CryoSat-2 was launched in April 2010 aiming to monitor Earth's cryosphere and, in particular, to measure the decline in land and sea ice in the polar regions in order to understand the role of climate in the retreat of polar ice. CryoSat-2 was placed on a non-Sun-synchronous orbit with a long repeat orbit of about 369 d. CryoSat-2 is carrying a Ku-band radar altimeter and is observing in three different acquisition modes up to a latitude of 88∘ N/S . The acquisition modes vary with application area and surface type with respect to a geographical mode mask (for more information, see https://earth.esa.int/eogateway/instruments/siral/description, last access: 14 February 2023).

The polar seas are predominantly sampled by the synthetic-aperture radar (SAR) mode with an along-track footprint size of about 300 m . Briefly summarized, the SAR mode combines frequency-shifted radar returns (i.e. Doppler effect) in the direction of flight from different look angles with respect to a predefined position on the surface. The result of combining different view angles is called a multi-look waveform and samples the surface with 20 Hz resolution.

The present investigation is based solely on SAR-mode-acquired multi-looked waveforms, covering major parts of the Arctic Ocean. In particular, CryoSat-2 Level-1B (L1B) Ice Baseline-D data are introduced to the processing chain. This data set comprises, in addition to the waveform data, information on waveform scaling as well as orbit positions. More information regarding Baseline-D can be found in the ESA CryoSat-2 Product Handbook and .

For the comparison of thin-ice thickness to CryoSat-2 waveforms, MODIS Level-1B-calibrated radiances are obtained from both NASA satellites, Terra and Aqua (MOD/MYD02; ), retrieved from the Level-1 and Atmosphere Archive and Distribution System (LAADS) Distributed Active Archive Center (DAAC) with a spatial resolution of 1km×1km at nadir and swath dimensions of 1354 km (across track) × 2030 km (along track).

Brightness temperatures were calculated from the calibrated radiances comprising MODIS channels 31 and 32 at 10.78 to 11.28 µm and 11.77 to 12.27 µm, respectively, following . Subsequently, the sea-ice surface temperature (IST) was computed following . All MODIS processing is based on MODIS Collection 6.1 data for nighttime only.

In order to compute corresponding thin-ice-thickness data from the IST data, additional data on the prevailing atmospheric conditions are necessary. Here, all necessary atmospheric fields are provided from the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth-generation reanalysis (ERA5) data acquired from the Copernicus Climate Data Store (CDS; ). These fields comprise the 2 m air temperature, the 10 m wind-speed components, the mean sea-level pressure, and the 2 m dew-point temperature in hourly resolution.

The ESA Copernicus C-band SAR missions Sentinel-1A and Sentinel-1B (S1-A/B) were launched in 2014 and 2016, respectively. At the time of full functionality, both satellites orbited Earth 180∘ apart to provide SAR imagery, unaffected by cloud cover, on a 6 d repeating cycle. SAR images from both missions are used for visual comparisons. Automatic thin-ice detection from SAR images is not applied in this study because this falls outside the main focus of the work. S1-A/B features a higher spatial resolution with regard to MODIS and, therefore, provides further information about different sea-ice surface types by making use of the backscattering properties of different surfaces. For instance, leads and polynyas appear very dark due to a very flat and less rough surface. In this case the incoming radar signal is scattered away from the receiver. However, caution must be taken by the interpretation of the backscattering pixel values in the presence of small-scale features like frost flowers (i.e. small ice crystals with the size of a few centimetres in diameter) that develop under cold and calm conditions, e.g. on nilas ice, as they can significantly increase the scattering resulting in brighter pixel values . Furthermore, brighter pixel values can also result from a roughened water surface due to strong wind influence in polynyas. More information regarding sea-ice surface type interpretation can be found in and .

In the present study, the Sentinel-1 comparison data set consists of Level-1 dual-polarized SAR extra-wide-swath mode data at medium resolution. The images are ground range detected and show a pixel resolution of 40m×40m and a swath width of 400 km. The spatial resolution is close to 100 m. The images are processed using SNAP (ESA Sentinel Application Platform) v8.0 (http://step.esa.int, last access: 14 February 2023) following the processing steps described in and but with an additional speckle filtering. Briefly summarized, the main processing steps follow standard routines (e.g. radiometric calibration, speckle filtering, map projection). The Level-1 data are gathered from the Alaska Satellite Facility Data Active Archive Center (ASF DAAC). In terms of the study area and period, the Sentinel-1A/B image pool represents a potentially usable size of approximately 500 scenes. Unfortunately, Sentinel-1B was decommissioned after an instrument failure in December 2021.

developed an unsupervised classification of altimeter waveforms that was primarily focused on the detection of open-water targets, such as leads and polynyas, without the use of training data or previously known information about the surface conditions. The classification can be applied to any kind of altimeter waveforms and missions. applied it to the non-SAR, conventional altimeter missions Envisat and SARAL (Satellite with ARgos and ALtiKa). Later, the classification approach was adopted to SAR altimeter waveforms and applied to CryoSat-2 and Sentinel-3A/B in the framework of the European Space Agency's Baltic+ Sea Level (ESA Baltic SEAL) project . However, none of these studies classified thin ice, since altimeter waveforms generated by this surface type are quite similar to open-water returns.

Briefly summarized, the unsupervised waveform classification (UWC) is based on an automatic clustering of a broad spectra of different waveforms by K-medoids classification e.g. defining a reference model with a certain number of clusters. After clustering, an assignment of the clustered waveforms as well as remaining waveforms to certain surface types (e.g. ocean, lead/polynya, or sea-ice conditions) is performed. The assignment of the waveform clusters to the different surface types is mainly based on the use of background knowledge about the physical backscattering properties of the individual surface types and statistical relationships (Fig. ). More detailed explanations of the cluster assignment can be found in . In the present investigation, the cluster number is set to 25. This number was found to produce optimal results in and led there to an overall agreement of about 97 %. Moreover, an internal misclassification rate of 1.13 % can be expected after performing a 10-fold cross validation .

The main input to the classification approach is parameters derived from the waveform shapes and information on the backscatter power. Altogether, they span the feature space, which is defined as follows see:

Maximum power (MP) – physical backscatter coefficient σ0 at the waveform maximum

Moreover, in the quantitative comparison (Sect. ) two additional features are included. The additional features are part of the CryoSat-2 waveform classification approach applied in the framework of ESA CCI:

Leading-edge width (LEW) – width in range bins between 95 % and the first bin at the leading edge exceeding 5 % of the waveform maximum power using a 10-time oversampled and smoothed waveform

Figure  shows the assignment of 25 clusters to 5 different surface types (compared to 4 in the original UWC approach): undefined, sea ice, thin ice, lead, and ocean. Clusters characterized by a very strong MP, a small Wwidth, and strong decay obtained by the fitting of an exponential function to the trailing edge of the waveform are labelled as lead clusters (i.e. 5, 10, 14). Clusters that were formerly assigned to sea ice are now divided into two groups (sea ice and thin ice) based on their different reflective properties. Following and thin ice covers nilas and young ice ranging from 0 to 0.30 m and is often covered by a flat layer of slush, which is ice crystals saturated with salt brine. Members of thin-ice clusters show characteristics in between lead clusters and clear sea-ice groups. They are characterized by a wider waveform shape, a weaker waveform decay, and a flatter trailing-edge slope than lead clusters. Moreover, they also have a slightly weaker MP than radar returns reflected from open, calm water . These properties correspond to clusters 4 and 19.

Undefined waveform clusters represent waveforms which cannot assigned unambiguously to certain surface conditions, for example if they are acquired in the direct vicinity of the coast or islands. They also show a bigger standard deviation compared to other clusters.

In order to compute the thin-ice thickness (TIT) from MODIS IST a simple surface energy balance model is employed, which utilizes the inversely proportional relation between IST and the thickness of thin sea ice . In the model, the net positive flux towards the atmosphere (i.e. positive corresponding to the direction from the warm ocean to the cold atmosphere) is equalized from the conductive heat flux through the ice. From this conductive heat flux, TIT is derived following Eq. (), where TIT is the thin-ice thickness; κi is the thermal conductivity of sea ice (2.03 W(mK)-1); IST and Tfp are the IST and the ice–ocean interface temperature (assumed to be at the freezing point of the ocean), respectively; and Qatm is the total heat flux to the atmosphere. 1TIT=κi×IST-TfpQatm

A detailed description of the TIT retrieval procedure as well as all necessary equations and related assumptions are thoroughly described in . These assumptions comprise the following: sea ice that is free of snow cover, a linear temperature gradient within the sea ice, a negligible ocean-heat flux, and cloud-free conditions assured by manual screening of all used MODIS swaths . While no state-of-the-art uncertainty analysis is available for our combination of MODIS thin-ice retrieval with ERA5 atmospheric reanalysis, state an average uncertainty of ±4.7 cm for ice thicknesses between 0.0 and 0.2 m using the NCEP2 reanalysis National Centers for Environmental Prediction;, substantially increasing for larger thickness ranges. Figure  exemplifies the underlying IST with its corresponding TIT. With regard to these uncertainty limitations in combination with the desire to maximize CryoSat-2/MODIS overlaps, all TIT analyses are limited to a maximum sea-ice thickness of 25 cm.

This section provides an initial visual intercomparison between CryoSat-2 classified open-water lead, thin-ice, and sea-ice observations on the one hand and either MODIS (Table ) or Sentinel-1A/B SAR imagery (Table ) on the other hand.

Figure  shows four subsets of two HH-polarized SAR images from February 2018 with their respective classification results from CryoSat-2 superimposed on them. Both SAR images feature at least one lead, which is recognized by the classification algorithm and highlighted by the cyan dots. Orange labels indicate thin-ice observations in the vicinity of leads and correspond to higher SAR backscatter values. Within the image, the areas appearing in light grey to almost white with their lead-like pattern represent former open-water areas that have recently frozen over. These areas of new ice can range in thickness from 10 to 30 cm and are often covered by a layer of slush . The CryoSat-2 classification results agree reasonably well with the SAR images; however, not all thin-ice surfaces and leads are always correctly detected (e.g. Fig. c and d). Potential reasons for this are two-fold: from the SAR point of view, a complete interpretation of the SAR pixel values is not possible. From the altimetry point of view, off-nadir effects, such as when a dominant and specular lead is not in the nadir direction, may overlay clear leads or thin-ice radar echoes, which hence prevents clear identification, in particular if the lead or thin-ice surface is very small, i.e. less then 1 % of the illuminated surface . These off-nadir effects can become noticeable in the waveform by the appearance of further dominant peaks in the backscatter signal, which later can lead to deviations in the height determination if a retracking algorithm specially modified for this problem is not used see e.g.. Since the observations are very close together in time, differences due to ice movement or over-freezing can be excluded.

A visual comparison between MODIS TIT estimates and thin-ice-assigned CryoSat-2 radar echoes are provided by Fig. . The sets of images were recorded in January 2014 and 2017, respectively. White areas in the north indicate either a lack of data due to present cloud cover or an ice-thickness estimate above 25 cm. Towards the south, thin-ice areas are bounded by either the coast line and/or the extensive presence of landfast sea ice . Northwards, leaving the respective coastline or fast-ice edges, MODIS TIT features a rather steady increase. The respective CryoSat-2 classification generally agrees with respect to the MODIS TIT, showing primarily lead and thin-ice classifications. Qualitatively, the respective classifications appear within expectations, in particular with lead classifications close to the coastline- or fast-ice-associated ice edge in the south, where the sea ice is thinnest, and thin-ice classifications further north, where MODIS features thicker thin-ice estimates (see Fig. c and d). However, in most cases a direct distinction between thicker sea-ice and thin-ice areas is not possible due to the coarse pixel resolution of MODIS and the variability in ice thickness within a MODIS pixel in comparison to CryoSat-2 which leads to the fact that one MODIS TIT pixel can contain up to three CryoSat-2 observations. Nevertheless, a general connection between thin-ice-labelled radar returns in the direct vicinity of thin sea ice can be recognized. This relationship is investigated more deeply using the full MODIS database.

Figure  displays a CryoSat-2, MODIS, and Sentinel-1A comparison from 1 March 2018 featuring acquisition time gaps less than 17 min (more details can be found in the Appendix). This gives the very rare opportunity to analyse observations of all three sensors within a 30 min time frame. It shows the different behaviour and dependencies of optical and microwave sensors with respect to different sea-ice surfaces and their physical properties (e.g. surface roughness). The scene shows very thin ice close to the landfast-ice edge near Taymyr in the northeastern part of the Laptev Sea region . The polynya observed by MODIS appears very bright in the SAR image and is likely caused by a high sea-ice surface roughness, potentially due to e.g. the presence of frost flowers or surface waves. In contrast to the impact this has on the side-looking SAR, the increase in diffuse surface scattering results in a wider waveform with smaller peak power for the nadir-looking CryoSat-2. We note here that this change in waveform properties can be caused by a change in roughness at the radar wavelength scale or large scales, e.g. by ice deformation. It is unlikely that larger areas covered solely by thin sheet ice have significant surface height variability or a considerable snow layer. It has been shown by that the increase in radar scale roughness can significantly affect CryoSat-2 waveform shape even for comparably flat surfaces when incoherent backscatter from radar scale roughness is taken into account. This effect may be so pronounced that several waveforms are assigned to the sea-ice category in an area where the SAR image indicates the presence of thin ice only. However, the low-backscatter region to the southeast (dark in the SAR image) featuring very thin ice is labelled correctly again as lead. While the CryoSat-2 unsupervised classification performs well in general, it was primarily developed to identify open water within sea-ice conditions. Hence, a clear distinction between thin and thick sea ice is not always possible due to a high variability in the surface roughness of thin ice. This comparison showcases how substantially the sea-ice surface can vary within small spatial scales but at the same time the potential and synergies for sea-ice investigations that lie within these multi-sensor collocations.

For the quantitative analysis, a total of about 21 300 CryoSat-2 observations are compared with MODIS TIT observations in the Laptev Sea for the winter months January through March between 2011 and 2020. This corresponds to about 4 % of the theoretically available matched MODIS versus CryoSat-2 along-track observations (total circa: 540 000). The small percentage of matches used is explained by (1) the frequent presence of cloud cover in the Arctic and (2) the availability of large flaw polynya openings with corresponding thin-ice surfaces, which occur near the landfast-sea-ice edge.

In total, 14 % of all 21 300 classifications were assigned to thin-ice surfaces and 1 % to leads. The largest proportion is attributed to thicker sea ice (85 %). With respect to valid overlaps (i.e. MODIS pixels with TIT information), about 51 % of CryoSat-2 classifications are assigned to open water and thin ice, while 45 % are assigned to other sea-ice types. Remaining waveforms are marked as undefined, e.g. due to the influence of land or instrument errors.

Besides a comparison of the CryoSat-2 classification results and the TIT from MODIS, the relationship between waveform-derived backscatter power as well as other waveform shape properties and different TIT categories is of peculiar interest. Therefore, the TIT data from MODIS are grouped into intervals of ±2 cm from 4 to 25 cm. These groups are then compared to corresponding CryoSat-2 radar waveforms, in particular, with the six waveform-derived features used in the classification and two additional waveform parameters (i.e. LEW and LEP) listed in Sect. .

Figure  shows the per-bin averages of the eight waveform features with their respective standard deviations indicated as grey bars in the background. The Pearson linear correlation coefficients with respect to the ice thickness are listed in the Appendix (Table ). With the exception of LES, there is a linear (or close to linear) dependency present with respect to an increasing TIT. This is especially evident in waveform features MP, Wwidth, and TES that are intended to characterize single-peak waveforms (e.g. radar reflections by a lead). Despite a very large standard deviation in the thinner-ice class bins, an increase with rising ice thickness is a physically explainable behaviour. In general, a rougher surface corresponds to an increase in surface scattering resulting in a diminishing return back to the sensor and at the same time an increase in received off-nadir scattering by the sensor. This leads to a broadening of the received waveform as well as a drop in maximum waveform power e.g. and, therefore, to the observed negative correlation with MP (-0.97) and the positive correlations with TES (0.94) and Wwidth (0.99). In the case of LES, which is the number of bins between the first waveform bin reaching 12.5 % and the bin of the waveform's MP , a linear relationship cannot be spotted. This might be due to a larger uncertainty associated with the first two TIT bins and their in general lower occurrence rates compared the thicker thin-ice bins or higher uncertainties in the LES processing related to very steep leading edges. Only the latter part, starting with the ±12 cm bin, features the expected behaviour. The remaining four waveform features, i.e. Wdecay, WfitMAD, LEW, and LEP, feature an apparent correlation; however, it is less clear than the ones we observed with MP, Wwidth, and TES. Similar to TES, physically one would expect a slower/smaller decay with an increase in surface roughness and therefore sea-ice thickness as well as an increase in the width of the leading edge (LEW; ) from thinner to thicker ice classes. In contrast, the LEP is expected to decrease with an increasing LEW going along with an increase in surface roughness. The median absolute deviation from the exponential fit to the waveforms is also decreasing for broader waveforms that result from additionally received backscatter from off-nadir areas due to an increased surface roughness leading to a strong negative correlation of -0.97.

Nevertheless, this comparison provides information on how different thin-ice scenarios affect the altimeter waveform. The shown dependencies between TIT and derived waveform parameters can be used e.g. to adapt and optimize altimeter waveform classifiers to thin-ice conditions and subsequently improve the sea-ice freeboard estimation in areas of frequently present thin ice.

We compare the surface type classification with the CryoSat-2 surface classification described in to assess how thin-ice class waveforms are represented in other CryoSat-2-based products. The classification by was developed for the CryoSat-2 contribution to the sea-ice-thickness data record of the ESA Climate Change Initiative , hereafter named the CCI classification. The algorithm is also used in the Alfred Wegener Institute (AWI) CryoSat-2 sea-ice product v2.4 which provides the necessary temporal coverage for this study. We use Level-2 intermediate (l2i) data, which provides the surface type flag for full-resolution orbit data for the months of October through April from November 2010 to April 2021 for the Arctic Laptev Sea regions (Fig. ). The flags in the l2i files are based on monthly thresholds for the backscatter coefficient sigma0, the LEW, and pulse peakiness as well as supported by sea-ice concentration data OSI-450 and OSI-430-b of the Ocean and Sea Ice Satellite Application Facility; as a sea-ice mask. The surface types used in are comparable to this study except for the missing thin-ice class and the fact that the ocean-waveform classification solely depends on the sea-ice mask and existing land/ocean flags.

The surface type classification is based on approximately 26.5×106 waveforms. The CCI classification lists 50.2 % of these in the sea-ice category, 10.9 % in the lead category, 38.7 % in the unknown category, and less then 0.1 % in the ocean category (Fig. a). Compared to the CCI classification, the unsupervised waveform classification algorithm (UWC) of this study has more sea-ice (79.7 %, +29.2 %) and ocean (3.9 %, +3.89 %) waveforms, as well as fewer lead type (1.9 %, -9 %) and unknown (i.e. undefined) waveforms (1.4 %, -37.3 %) in addition to the 13.0 % thin-ice waveforms (Fig. b). The classification matrix (Fig. c) shows that the UWC thin-ice waveforms are mostly distributed in CCI unknown (46.3 %) and CCI lead (53.4 %) surface types with a negligible contribution of CCI sea-ice waveforms (0.3 %). UWC lead classifications are almost exclusively (96.8 %) in the CCI lead class, showing a good agreement in the identification of open-water leads. UWC sea-ice classification not only has a good agreement with CCI sea-ice classifications (61.9 %) but also includes waveforms the CCI algorithm labels as unknown (35.6 %).

Between the two surface type classifications algorithms, the UWC results in far fewer unknown/undefined waveforms than the CCI algorithm and, thus, provides more usable information for sea-ice freeboard and thickness retrieval. The distinction of leads and thin ice by the UWC algorithm, which are partly seen as leads in the CCI algorithm, reduces the number of sea-surface height observations but increases their reliability. It should be noted that we define a lead here in the sense of satellite altimetry as an open-water lead, which provides a true sea-surface height observation without any bias introduced by thin-ice freeboard. The sea-ice-thickness bias introduced by using thin-ice freeboard as sea-surface height on the surrounding sea ice is of the order of the TIT itself and with a maximum of 25 cm a significant fraction of typical first-year ice thickness. The fact that the CCI algorithm labels a significant portion of the UWC thin-ice waveforms as unknown demonstrates that these were rightfully excluded from either lead or sea-ice class. The latter sea-ice class is treated as an ice surface, for which range corrections for the full climatological snow cover are applied, which would also result in range biases. The distinction between open-water lead and thin-ice classes, therefore, introduces the possibility of improving both the sea-surface height and radar freeboard retrieval.

Finally, it must be noted that the official definition of the World Meteorological Organization (WMO) for the term lead includes thin ice with a thickness of up to 30 cm . To obtain lead fractions according the WMO definition or to compare lead fractions with other remote-sensing data, the thin-ice class may be added to the open-water lead class.