Evaluation of Summertime Passive Microwave and Reanalysis Sea‐Ice Concentration in the Central Arctic

Passive microwave (PM) observations have been used to monitor ice retreat in the Arctic. However, various PM sea ice concentration (SIC) algorithms are prone to underestimate ice fraction during summer. We evaluated the accuracy of 2002–2019 low SICs in the Central Arctic Ocean of four PM products from the University of Bremen, the National Snow and Ice Data Center (NSIDC), and the Ocean and Sea Ice Satellite Application Facility (OSI SAF), and two reanalysis data sets from the fifth generation of European ReAnalysis (ERA5) and the Modern‐Era Retrospective analysis for Research and Applications, Version 2 (MERRA‐2). Three reference fields were used: (a) Moderate Resolution Imaging Spectroradiometer (MODIS) and Visible Infrared Imaging Radiometer Suite (VIIRS) true‐color composites, (b) MODIS sea ice extent, and (c) multi‐product ensemble (MPE‐SIC) comprising the median of collocated SIC estimates. Our results indicate SICs derived from the Advanced Microwave Scanning Radiometer ‐ Earth Observing System (AMSR‐E) and the Advanced Microwave Scanning Radiometer 2 (AMSR2) high frequency channels have the best accuracy. Reanalysis SICs indicate almost identical patterns as their remote sensing inputs. The assessment shows that the Bremen (+1.06%) and NSIDC (+0.99%) SICs are higher than the median field, while the OSI‐401 (−6.65%) and OSI‐408 (−4.64%) have negative mean deviations. The mean error of MODIS‐derived SIC (−0.80%) is smaller than PM SICs. These small mean values belie wide distributions of values. The correlation coefficients of pairs of time series of Low sea‐Ice Concentration Index range from 0.37 to 0.96.


Introduction
Sea-ice is a crucial component in the Earth's system.The rapid decrease of Arctic sea ice cover within the past few decades is a convincing signal of climate change and Arctic Amplification which is mainly indicated by the rising surface air temperature (SAT) (Cohen et al., 2014;Graversen et al., 2008;Johannessen et al., 2004;Polyakov et al., 2002;Serreze & Francis, 2006).Satellite observations showed that there has been a downward trend in the annual Arctic minimum sea ice extent (SIE) and sea ice area (SIA) since 1979 (Comiso et al., 2017;Serreze & Meier, 2019;Wang et al., 2019).The SIE is defined as the total region with at least 15% ice cover.The SIA is defined as the total area covered by sea ice.Meanwhile, the pronounced interannual retreat of multiyear-ice (MYI) and the increasing extent of first-year ice (FYI) make a "seasonal ice free" Arctic possible in the future (Jahn et al., 2016;Stroeve & Notz, 2015), which would result in a profound influence on the global climate (Curry et al., 1995;Graversen & Wang, 2009;Katlein et al., 2019) and regional ecosystems (Moline et al., 2008;Sweetman et al., 2017;Tynan & DeMaster, 1997).Therefore, it is essential to monitor sea ice change, especially during melting season, before this great transformation.
Satellite remote sensing detects electromagnetic radiation from features on the Earth's surface and in the atmosphere without requiring direct contact.Since sea-ice has a higher albedo than the surrounding ocean, it reflects more solar radiation and is therefore represented as a brighter object in spaceborne visible imagery such as from the Moderate Resolution Imaging Spectroradiometer (MODIS; Guenther et al., 2002) and Visible Infrared Imaging Radiometer Suite (VIIRS; Xiong et al., 2014).However, clouds and darkness frequently prevent the observation of sea ice from visible sensors.Passive microwave (PM) radiometry can detect sea-ice since the surface emissivity, the ratio of emitted energy from a surface to that of a perfect emitter, is different than that of liquid water.The surface emissivity of water, ice and snow are close to unity in the thermal infrared (wavelengths, λ, of 8-14 μm) (Sobrino & Cuenca, 1999) but are much more variable at microwave frequencies, depending on wavelength and polarization.

10.1029/2023EA003214
2 of 20 The sea-ice concentration (SIC) is defined as the proportion of an ocean area that is ice-covered and has been derived from PM measurements, expressed as brightness temperature (Tb), since the 1970s.The Electrically Scanning Microwave Radiometer (ESMR) on Nimbus-5 provided the first global sea-ice cover data (Parkinson et al., 1987).ESMR measured radiation at 19.35 GHz and this leads to a limited accuracy of the retrieved sea-ice cover because the ambiguity caused as well by the variations of surface emissivity and temperature as by atmospheric water vapor and cloud liquid water cannot be interpreted correctly from measurements taken at a single frequency.The Scanning Multichannel Microwave Radiometer (SMMR) on Nimbus-7 was in operation from November 1978 to August 1987 and collected sea-ice data with improved accuracy compared to its predecessors due to its dual-polarized microwave channels (Cavalieri et al., 1984).Beginning in 1987, SMMR was replaced by a series of similar sensors called the Special Sensor Microwave/Imager (SSM/I) and the Special Sensor Microwave Imager/Sounder (SSMIS).The SSMISs are conical scanning sensors, as were SMMRs and SSM/Is, and the Instantaneous Fields of Views (IFOVs) of the SSMIS range from 13.1 × 14.4 km at 91.655 GHz to 45 × 68 km at 19.35 GHz, determined by the antenna dimensions of 61 × 66 cm.The Advanced Microwave Scanning Radiometer -Earth Observing System (AMSR-E) was launched on Aqua in May 2002.It measured horizontally (H) and vertically (V) polarized radiation in six channels: 6.9 GHz,10.7 GHz,18.7 GHz,23.8 GHz,36.5 GHz,89 GHz.Its successor, the Advanced Microwave Scanning Radiometer 2 (AMSR2) on the Japan Aerospace Exploration Agency (JAXA) Global Change Observation Mission-Water (GCOM-W), has the same frequencies with the addition of a 7.3 GHz channel that is used for radio frequency interference (RFI) mitigation for sea-surface temperature retrievals.AMSR-E had a 1.6 m antenna, increased to 2.0 m for AMSR2, so the spatial resolutions are improved approximately threefold over those of SMMR and SSM/I.
The annual variations of SIE and SIA are similar, but SIA is always the smaller and is more sensitive to the summertime SIC (Ivanova et al., 2014).However, the seasonal and decadal trends of SIA and SIE produced by different algorithms have discrepancies since each algorithm has different sensitivities to surface emissivity and atmospheric effects (Andersen et al., 2007;Comiso et al., 2017).When assimilating SIC product into climate models, an inaccuracy of 10% in SIC is usually assumed (Kimmritz et al., 2018;Tietsche et al., 2012).Nevertheless, various surface properties (e.g., ice type, melt ponds, leads), can contribute ∼30% inaccuracy in satellite derived summer SICs.A study by Han and Kim (2018) evaluated the performance of four PM SIC algorithms of the summertime Chukchi Sea by comparison with 78 KOrean Multi-Purpose SATellite-5 (KOMPSAT-5) enhanced wide-swath X-band high resolution Synthetic Aperture Radar (SAR) images.Their results showed mean biases in the NASA Team algorithm (NT; Cavalieri et al., 1984) of −25.65%, the Bootstrap algorithm (Comiso, 1986) of +1.53%, OSI SAF (Breivik et al., 2001) of −7.59% and Arctic Radiation and Turbulence Interaction STudy (ARTIST) Sea Ice (ASI; Spreen et al., 2008) of −8.53% over the consolidated pack ice zone with 100% ice concentration.In a case study by Rösel and Kaleschke (2012b), three SIC images from AMSR-E, derived with the ASI, the enhanced NASA Team algorithm (NT2; Markus & Cavalieri, 2000), and Bootstrap algorithms for the area of the Canadian Archipelago, were compared with MODIS-derived SIC and melt pond fraction (MPF).The MPF is defined as the ratio of melt pond areas to SIA.In the same region with mean 93% ice cover and around 40% MPF determined from MODIS data, the ASI algorithm had a 45% mean ice concentration, the NT2 result was 65%; and the Bootstrap algorithm showed 55%.Although in this case the NT2 algorithm was closest to the MODIS result, it was still far from the 93% ice concentration determined from the MODIS data.The misinterpretation of sea ice with melt ponds has been found among 13 SIC algorithms (Ivanova et al., 2015).
The long-term PM SICs play important roles in representing Arctic climate change and in evaluating climate models.Hence, a concern emerges regarding our confidence in the extent and distributions of low ice concentration or ice-free sea surface indicated by satellite observations.Although previous studies have concluded that in addition to there being a general underestimation of SIC during summer conditions, the size of the discrepancy is likely to be dependent in the SIC itself, with increasing errors as SIC declines.Even though some ice retrieval methods use dynamic tie points (values for pure surface types), the tie-point defined for 100% ice during summer are likely to contain melt ponds, so that the resulting ice concentration uncertainty is correlative to the onset of melt ponds.Furthermore, research focused on small areas, usually along the ice pack edge that is affected by open ocean processes (Wadhams, 1986), known as the marginal ice zone (MIZ), and/or short sampling times, does not necessarily support indications of sea ice change in the Central Arctic, an area which used to be covered by high concentration ice with different ice types, but where reliable observations are rare compared with the MIZ.The uncertainty in SIC retrievals from various sensors and algorithms mainly results from the inaccurate interpretation of measurements of radiative energy which is influenced by the spatial heterogeneity of the atmosphere and of the surface (Andersen et al., 2006(Andersen et al., , 2007)).And the different algorithm sensitivities to atmospheric and surface conditions are likely to cause different errors in the low and high SIC regions (Han & Kim, 2018).Therefore, by analyzing the agreement of PM SIC products we have the chance to explore relative sensitivities of measurements in various microwave channels to the presence of melt ponds, which can give us further knowledge to optimize SIC retrieval methods.
The lack of assessment of reanalysis SIC products has the potential to be problematic since ice cover from operational reanalysis data sets, for example, the fifth generation European ReAnalysis (ERA5; Hersbach et al., 2020) and the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2; Gelaro et al., 2017), offers temporally and spatially complete representation of sea ice, but biases and uncertainties of reanalysis SIC data sets are not well understood.Even though Graham et al. (2019) evaluated the performance of six reanalysis data sets over Arctic sea ice, only atmospheric variables, such as the 2-m temperature, 10-m wind speed, and total column water vapor, were validated using observations from the Norwegian Young Sea Ice campaign.In this study, we investigated the performance of two reanalysis SIC and four PM SIC products using the same criteria; this provides valuable knowledge about the accuracy of daily reanalysis SICs.
The rest of the paper is organized as follows: Section 2 describes the research area and evaluated SIC data sets.Section 3 introduces the MODIS SIC retrieval algorithm, Low sea-Ice Concentration Index (LICI), and the evaluation methods of this study.The correlation results of LICI and the accuracy evaluation of SIC products via different methods are presented in Section 4. Section 5 is a discussion and Section 6 summarizes the work and resulting conclusions as well as giving some suggestions for future research.

Research Area
There are several definitions of the Central Arctic Ocean (CAO) based on hydrography, international accord, and absolute coordinates.We focus on the SIC retrieval within the zone between 84°N and 88.3°N-hereinafter referred to as CAO.The southern limit is set to 84°N to eliminate areas with land ice.The northern limit removes the influence of missing data near the North pole due to the combination of satellite orbital geometry and swath widths of the microwave radiometers.The summertime is defined here to be from June 1 to October 31.

ARTIST Sea Ice (ASI) SIC Product From AMSR-E/AMSR2
Researchers at the University of Bremen applied the ASI algorithm to swath AMSR-E L1A and AMSR2 L1B data and mapped swath-width SIC for each calendar day (UTC) into a 6.25 km polar stereographic grid, a resolution based on considering the size of IFOV of AMSR-E 89 GHz (Spreen et al., 2008).The ASI algorithm uses the Tb differences at 89V and 89H to retrieve SIC because different ice surfaces show similar emissivity differences while water has a much larger value.Since high frequency channels are used, the ASI algorithm is sensitive to weather conditions.In this study, we used ASI SIC products from 2002 to 2019 and this data set is hereafter referred as Bremen.

NASA-Team2 (NT2) SIC Product From AMSR-E and AMSR2
The NSIDC provides daily SIC products with a grid scale of 12.5 km based on measurements of AMSR-E (Data Set ID: AE_SI12) (Cavalieri et al., 2014) and AMSR2 (Data Set ID: AU_SI12) (Meier et al., 2018).These products use the NT2 algorithm which assumes three surface types (first-year ice, multi-year ice, and open water) and estimates SIC by applying a set of coefficients to the observed polarization ratio (PR) of 19 GHz and the spectral gradient ratio (GR) between 19 and 37V.The difference between GR (85V/19V) and GR (85H/19H) are used to resolve the errors due to surface snow effects of the NT algorithm.The time periods are from 1 June 2002 to 4 October 2011 and 2 July 2012 to 2019, respectively.These products are hereafter referred as NSIDC.

OSI-SAF SSMIS SIC Product
The OSI-401-b data set (identified as OSI-401-d from 25 April 2023), hereafter OSI-401, is one of the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) Ocean and Sea Ice Satellite Application Facility (OSI-SAF) global SIC products (Tonboe & Lavelle, 2016).It is derived from SSMIS observations 10.1029/2023EA003214 4 of 20 using the OSI SAF algorithm.Prior to calculating SIC, Tb measurements were corrected for wind roughening over open water and water vapor in the atmosphere using several variables from the ECMWF weather forecast fields: surface wind speed, 2 m air temperature, total column water vapor, and total column cloud liquid water.The OSI SAF algorithm is a hybrid of the Bootstrap frequency (BF) mode (Comiso, 1995) and the Bristol algorithm (Smith, 1996).The BF algorithm assumes two surface types (sea ice and open water) and uses Tbs of 19 and 37V to estimate SIC.The Bristol algorithm uses both PR and GR information from 19V, 37V and 37H.If the BF algorithm indicates open water (SIC BF = 0), then SIC OSISAF = SIC BF .For ice concentration up to 40%, SIC OSISAF is the average from the BF and Bristol algorithms.When the BF algorithm indicates SIC > 40%, the SIC OSISAF = SIC Bristol .This algorithm has been in operation since 1 March 2005.The spatial resolution of this SIC product is 10 km.However, it is an over-sampled grid since the footprints of 19 and 37 GHz channels of SSMIS are 73 × 47 km and 41 × 31 km.This data set has been the remote sensing input to the ERA5 SIC since September 2007, and MERRA-2 SIC since April 2006.Both ERA5 and MERRA-2 data sets will be discussed below.

OSI-SAF AMSR2 SIC Product
The OSI-408 data set (identified as OSI-408-a from 25 April 2023), here after OSI-408, is another operational SIC product from the EUMETSAT OSI-SAF (Tian et al., 2015) which uses AMSR2 observations as an input.The Tb correction approach is as the same as the one described in Section 2.2.3.The SIC retrieval algorithm was developed at the Technical University of Denmark (TUD) and utilizes the 19 GHz, 37 GHz, and 89 GHz channels.First, the SIC is estimated from the BF algorithm at a low spatial resolution and then by a linear function of Tbs at 89V and 89H.The final SIC is the geometric mean of the two values.Therefore, the TUD hybrid algorithm reduces the atmospheric sensitivity inherent in measurements near 90 GHz while providing increased resolution for concentrations above 10%-20% (Andersen et al., 2006).The SIC estimates are gridded on the same 10 km grid as the OSI-401 and are also over-sampled.The time coverage of this product is from 19 September 2016.

ECMWF ERA5 SIC Product
ERA5 is the fifth-generation atmospheric reanalysis released by ECMWF (Hersbach et al., 2020).The ERA5 SIC has 0.25° × 0.25° spatial resolution and the values are updated once per day.The ERA5 is based on ECMWF Integrated Forecasting System (IFS) Cy41r2 and ingested the Operational Sea-surface Temperature and Sea Ice Analysis (OSTIA; Good et al., 2020) data set, which uses OSI-401 for SIC, from 2007 to present.

MODIS SIC Retrieval
To calculate the MODIS SIC, we adapted the approach used by Cavalieri et al. (2010).They retrieve SIC from broadband top-of-atmosphere (TOA) reflectance from three MODIS bands.Cavalieri et al. (2010) first calculated the broadband albedo (0.46-0.67 μm) from MODIS bands 1, 4, and 3 corresponding to the red, green, and blue parts of visible spectrum using the following weights derived by Liang et al. (1999): broadband TOA albedo = band1 * 0.3265 + band4 * 0.2366 + band3 * 0.4364 (1) Then, they use the same thresholds as Cavalieri et al. (2006) to classify surface cover into four different types (open water, new ice, young ice, and first-year ice).For our study, we simplified the thresholds to provide a binary classification map.If albedo <0.06, the pixel is evaluated as pure water, and if albedo >0.60, it is pure ice (Perovich, 1996).The final step is to project MODIS SIC onto the target resolution grid.

Low Sea-Ice Concentration Index
The Low sea-Ice Concentration Index (LICI) proposed by Li et al. (2018) describes the proportion of low SIC values within an area.Following Li et al. (2018), we put 15%-75% as the low SIC range and calculated the ratio of low SIC area and the area of the Central Arctic.The formula is defined by: where A i is the area of each grid cell, C i is estimated SIC in each cell.
The LICI time series generated from daily LICI values provides an effective way to quantify the progression of melting sea ice and greatly simplifies the comparisons of SIC products with different resolutions.Peaks in the LICI time series, detected using a 7-day window and 5% threshold (at least 5% area of SICs in the Central Arctic are <75%), will be used to obtain a selection of low ice concentration cases for validation of the accuracy of the satellite retrievals of SIC.

Correlation Analysis
Firstly, the linear relationships of LICI time series (four from PM SICs and two from reanalysis SICs) were investigated by analyzing Pearson's correlation coefficient (CC), r XY : The value of r XY lies between −1 and +1 indicating the extent two variables are linearly related.A symmetrical autocorrelation matrix is obtained by calculating CC of each pair of LICI time series.To further assess the temporal variability, that is, "leader-follower" relationships, of highly related signals, we use Time Lagged Cross Correlation (TLCC) which is derived by incrementally shifting one of the time series vectors in time and repeatedly calculating the correlation between two signals.If the peak correlation is where the offset = 0, it indicates the pair of time series is mostly synchronized.However, the peak correlation may be at a different offset if one signal leads the other.

Human-Inspection Based on Composite True-Color Imagery
NASA Worldview (https://worldview.earthdata.nasa.gov/)provides near real-time, true-color imagery from both MODIS and VIIRS.This imagery is termed as "corrected reflectance" because it is generated from L1B radiances using a simple atmospheric correction algorithm to remove gross atmospheric effects, such as Rayleigh scattering, but ignoring aerosol effects.For MODIS, Band 1 (red) at 250 m resolution is used to sharpen Bands 10.1029/2023EA003214 6 of 20 3 (blue) and 4 (green) at 500 m resolution so the resulting geometric imagery resolution is 250 m; the temporal resolution of composite reflectance imagery is daily and is available since 24 February 2000 for MODIS on Terra and 3 July 2002 for MODIS on Aqua.The corrected reflectance gives a true color representation of the Earth's surface and atmospheric features, but it is subject to loss of clarity due to uncorrected atmospheric effects.In contrast, the MODIS land surface reflectance product (MOD09, described below) is based on a more complete atmospheric correction algorithm including an aerosol correction (Vermote & Kotchenova, 2008), made it also available over sea ice.So, the MODIS corrected reflectance imagery and MODIS land surface reflectance product are very similar in clear atmospheric conditions, which facilitates our assessment, but they will be different when aerosols are present.As for VIIRS imagery visualized in Worldview, band I1 (red), band M4 (green) and band M3 (blue) are used.The sensor resolution is 750 m for the M Bands and 375 m for the I Band, and imagery resolution is 250 m.The VIIRS pixels have limited growth in the scan direction away from nadir through the process of pixel aggregation (Minnett et al., 2020;Schueler et al., 2013).
The preliminary evaluation was based on the spatial distribution of sea ice shown in the corrected reflectance imagery from MODIS and VIIRS.By visual inspection, it was straightforward to identify ice and open water in a true-color image, however, dark nilas might be hard to discern from open water in rare cases.This supports the idea that people can make use of the landscape scale (1-10s km) organization of sea ice from MODIS and VIIRS corrected reflectance imagery from NASA Worldview to estimate SIC under clear-sky conditions.Table 2 lists some common sea ice organization types and corresponding characteristics Sea Ice Glossary (n.d).By identifying the spatial distribution of ice, we can obtain a reference range of SIC values.
In Figure 1, the left panel shows SIC derived using the ASI algorithm and the image on the right is the MODIS/ Aqua corrected reflectance corresponding to the region inside the black box in the SIC map on the left.The Name of sea ice type Characteristics Floe Any relatively flat piece of sea ice 20 m or more across.
Lead A long narrow passage through pack ice, navigable by surface vessels.
Open pack ice Pack ice in which the concentration is 4/10 to 6/10, with many leads and polynyas, and the floes generally not in contact with one another.
Close pack ice Pack ice in which the concentration is 7/10 to 8/10, composed of floes mostly in contact.
Very close pack ice Pack ice in which the concentration is 9/10 but less than 10/10.

Compact pack ice
Pack ice in which the concentration is 10/10 and no water is visible.

Consolidated pack ice
Pack ice which covers 10/10 of the sea surface and the floes are frozen together.

Table 2
Glossary of Sea-Ice Distribution Figure 2, however, is an example of disagreement between ice cover determined by PM algorithms and from visible images.The corrected reflectance from MODIS/Aqua on the right indicates typical consolidated pack ice in which the floes are frozen together with some cracks or rifts.Though there is a subregion showing less reflectance/albedo probably due to melt ponds, the ice cover is practically 100%.With this information, we can confirm that the lower PM-derived SIC (50%-70%) in the selected region underestimates the human-derived ice cover by at least 30%.The underestimations might be from the melting surface which makes its characteristics close to open water in the microwave range.
We repeated this evaluation process for LICI time series peaks which correspond to independent low SIC cases.
Images within a 7-day window (±3 days from the date when low SICs occurred) were taken into consideration to reduce the effect of cloud contamination.We classified our results into four groups based on the difference between visually inspected SIC and the SIC estimates to be validated: Accurate (−20% to +20%), Inaccurate (underestimated if <−20% and overestimated if >+20%) and Mixed (contain two or more categories).

Validation Using MODIS SIE Product
MODIS/Terra and MODIS/Aqua SIE Daily L3 Global 1 km Equal Area Scalable Earth Grid (EASE-Grid) Day (MOD29P1D and MYD29P1D), Version 5, was the second validation reference (Hall et al., 2006).The EASE Grids (Brodzik et al., 2012) are intended to minimize the amount of areal distortion over the poles so that comparisons and analyses of different fields are facilitated.The SIE field was provided as tiles of data gridded in the original EASE-Grid Lambert Azimuthal Equal Area map projection, with 1 km cell size and 951 × 951 cells of each tile.The "MOD" prefix represents Terra-derived data and "MYD" means Aqua-derived.The ice detection algorithm of this product assumes that sea ice is snow covered and snow dominates the reflectance characteristics (Riggs et al., 1999).It uses the normalized difference snow index (NDSI) as the main criterion.Since snow has high reflectance at visible wavelengths and low reflectance at wavelengths of ∼1.6 μm, the MODIS NDSI is defined as the ratio of the difference between band 4 (Green) and band 6 (Short Wave Infrared) and their sum.The details of this algorithm can be found in Riggs et al. (1999).
To validate all LICI peak cases using daily MODIS SIE, we firstly mask out clouds and assign a value of 1 to ice pixels and 0 to ocean pixels.Then, we re-project and down-sample cloud-free MODIS SIE into the target resolution grids (Bremen, NSIDC and OSI-408 polar stereographic grids, respectively, 6.25, 12.5 and 10 km; ERA5: 0.25°).We use ERA5 as a proxy of OSI-401 and MERRA-2 due to high correlations among those three data sets (see details in Section 4.2).Then, if more than 10 pixels show low ice concentrations (<75%), we calculate the mean of these pixels and use the outcome to compare with the means of the target data sets (Bremen, NSIDC, OSI-408, and ERA5) using the same array of pixels.On the contrary, if fewer cells (<10) show low ice concentrations, we use the mean of all valid pixels to compare with the average of the target data sets with the same array of pixels.Finally, a simpler criterion was used to evaluate the SIC accuracy based on the mean SIC difference: if the difference is within the range of ±20%, the evaluated case was considered to be Accurate, and if the absolute value of the difference exceeds 20%, the evaluated case was classified as Inaccurate.

Validation Using Multi-Product Ensemble SIC (MPE-SIC)
Since optical data are rendered problematic by the effects of clouds, we devised a way of using the median values of all visible and PM SICs in a common grid to determine the relative accuracy of the individual SICs.This method is taken from the GHRSST multi-product ensemble (Martin et al., 2012) which used the median field of independent SST retrievals as the reference to assess the relative accuracy of each retrieved SST.
The MODIS/Terra and MODIS/Aqua Surface Reflectance Daily L2G Global 1 km and 500 m sinusoidal grid (MOD09GA and MYD09GA), Version 6 was used to retrieve MODIS SIC (details in Section 3.1).The Level 2G format was developed by mapping Level 2 granules onto a geolocated grid based on sinusoidal projection without compositing and averaging results.The grid consists of 460 nonoverlapping tiles which measure approximately 10° × 10°.Each tile can be located by its horizontal and vertical indices.For the Central Arctic, we downloaded four tiles: h16v00, h17v00, h18v00, and h19v00.
The first step to retrieve MODIS SIC was to re-project L2G MODIS surface reflectance maps on a 1 km polar stereographic grid and generate one mosaic map covering the Central Arctic from the four tiles.Cloud information was then derived from the Quality Assessment (QA) values to generate the cloud mask for the mosaic map.Secondly, the SICs within clear sky pixels were derived using the methodology described in Section 3.1.
After obtaining 1 km MODIS SIC, the data were remapped into the coarsest resolution cells (12.5 km).SIC data sets at finer resolutions, that is, Bremen, OSI-401 and OSI-408, were downscaled into the 12.5 km grid as well.Once all data sets had the same projection and grid scale, the median value of each 12.5 km cell was calculated to generate the multi-product ensemble (MPE) SIC field which was used for intercomparisons.
Figure 3 shows the four remapped SIC maps and their median field (MPE-SIC) for 1 July 2008.All images are on 12.5 km polar stereographic grids.We overlayed the MODIS cloud mask on PM SIC maps to display the common cloud-free, blind-hole-free regions, so the shape of MODIS tile is outlined on the polar stereographic grids.For our study, we only use data within the 84°N, so the shape of the tile would not impact analyses.The invalid pixels, that is, North Pole blind holes and pixels in the cloud mask are black, and the exterior regions are colored brown.The mean deviation of satellite derived SICs with respect to the reference inside the 84°N circle was calculated.
The deviation distribution and root mean square error (RMSE) of the samples were statistically analyzed, as well as further inspection of the human-derived accuracy labels was conducted.Figure 7 summarizes the evolution of the summer LICI starting in 2002.The x-axis is selected summer periods (June-October) from 2002 to 2019.The y-axis indicates the six SIC products.There are several missing days of OSI-401, Bremen, and NSIDC, so gaps can be seen along their timelines-the most evident one is from October 2011 to June 2012, the observation time gap between AMSR-E and AMSR2.This plot also reveals the similarity

Cross-Correlation of SIC LICIs
CC was calculated for 18-year LICIs, providing the general relationships among various SIC products.The correlation matrix is shown in    The LICIs of ERA5, MERRA-2 and OSI-401 are highly correlated which also indicates both reanalysis products introduce little improvement to OSI-401.Hence, ERA5 LICI peaks can be used as a representative of the other highly correlated time series for the next step, which is accuracy assessment.

Evaluation Through Human Inspection
During 2002-2019, there are 96 ERA5 LICI peaks of which 65 have available matches with composite true-color imagery from MODIS and VIIRS.As a result of human-inspection, 35 of 65 daily ERA5 SIC estimates are considered Accurate, 29 are identified as Underestimated, and one case is Overestimated.The comparisons are summarized in Table 4.
Bremen has 48 LICI peaks in the same time period.The number of peaks is half that of ERA5 and 37 peaks match with valid MODIS and VIIRS imagery.In these 37 cases, 84% are considered Accurate and 16% are Underestimated.
For NSIDC, 27 of a total of 43 LICI peaks match those in MODIS data in the same time period.About 70% are Accurate, 15% are Underestimated and the remaining 15% contain more than one condition which makes it difficult to classify low SIC estimates into a single class.Based on SIC estimates from the spatial distribution shown in the composite true-color imagery, all SIC products tend to underestimate summer ice concentration, but SIC products retrieved from AMSR-E/AMSR2 Tb have better performance compared to reanalysis SIC products, though Bremen, NSIDC, and OSI-408 use three different retrieval algorithms and are at various spatial resolutions.

Evaluation Using MODIS SIE
Since the cloud mask used in MODIS SIE product has a 14.2% false positive rate (false cloud) and 7.1% false negative rate (missing cloud) during polar day in summer (Frey et al., 2019), we have fewer cloud-free pixels identified than occur in nature and fewer reference samples to be used in the validation.
The comparisons with MODIS SIE used as the reference are summarized in Table 5. ERA5, Bremen and NSIDC have similar outcomes compared to the values in Table 4, but lower accuracies.The relatively low accuracy probably results from the difference between the MODIS sea ice identification method based on NDSI and PM SIC algorithms using Tb properties.As for OSI-408, all seven cases are considered as Inaccurate.This result is inconsistent with 77% Accuracy of the human-inspection, which may be due to the false positives in cloud masking, as well as a small sample size.

Evaluation Based on Ensemble SIC (MPE-SIC)
We summarized LICI peaks for ERA5, Bremen, NSIDC, and OSI-408 and there is a total of 75 LICI peak cases.
The scatter plot (Figure 10) shows the deviations of 75 cases with respect to the median fields, excluding 14 cases with data error, illumination issues, or cloud contamination.The OSI-401 (orange) and OSI-408 (dark gray) points almost all lie below zero, which means these two products usually have lower ice concentrations than the median values.Many Bremen (blue) and NSIDC (magenta) points have mostly positive deviations meaning they    4) and contains 21 cases, the mean deviation is +1.3%.Rösel and Kaleschke (2012a) investigated the effects of melt ponds on PM SICs in the Canadian Archipelago on 18 June 2011 and presented SIC maps derived from MODIS and AMSR-E using ASI, NT2 and Bootstrap algorithms.In the areas without melt ponds identified in MODIS data, the PM SICs were larger than the MODIS SIC.Thus, a reason for the mean negative deviation and large variance of the MODIS SIC compared to the MPE-SIC in our analysis is likely to be that SICs derived from MODIS are smaller than the PM SICs in regions free of melt ponds.
The mean of Bremen and NSIDC deviations are 1.06% and 0.99%, respectively and the greatest negative deviation is around −6%.The standard deviation of NSIDC is a little larger than that of Bremen, excluding the outliers.The mean deviations of OSI-401 and OSI-408 are −6.65% and −4.64%, respectively.

Discussion
Accurate SIC measurement is necessary in terms of monitoring, understanding, and modeling Arctic Amplification.PM SIC products provide daily distribution of ice cover and open water, determining the regions where SST can be estimated.Although the surface temperature of ice and water can be very close in the summer melt season, their different albedos result in contrasting levels of solar radiation absorption and distinct contributions to the Arctic radiation budget.By incorporating SIC into climate models, scientists can better understand the mechanisms of surface energy budget and project future Arctic warming.Our study provides a comprehensive comparison and evaluation of four PM and two reanalysis SIC data sets.The limitations of this study are as follows.1.The statistics of SIC accuracy assessments are influenced by several factors including the size and randomness of the sample.In this study, we detect peaks of LICI time series and assign multiple peaks that happened within 7 days as one low SIC event.For different SIC products, we have different numbers of events that are used in the accuracy validation.Larger sample sizes tend to produce higher confidence level results and vice versa.Another influence relevant to low SIC samples is that we cannot prevent missing matches due to the unavailability of optical imagery.2. Since we derive SIC from MODIS surface reflectance, the values are, to some extent, sensitive to the selections of reflectance thresholds for water and ice.We also recognize that the effects of clouds may have impacts on the validation when using SIC estimated from MODIS SIE and broadband albedo.We assume that the geophysical value of pixels under clouds within a retrieval grid could be represented by the value of adjacent or nearby clear-sky pixels.This may also introduce errors into the SIC from MODIS and MPE-SIC.3. Another limitation of this study is that using MPE-SIC as reference might provide biased results since this is not perfect independent validation data, though this method is good at identifying individual outliers and algorithms that give "out-of-family" results.
Nevertheless, these assessments have several significant consequences for future sea ice studies.
1.Many sea ice studies used MODIS-derived SIC as the reference to validate the accuracy of PM SICs (Cavalieri et al., 2010;Rösel & Kaleschke, 2012b;Shi & Su, 2018).However, the limitations of the MODIS SICs, such as being prone to underestimate ice cover when the ice is thin (Ludwig et al., 2020), should be kept in mind in evaluating their analyses as well as ours.2.Even though all PM SIC algorithms appear likely to underestimate ice cover with very high concentration values, the likelihood varies with algorithms more than with sensors.The BF and Bristol SIC algorithms appear to be more sensitive to a wetter surface condition, indicating that algorithms using Tb gradient difference and polarization difference at low frequencies may not correctly retrieve SIC in the presence of melt ponds.The ASI and NT2 algorithms which utilize polarization ratio (PR) at 89 or 85 GHz provide more Accurate matches with respect to the validating data.Thus, the polarization difference or polarization ratio at high frequencies are probably more robust when the surface becomes wetter in summer.But the modification by a linear expression of the 85 GHz polarization difference in the TUD algorithm seems inadequate.Future work could use radiative transfer models to investigate the sensitivity of PM Tb to the presence and area of melt ponds and the effectiveness of tie points in ASI and NT2 algorithms.3. Further, a more fundamental question is how to exploit the strengths of optical and microwave sensors to obtain PM SIC retrievals with errors consistently <10%?A traditional approach is to improve the algorithm by tuning the tie points for sea ice, but the outcomes vary spatially and temporally (Hao & Su, 2015).Since MODIS SIC is derived from a few optical channels with 500 m resolution, some physical mechanisms related to the sea ice features, such as melt ponds, can probably be better described.The merged SIC provides another approach that can be used as an ensemble SIC to investigate the evolution of melt ponds.

Conclusions
Comparisons of summer-time CAO sea-ice fields derived from PM and optical remote sensing data show similarities, but also marked differences.The differences are dependent not only on the method of measurements but also on the algorithms to derive the sea-ice fields, especially on ice surface properties, including the presence of melt-ponds.The extent of low sea-ice concentrations in the summer CAO was investigated using Low sea-Ice Concentration Index (LICI) time series calculated from four PM products and two reanalysis data sets (Figures 4-6).Pearson's correlation coefficients (CC, The accuracies of low ice concentration cases with respect to three reference fields in the CAO in the summers from 2002 to 2019 were evaluated.Results regarding the likelihood of a SIC product misinterpreting summer ice cover are summarized in Table 6. Using SIC estimates from the sea ice distribution shown in the optical imagery as the reference, all PM SIC products were found to underestimate ice fraction (Table 4).The Accurate cases of ERA5 only account for 53.9%.SIC products retrieved from AMSR-E/AMSR2, that is, using the Bremen, NSIDC, and OSI-408 algorithms, provide higher accuracies 83.8%, 70.4%, and 76.9%).
MODIS SIE was used as the validation reference revealing all PM and reanalysis SICs have less Accurate cases: ERA5 (36%), Bremen (69%), NSIDC (53%), OSI-408 (0%).When compared to human inspections, the accuracy values are lower.This may result from the reduced amount of LICI peak cases which are able to be matched with cloud-free MODIS SIE, as well as the ice identification method employed in the MODIS SIE product.
We also estimate SIC from MODIS broadband surface albedo and obtain a median SIC field from PM SICs and MODIS-derived SIC.Using the median field as a representative reference, the ice concentration deviations of each product were analyzed.From 64 valid cases, the majority of Bremen and NSIDC deviations are positive meaning they are likely to produce higher ice concentrations than the median.The mean deviations of Bremen (1.06%) and NSIDC (0.99%) are small.In contrast, OSI-401 and OSI-408 are prone to have lower values of ice concentration and their mean deviations are −6.65% and −4.64%, respectively.The errors of MODIS-derived SIC have a complicated pattern with a mean deviation −0.8%, but this results from the compensation of two clusters in which (a) PM SIC is Accurate/Overestimated, and (b) PM SIC is Inaccurate/Underestimated, giving mean deviations of these clusters MODIS SIC of −2.1% and +1.3% compared to the median.This probably indicates that ice concentrations derived from MODIS could have distinct biases due to the influence of ice thickness (Ludwig et al., 2020) and melt pond fractions (Kern et al., 2020).The root mean square errors (RMSE) of these five SICs with respect to the MPE-SIC are: MODIS (4.44%), Bremen (3.57%), NSIDC (3.48%), OSI-401 (8.15%) and OSI-408 (6.86%) (Table 6).
The recognition that the properties of SIC in the central Arctic Ocean is an important factor in the response of the changing Arctic, and that satellite remote sensing is the only feasible method of monitoring the seasonal and interannual changes, we have quantified the accuracies of several widely used SIC products.We have introduced the concept of a median SIC field as a reference.Our results could guide future analyses and interpretations of the satellite-derived SICs.

Data Availability Statement
The python codes used for this study have been made available to the public by the authors in a Zenodo repository (Song, 2023).The ASI SIC can be accessed from PANGAEA data repositories (Melsheimer & Spreen, 2019, 2020).The NT2 SIC are archived by NSIDC (Cavalieri et al., 2014;Meier et al., 2018).The OSI-401 (OSI SAF, 2017b) and OSI-408 (OSI SAF, 2017a) were provided by EUMETSAT OSI SAF.MODIS SIE L3 data can be accessed from NSIDC (Hall et al., 2006).MODIS surface reflectance Daily L2G data were provided by the USGS (Vermote & Wolfe, 2015).ERA5 data were obtained from the Copernicus Climate Change Service (Hersbach et al., 2023

Figure 1 .
Figure 1.Left is daily SIC map from Bremen for 08/23/2012.Right is corrected reflectance image from an overpass of MODIS/Aqua on the same day in the relatively low SIC regions inside the black box in the left image.

Figure 2 .
Figure 2. Left is daily SIC map from Bremen for 07/01/2008.Right is corrected reflectance image from an overpass of MODIS/Aqua on the same day in the relatively low SIC regions inside the black box in the left image.

Figure 3 .
Figure 3. First row: MODIS-derived SIC and Bremen SIC.Second row: OSI-401 SIC and NSIDC SIC.Bottom: the multi-product ensemble (MPE) SIC generated by calculating the median field from the four maps above.All images are on 12.5 km polar stereographic grids.The exterior region is colored brown.North Pole blind holes and cloud mask are in black.The yellow dotted circle highlights latitude = 84°N.

Figure 5 .
Figure 5. 2008-2013 LICI time series.SIC Data sets are the same as those in Figure 4.

Figure 6 .
Figure 6.2014-2019 LICI time series.SIC Data sets are the same as those in Figure 4 except for the black line representing OSI-408 which is available since September 2016.

Figure 7 .
Figure 7.A Hovmöller-like diagram of LICI time series from June 2002 to October 2019.The values scaled to a blue-red color-map are the same as the above line plots.The gap between 2011 and 2012 is due to the discontinuity of operational SIC products.

Figure 8 .
Figure 8. Yearly Time Lagged Cross Correlation (TLCC) of OSI-401 and ERA5 LICI.The top panel is from 2005 to 2012.The bottom panel is from 2013 to 2019.The 0 offset is labeled by a vertical black dashed lines.The correlation peaks since 2007 are highlighted by the vertical red dashed line.Note that if two signals are synchronized, the black line will be covered by the red dashed line (offset = 0).

Figure 10 .
Figure 10.Plot of the mean deviations of 75 LICI peak cases with respect to the MPE-SICs.The x-axis is case index.The y-axis is deviations in percentage.The colors correspond to five satellite-derived SICs.

Figure 11 .
Figure 11.Box plot of deviations of the LICI cases of five satellite-derived SIC products with respect to the MPE-SIC.The mean is marked by a cross.Light gray: MODIS, blue: Bremen, orange: OSI-401, magenta: NSIDC and dark gray: OSI-408.
starting 1 April 2006.The daily MERRA-2 SIC product has a horizontal resolution of 0.5° × 0.66° in latitude and longitude.The properties of the data used here, including the reanalysis fields, are summarized in Table1.
Table 3 which provides quantitative results of the linear relationship between every pair of SIC products.LICIs of two reanalysis data sets and OSI-401 have high positive correlations (r OSI- NSIDC CCs are in most cases lower (from 0.37 to 0.61), with the exception Bremen (0.68).Annual TLCC analyses were used to elucidate whether "leader-follower" relationships exist between OSI-401 and ERA5 (MERRA-2).We only selected OSI-401 because we observed that the LICI time series of OSI-401, ERA5, and MERRA-2 demonstrate almost the same patterns from 2013 onwards, but with a little temporal offset from 2008 to 2012 (OSI-401 vs. ERA5) and 2007 to 2012 (OSI-401 vs. MERRA-2).The TLCC peak value can infer the temporal offset between two LICI time series at a specific year.LICI of Bremen, NSIDC, and OSI-408 were

Table 3
Pearson's Correlation Coefficients of 2002-2019 LICI Time Series OSI-408 is available for only the last four years of the study, and 13 peaks are used in the comparison.The percentage of Accurate cases is 77%.Underestimated cases account for 23%.This is better than ERA5, but worse than Bremen and NSIDC.

Table 5
Validation Results From Comparing With MODIS SIE Ludwig et al. (2019)ated MODIS and PM images to build a training data set, machine learning methods may offer a means of classifying open water and different types of sea ice with little concern about tie point selection(Chi et al., 2019).Ludwig et al. (2019)merged MODIS SIC and AMSR2 SIC by each 5 km by 5 km box-if MODIS data are available, the grid value is the MODIS SIC plus the difference between the mean of MODIS SIC and the mean of AMSR2 SIC; if MODIS are not available, the grid value is the AMSR2 SIC.

Table 3
. 2013-2019, LICI of ERA5 and MERRA-2 show identical patterns as the OSI-401 from which we can infer that both reanalysis SICs directly interpolate OSI-401 into their target grids.
) indicate that LICIs of OSI-401, OSI-408, ERA5 and MERRA-2 fields are highly correlated (>0.8), while correlations of other sets range between 0.37 and 0.74.The LICI time series in together with the results of Time Lagged Correlation Coefficients (TLCC, Figures8 and 9) show the development of reanalysis SIC products: a) 2002-2006, ERA5 and MERRA-2 have different inputs of PM SIC and the LICIs have independent features.b)2007/2008-2012, LICIs are highly correlated but indicate 1-day offset compared to OSI-401 LICI.c

Table 6
). MERRA-2 data were obtained from the Goddard Earth Sciences Data and Information Services Center (GES DISC) (Global Modeling and Assimilation Office, 2015).Accuracy Evaluation Results of PM, Reanalysis, and MODIS Retrieved SIC