Like in Kern et al. (2019), we consider 10 different sea-ice concentration products which we very briefly summarize in Table 1. More information about these products is given in Kern et al. (2019, Appendix 7.1–7.6). 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, (3) accessibility and sustained extension, and (4) overlap with the melt pond fraction evaluation data set. Due to these criteria we have not selected products with < 10 years coverage or with a grid resolution < 12.5 km.

The algorithms used to generate the 10 products can be distinguished by their general approach to derive the SIC. We took advantage of this fact and assigned products to four different groups: I to IV (see Table 1). Algorithms of group I (OSI-450) and the three SICCI algorithm versions employ a self-optimizing hybrid approach combining an algorithm with superior precision over open water with an algorithm with superior precision over consolidated sea ice (see e.g. Ivanova et al., 2015; Lavergne et al., 2019). In addition, all products of group I utilize an optimized tie point retrieval scheme mitigating inter-sensor inconsistencies. Algorithms of group II employ an advanced bootstrap technique to compute the SIC in a two-dimensional space of either dual-polarization 37 GHz TBs or vertically polarized TBs at 19 and 37 GHz (see Comiso and Nishio, 2008); the group hence includes data derived with the Comiso bootstrap algorithm from two different PMW TB data sets. Group II includes the National Oceanographic and Atmospheric Administration (NOAA) National Snow and Ice Data Center (NSIDC) SIC CDR because it is largely determined by the input Comiso bootstrap algorithm. Group III includes those algorithms of our set of 10 that derive the SIC mainly from the TB polarization difference at 19 GHz (NT) or near 90 GHz (ASI). Also, these two products use constant tie points. Even though the results of this paper suggest that ASI appears to fit better into group I, as will be briefly discussed later, we keep that product in group III to avoid confusion with Kern et al. (2019). Finally, group IV includes one product only, the enhanced NASA Team (NT2) algorithm. While the NT2 advances the NT algorithm, e.g. by adding near-90 GHz TBs, the SIC retrieval itself differs fundamentally from that of all other nine algorithms. We refer to Kern et al. (2019) and the references therein for further reading.

In the following few paragraphs we provide some more general remarks on the satellite PMW data products used. We refer to Lavergne et al. (2019) and Kern et al. (2019) for further information.

The difference in microwave TBs observed over open water (low) and land (high) combined with the diameter of the field of view of several kilometres to a few tens of kilometres can cause spurious sea-ice concentrations to appear along coasts (e.g. Lavergne et al., 2019). In this paper, we neither further correct potential differences between the 10 products caused by this effect nor pay particular attention to this effect.

Atmospheric moisture and wind-induced roughening of the ocean surface can cause spurious sea-ice concentrations in areas that are actually ice free. To mitigate this noise, different kinds of weather filters are applied in the 10 products used. These and their effects on SIA and SIE estimated from the sea-ice concentration data are discussed in Kern et al. (2019). The focus of this paper is on the performance of the 10 products during summer conditions over consolidated ice, where the weather filters have no effects. Therefore, we do not further discuss weather filters in this paper.

In near-100 % and near-0 % sea-ice concentration conditions, most retrieval algorithms will naturally retrieve a bell-shaped distribution of sea-ice concentration values, returning values both below and above 100 % or 0 % sea-ice concentration (e.g. Ivanova et al., 2015). While the EUMETSAT-OSI SAF and ESA-CCI products (group I; see Table 1) allow use of the naturally retrieved sea-ice concentration on either side of 100 %, the others do not. In those other products any sea-ice concentration values retrieved as being larger than 100 % are set to 100 % and lost to the user. The availability of these “off-range” estimates in the four group I products was used in Kern et al. (2019) to demonstrate how the off-range distribution can effectively be reconstructed a posteriori for most of the other products from their truncated sea-ice concentration distributions. Kern et al. (2019) illustrated that products with overestimated sea-ice concentration (modal value of the non-truncated distribution larger than 100 %) would obtain better validation statistics (smaller bias and RMSE) than products with no overestimation (modal value of the non-truncated distribution exactly at 100 %). The larger the overestimation, the better the statistics would be. We briefly discuss this issue and its relevance for our comparison with the MODIS data set in Sect. S3.1 in the Supplement.

We will mainly focus our discussion of the results obtained (Sects. 3 and 4) on products that we selected to be representative of the four groups in Kern et al. (2019). These products are OSI-450 for group I, CBT-SSMI for group II, NT1-SSMI for group III, and NT2-AMSR-E for group IV (see Table 1 for the product acronyms used). We refer to the Supplement where, starting with Fig. S3, we show some of the results for all 10 products.

We use the MODerate resolution Imaging Spectroradiometer (MODIS) Arctic melt pond fraction data set developed by Rösel et al. (2011, 2012a): Rösel et al. (2015), http://doi.org/10.1594/WDCC/MODIS__Arctic__MPF_V02, last access: 19 May 2020. This data set is provided for the Arctic Ocean north of 60∘ N with 8-daily temporal resolution on the NSIDC polar-stereographic grid with 12.5 km × 12.5 km grid resolution at 70∘ N. It extends from day of year (DOY) 129, i.e. 9 May (8 May for leap years) to DOY 256, i.e. 13 September (12 September for leap years), and hence covers pre-melt, melt advance, peak-melt, and end-of-melt conditions.

The melt pond fraction retrieval is based on the calibrated and atmospherically corrected reflectance values measured by MODIS channels 1, 3, and 4 available in the MOD9A1 8 d product. For this product, reflectance values measured during 8 consecutive days were reprojected from the original MODIS tiles into the NSIDC polar stereographic grid with 500 m × 500 m grid resolution, composited over the 8 d period, and combined with the cloud and land masks provided with the MOD09 product. Composited means that a cloud-free section in a MODIS tile of a more recent satellite overpass is preferred over an older satellite overpass within the 8 d period. For the retrieval, it is assumed that each 500 m grid cell is solely covered by fractions of three surface types: open water in leads and openings between ice floes, melt ponds, and sea ice and snow. The sum of these fractions is assumed to equal 1. Via a spectral un-mixing approach and an artificial neural network, the measured reflectance values are converted into the fractions of these three surface types per grid cell, followed by the interpolation onto the 12.5 km grid used for the final product.

The product contains the melt pond fraction (MPF), the open-water fraction (OWF), the standard deviation of the MPF values at 500 m grid resolution, and the number of valid 500 m MPF estimates. This latter number is a measure of the number of clear-sky 500 m grid cells. In addition the product contains so-called “clear-sky” versions of the 12.5 km gridded MPF and OWF data computed only for those 12.5 km grid cells where more than 90 % of the input 500 m grid cells are denoted clear sky. We note that the MPF is a measure of the melt pond fraction per grid cell. No MPF values are provided for 12.5 km grid cells with an OWF larger than 85 %.

Rösel et al. (2012a) reported root-mean-squared errors (RMSEs) between ∼ 4 % and 11 % compared to airborne data. Kern et al. (2016) compared daily estimates of the MPF for June to August 2009 with ship-based observations of the MPF and reported RMSE values between ∼ 6 % and ∼ 15 %. Istomina et al. (2015) and Marks (2015) confirmed the validity of the MODIS MPF data set with different independent observations of melt ponds. Zhang et al. (2018) evaluated the MODIS MPF data set with independent high-resolution satellite observations. Experience working with these data led us to conclude that the MPF estimates are accurate to within a few percent. MODIS SIC and MODIS ISF share the same accuracy as MPF and are taken to be as accurate as 5 % in our study (see also Kern et al., 2016).

Besides unaccounted for cloud influence there is another limitation that needs to be kept in mind when using this data set. The used approach is based on three channels, which limits the maximum number of surface types to be discriminated to three. Ponds on first-year ice, however, have different spectral characteristics than ponds on multi-year ice: while the latter appear and remain bluish and relatively bright, the former become darker with advancing melt season until they eventually melt through the ice. As a consequence, towards the end of the melt season melt ponds on first-year ice might be assigned to the class open water. During the same time of the melting season, melt ponds might be covered by a slush or thin ice layer. Depending on the properties of this layer, the melt pond is either still assigned to the class melt pond, or it is assigned to the class ice. In addition, new ice forming between the ice floes in the high Arctic towards the end of the melt season could be classified as melt ponds (see also Rösel et al., 2012a). Because of these ambiguities in the retrieval of the melt pond fraction, it is likely that the accuracy of the parameters derived is poorer towards the end of the melt season, i.e. September.

We note that – due to the 8 d compositing (see above) – this product is less well suited to define melt onset or the length of the melt period with daily temporal resolution. Later on we will work with four distinct phases of the summer melt period. Our definition of theses phases is not driven by exact dates but by changes in the overall pan-Arctic melt pond fraction evolution (see below). Therefore we are confident that eventual biases that might occur due to the 8 d compositing, e.g. a melt pond fraction map of an 8 d period is not representative of the entire 8 d period but of the last 1–2 d of it, does not influence our results – except potentially increasing the noise. The same applies to issues such as melt–refreeze cycles.

For this paper, we used the clear-sky versions of MPF and OWF. In addition, we exclude all those MODIS data set grid cells where the ratio between the 12.5 km gridded MPF value and the standard deviation of the 500 m MPF values is smaller than 1. While this step filters out grid cells with an actual true large MPF variability, at the same time it reduces the influence of cloud cover artefacts. A similar filtering effect could have been achieved by increasing the percentage of 500 m grid cells required to consider a 12.5 km grid cell value clear sky from 90 % to, for instance, 95 %. However, in that case the number of valid MODIS product data would have decreased drastically.

We are interested in the fraction of ice detectable with PMW sensors. We call this the net ice surface fraction (ISF). ISF is related to OWF and MPF as follows: ISF + MPF + OWF = 1. We thus derive two parameters from the MODIS data set: the MODIS sea-ice concentration, MODIS SIC, which is 1 - OWF, and the MODIS ice surface fraction, MODIS ISF, which is 1 - OWF - MPF.

Sea-ice concentrations of the 10 products (Sect. 2.1) are co-located with the MODIS parameters via finding the grid cell pairs with the minimum difference (in kilometres) between the grid-cell centres. For this step, we converted the latitude and longitude coordinates of both data sets, i.e. the PMW products and the MODIS products, into metric coordinates using the WGS84 ellipsoid, allowing the computation of the minimum distance via simple geometry. We do not interpolate any of the data sets. We do not perform any averaging in case multiple (small) grid cells of one product fall into one (large) grid cell of the other product. All comparisons are carried out at the native grid resolution. When compared to the 25 km products, this results in a lower number of co-located grid cells for SICCI-50km and a higher number for SICCI-12km and ASI-SSMI. Finally, the collocated PMW SIC data are averaged in time over the same 8 d used in the respective 8-daily MODIS product; i.e. for the MODIS product of DOY = 129 we average over data from DOY 129 through 136. If valid sea-ice concentrations of fewer than 3 d within this 8 d period are available, this grid cell is discarded from further analysis.

In Fig. 2 we illustrate the melt pond development in the Arctic Ocean as relevant for this paper. The maps show melt pond distributions of a DOY representative of the four periods considered in this paper: pre-melt, melt advance, peak melt, and end of melt in the maps of Fig. 2a–d, respectively. For these maps, we selected years where the data coverage is particularly good, i.e. with only a few grid cells discarded as potentially cloud contaminated. Below each map we show histograms of the melt pond fraction of the respective DOY of the years 2003 to 2011, to illustrate the inter-annual variability.

Figure 4 exemplifies how the difference of PMW SIC minus MODIS SIC changes as a function of the stage of melt for the four groups. For this illustration, we select the same 8 d periods as used in the maps shown in Fig. 2. The four rows represent stages of melt: pre-melt (DOY 129, 9–16 May), melt advance (DOY 169, 18–25 June), peak melt (DOY 201, 20–27 July), and end of melt (DOY 241, 29 August–5 September). The four columns represent groups I to IV by showing results of OSI-450 (group I), CBT-SSMI (group II), NT1-SSMI (group III), and NT2-AMSR-E (group IV). These examples are taken from different years, chosen because of a relatively small number of invalid or missing data. Figure 5 shows two-dimensional (2-D) histograms of PMW SIC (y axis) versus MODIS SIC (x axis) corresponding to the SIC maps used for the differences shown in Fig. 4. Note the logarithmic scale of the count. Similar histograms but based on SIC data of the years 2003 to 2011 are shown in Fig. S5 in the Supplement. We omit the pre-melt examples in Fig. 5 (and Fig. S5) because they exhibit limited additional information but show them for completeness in Fig. S6 in the Supplement.

Melt ponds have the largest impact on PMW SIC because of the inability – at the microwave frequencies used – to discriminate between open water in the form of melt ponds on the ice floes and open water in the form of leads and openings between the ice floes. As detailed in the introduction, based on physical principles a sea-ice concentration retrieval algorithm should provide a value of 60 % for a case A, 100 % sea-ice concentration with 40 % melt ponds, and a case B, 75 % sea-ice concentration with 15 % melt ponds; in other words the algorithm should provide the net ice surface fraction. Therefore, a logical next step to better understand the causes of the SIC differences reported in Sect. 4.1 is to investigate how PMW SIC compares to ISF, as derived, e.g., from MODIS (Sect. 2.2). The inter-comparison between PMW SIC and MODIS ISF is carried out similarly to the inter-comparison to MODIS SIC (Sect. 4.1). We organize the results in exactly the same structure as in Sect. 4.1. We present in Fig. 7 a set of maps of the differences of PMW SIC minus MODIS ISF for the previously selected 8 d periods (compare Fig. 4), complemented by the respective 2-D histograms shown in Fig. 8 (compare Fig. 5) and extended to the entire period 2003–2011 in Fig. S8 in the Supplement (compare also Fig. S5).

The main motivations for this paper are to evaluate the performance of PMW SIC products during summer conditions and to better understand why PMW SIC products usually do not provide the net ice surface fraction – which they should following physical principles. The results presented so far document that none of the 10 PMW SIC products provide a faithful picture of the ISF, nor are they accurate measures of the summer SIC. The discussion given further below in Sect. 5 not only reveals possible explanations of the diversity of evaluation results but also demonstrates the complexity involved in a potentially planned improvement of the used algorithms – be it by further development of the algorithm itself or via application of more advanced ice tie point retrieval approaches. Here we discuss potential ways forward in the short to medium term (using existing PMW products) and in the longer term (preparing and using improved PMW SIC products).

For groups I and III, our comparison between PMW SIC and MODIS SIC (Sect. 4.1) and between PMW SIC and MODIS ISF (Sect. 4.2) suggests linear functional relationships. In the short term, these offer the prospect for users of the existing PMW SIC data sets from these two groups to perform bias corrections of the PMW SIC towards either true SIC (representative of the sea-ice area fraction of the geophysical model at hand) or net ISF (representative of the ice surface clear of melt ponds). The mean slope and intercept values prepared in Tables 3 and 4 but also slope and intercept of the individual linear regression lines (e.g. Figs. 5 and 8) could allow such a bias correction, noting all the limitations of these parameter values that are derived at pan-Arctic and, as presented in Tables 3 and 4, multi-year scales. For example, we find values of the linear correlation larger than 0.85 and slope close to 1 (see Table 4) with respect to MODIS ISF. With such a bias correction one might be able to get closer to the physically more meaningful result of a PMW SIC which equals the net ISF.

We do not explore or comment at length on a bias correction of PMW SIC towards true SIC with values in Fig. 5 (or Table 3). As predicted by physics, the bias correction towards true SIC is less skilled than towards net ISF, as can be assessed by the lower correlation values R in Fig. 5 (SIC) compared to Fig. 8 (ISF). A bias correction towards SIC would attempt to force the PMW SIC product to represent open water in two different ways: as sea ice when it is a melt pond and as true open water when it is a lead/opening between the ice floes, despite the fact that the surface emissivity and hence the observed TB are determined by the overall total amount of liquid water at the surface.

We hence only use linear regression equations obtained from the comparison between PMW SIC and MODIS ISF for a bias correction of PMW SIC towards MODIS ISF. We first test how well the bias correction works in comparison to MODIS ISF, i.e. investigate whether the difference between PMW SIC and MODIS ISF is reduced to zero, and subsequently compare the bias-corrected PMW SIC to MODIS SIC. This bias correction is exemplarily carried out for OSI-450 (group I), CBT-SSMI (group II), and NT1-SSMI (group III) for peak melt (DOY 201, year 2009) in Fig. 10 and for melt advance (DOY 169, year 2010) in Fig. S11 in the Supplement. Note that we use slope and intercept values obtained exactly for these examples, i.e. from Fig. 8, and not from Table 4.

The bias correction works well with respect to MODIS ISF for peak melt. The majority of the differences of bias-corrected PMW SIC minus MODIS ISF have a magnitude less than 5 % (Fig. 10d–f). The linear correlations are as high as for the uncorrected case and the RMSD decreases to around 6 %–7 % (compare Fig. 10a–c with Fig. 8b, e, h); the slope is almost identical to the identity line for OSI-450 and NT1-SSMI. We note that if the results of this bias correction prove to be of equal quality for other parts of the peak-melt period and other years, one could use the respective equations to obtain an independent estimate of the ISF from the entire PMW SIC data record, i.e. from 1979 to today. This could serve as an important boundary condition for the estimation of the surface albedo independent of daylight and cloud cover, complementing existing data sets and aiding in their evaluation (e.g. Riihela et al., 2010, 2017). For melt advance (Fig. S11a–f, Supplement), differences between bias-corrected PMW SIC and MODIS ISF are considerably larger than for peak melt, especially for CBT-SSMI and NT1-SSMI. While the slopes all agree quite well with the identity line, RMSD values are much larger than for peak melt. This is also evident from the larger scatter of value pairs in the respective 2-D histograms. During melt advance it appears advisable to use non-truncated SIC values if available, because the fraction of SIC larger than 100 % is the highest during the summer melt cycle (see Sect. S3.1 in the Supplement); at this stage we did, however, not further quantify the effect this may have on the results of the bias correction performed.

As expected, the difference of bias-corrected PMW SIC minus MODIS SIC is negative all over and has a magnitude of about 25 %. We find a relatively homogeneous distribution of differences (Fig. 10j–l). We find value pairs in the respective 2-D histograms to be confined below the identity line around a linear regression line with a slope slightly larger than 1 and linear correlations comparable to the uncorrected PMW SIC (Fig. 5b, e, h). Most striking is the similarity of the distributions in the maps and 2-D histograms across the three products and the fact that the RMSD between bias-corrected PMW SIC and MODIS SIC not only agrees within 1 % among the three products but also agrees with the modal MPF of 25 % for DOY 201 of the year 2009 (see Fig. 2c). Thus, the bias correction towards ISF reconciles the various PMW SIC products towards a consistent difference of PMW SIC minus MODIS SIC of the same order of magnitude as the average MPF. In contrast, during melt advance with melting and frozen and wet and dry surfaces co-existing, the results of the bias correction of PMW SIC appear less convincing (Fig. S11g–l, Supplement). Here CBT-SSMI provides a difference bias-corrected PMW SIC minus MODIS SIC, which in the central Arctic Ocean is uniform at about 10 %. While this value matches well with the MPF map and the first mode (9 %) of the bimodal MPF distribution for DOY 169 of the year 2010 (Fig. 2b), the other differences range between -40 % and 10 %, demonstrating that during melt advance a bias correction as proposed is potentially of limited value.

A logical next step would be to use the mean values of slope and intercept (Table 4) instead of the individual values (see above). We note that the mean values (Table 4) differ considerably from the individual values. For example, for OSI-450 during the 8 d period beginning at DOY 201 in year 2009 we have individual values of intercept and slope of 27.3 % and 1.01, respectively, while the respective mean values for group I during peak melt are 30.3 % and 0.86 (Table 4). We did not yet apply these, however, because we regard these first attempts as a feasibility study only. To carry out a comprehensive study about the potential of a bias correction of PMW SIC towards MODIS ISF would require a well-thought concept about how to adequately evaluate the bias-corrected SIC; this is beyond the scope of this paper.

After such a study, in the short term, values given in Table 4 could allow users of the existing PMW SIC data sets to bias-correct these products towards net ISF. Such a bias correction is however not necessarily useful in practice. Indeed, users must now rely on additional sources of information to link their SIC (e.g. from a geophysical model) to a measure of the ISF. This for example requires a trustworthy representation of the evolution of melt ponds on sea ice in their model. Several such melt pond schemes are being developed (e.g. Pedersen et al., 2009; Flocco et al., 2010; Scott and Feltham, 2010; Holland et al., 2012; Skyllingstad et al., 2015; Popović and Abbot, 2017), but their application and evaluation reveal some challenges remain (e.g. Light et al., 2015; Tsamados et al., 2015; Zhang et al., 2018; Burgard et al., 2020; Dorn et al., 2019). Still, in the long run, using PMW SIC as an observation of net ISF should be favoured, as it is more meaningful and will be more accurate. This will especially be the case when producers of PMW SIC data sets put additional effort into improving their algorithms and/or ice tie point selection schemes to actually retrieve unbiased observations of the net ISF. There is furthermore no doubt that both improving melt pond schemes in models and designing better PMW-based SIC algorithms in summer will benefit from better accuracy and availability of Earth-observation-based melt pond fraction CDRs from visible–infrared imager instruments such as NASA MODIS (e.g., Rösel et al., 2012), the European Space Agency's MEdium Resolution Imager Sensor (MERIS) (e.g., Istomina et al., 2015; Zege et al., 2015), or the Copernicus Ocean and Land Colour Imager (OLCI). There is a critical Earth observation (EO) gap to be filled here in order to further improve the Sea Ice essential climate variable (ECV).

Independent of the way forward and future attempts to get closer to what appears to be physically more correct when using satellite PMW data for SIC retrieval, we note that there might be applications which require an accurate SIC including the melt ponds on top, i.e. without the need to understand why the PMW SIC does not match the actual net ISF. The classical application would be the computation of the SIA, the sum of the area of all ice-covered grid cells weighed by SIC. We demonstrated in Sect. 4.1 which groups over- and/or underestimate MODIS SIC where and by which amount (Figs. 4, 5 and S5, Supplement). We illustrated that on a pan-Arctic scale, averaged over the years 2003–2011, group I exhibits a near-0 % bias, while group III appears to underestimate MODIS SIC by 5 %–10 % during peak melt and end of melt, and group II appears to overestimate MODIS SIC by around 10 % (see Fig. 6). This finding holds for melt pond fractions up to 30 % and for NT1-SSMI and group II products even up to 40 % (Fig. 11a). In addition, Fig. 11b further illustrates how well the difference of PMW SIC minus MODIS ISF can be seen as a linear function of the MPF for group I – at least up to a MPF of ∼ 30 %.

Coming back to the computation of SIA and the potential influence of melt ponds, as shown in Kern et al. (2019) and Ivanova et al. (2014), the choice of the product for the computation of SIA from PMW SIC data makes a difference. For the months July through September of the years 2002–2011, the SIA computed from PMW SIC of group I products is ∼ 400 000 km2 larger than SIA computed from NT1-SSMI (group III) and ∼ 600 000 km2 smaller than SIA computed from group II products (Kern et al., 2019, Fig. G2g–i). The average pan-Arctic MODIS SIC for these months is between 85 % and 90 % (Figs. 6 and S7, Supplement). Considering a value of 90 % and assuming an extent of 6 million square kilometres to be covered by some amount of sea ice on average for these months, we end up with a SIA of about 5.4 million square kilometres based on MODIS. Group I products, exhibiting zero bias to MODIS SIC (Figs. 6a, S07a–d) yield the same SIA estimate. NT1-SSMI, exhibiting a negative bias of 5 %–10 % (Figs. 6c, S7i), say 7 %, i.e. a pan-Arctic average SIC of 83 %, yields a SIA of 5.0 million square kilometres. Group II products, exhibiting a positive bias of ∼ 10 % (Figs. 6b, S7e–g), i.e. a pan-Arctic average SIC of 100 %, yield a SIA of 6.0 million square kilometres. Based on these considerations we can conclude that the summertime differences between the SIA estimates of the 10 products presented by Kern et al. (2019) can be explained well with the differences between PMW SIC and MODIS SIC presented in this paper.

Following up on the release of three new global sea-ice concentration (SIC) climate data records (CDRs) described in Lavergne et al. (2019), this paper focuses on an inter-comparison of these three CDRs and seven other SIC products (see Kern et al., 2019) with estimates of the SIC and the net ice surface fraction (ISF) in the Arctic during summer (May through September) for the years 2003 through 2011 obtained from satellite observations by the MODIS sensor. The motivation for this dedicated paper is the fact that it is particularly challenging to derive the SIC of melting sea ice. It is impossible with the current microwave radiometer sensors to distinguish water in melt ponds on top of the sea ice from the water in the leads between the sea-ice floes. What we expect to measure with the microwave radiometer sensor is therefore the ISF even though this is not what scientists normally relate to the term “sea-ice concentration”. The ISF radiometric signature and especially its variability are difficult to characterize when the sea ice is melting and this results in large random and systematic uncertainties when retrieving the SIC and ISF from PMW observations. Our study employs 10 SIC products which we assign to four groups based on their retrieval algorithm (see Table 1) – like we did in our previous study (Kern et al., 2019). Our results document that none of the 10 PMW SIC products provide an accurate measure of the summer SIC, or a faithful picture of the ISF.

Overall we find group I products (SICCI and OSI-450; see Table 1) exhibit a near-0 % bias to the MODIS Arctic average SIC – independent of melt pond fractions up to ∼ 35 % (Fig. 11a). Group II (CBT-SSMI, CBT-AMSR-E and NOAA-CDR) and IV (NT2-AMSR-E) products have a positive bias of 5 %–10 %, and NT1-SSMI (group III) has a negative bias of 5 %–10 %. However, these small overall biases are the result of widespread, spatio-temporally varying positive and negative differences of substantial magnitude which cancel out in a pan-Arctic mean for some of the products. Magnitudes of these biases frequently reach up to 20 %–25 % for groups I and III and up to 30 %–35 % for groups II and IV. Unlike what is generally accepted and reported in the literature, we observe that several PMW SIC products significantly overestimate true SIC.

By comparing PMW SIC with MODIS ISF and the MODIS melt pond fraction (MPF) we find that SIC products of all four groups substantially overestimate MODIS ISF. This overestimation is generally related to the MPF but the degree of overestimation varies between the groups. On a pan-Arctic scale, group I products overestimates MODIS ISF by almost exactly the overall mean MPF for values below ∼ 30 % (Fig. 11b). In contrast, groups II and IV overestimate MODIS ISF by an amount 5 %–10 % higher than the mean MPF while NT1-SSMI (group III) overestimate MODIS ISF by an amount 5 %–10 % smaller than the mean MPF. ASI-SSMI, albeit assigned to group III based on its SIC retrieval approach, performs considerably different to the other product assigned to group III: NT1-SSMI. Results for ASI-SSMI actually resemble a combination of our findings for group I and group IV (see Figs. 11, S7 and S10 in the Supplement).

The observed differences between PMW SIC and MODIS SIC or ISF cannot be explained by the presence of melt ponds alone. Often regions exhibiting high MPF values do not coincide with regions of large overestimation of MODIS ISF by PMW SIC. For example, we find regions with near-100 % PMW SIC coinciding with MODIS ISF and MODIS SIC of 55 % and 85 %, respectively. The associated MPF is only ∼ 30 %, and with that overestimation of MODIS ISF is 15 % larger than the MPF. By taking into account the different PMW data used by the various algorithms and relevant surface properties other than melt ponds – such as wet snow, (refrozen) coarse grained snow or a frozen surface in general – we discuss potential reasons for our observations. For the near-19 GHz and near-37 GHz frequency channels often used for SIC retrieval (see Table 1), open water in the form of melt ponds reduces the observed PMW brightness temperatures. However, during summer the surface/snow between melt ponds is likely wet, which results in an increase in their brightness temperatures compared to typical winter and spring conditions. The two effects counteract and might result in a PMW SIC close to 100 % despite a considerably smaller ISF of, e.g., 80 % caused by the melt ponds. This applies in particular when the ice tie point does not represent wet snow conditions well. Another scenario that would have the same effect is that the ice tie point does represent wet snow conditions between the melt ponds well but does in addition include an unknown amount of open water due to melt ponds, i.e. does not represent 100 % melt-pond-free sea ice. Our results illustrate that of the two groups of products employing advanced ice tie point retrieval methods, i.e. groups I and II, the methods of group I are considerably more successful in mitigating the unwanted influence of surface properties other than melt ponds.

Our inter-comparison reveals similarity in the results between group I and III products on the one hand and between group II and IV products on the other hand. This similarity is particularly interesting because ice tie point estimation differs substantially between groups I and III and between groups II and IV. While groups I and II have comparably advanced schemes to derive the ice tie point at a daily temporal scale, ice tie points are fixed throughout the year for algorithms of the other two groups. This appears to call for a revision of the currently used concepts to derive and use ice tie points during summer. One potential solution to reduce SIC biases reported in this paper would be to add regional variation by, e.g. incorporating the different regionally varying stages of melt into the ice tie point estimation. This could be done, e.g., by using maps of melt onset derived from PMW observations (e.g. Stroeve et al., 2014; Markus et al., 2009) – possibly in combination with atmospheric reanalysis data or observations of the ice surface temperature. Another solution could be to simplify the entire SIC retrieval process by, e.g., assuming melt conditions globally and derive a global ice tie point for melting conditions. The smaller sensitivity of lower-frequency channels, i.e. near 7 GHz or near 1 GHz, to changes in snow grain size or snow wetness makes these particularly good candidates for ice tie point optimization during summer conditions. Such channels are for example offered by AMSR-E, AMSR2, the Soil Moisture and Ocean Salinity (SMOS) mission and the planned Copernicus Imaging Microwave Radiometer (CIMR) mission.

One goal of such an optimization could be to further support the switch from sea-ice extent (SIE) to sea-ice area (SIA) as the main parameter to monitor long-term changes of the Arctic sea-ice cover. Sea-ice covers sharing the same sea-ice edge provide the same SIE regardless of how open the sea-ice cover inside the ice edge actually is. In contrast, SIA allows one to distinguish between a comparably open sea-ice cover equalling low SIA and a highly compact sea-ice cover equalling large SIA. Hence the SIA clearly outperforms SIE in terms of providing information about the status of the sea-ice cover inside the ice edge (e.g. Notz, 2014), but it is also much more affected by systematic summer biases as documented here for all 10 algorithms. Another goal could be to support moving away from retrieving sea-ice concentrations during winter and some highly inaccurate, ill-defined quantity during summer, still called sea-ice concentration, and rather retrieve net ice surface fraction year-round – the quantity which by physical means is the one accessible with these microwave radiometry frequencies year-round. A starting point of such a switch could be based on the obtained linear relationships between PMW SIC and MODIS ISF which appeared to be robust enough for our attempt to perform a bias correction of the PMW SIC during peak-melt conditions. In any case, such a switch will require improved algorithms for PMW observations, and improved melt pond formulations in geophysical models. In turn, this will require preparing improved, error-characterized, longer and sustained melt pond fraction data sets derived from satellite observations in the visible–near-infrared frequency range (MODIS, MERIS, OLCI, etc.). To have the most impact, these MPF Earth observation products should classify the ocean surface in at least three classes, ocean, ice, and melt ponds, so that they can address both true SIC and MPF. We recommend that the sea-ice communities work towards such a switch and enhanced data sets of true SIC and MPF to improve sea ice as an essential climate variable (ECV).