A Preliminary Investigation of Arctic Sea Ice Negative Freeboard from in-situ Observations and Radar Altimetry

LI Shutong, DOU Tingfeng, and XIAO Cunde

A Preliminary Investigation of Arctic Sea Ice Negative Freeboard fromObservations and Radar Altimetry

LI Shutong1), 2), DOU Tingfeng2), 1), *, and XIAO Cunde3), 1)

1),,,730000,2),,100049,3),,100875,

The negative freeboard of sea ice (., the height of ice surface below sea level) with subsequent flooding is widespread in the Southern Ocean, as opposed to the Arctic, due to the relatively thicker ice and thinner snow. In this study, we used the observations of snow and ice thickness from 103 ice mass balance buoys (IMBs) and NASA Operation IceBridge Aircraft Missions to investigate the spatial distribution of negative freeboard of Arctic sea ice. The Result showed that seven IMBs recorded negative freeboards, which were sporadically located in the seas around Northeast Greenland, the Central Arctic Ocean, and the marginal areas of the Chukchi–Beaufort Sea. The observed maximum values of negative freeboard could reach −0.12m in the seas around Northeast Greenland. The observations from IceBridge campaigns also revealed negative freeboard comparable to those of IMBs in the seas around North Greenland and the Beaufort Sea. We further investigated the large-scale distribution of negative freeboard using NASA CryoSat-2 radar altimeter data, and the result indicates that except for the negative freeboard areas observed by IMBs and IceBridge, there are negative freeboards in other marginal seas of the Arctic Ocean. However, the comparison of the satellite data with the IMB data and IceBridge data shows that the Cryosat-2 data generally overestimate the extent and magnitude of the negative freeboard in the Arctic.

Arctic sea ice; negative freeboard; ice mass balance buoy; IceBridge; CryoSat-2

1 Introduction

When the ratio of snow depth to sea ice thickness exceeds a certain value (usually 0.25 to 0.5, depending on the snow density), the sea ice surface is depressed below sea level due to snow weight, and then seawater may flood onto sea ice and a snow-water mixture layer (slush) is formed; this phenomenon is called flooding (Ackley., 1990). The negative freeboard of sea ice associated with flooding is typical in the Antarctic sea ice zone, owing to the thick snow and thin sea ice, which makes it easy for the ice surface to be depressed below sea level, and the strong seawater advection (Lange., 1990; Eicken, 1994; Jeffries., 1994; Kawamura., 1997). Mean- while, during the cold season, the slush layer will refreeze and eventually lie on top of the original sea ice, a pheno- menon known as snow-ice formation. Flooding and snow- ice formation substantially contribute to sea ice mass ba- lance in the Southern Ocean (Haas., 2001). During the sea ice freezing period, flooding helps the rapid conversion of snow into sea ice and accelerates the ice growth.However, in the melting period, flooding carries the heat of seawater into the snow-ice interface, promoting the ice melting and the formation of ponds. In addition, flooding alters the optical properties of sea ice and affects physical and biological processes (Arndt., 2017; Fernández- Méndez., 2018).

Since the ratio of snow depth to sea ice thickness is usually low in the Arctic Ocean (Sturm and Massom, 2010; Vihma., 2013), it was believed that the negative freeboard of sea ice in the Arctic Ocean is not prevalent, but this may change with the dramatic thinning of sea ice (Laxon., 2003; Kwok and Rothrock, 2009; Renner.,2014; Lindsay and Schweiger, 2015) under climate warming. Previous studies based on field measurements during the N-ICE2015 expedition have found that negative freeboard and snow-ice formation widely exists in the Atlantic Sector where thicker snow and thinner sea ice favor negative freeboard (Kwok and Rothrock, 2009; Hansen., 2013; Gallet., 2017; Merkouriadi., 2017b). Researchers have evaluated the influence of the negative freeboard on snow-ice formation by drilling holes on level ice (Rösel., 2018), monitoring temperature profiles (Provost., 2017), and determining oxygen isotope (δ18O) in sea ice cores (Granskog., 2017). In addition, Merkouriadi. (2017a) used a 1-D snow/ice thermodynamic model to simulate the contribution of snow- ice formation to ice mass balance. In a region with thick snowpack on relatively thin ice, the contribution of snow- ice formation to the sea ice mass balance is non-negligible (Merkouriadi., 2017b; Wang., 2019). The negative freeboard and subsequent flooding have also been considered important in landfast ice (Kawamura.,2001; Granskog, 2004; Uusikivi., 2011) and some mar- ginal seas (Ukita., 2000).

The snow depth and sea ice thickness data measured by sea ice mass balance buoys (IMBs) can be used to estimate freeboard in the Arctic Ocean. The CRREL-Dartmouth Mass Balance Buoy Program provides thermodynamic mass balance and motion of sea ice (comprising changes in snow depth, ice thickness, ice temperature and position) using autonomous buoys (Perovich., 2017). In addition, IceBridge has observed sea ice freeboard, snow depth, and sea ice thickness in the western Arctic, and the observations have been used to validate satellite data (Kurtz., 2014; Xia and Xie, 2017) and assess changes in snow cover on sea ice (Webster., 2014). In the current study, we first used IMB observations and airborne radar observations to investigate the sea ice negative freeboard over the measurement area, and then we analyzed the large-scale distribution of the negative freeboard using CryoSat-2 in the Arctic. Finally, we validated the satellite data with the field observations during N-ICE2015 and the initial freeboard recorded by IMBs.

2 Data and Methods

2.1 Data

Since 2000, a large number of IMBs have been deploy- ed across the Arctic, in regions such as the Central Arctic, the Beaufort Sea, the Chukchi Sea, the Laptev Sea, the North Pole, Canadian Islands, and Svalbard (Perovich., 2017; http://imb-crrel-dartmouth.org/archived-data/). Sea ice thickness and snow depth were measured autonomously by these instruments from 2000 to 2016. The mass balance data were recorded at 2- or 4-h interval, and position data were recorded at 1 or 4h. In this study, we used data from 103 IMBs deployed in these regions to calculate ice freeboard. The trajectories of IMBs are displayed in Fig.1.

We also used the dataset of IceBridge L4 Sea Ice Free- board, Snow Depth, and Thickness, Version 1 (Kurtz., 2015) from the National Snow and Ice Data Center (NSI- DC: https://nsidc.org/data/IDCSI4/versions/1). This dataset contains derived geophysical data products including sea ice freeboard, snow depth, and sea ice thickness mea- surements retrieved from IceBridge Snow Radar, Digital Mapping System (DMS), Continuous Airborne Mapping By Optical Translator (CAMBOT), and Airborne Topographic Mapper (ATM). This campaign spanned from 2009 to 2013 in the Western Arctic. The trajectories of IceBridge ice freeboard observations are shown in Kurtz. (2013). We used the mean freeboard from the combined ATM and DMS dataset to determine the distribution of negative freeboard.

To investigate the large-scale distribution of negative freeboard over the Arctic Ocean, we also used the data of CryoSat-2 Level-4 Sea Ice Elevation, Freeboard, and Thick- ness, Version 1 (Kurtz and Harbeck, 2017) from NSIDC (https://nsidc.org/data/RDEFT4). CryoSat-2 carried a Ku- band Synthetic Aperture Interferometric Radar Altimeter (SIRAL) to measure the elevation of the main scattering horizon from a waveform. Sea ice freeboard was then defined by subtracting the sea surface elevation from the sea ice floe elevation and applying the radar propagation speed correction where snow depth data were available (Kurtz., 2014).

Fig.1 Drift trajectories of IMBs from CRREL-Dartmouth Mass Balance Buoy Program in 2000 to 2016, with the records of snow depth and sea ice thickness.

The field observations obtained during N-ICE2015 (Di- vine., 2017; Rösel and King, 2017) and initial ice freeboard recorded by IMBs were compared with freeboard observations from CryoSat-2.Divine. (2017) used laser leveling to measure freeboard in February and April 2015. Rösel and King (2017) conducted a detailed survey through coring/drilling from January to April 2015. Both studies were conducted in the North of Svalbard. In addition, there are six IMBs recording the initial freeboardof sea ice, which can be used to verify CryoSat-2 data. They are located in the Western Arctic, and their recording spans from 2011 to 2016. All these observations were used to verify the freeboard retrieved from CryoSat-2.

2.2 Methods

Ice mass-balance buoys (IMBs) have been deployed in the sea ice area over the Central Arctic, Beaufort Sea, Lap- tev Sea, Canadian Islands, Baffin Bay, Greenland Sea and Chukchi Sea since 2000. These buoys measure snow depth, ice thickness, floe position and meteorological parameters (Perovich., 2017). To calculate sea ice freeboard based on the records of snow depth and sea ice thickness, we established a theoretical model (Fig.2) to describe the re- lationship of freeboard with snow and ice thickness under hydrostatic equilibrium.

The sea ice thicknesshand snow depthhrecorded by IMBs are shown in Fig.2. If sea ice freeboardhis negative, the system follows hydrostatic equilibrium law, sa- tisfying Eq. (1),

where snow density, sea ice density, and seawater densityare taken as 320, 915, and 1024kgm−3, respectively. Note that these density approximations are from Kurtz. (2013) to be consistent with the IceBridge data. Thus, the negative freeboard of sea icehis calculated using Eq. (2).

Fig.2 Schematic of negative freeboard of sea ice under hydrostatic equilibrium.

3 Results

3.1 Negative Freeboard from IMBs

Based on the snow depth and sea ice thickness recorded by 103 IMBs spanning from 2000 to 2016, the theoretical model as mentioned above was applied to calculate the sea ice freeboard. Figs.3 and 4 show the trajectories and values of negative freeboard recorded by seven buoys from 2007 to 2015, respectively.

The results of IMB-2007C showed negative freeboard from October 2007, to December 2007, when the sea ice thickness was 1.6m, snow depth was approximately 0.6m, and sea ice negative freeboard was 0.04m. During this period, the negative freeboard of sea ice became deeper with increasing snow depth. The results of IMB-2012D showed negative freeboardin October 2012. In mid to late October 2012, the snow depth tended to be 0.7m, and the sea ice thickness remained at 0.9 to 1.0m, so that very deep negative freeboard of sea ice (0.08 to 0.12m) was attained, induced by snow load. Moreover, IMB-2015D recorded a short appearance of negative freeboard between November 17 and 24, 2015, with a value reaching 0.08m. These three buoys were all set in the Central Arctic initially, and located in the north of Fram Strait when signi- ficant negative freeboard of sea ice appeared (Fig.3). This drift trajectory allows plenty of water vapor from the Atlantic Ocean to increase the snowfall on ice surface, and the snow weight leads to sea ice negative freeboard, which is consistent with previous reports (Gallet., 2017; Merkouriadi., 2017b; Rösel., 2018).

Furthermore, IMB-2012I was initially set in the Chukchi Sea and negative freeboard occurred when it was in the north of 80˚N (Fig.3) between October and December 2012. The sea ice thickness in this period increased from 0.6 to 0.8m, and the snow depth also accumulated from 0.2 to 0.4m; the negative freeboard of sea ice reached 0.06m when the snow depth became thicker. IMB-2012J was initially from the Laptev Sea, and negative freeboard occurred when it was drifted in the north of 80˚N (Fig.3) during November and December 2012. The sea ice thickness ranged from 0.7 to 0.8m; the snow depth was relatively thinner, within 0.2 to 0.3m; and very shallow negative freeboard, which was not more than 0.01m, was recorded.

Fig.3 Locations of IMBs that observed negative freeboard (dots).

IMB-2013F and IMB-2015H were both located in the Beaufort Sea (Fig.3). The former recorded negative freeboard from October 2013 to June 2014, which spanned the entire period of sea ice growth, when the sea ice thickness increased from 1.2 to 1.7m. During this freezing period, the snow depth increased from 0.5 to 0.8m, and the negative freeboard reached 0.06m. The latter buoy recorded for a shorter period, during October 2015, when the sea ice thickness changed between 0.4 and 0.5m, snow depth increased slightly from 0.3 to 0.4m, and the value of negative freeboard was between 0.05 and 0.07m.

Overall, sea ice floe located in the Atlantic Sector tends to feature deeper negative freeboard more easily. Consi- dering the slower variations of sea ice thickness than that of snow depth, high frequency variations of snow cover seems to dominate the sea ice freeboard during a relatively short period, such as in IMB-2007C, IMB-2012D, and IMB-2015H (Fig.4). However, when the sea ice thickness gradually increases during the cold season, such as for recordings of IMB-2012I and IMB-2013F (Fig.4), the value of ice freeboard increases as a result of large buoyancy.

3.2 Negative Freeboard from IceBridge

Data from IceBridge campaigns are widely used in studies on Arctic snow and sea ice thickness (Kurtz., 2014; Webster., 2014). Therefore, we used freeboard data from IceBridge to identify negative freeboard in the Arctic Ocean. As shown in Fig.5, negative freeboard exists in the seas around Greenland, and the Chukchi-Beaufort Sea, spanning from March to April in 2011 and 2013. In the edge of the Chukchi-Beaufort Sea, IceBridge observed a negative freeboard with a value of up to 0.07m, which is consistent with the IMB-2013F recording; and in the seas around Greenland, negative freeboard with a value up to 0.10m was observed, which is consistent with the IMB- 2012D recording.

Fig.4 Snow depth (dark blue lines) and sea ice thickness (light blue lines) observed by seven IMBs that recorded negative freeboard. The locations of IMBs are shown in Fig.3. The ice freeboard (red lines) calculated based on hydrostatic equilibrium law is also shown. The black dotted lines represent the level where the ice freeboard is equal to zero. The numbers on the abscissa indicate how many records were obtained during this period; the start and end dates are shown below the numbers. Note that these seven IMBs recorded snow depth and sea ice thickness every four hours.

3.3 Spatial Distribution of Freeboard from CryoSat-2

We further explored the large-scale distribution of ne- gative freeboard in the Arctic Ocean using the freeboard data from CryoSat-2. The monthly mean freeboard values from 2010 to 2019 were calculated to investigate the spatial distribution of the negative freeboard. As shown in Fig.6, the positive freeboard was mainly distributed in the Central Arctic. The negative freeboard mainly existed in the Arctic peripheral seas, especially in the Atlantic Sector, where negative freeboard existed from November to April.

The scattering layer of CryoSat-2 is assumed to be the snow-ice interface, which can induce large uncertainty of ice freeboard estimation. Previous studies have investigated the influence of this assumption (Willatt., 2011; Armitage and Ridout, 2015; Ricker., 2015; Nandan., 2017; King., 2018), and the findings emphasized that the impact of the snow layer on Ku-band penetration is not negligible for different snow properties. Except for the penetration of radar signal, retracking methods also contribute to the error budget. In threshold me- thods, the choice of retracker thresholds has a significant impact on the magnitudes of the sea ice freeboard (Laxon., 2013; Kurtz., 2014; Ricker., 2014, 2015; Xia and Xie, 2017; King., 2018). For waveform fitting retracking, Kurtz. (2014) illustrated that the sea ice freeboard from CryoSat-2 NASA products agreed well with IceBridge data in the Western Arctic; the mean freeboard error for this dataset was estimated to be within 6.5cm.

Fig.5 Location and magnitude of negative freeboard from IceBridge. Blue, red, and green dots represent 2011, 2012, and 2013, respectively.

Fig.6 Spatial distribution of monthly sea ice freeboard from 2010 to 2019. The gray shading indicates areas not verified by in situ observation data.

In this study, we used freeboard records fromobservations to verify CrySat-2 satellite data. Compared with observations from Rösel and King (2017), CrySat-2 tends to overestimate freeboard in the North of Svalbard, attributed to the radar freeboard assumption. Nonetheless, it agrees well with two records from Divine. (2017) in the same region. CryoSat-2 freeboard in the Western Arctic is comparable to that of the initial freeboard recorded by IMBs, except for one point located at 73˚N. In addition to the errors of satellite altimeter, another reason for these differences is the inconsistent time resolution be- tween CryoSat-2 and in situ observation. CryoSat-2 can capture the basic characteristics of freeboard, in terms of magnitude and sign, but it tends to overestimate the absolute value, both for negative freeboard and positive free- board.

4 Conclusions

In this study, the negative freeboard of sea ice in the Arctic under hydrostatic equilibrium was investigated based on the observations of sea ice thickness and snow depth from IMBs archived at the CRREL-Dartmouth Mass Balance Buoy Program. The ice buoy records illustrate that negative freeboard of sea ice existed in the Beaufort Sea, the seas around Northeast Greenland, and the central Arctic Ocean between 2007 and 2015. Although the negative freeboard only occurred in the local area, its maximum value could reach −0.12m. The IceBridge observations also revealed negative freeboard in the marginal waters of the Chukchi-Beaufort Sea and the seas around Greenland from March to May during 2009 and 2013.

Fig.7 Comparisons of sea ice freeboard from CryoSat-2 with that from field observations in N-ICE2015 by Divine et al. (2017), Rösel and King (2017), and IMBs.

To analyze the spatial distribution of negative freeboard over the whole Arctic Ocean, we employed CryoSat-2 radar altimeter data, which were validated by in situ observations of N-ICE2015 and IMBs. The results indicate that the negative freeboard was predominant in most marginal seas of the Arctic Ocean, especially in the Atlantic sector from November to April. Comparison with the field measurements demonstrated that the extent and magnitude of the negative freeboard were both overestimated in NASA CryoSat-2 product, which does not deny the existence of negative freeboard.

For the seas around Northeast Greenland and the marginal areas of the Chukchi-Beaufort Sea, we suggest that the ice negative freeboard should not be ignored in the retrieval of Arctic sea ice thickness, and more field measurements of snow depth, ice thickness, and freeboard are needed to verify the satellite data. The snow-ice produced by negative freeboard and flooding should be parameterized in the sea ice dynamics model, since the negative freeboard may increase in the Arctic with the dramatic thinning of sea ice in the future under climate warming.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (No. 2018YF C1406104); and the National Natural Science Foundation of China (Nos. 41425003 and 41971084). We would like to thank the NSIDC and the Norwegian Polar Data Center for providing IceBridge, CryoSat-2 data and N-ICE2015 data, respectively.

Ackley, S. F., Lange, M. A., and Wadhams, P., 1990. Snow cover effects on Antarctic sea ice thickness. In:. Ackley, S. F., and Weeks, W. F., eds., Cold Re- gions Research and Engineering Laboratory, Hanover, 16-21.

Armitage, T. W. K., and Ridout, A. L., 2015. Arctic sea ice freeboard from AltiKa and comparison with CryoSat-2 and Operation IceBridge., 42 (16): 6724- 6731.

Arndt, S., Meiners, K. M., Ricker, R., Krumpen, T., Katlein, C., and Nicolaus, M., 2017. Influence of snow depth and surface flooding on light transmission through Antarctic pack ice., 122 (3): 2108-2119.

Divine, D., King, J., Rösel, A., Itkin, P., Haapala, J., and Gerland, S., 2017. N-ICE2015 Sea-ice and snow surface elevation from laser leveling exercises (Data set). Norwegian Polar Institute. https://doi.org/10.21334/npolar.2017.69ec354f.

Eicken, H., 1994. Structure of under-ice melt ponds in the cen- tral Arctic and their effect on the sea-ice cover., 39 (3): 682-694.

Fernández-Méndez, M., Olsen, L. M., Kauko, H. M., Meyer, A., Rösel, A., Merkouriadi, I., Mundy, C. J., Ehn, J. K., Johansson, A. M., Wagner, P. M., Ervik, Å., Sorrell, B. K., Duarte, P., Wold, A., Hop, H., and Assmy, P., 2018. Algal hot spots in a changing Arctic Ocean: Sea-ice ridges and the snow-ice in- terface., 5: 1-22.

Gallet, J. C., Merkouriadi, I., Liston, G. E., Polashenski, C., Hud- son, S., Rösel, A., and Gerland, S., 2017. Spring snow con- ditions on Arctic sea ice North of Svalbard, during the Nor- wegian Young Sea ICE (N-ICE2015) expedition., 122: 10820-10836.

Granskog, M. A., 2004. Seasonal development of the properties and composition of landfast sea ice in the Gulf of Finland, the Baltic Sea., 109 (C2): C02020.

Granskog, M. A., Rösel, A., Dodd, P. A., Divine, D., Gerland, S., Martma, T., and Leng, M. J., 2017. Snow contribution to first-year and second-year Arctic sea ice mass balance North of Svalbard., 122 (3): 2539-2549.

Haas, C., Thomas, D. N., and Bareiss, J., 2001. Surface proper- ties and processes of perennial Antarctic sea ice in summer., 47 (159): 613-625.

Hansen, E., Gerland, S., Granskog, M. A., Pavlova, O., Renner, A. H. H., Haapala, J., Løyning, T. B., and Tschudi, M., 2013. Thinning of Arctic sea ice observed in Fram Strait: 1990– 2011., 118 (10): 5202- 5221.

Jeffries, M. O., Shaw, R. A., Morris, K., Veazey, A. L., and Krouse, H. R., 1994. Crystal structure, stable isotopes (δ18O), and de- velopment of sea ice in the Ross, Amundsen, and Belling- shausen Seas, Antarctica., 99(C1): 985-995.

Kawamura, T., Ohshima, K. I., Takizawa, T., and Ushio, S., 1997. Physical, structural, and isotopic characteristics and growth processes of fast sea ice in Lützow-Holm Bay, Antarctica., 102 (C2): 3345- 3355.

Kawamura, T., Shirasawa, K., Ishikawa, N., Lindfors, A., Rasmus,K., Granskog, M. A., Ehn, J., Leppäranta, M., Martma, T., and Vaikmäe, R., 2001. Time-series observations of the structure and properties of brackish ice in the Gulf of Finland., 33 (1): 1-4.

King, J., Skourup, H., Hvidegaard, S. M., Rösel, A., Gerland, S., Spreen, G., Polashenski, C., Helm, V., and Liston, G. E., 2018. Comparison of freeboard retrieval and ice thickness calcu- lation from ALS, ASIRAS, and CryoSat-2 in the Norwegian Arctic to field measurements made during the N-ICE2015 expedition., 123 (2): 1123-1141.

Kurtz, N. T., and Harbeck, J., 2017. CryoSat-2 level-4 sea ice elevation, freeboard, and thickness, version 1. NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado, https://doi.org/10.5067/96JO0KIFDAS8.

Kurtz, N. T., Farrell, S. L., Studinger, M., Galin, N., Harbeck, J. P., Lindsay, R., Onana, V. D., Panzer, B., and Sonntag, J. G., 2013. Sea ice thickness, freeboard, and snow depth products from Operation IceBridge airborne data., 7 (4): 1035-1056.

Kurtz, N. T., Galin, N., and Studinger, M., 2014. An improved CryoSat-2 sea ice freeboard retrieval algorithm through the use of waveform fitting., 8 (4): 1217-1237.

Kurtz, N. T., Studinger, M., Harbeck, J., Onana, V., and Yi, D., 2015. IceBridge L4 sea ice freeboard, snow depth, and thick- ness, version 1. NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado,http:// doi.org/10.50 67/G519SHCKWQV6.

Kwok, R., and Rothrock, D. A., 2009. Decline in Arctic sea ice thickness from submarine and ICES at records: 1958–2008., 36 (15): 1-5.

Lange, Μ. A., Schlosser, P., Ackley, S. F., Wadhams, P., and Dieckmann, G. S., 1990.18O Concentrations in sea ice of the Weddell Sea, Antarctica., 36 (124): 315- 323.

Laxon, S., Peacock, N., and Smith, D., 2003. High interannual variability of sea ice thickness in the Arctic region., 425 (6961): 947-950.

Laxon, S. W., Giles, K. A., Ridout, A. L., Wingham, D. J., Willatt, R., Cullen, R., Kwok, R., Schweiger, A., Zhang, J., Haas, C., Hendricks, S., Krishfield, R., Kurtz, N., Farrell, S., and Davidson, M., 2013. CryoSat-2 estimates of Arctic sea ice thickness and volume., 40 (4): 732-737.

Lindsay, R., and Schweiger, A., 2015. Arctic sea ice thickness loss determined using subsurface, aircraft, and satellite obser- vations., 9 (1): 269-283.

Merkouriadi, I., Cheng, B., Graham, R. M., Rösel, A., and Granskog, M. A., 2017a. Critical role of snow on sea ice growth in the Atlantic Sector of the Arctic Ocean., 44 (20): 10479-10485.

Merkouriadi, I., Gallet, J. C., Liston, G. E., Polashenski, C., Hudson, S., Rösel, A., and Gerland, S., 2017b. Winter snow conditions on Arctic sea ice North of Svalbard during the Nor- wegian Young Sea ICE (N-ICE2015) expedition., 122 (20): 10837-10854.

Nandan, V., Geldsetzer, T., Yackel, J., Mahmud, M., Scharien, R., Howell, S., King, J., Ricker, R., and Else, B., 2017. Effect of snow salinity on CryoSat-2 Arctic first-year sea ice free- board measurements., 44 (20): 10419-10426.

Perovich, D., Richter-Menge, J., and Polashenski, C., 2017. Ob- serving and understanding climate change: Monitoring the mass balance, motion, and thickness of Arctic sea ice. http:// imb-crrel-dartmouth.org.

Provost, C., Sennéchael, N., Miguet, J., Itkin, P., Rösel, A., Koenig, Z., Villacieros-Robineau, N., and Granskog, M. A., 2017. Observations of flooding and snow-ice formation in a thinner Arctic sea-ice regime during the N-ICE2015 cam- paign: Influence of basal ice melt and storms., 122 (9): 7115-7134.

Rösel, A., and King, J., 2017. N-ICE2015 Ice thickness, snow thickness, and freeboard from thickness drillings (Data set). Norwegian Polar Institute. https://doi.org/10.21334/npolar.2017. 25f70db1.

Rösel, A., Itkin, P., King, J., Divine, D., Wang, C., Granskog, M. A., Krumpen, T., and Gerland, S., 2018. Thin sea ice, thick snow, and widespread negative freeboard observed During N-ICE2015 North of Svalbard., 123 (2): 1156-1176.

Renner, A. H. H., Gerland, S., Haas, C., Spreen, G., Beckers, J. F., Hansen, E., Nicolaus, M., and Goodwin, H., 2014. Evi- dence of Arctic sea ice thinning from direct observations., 41 (14): 5029-5036.

Ricker, R., Hendricks, S., Helm, V., Skourup, H., and Davidson, M., 2014. Sensitivity of CryoSat-2 Arctic sea-ice freeboard and thickness on radar-waveform interpretation., 8 (4): 1607-1622.

Ricker, R., Hendricks, S., Perovich, D. K., Helm, V., and Gerdes, R., 2015. Impact of snow accumulation on CryoSat-2 range retrievals over Arctic sea ice: An observational approach with buoy data., 42 (11): 4447-4455.

Sturm, M., and Massom, R., 2010. Snow on sea ice. In:. Thomas, D., and Dieckmann, G., eds., Wiley-Black-Well, Chi-chester, 153-204.

Ukita, J., Kawamura, T., Tanaka, N., Toyota, T., and Wakatsuchi, M., 2000. Physical and stable isotopic properties and growth processes of sea ice collected in the southern Sea of Okhotsk., 105 (C9): 22083-22093.

Uusikivi, J., Granskog, M. A., and Sonninen, E., 2011. Meteoric ice contribution and influence of weather on landfast ice grow- th in the Gulf of Finland, Baltic Sea., 52 (57): 91-96.

Vihma, T., Pirazzini, R., Renfrew, I. A., Sedlar, J., Tjernström, M., Nygård, T., Fer, I., Lüpkes, C., Notz, D., Weiss, J., Mar- san, D., Cheng, B., Birnbaum, G., Gerland, S., Chechin, D., and Gascard, J. C., 2013. Advances in understanding and pa- rameterization of small-scale physical processes in the marine Arctic climate system: A review., 13 (12): 32703-32816.

Wang, C., Graham, R. M., Wang, K., Gerland, S., and Granskog, M. A., 2019. Comparison of ERA5 and ERA-Interim near- surface air temperature, snowfall and precipitation over Arctic sea ice: Effects on sea ice thermodynamics and evolution., 13: 1661-1679.

Webster, M. A., Rigor, I. G., Nghiem, S. V., Kurtz, N. T., Farrell, S. L., Perovich, D. K., and Sturm, M., 2014. Interdecadal changes in snow depth on Arctic sea ice., 119 (8): 5395-5406.

Willatt, R., Laxon, S., Giles, K., Cullen, R., Haas, C., and Helm, V., 2011. Ku-band radar penetration into snow cover on Arc- tic sea ice using airborne data., 52 (57): 197-205.

Xia, W., and Xie, H., 2017. Assessing three waveform retrackers on sea ice freeboard retrieval from Cryosat-2 using operation IceBridge Airborne altimetry datasets., 204: 456-471.

November 5, 2019;

March 26, 2020;

December 16, 2020

© Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2021

. E-mail: doutf@ucas.ac.cn

(Edited by Chen Wenwen)