dataesr/scientific-paragraphs-categorization huggingface dataset:
The paper is organised as follows: -First, we detail the methodology to process the ASD product and present all the datasets used in this study. -Section 4 compares ASD with the other main existing snow depth satellite and model data in both hemispheres. -The datasets are then assessed against OIB, CryoVEx and IMB validation data in the Arctic in Sect. 5. -To circumvent the temporal limitation induced by SARAL, we propose in Sect. 6 a preliminary snow depth climatology based on ASD. -Section 7 aims to quantify the SIT level of uncertainty due to the snow depth from an ensemble of SIT estimations calculated from the satellite and model snow depth datasets presented in the previous sections. -We finally discuss and conclude, emphasising current needs for snow depth data in sea ice studies. 2 Data processing of ASD + MSS + tide ocean + tide bar )), ( 1 ) where alt is the satellite altitude, range is the altimetric range retracked from the waveforms, tropo dry is the dry tropospheric correction, tropo wet is the wet tropospheric correction, iono is the ionospheric correction, MSS is the DTU15 mean sea surface correction  (Andersen and Knudsen, 2015) , tide ocean is the oceanic tide corrections, and tide bar is the barometer tide correction.
A 25 km median filter is then applied to the 20 Hz along-track surface height of sea ice floes and sea ice leads. For each observation, the sea level anomalies (SLAs) under floes are calculated as the median value of all leads in a 25 km radius around the considered along-track point. Freeboard heights are computed by fb = H floe -H lead , where H floe is the heights of the ice floes and H leads the heights of the leads. Finally, a 25 km radius median smoothing is applied to the retrieved freeboards. The reason is that we assume that the ASD product should not be able to provide relevant information at smaller scales. However, additional analyses and comparisons with validation data would be necessary to properly characterise this point. Note that the ability to consistently observe small scales would certainly be significantly improved in the future dual-frequency snow depth products from the CRISTAL mission.
In the first ASD data version  (Guerreiro et al. , 2016) , snow depths were only calculated at CS-2 and SARAL crossing track points. For this version, snow depths are calculated from the difference between monthly EASE2 gridded freeboards as sd r = fb Ka -fb Ku , where sd r is a radar snow depth. Furthermore, to compute snow depth (sd), we need to take into account the decrease in the Ku radar echo velocity as it penetrates into the snow pack  (Ulaby et al. , 1986; Kwok and Cunningham, 2015) : sd = sd r × (1 + 0. 51 × ρ s ) (-1. 5) , (3) where ρ s is the snow density, set to 300 kg/m 3. Note this formulation agrees with the conventional interpretation to correct for the slower wave propagation speed through snow, as recently shown in  Mallett et al. (2020). To estimate snow depth uncertainties, we assume that errors are unbiased, uncorrelated and follow the Gaussian propagation law.
DuST The DuST  (Lawrence et al. , 2018)  data are provided in the Arctic on a 1. 5   data; see Sect. 2), the DuST product uses SAR mode freeboard estimates of CS-2. The CS-2 and SARAL (LRM data) data are then calibrated against data from National Aeronautics and Space Administration's (NASA's) OIB airborne measurements to align the freeboard observations from SARAL/Altika with the snow-air interface and the freeboard observations from CS-2 with the snow-ice interface. Although this method provides a generic approach adaptable to different footprints (e. g. ICESat-1 and 2), it has the disadvantage of being dependent on the OIB data which are mainly located near the Canadian Archipelago and the Beaufort Sea and are only obtained during March and April.
Because of this limitation, we mainly focus on the Bremen AMSR2B product  (Rostosky et al. , 2018)  developed at the Institute of Environmental Physics of the University of Bremen. This product is available on a daily basis from November 2012 to April 2018 on a polar stereographic grid with a 25 km × 25 km resolution. Unlike in AMSR2-NSIDC, March and April snow depth data are also calculated over MYI for AMSR2B. Other months are only available over FYI. Note that the algorithm used to calculate snow depth over MYI is also calibrated with observations from OIB.
NESOSIM The NASA Eulerian Snow On Sea Ice Model (NESOSIM) is a 3D snow budget model configured to produce snow depth and density over sea ice in the Arctic Ocean. Data used in this paper are snow depth monthly mean maps provided on a 100 km × 100 km stereographic polar grid issued from the NESOSIM 1. 0 configuration  (Petty et al. , 2018). It is freely available at https://earth. gsfc. nasa. gov/ cryo/data/nasa-eulerian-snow-sea-ice-model-nesosim (last access: March 2021). Snowfall data forcing fields are the ECMWF ERA-Interim global reanalysis and a median of three reanalyses: the 55-year reanalysis of the JRA, NASA's MERRA and ASR, version 1.
CryoSat Validation EXperiment (CryoVEx) These airborne data are a joint effort of the DTU National Space Institute and ESA (in cooperation with AWI). The main goal of the project is to quantify and vali- date CS-2's ability to measure SIT. Since 2003, the Cry-oVEx missions have provided both laser (ALS, airborne laser scanner) and Ku-band radar (ASIRAS, ESA airborne Ku-band interferometric radar) altimetric measurements. In addition, in 2017, the data include for the first time along-track total freeboards from the Ka-band KAREN altimeter  (Haas et al. , 2017)   2015). Snow depth data are collected at 4 h intervals from acoustic sounders. In this study we analyse the data of three winters  (2013-2014, 2014-2015 and 2015-2016). Note that we do not use the data of 2017 and 2018 because they are still provisional and subject to revision.
Methodology Model and satellite snow depth estimations are projected onto a 12. 5 km pixel size EASE2 grid (similar to ASD) using a linear 2D multivariate interpolation. For each product we compute monthly mean maps for the 6 winter months (November-April in the Arctic and May-October in the Antarctic) for both hemispheres from March 2013 to October 2019. These maps are provided for 2015 in the Supplement (Figs. S1 to S13). Note that to improve the consistency of the analyses we always use the larger common time period for all the compared products. Thus, the covered time periods may vary depending on the availability of the snow depth products. Three statistical diagnoses are used to characterise the differences between snow depth datasets: 1. The climatic annual mean is simply the average of all monthly snow depth maps from all years.
g. Queen Elizabeth Islands region). Except in the MYI zones, AMSR2B data are quite smooth and characterised by a weak variability compared to that of the two altimetric products. In MYI zones (towards Queen Elizabeth islands) AMSR2B has the highest snow depths. We assume that it might be related to the snow depth retrieval algorithm, inadequate over thick ice. Indeed, the statistical results which are presented in the Appendix (Table  A1 ) show that the two Ka-Ku products (ASD and DuST) are in good agreement in terms of spatial variability and the magnitude of their annual cycle considering the entire set of data over the 6 winter months. Note that DuST presents the highest climatic "seasonal" mean solution, even higher than W99m (see also Fig. 2 ). In addition, DuST and ASD spatial distributions are comparable, showcasing that the difference between the two Ka-Ku altimetric products is likely a bias resulting from the re-calibration of the DuST data with OIB (this point will also be discussed in the next sections).
This underlines the consistency of this methodology used to compute bi-frequency snow depth estimations in the absence of external data (ASD) since DuST calibration is limited by the spatial and temporal availability of OIB. Figure  4  compares the ASD snow depth estimations with the outputs of three sea ice models in the Arctic (NESOSIM, MERCATOR and PIOMAS). The statistical diagnoses presented in Sect. 4. 1 are used. They are summarised in Ta-ble A1. Amongst the three models, the MERCATOR model provides lower snow depth estimations throughout with a climatic mean of 7. 4 cm and lower mean interannual and annual variability of about 3 cm. On the contrary, climatic means of PIOMAS and NESOSIM are similar both in terms of spatial distribution and pan-Arctic mean (with values of respectively 15.
The ASD data climatic mean is lower (12. 3 cm), and zones of thin snow layers (e. g. around 120 • E) are less pronounced in models (except by MERCATOR, where snow depth is low everywhere). Models also present higher variability. However, in all datasets the maximum variability occurs between 0 and 90 • E, which is relevant because of the proximity to the open ocean and the existence of strong meteorological events (e. g. Semenov et al. , 2019; Dong et al. , 2019). Although investigating what causes these discrepancies is beyond the scope of this article, the strong sensitivity of the models to the reanalysis snowfall forcing data (e. g. Boisvert et al. , 2018; Petty et al. , 2018)  could play a predominant role here.
As in the Arctic, AMSR2-NSIDC annual and interannual variability is lower and much more localised than in the ASD data. ASD and AMSR2-NSIDC rehttps://doi. org/10. 5194/tc-15-5483-2021 The Cryosphere, 15, 5483-5512, 2021 produce well the thin snow pattern of the Ross Ice Shelf. One other relevant difference between these two datasets is the systematic decrease in snow depth in October in the AMSR2-NSIDC data (see Table  A2 ). The presence of thicker snow in East Antarctica for ASD is consistent with  Worby et al. (2008b)  in that comparisons with ARISE in situ data have shown radiometric measurement snow depth underestimations. Wet-snow conditions due to flooding might be responsible for radiometric brightness temperature contrasts. The low variabilities in the Weddell Sea for ASD were not expected since winter snow properties are extremely variable  (Massom et al.
The OIB data are almost within the ASD envelope of uncertainties (in shaded red) at all times. These consistencies between OIB and ASD data are also demonstrated in several other OIB tracks provided in the Supplement (Figs. S14 to S17). The DuST Ka-Ku data present an along-track variability similar to ASD but tend to overestimate snow depth compared to OIB. This reinforces the hypothesis that the main difference between ASD and DuST is a bias. The AMSR2B data also reproduce the large-scale snow depth variability quite well but overestimate at a level comparable with DuST when compared to OIB. The DuST and AMSR2B overestimations are quite consistent with  Kwok et al. (2017) , who found that this OIB product tends to have thinner snow than the NOAA Wavelet Airborne Snow Radar dataset, which has been used for re-calibrations.
In fact, it is important to be aware that various OIB datasets have been produced, leading to a variety of snow estimations that can reach 7 cm on FYI and 12 cm on MYI  (Kwok et al. , 2017). The variabilities in snow properties from OIB daily basis data to the monthly means of the other datasets certainly explain some of the deviations. Models hardly represent the along-track variability and do not reproduce small-scale patterns. A resolution that is too coarse could partly explain this feature. As expected, the MERCATOR model snow thicknesses are far below the others, whereas the PIOMAS and NESOSIM solutions provide comparable results (see also Table  1 ). As expected, the W99m climatology strongly overestimates snow depths and is clearly a less optimal solution in this case.
However, the along-track variability is not well reproduced by any dataset. The MERCATOR and NESOSIM models also show similar magnitudes as the CryoVEx snow depth estimations (ALS/ASR and Ka/ASR), while PIOMAS and the W99m climatology clearly overestimate. AMSR2B and DuST overestimate snow depth, while the DuST along-track variability is comparable to ASD.
In particular, an important point would be to provide a relevant snow product representing the Envisat era. Since the W99m can be considered as relatively consistent until the year 2000, a mixed ASD and W99m product (ASD-W99m), including, for instance, a time dependency, could be considered. Also, it could be relevant to take into account the sea ice type interannual variability as is done for W99m. Another critical point of the ASD data (for instance for sea ice volume estimations) is the reduced spatial coverage due to the SARAL orbit. While during the time period of Envisat, this does not become an issue since its orbit is equivalent to that of SARAL; the absence of data north of 81. 5 • N is a major limitation to SIT estimations. A combination of ASD with W99m and/or model data could be done to extrapolate the data.
Potentially, one could also investigate a combination of ASD with W99m and/or models to extrapolate the data. In the Antarctic, we do not encounter the same issue since the orbit does not reduce the spatial coverage, and FYI is generally considered to be the only sea ice type present in the Southern Ocean. Then, such a climatology would be a solution to compute SIT estimations over the Envisat and CS-2 time period provided that the temporal variability in precipitation is investigated. Note that experimental SIT estimations  (Hendricks et al. , 2018)  have already been done in the Antarctic in the framework of the Sea Ice Climate Change Initiative (SI-CCI). These data used a snow climatology elaborated from AMSR-E and AMSR2 data in a nearly equivalent manner to what has been presented here.
Impacts of snow depth on SIT estimation Since there is still no validated freeboard product in the Antarctic, this analysis has only been performed in the Arctic. From the CS-2 radar freeboard product presented in  Guerreiro et al. (2017) , extended to 2019, we have computed SIT estimates using the various snow depth datasets presented in this study. They are calculated from the CS-2 L1b ESA Baseline-C SAR waveforms  (Bouffard et al. , 2018b)  with the methodology presented in Sect. 2. Freeboard heights are converted into SIT assuming hydrostatic equilibrium between snow-covered sea ice and the ocean (Eq. 8).
SIT = ρ wfb ice + ρ s sd ρ w -ρ i (8) As in  Ricker et al. (2014) , we assume the seawater density (ρ w ) is set to 1024 kg/m 3. Consistent with the approach of  Laxon et al. (2013) , sea ice density (ρ i ) is set to 882 kg/m 3 for MYI and 917 kg/m 3 for FYI  (Alexandrov et al. , 2010). Furthermore, the snow density (ρ s ) is set to 300 kg/m 3. A distinction between FYI and MYI follows the EUMETSAT OSI SAF sea ice type classification. The sea ice freeboard fb ice is calculated from the radar freeboards, taking into account the reduction in radar velocity within the snow layer, which depends on snow depth data following Eq. (3). SIT monthly maps are calculated for each snow depth product presented in previous sections. These monthly maps are provided for the winter of 2015 in the Supplement (Figs.
1 ) have strong impacts on the freshwater budget. Although this provides a relevant overview, such largescale pan-Arctic means do not show the spatial and temporal variability in the various SIT solutions. For instance, while DuST and W99m provide comparable SIT pan-Arctic mean estimations, the spatial and temporal information included in these two datasets are very different (e. g. Figs. 2  and 3 ). To better characterise the impacts of snow depth on SIT, we propose to consider the deviations between these SIT estimates for each month of each year and at each grid point. Such an ensemble of SIT solutions will allow us to characterise the level of uncertainty due to discrepancies between the different snow depths. For the month m of year y, the standard deviation (SD y, m (SIT)) and the maximum deviation (maxdev y, m (SIT)) maps are calculated with Eqs.
Discussions and conclusions In this study, we have presented a Ka-Ku snow depth product computed, in both hemispheres, from the data obtained by altimeters on board the satellites SARAL (Ka-band) and CS-2 (Ku-band). This product has been compared over the period 2013-2019 with the other Ka-Ku snow depth product (DuST, only in the Arctic), AMSR2 passive radiometer snow depth estimations, W99m (only in the Arctic) and snow depth solutions of the models PIOMAS (GIOMAS in the Antarctic), MERCATOR and NESOSIM (only in the Arctic). Thereafter, all these products have been evaluated, in the Arctic, against OIB airborne data, IMB snow buoys and CryoVEx airborne campaign data, including Ka-Ku, as well as ALS and Ku, snow depths. In the Antarctic, the lack of validation data remains a major obstacle to the assessment of sea ice products.
It is currently a primary focus of the ESA CSAO+ project. In the Arctic, we observed a good agreement between the two Ka-Ku products (ASD and DuST) in terms of spatial dis-tributions and annual and interannual variability, but DuST is always high biased by about 6. 5 ± 0. 5 cm (see Table  A1 ). Although this is likely due to the re-calibration of the DuST product with OIB data mainly measuring thick snow, this bias probably also indicates variabilities in Ku-band penetration related to snow properties. Only the surface roughness is considered in the ASD calculation, but the impact of other snow properties should be analysed and considered. The AMSR2B (and also AMSR2-NSIDC over FYI) data also tend to overestimate snow depths compared to ASD in the Arctic. This overestimation is lower than DuST, on average of about 3 cm, and does not seem to only be a bias since AMSR2B spatial patterns present noticeable differences.
We found a RMSE of about 6 cm with a correlation coefficient of 0. 66. By comparison, the DuST product has a RMSE of 8. 7 cm and AMSR2B of 7 cm. Note that this higher RMSE for DuST, in spite of a re-calibration, probably comes from the OIB version used for re-calibrating. Indeed, DuST is recalibrated against the OIB NOAA Wavelet Airborne Snow Radar dataset which is expected to present higher snow depth values. In addition, further analysis could be done in order to link the space and time variability in these biases with snow properties The various snow depth products are less consistent when comparing with IMB, although ASD mean values present a consistent order of magnitude. Due to the data coverage, validation with CryoVEx has been limited to one single track (where both Ku-band radar (ASIRAS), Ka-band radar (KAREN) and lidar scanner (ALS) were available).
We observed that KAREN and ASIRAS snow depth estimations are low, including a non-negligible amount of negative values. ASD data always remain in between the laser-Ku (ALS-ASR) and Ka-Ku (Ka/ASR) CryoVEx snow depth estimations. Since the results of such comparisons with validation data can vary from one methodology to another (e. g. grid sizes, smoothing kernel, dataset versions), they do not aim to assess the best snow depth product. However, they demonstrate how ASD provides a relevant snow depth solution, in good agreement with several validation data, and that ASD allows for the characterisation of the deviations between the different snow depth products. A more refined comparison with the CryoVEx data (including various tracks) is mandatory to understand the relative impacts of roughness and penetration and their link with snow properties.
, 2019). These comparisons highlight snow properties in the Antarctic that are very different than in the Arctic. Such opposite model behaviours in the two hemispheres argue that a single model tuning of parameters may not be adapted for a global configuration. In the context of data assimilation, the positive impacts of the integration of SIT  (Fiedler et al. , 2021; Massonnet et al. , 2015)  could also be enhanced using ASD either by improving the SIT observations or by enabling the simultaneous use of freeboard and snow depth data to constrain the models. An important limitation of the ASD snow depth data is its temporal coverage, imposed by SARAL which has only been available since 2013. To circumvent this limitation, we have shown that a simple monthly climatology, constructed as the average of ASD snow depth maps over the 2013-2019 period, could be a relevant option.
Deviations between SIT estimations reached up to 77 cm (55 % of pan-Arctic mean SIT) in marginal and coastal zones. We have highlighted in this study that the DuST and ASD products, albeit computed from data acquired by the same sensors at the same time, present some significant differences due to the methodology applied. The main difference is that for ASD we compare LRM data (PLRM for CS-2), while DuST compares LRM data with SAR data. The advantage of comparing LRM data together is that they have comparable footprint sizes, by which the difference reduces the effects of surface roughness to highlight the effects of volume backscatter and penetration. DuST, on the other hand, relies on the calibration of the measurements on OIB without taking into account effects of the surface roughness.
Comparison with in situ and airborne data 4. 3. 1 OIB OIB data are compared to all the datasets presented in the previous sections. We only consider OIB observations below 81. 5 • N from the 2014-2018 campaigns. Figure 6 shows an along-track example from the OIB flight on 29 March 2015, and Fig. 7 presents scatter plots comparing the various snow depth products with the OIB data over the entire 2014-2018.
Acknowledgements. This research is supported by the  ESA PO-LAR+ Snow on Sea Ice , the  CryoSat+ Antarctic Ocean projects (CSAO+)  and the CryoSat SciEnce-oriented data ANalysis over  Sea-ICE areas (CryoSeaNICE). It has benefited from the support of the  CNES TOSCA   CASSIS  project and the  ESA  living planet fellowship. The work has also been supported by the  Programme Nationale de Télédétection Spatiale  (PNTS, http://programmes. insu. cnrs. fr/pnts/, last access: March  2021 ), grant no. PNTS-2020-11. We also thank the  Center for Topographic studies of the Oceans and Hydrosphere (CTOH) at LEGOS. Financial support. This article has benefited from the financial support of the  CNES TOSCA CASSIS , the  ESA Living Planet Fellowship , the  ESA POLAR+ Snow on Sea Ice  project and the  Programme Nationale de Télédétection Spatiale  (PNTS, http:// programmes.
4. 3 3 Comparison with in situ and airborne data 4. 3. 1 OIB OIB data are compared to all the datasets presented in the previous sections. We only consider OIB observations below 81. 5 • N from the 2014-2018 campaigns. Figure 6 shows an along-track example from the OIB flight on 29 March 2015, and Fig. 7 presents scatter plots comparing the various snow depth products with the OIB data over the entire 2014-2018.
OIB snow depth data presented in this paper are the NSIDC OIB Quicklook version (Kurtz et al. (Richter-Menge et al. , 2006; Ku snow depth estimations. These data have been develhttps://doi. org/10. 5194/tc-15-5483-2021TheCryosphere,15,5483-5512,2021Cryosphere,15,5483-5512,F. , 2012;; King et al. , 2015)validated from in situ data of the BROMEX campaign(Nghiem et al. , 2013). These data are available at https://daacdata. apps. nsidc. org/pub/DATASETS/ICEBRIDGE/Evaluation_Products/(lastaccess:March2021). For comparison with the ASD dataset, we use all spring campaigns during the period of 2014-2018. For comparison with the ASD climatology, we use all OIB spring campaigns during 2009-2012. 3. 3. 3Icemassbalance(IMB) buoysIMB data(Perovich et al. , 2021)are issued from the US Army CRREL-Dartmouth Mass Balance Buoy Program.