14a). The rows “Gaussian” show the mean difference of the modal value of Gaussian fit to satellite SIC ≤ 99 % (compare Fig. 3) minus near-100 % reference SIC (RRDP2 SIC) ± 1 sigma of the Gaussian fit (see Fig. 14a). The rows “Non-truncated” show the mean difference satellite SIC minus RRDP2 SIC ± 1 standard deviation of the difference for SICCI and OSI-450 products. The rows “Truncated” show the mean difference of satellite SIC constrained to a maximum value of 100 % minus RRDP2 SIC ± 1 standard deviation of the difference. All values in these rows are given in percent sea-ice concentration. Values in rows denoting the periods 2007–2015 and 2007–2011 contain the number of valid data pairs. See text for meaning of ^* in the column “NT2–AMSR-E”.

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Figure 14a confirms our hypothesis that those products where the cumulative distributions seem to contain a large fraction of sea-ice concentrations larger than 100 % set to 100 % (Fig. 13a), i.e. the group II products, and NT1–SSMI are likely to overestimate the actual sea-ice concentration. The overestimation is particularly high for NOAA CDR with a modal sea-ice concentration of ∼ 103 % (see also Table 3). The group I products exhibit modal sea-ice concentrations that are slightly below and closest to the near-100 % reference. The Gaussian fit also almost perfectly matches the actually observed non-truncated sea-ice concentration for SICCI-50km in terms of the standard deviation (compare blue and black symbols in Fig. 14a and Table 3). The match is less accurate for OSI-450 and SICCI-25km.

In addition, Fig. 14a and Table 3 confirm our hypothesis that the group II products and NT1–SSMI are likely to have a standard deviation that is lowered by truncating sea-ice concentrations to a maximum of 100 %. This is illustrated by the standard deviations of the non-truncated and the truncated sea-ice concentration for group I products (Table 3). Under the assumption that the standard deviation of the Gaussian fit is a better measure of the spread in sea-ice concentrations near (but below) 100 %, we state that the CDRs of group I (SICCI-50km, OSI-450, and SICCI-25km) allow a better precision than group II products. We also confirm the findings of Lavergne et al. (2019) that the group I products are slightly – but significantly – biased low.

For ASI–SSMI and NT2–AMSR-E, the application of a Gaussian fit is potentially not justified given the way sea-ice concentrations are retrieved. ASI–SSMI is non-linear near 100 % (Kaleschke et al., 2001) while no statement about the functional relationship of the input satellite data and the retrieved sea-ice concentrations can be made for NT2–AMSR-E (Markus and Cavalieri, 2000; Brucker et al., 2014). Our analysis, however, results in a reasonable Gaussian fit for ASI–SSMI (see Appendix H, Fig. H1a). We are confident therefore that the values taken from the fit and shown in Fig. 14a and Table 3 can be used. In contrast, the NT2–AMSR-E sea-ice concentration distribution does not allow reasonable application of a Gaussian fit (see Appendix H, Fig. H1j) and we do not report it along with the others in Fig. 14a. We note that Andersen et al. (2007) reported a mean NT2 sea-ice concentration of ∼ 105 % with a standard deviation of ∼ 5 % at near-100 % sea-ice concentrations for their unconstrained version of this algorithm.

Figure 14Summary of the results of the inter-comparison to the near-100 % reference SIC (RRDP2) for (a) the Arctic and (b) the Antarctic. Shown for each sea-ice concentration product in black is the centre of the Gaussian fit of the sea-ice concentration ≤ 99 % at the respective RRDP2 locations (see Fig. 4). Bars denote ± 1 standard deviation of the Gaussian fit. For symbol pairs (all products but CBT–AMSR-E and NT2–AMSR-E) the left symbol is based on data of the years 2007–2011 and the right one on data of the years 2007–2015. Blue symbols denote the mean non-truncated sea-ice concentration at the near-100 % reference SIC for OSI-450 and SICCI products; blue bars denote the respective sea-ice concentration standard deviation. Roman numbers at the top denote product groups (see Table 2). No values are shown for NT2–AMSR-E because a Gaussian fit could not be adequately applied.

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4.2 Antarctic

For the Antarctic (Fig. 13b), we find more similarities in the cumulative fractions of the deviation (bias) from 100 % than for the Arctic. Common to all products, except NT2–AMSR-E and ASI–SSMI, is a notable step change in the cumulative fraction between bin −1.5 % … −0.5 % and the last bin. This step change is least pronounced for NT1–SSMI and most pronounced for NOAA CDR, exhibiting cumulative fractions of ∼ 0.8 and ∼ 0.4, respectively, in the last bin. Step changes are slightly larger for the two CBT products than for group I products (see also F₉₉ values in Fig. 3d, e). For ASI–SSMI the cumulative fraction levels off before the last bins (see also the F₉₉ value in Appendix H, Fig. H2a). A total of 93 % of the ASI–SSMI sea-ice concentrations at the near-100 % reference sea-ice concentration locations are below 99.5 %. The distribution for NT2–AMSR-E is extremely narrow. About 75 % of the NT2–AMSR-E sea-ice concentrations at the near-100 % reference sea-ice concentration locations are above 99.5 %. This behaviour is, like for the Arctic, completely different from all other products and agrees with the findings of Ivanova et al. (2015); see also our discussion in Sect. 4.1.

Table 4As Table 3 but for the Antarctic (see Fig. 14b).

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Group I and II products provide a modal sea-ice concentration which deviates by less than ∼ 1 % from 100 % (Fig. 14b, Table 4). While group II products tend to exhibit a modal sea-ice concentration > 100 %, group I products exhibit modal sea-ice concentrations < 100 %. Modal sea-ice concentrations obtained with the Gaussian fit agree within 0.5 % with the actually measured mean sea-ice concentration derived from the non-truncated values of group I products (compare black and blue symbols in Fig. 14b). Respective standard deviations match better in the Antarctic than the Arctic and are systematically smaller for the truncated than the non-truncated results (compare black and blue bars in Fig. 14a and b as well as Tables 3 and 4). For group II products, using the Gaussian fit method suggests standard deviations between ∼ 4.5 % and ∼ 5.5 % while using the truncated values results in a standard deviation between 2.0 % and 2.5 %. Following our assumption in Sect. 4.1, we state a better precision for group I products (SICCI-50km, SICCI-25km, and OSI-450) than group II products. Similarly but to a lesser extent than in the Arctic, group I products are slightly biased low with respect to the validation data set.

4.3 Summary and discussion of the evaluation near 100 %

In near-100 % sea-ice concentration conditions, most retrieval algorithms will naturally retrieve some distribution of values around 100 % sea-ice concentration, i.e. also values > 100 %. However, these values are almost never accessible to the user and thus generally not accessible for validation. Here, we used the availability of these “off-range” estimates in the group I products to demonstrate how the entire distribution around 100 % can effectively be reconstructed a posteriori from the products with truncated sea-ice concentration distributions (Fig. 3, Appendix H). This Gaussian fit methodology allows us to go deeper in the analysis of near-100 % conditions. Indeed, if the analysis had been limited to the truncated distributions only (Fig. 13), algorithms that overestimate sea-ice concentration (modal value of the non-truncated distribution larger than 100 %) would obtain better validation statistics (smaller bias and RMSE) than products without such overestimation. The larger the overestimation, the better the statistics would be. Using the Gaussian fit, we unveil a possible overestimation of several sea-ice concentration products, including NT1–SSMI, CBT–SSMI, and NOAA CDR in the Arctic and NOAA CDR (but only slightly) in the Antarctic. This Gaussian fit methodology also confirms that group I products are slightly low biased in the Arctic (see Lavergne et al., 2019). We find the worst of these biases in the Arctic for SICCI-12km, which was not openly distributed at the end of the ESA CCI Sea Ice Phase 2 project, partly based on these results.

Our results suggest that group I products, i.e. the three CDRs OSI-450, SICCI-25km, and SICCI-50km, are more accurate and have a higher precision than the fourth CDR investigated: NOAA CDR; this applies to both hemispheres. Group I products can be regarded as being superior, in terms of the precision and accuracy, to NT1–SSMI and CBT–SSMI as well. Our results furthermore confirm earlier work (Andersen et al., 2007; Ivanova et al., 2015) that the accuracy of NT2 algorithm products near 100 % cannot be quantitatively assessed. We hypothesize that this is merely caused by the fact that sea-ice concentrations are constrained to a maximum of 100 % by the algorithm concept. This is fundamentally different from the other nine products investigated. In the iterative retrieval used in the NT2 algorithm, sea-ice concentrations are only allowed to converge at 100 % from one side, i.e. < 100 % – in contrast to other iterative algorithms such as the polynya signature simulation method (PSSM) (Markus and Burns, 1995). Another element of the NT2 algorithm, which complicates quantitative assessment of the accuracy near 100 % sea-ice concentration, is the usage of model atmospheres to create lookup tables from which the sea-ice concentration is retrieved. This approach likely reduces the natural variability of the obtained sea-ice concentration. We refer to Brucker et al. (2014) for more details of NT2 algorithm sea-ice concentration uncertainty.

The results of the comparison in Sect. 4.1 and 4.2 are based on winter data (see Sect. 2.2). But also during winter temperatures can get close to 0 ^∘C, influencing the brightness temperatures used to compute the sea-ice concentration and questioning the assumption of freezing conditions for generation of the near-100 % reference sea-ice concentration data set. By using the co-located air temperature from ERA-Interim reanalysis data included in the RRDP2 data set (Pedersen et al., 2019), we repeated the analyses for cold cases, i.e. air temperatures below −10 ^∘C. We find that biases between satellite and reference sea-ice concentrations change by less than 0.1 % for all products except NT1–SSMI. For NT1–SSMI constraining the analyses to cold cases yields a bias reduction by ∼ 0.4 % for the Arctic and ∼ 0.7 % for the Antarctic, indicating that this particular algorithm is more sensitive than others to variability of air temperature.

5.1 Arctic

Overall, for the Arctic, all 10 products compare reasonably well to the ship-based observations (Fig. 15, Table 5). At high concentrations ($>\sim$ 80 %), group I products and ASI–SSMI (Fig. 15a–d, h) exhibit the most symmetric distributions around the identity line. NT1–SSMI (Fig. 15i) shows an asymmetric distribution with a considerable fraction of satellite sea-ice concentrations even below 60 %, translating into a difference between satellite- and ship-based sea-ice concentrations of up to 40 %. Group II and IV products (Fig. 15e–g, j) show an asymmetric distribution with more high satellite-based than high ship-based sea-ice concentrations. Most products have more data pairs below the identity line; i.e. satellite-based are smaller than ship-based sea-ice concentrations as illustrated by a negative overall bias and regression lines located below the identity line for six of the 10 products (Table 5). Group II and IV products provide the smallest absolute overall bias of < 1 %. Biases are larger for group I, but at the same time the standard deviation of the difference (SD) is smallest for group I products. The highest correlations are obtained for CBT–AMSR-E and group I products, except OSI-450. We find the best linear fits, i.e. slopes closest to the identity line, however, for CBT–SSMI and NOAA CDR.

Figure 16As Fig. 15 but for the Antarctic.

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Table 6As Table 5 but for the Antarctic (see Fig. 16, black symbols).

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How do results of the entire year compare to those obtained separately for winter or summer months (see Fig. 5 for differences in the location of the ship-based observations)? For all products, the correlation is lower in winter than summer and the entire year. This can be explained by fewer observations during winter in general and by substantially fewer low sea-ice concentrations; most observations during winter are > 75 %. Except for ASI–SSMI, the differences in the bias between summer, winter, and the entire year are small (mostly < 1 %). All products except SICCI-12km and ASI–SSMI provide a lower SD in winter than summer. Compared to the other groups, group I exhibits the smallest SD in summer while group II does so in winter. OSI-450 stands out with the smallest inter-seasonal change in bias and SD of only ∼ 0.1 % (Table 5; see also Sect. 6.1.4).

We want to better visualize the average distribution of the two data sets and investigate the partitioning of the data into sea-ice concentration bins of 10 % width – the average accuracy of the ship-based sea-ice concentration observations. For this purpose we bin sea-ice concentrations of one data set, e.g. ship observations, into 10 % wide bins and compute the mean sea-ice concentration of the other data set (Fig. 15, red symbols) and vice versa (blue symbols). The binned values and associated regression lines illustrate even better the above-mentioned asymmetry in the distribution of the data pairs. For instance, NT1–SSMI (Fig. 15i) sea-ice concentration range between 60 % and 100 % over a ship-based observations range of 80 % to 100 %. Consequently, the average NT1–SSMI sea-ice concentration for the ship observation bin 95 %–100 % is ∼ 85 % (uppermost red triangle), while the average ship-based sea-ice concentration for the NT1–SSMI bin 95 %–100 % is ∼ 95 % (uppermost blue square). For two equally well-distributed data sets, one would expect that red and blue symbols and regression lines are close to each other. This is not the case and we refer to Sect. 6.1.4 for more discussion of this issue.

5.2 Antarctic

The scatterplots of the daily average along-track mean sea-ice concentrations for the Antarctic (Fig. 16) reveal, for sea-ice concentrations $>\sim$ 80 %, mostly symmetric distributions for seven of the 10 products. NT1–SSMI (Fig. 16i) has considerably more low than high sea-ice concentration values (compare Fig. 15i). NT2–AMSR-E (Fig. 16j) has almost no data points below the identity line at $>\sim$ 80 % with data pairs concentrated at 100 % satellite sea-ice concentration. A considerable drop in the count of data values above the identity line at lower concentrations results in a highly asymmetric distribution at concentrations below ∼ 50 %. Group II products have the lowest overall biases (Table 6) but slopes of the linear regression are considerably steeper than the identity line (Fig. 16e–g) in contrast to group III products (Fig. 16h, i) and OSI-450 (Fig. 16d). We find the largest bias for NT1–SSMI: −11.0 %. NT2–AMSR-E shows a considerable positive bias: +4.5 %. We find highest correlations between ship- and satellite-based observations for group I products and CBT–AMSR-E, the lowest SD values for group I products as well.

In contrast to the Arctic, correlations between ship- and satellite-based sea-ice concentrations are smaller in summer than winter when correlations are even higher than for the entire year for most products (Table 6). For all products, except group III, biases are smaller in winter than summer by mostly < 2 %. NT2–AMSR-E is the only product with a positive bias in both seasons. We find the largest inter-seasonal bias change for CBT–AMSR-E (2.7 %) and SICCI-25km (2.9 %) and the smallest for CBT–SSMI (0.4 %). For all products, the SD is smaller by 3 %–5 % (larger by 2 %–3 %) compared to the entire year in winter (in summer). Inter-seasonal SD changes are hence considerably larger in the Antarctic than in the Arctic (compare Tables 5 and 6).

Binning the sea-ice concentrations like described in Sect. 5.1 (red and blue symbols in Fig. 16) leads to the following main observations. (1) All products – except NT1–SSMI and NT2–AMSR-E – have the best agreement with ship-based observations in the sea-ice concentration range from 60 % to 80 %. (2) All products underestimate ship-based sea-ice concentrations for concentrations $<\sim$ 50 %. (3) The negative bias of ∼ 10 % observed for NT1–SSMI applies to the entire sea-ice concentration range. (4) NT2–AMSR-E is the only product overestimating ship-based sea-ice concentrations considerably; this overestimation reaches 10 % for the range 60 %–80 %. Apart from that, we find, like for the Arctic, that blue regression lines exhibit a considerably steeper slope than the red ones, suggesting that in the Antarctic the distribution of the data over the range 0–100 % is also asymmetric (see Sect. 6.1.4).

5.3 Summary and discussion of comparison against ship-based observations

Group II products provide the smallest overall difference from the ship-based observations: around 0 % (Arctic) and around −2 % (Antarctic). Group I products provide differences around −7.5 % (Arctic) and −3.5 % (Antarctic). Group I and II products share similar average correlations (R²) in the Arctic, 0.77 and 0.76, and in the Antarctic, 0.74 and 0.72. Standard deviations for group I products are smaller – by 1 % in the Arctic and by 2 % in the Antarctic – than for group II products. On average, these results are more accurate than those obtained for group III and IV products. We refrain from giving a ranking or recommendation as to which product is the best when compared to ship-based observations.

We find the lowest correlation for ASI–SSMI (group III) in both hemispheres. However, it is the product with the largest improvement in the inter-comparison results between winter and summer in the Arctic: correlation increases and difference and standard deviation decrease. This could be attributed to the higher fraction of intermediate sea-ice concentrations during summer for which the comparably fine grid resolution of 12.5 km of the ASI–SSMI product could be advantageous. There is evidence that this behaviour is coupled to the usage of the near-90 GHz channels because we observed a similar, albeit less pronounced, behaviour for SICCI-12km, which also employs near-90 GHz data and is provided at 12.5 km grid resolution (Table 2). Because in the Antarctic the sea-ice cover is more open year-round, it is plausible that we did not find similar behaviour there for these two products.

There are a few points to discuss. First of all, Figs. 15 and 16 reveal quite a high relative occurrence of sea-ice concentrations in the range from 95 % to 100 %. This might have biased our results. We therefore repeated our comparison by discarding all data pairs with daily mean sea-ice concentrations ≥ 95 %. The main results (not shown) are an overall increase in the differences by about 2 % and in the standard deviations by ∼ 1 % (group I) and 2 %–3 % (group II) and a reduction of the correlation by ∼ 0.08. Ranking between groups is otherwise not changed. Secondly, the results obtained for group I products are based on the truncated sea-ice concentrations. Using the non-truncated data does not considerably change our findings (not shown). Differences between satellite-based and ship-based sea-ice concentrations decrease by between 0 % and 0.3 % with a concomitant increase in the standard deviation of up to 0.2 %; this applies primarily to winter when the fraction of near-100 % sea-ice concentrations is large. Thirdly, application of the Gaussian fit method (see Sects. 2.1.4 and 6.1.3) seems inappropriate given the sea-ice concentration range considered in this inter-comparison. Even if it were, we can assume that differences and standard deviations obtained for the other products would change by less than 1 %. All these changes would be small compared to the accuracy of the ship-based sea-ice concentrations (see Sect. 2.3, beginning of Sects. 5, and 6.1.4).

In Figs. 15 and 16, several of the products exhibit points along the y=0 % sea-ice concentration line, i.e. conditions where sea ice is reported by the ship while the satellite estimates exactly 0 %. This applies mostly to group II products and ASI–SSMI (Fig. 15e–h). These points with zero daily mean sea-ice concentration are very likely the result of the weather filters applied (Sect. 2.1.3), which, in addition to removing false sea ice caused by atmospheric effects, also remove true sea ice (Ivanova et al., 2015; Lavergne et al., 2019). The combination of explicit atmospheric correction and dynamic tuning of the weather filter in group I products seems to reduce the occurrence of such cases notably (Figs. 15a–d; 16a–d).