Sea ice thickness estimations from ICESat Altimetry over the Bellingshausen and Amundsen Seas,

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1 JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, , doi: /jgrc.20179, 2013 Sea ice thickness estimations from ICESat Altimetry over the Bellingshausen and Amundsen Seas, Hongjie Xie, 1 Ahmet Emre Tekeli, 1,2 Stephen F. Ackley, 1 Donghui Yi, 3 and H. Jay Zwally 4 Received 29 August 2012; revised 27 February 2013; accepted 25 March 2013; published 10 May [1] Sea ice thicknesses derived from NASA s Ice, Cloud, and Land Elevation Satellite (ICESat) altimetry data are examined using two different approaches, buoyancy and empirical equations, and at two spatial scales ICESat footprint size (70 m diameter spot) and Advanced Microwave Scanning Radiometer (AMSR-E) pixel size (12.5 km by 12.5 km) for the Bellingshausen and Amundsen Seas of west Antarctica. Ice thickness from the empirical equation shows reasonable spatial and temporal distribution of ice thickness from 2003 to Ice thickness from the buoyancy equation, however, additionally needing snow depth information derived from the AMSR-E, shows an overestimation in terms of maximum, mean (+63% to 75%), and standard deviation while underestimation in modal thickness ( 20%) as compared with those from the empirical equation approach. When ICESat snow freeboard is used as the snow depth in the buoyancy equation, i.e., the zero ice freeboard assumption, the derived ice thicknesses match well with those from the empirical equation approach, within 5% overall. The AMSR-E, therefore, may underestimate snow depth and accounts for ~95% of the ice thickness overestimation as compared with the buoyancy approach. The empirical equation derived ice thickness shows a consistent asymmetrical distribution with a long tail to high values, and seasonal median values ranging from 0.8 to 1.4 m over the period that are always larger than the corresponding modal values ( m) and lower than the mean values ( m), with standard deviation of m. An overall increasing trend of 0.03 m/year of mean ice thickness is found from 2003 to 2009, although statistically insignificant (p = 0.11) at the 95% confidence level. Starting from autumn, a general picture of seasonal mean, modal, and median ice thickness increases progressively from autumn to spring and decreases from spring to the following autumn, when new thin ice dominates the ice thickness distribution. The asymmetric shape of the thickness distribution reflects the key role of ice deformation processes in the evolution of the thickness distribution. The statistical properties of the thickness distribution interannually (high range of mean thickness and standard deviation) indicate the variability of deformation processes. However, spring ice volume, the product of ice mean thickness and areal extent computed for the spring maximum, shows variability year to year but is primarily dominated by ice extent variability, with no increasing or decreasing trend over this record length. The dependence of the volume on the ice extent primarily suggests that ice thickness changes have also not covaried with the ice extent losses seen over the satellite record in this region, unlike the Arctic. These properties reflect the interactive processes of ice advection, thermodynamic growth and ice deformation that all substantially influence ice mass balance in the Bellingshausen-Amundsen Seas region. Citation: Xie, H., A. E. Tekeli, S. F. Ackley, D. Yi, and H. J. Zwally (2013), Sea ice thickness estimations from ICESat Altimetry over the Bellingshausen and Amundsen Seas, , J. Geophys. Res. Oceans, 118, , doi: /jgrc Laboratory for Remote Sensing and Geoinformatics, Department of Geological Sciences, University of Texas at San Antonio, TX, 78249, USA. 2 Civil Engineering Department, King Saud University, Riyadh, 11421, Saudi Arabia. 3 SGT Inc., Cryospheric Sciences Laboratory, Code 615, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA. 4 Cryospheric Sciences Laboratory, Code 615, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA. Corresponding author: H. Xie, Laboratory for Remote Sensing and Geoinformatics, Department of Geological Sciences, University of Texas at San Antonio, TX, 78249, USA. (hongjie.xie@utsa.edu) American Geophysical Union. All Rights Reserved /13/ /jgrc Introduction [2] Satellite remote sensing has been the main operational means of monitoring changes in sea ice cover in the Arctic and Antarctic. Sea ice extent has been studied since 1979 by satellite remote sensing in a detailed manner using various portions of the electromagnetic spectrum including visible and infrared but primarily from the microwave portions of the spectrum [Cavalieri and Parkinson, 2008; Comiso and Nishio, 2008]. Besides sea ice extent, other parameters such as thickness, concentration, motion, deformation, surface temperature, and snow depth can be monitored from satellites, 2438

2 and all data contribute to a better understanding of sea ice processes [Markus and Cavalieri, 2000; Forsberg and Skourup, 2005; Kwok et al., 2006; Kurtz et al., 2008; Kwok and Cunningham, 2008; Zwally et al., 2008; Connor et al., 2009; Markus et al., 2011; Scott et al., 2013]. Sea ice thickness and snow depth are important parameters both for volume and heat flux computations and are sensitive indicators of climate change [Laxon et al., 2003; Screen and Simmonds, 2010]. However, there has been a lack of comprehensive sea ice thickness and snow depth data availability for the Antarctic, despite the compelling need for up-to-date spatial distributions of them [Kwok et al., 2009; Wang et al., 2013]. Ship-based ice observations based on the Antarctic Sea Ice Processes and Climate (ASPeCt) protocol [Worby and Allison, 1999] are still the most important means to provide sea ice thickness and snow cover information for the Antarctic sea ice zone, but the Bellingshausen and Amundsen Seas (BA) sector has the largest data gaps in all seasons [Worby et al., 2008a]. Unfortunately, icebreakers typically avoid the thickest ice during cruises, which may result in a bias towards thin ice and leads as indicated by Perovich et al. [2009], and, therefore, yield sea ice thickness results that tend to be biased toward the thinner end of the overall distribution [Zwally et al., 2008]. [3] The importance of sea ice and especially its thickness and snow depth over sea ice for the polar regions arises from the fact that sea ice regulates the energy flux exchange between atmosphere and the underlying sea surface both with its high albedo and low thermal conductivity [Laxon et al., 2003; Perovich, 2011; Weeks, 2010; Lytle and Ackley, 1996]. Dependence of heat and salt fluxes on sea ice is discussed in Dierking and Busche [2006] showing regional flux variability, largely controlled by spatial distribution of leads, polynyas, and where ice is newly formed and thin. Smith et al. [1990] emphasized the importance of sea ice and the net heat transfer through new and thin ice (thickness <0.4 m) that is up to two orders of magnitude larger than the heat flux through thicker ice (> 0.8 m). Kurtz et al. [2009] also mentioned the nonlinear dependence of heat flux on ice thickness and the possibility of variation in heat fluxes as high as one third due to different thickness assumptions. [4] Even though sea ice thickness determinations from space have been desired for a long time, some inherent limitations have prevented ice thickness calculations from satellite remote sensing. NASA s Ice, Cloud, and Land Elevation Satellite (ICESat), covering most sea ice area in the Arctic and all sea ice in the Antarctic, has provided a new tool for studying sea ice freeboard and thickness [Zwally et al., 2008]. Since ICESat measures the surface elevation of snow-air interface over sea ice, relative to an ellipsoid reference level, the initial step is the determination of the surface elevation relative to local sea level, defined as snow freeboard [Zwally et al., 2008; Xie et al., 2011]. Ice thickness can then be derived from a buoyancy equation, a function of freeboard, snow depth, and snow, water, and ice densities [Massom et al., 1997; Kurtz and Markus, 2012]. [5] Studies by Kwok et al. [2004, 2006, 2007], Kwok and Cunningham [2008], Forsberg and Skourup [2005], and Kurtz et al. [2009] showed the suitability of ICESat for sea ice thickness determination. However, the above studies were mostly performed over the Arctic. Several papers [Zwally et al., 2008; Yi et al., 2011; Xie et al., 2011; Worby et al., 2011; Markus et al., 2011; Kurtz and Markus, 2012] have discussed sea ice thickness determination for the Antarctic. Kurtz and Markus [2012] showed their ICESatderived ice thickness datasets for the entire Antarctic circumpolar region using the zero ice freeboard assumption of the buoyancy theory. Our motivations for the present paper are: (1) to compare the different methods or algorithms used in these Antarctic papers in determining best practices for converting ICESat elevation data into ice thickness for the Antarctic; and (2) to analyze the entire ICESat record ( ) for the ice thickness characteristics for the Bellingshausen-Amundsen Sea sector. [6] In particular, the paper compares sea ice thickness derived by two methods. The first method is based on the buoyancy equation [Zwally et al., 2008; Yi et al., 2011] using estimates of snow depth determined from the Advanced Microwave Scanning Radiometer (AMSR-E) passive microwave system together with ICESat freeboard. The second method uses field-based empirical equations [Xie et al., 2011; B. Ozsoy-Cicek et al., Sea ice thickness retrieval algorithms based on in-situ surface elevation and thickness values for application to altimetry, submitted to Journal of Geophysical Research: Oceans, 2013], which only rely on ICESat freeboard with no other information needed from other systems. Differences between the two methods are evaluated and a rationale is given for preferring the empirical equation method. We then discuss ice thickness results determined from ICESat surface elevation from using this empirical equation method for the Bellingshausen-Amundsen Sea sector. The results are also compared with those from Kurtz and Markus [2012] and from ASPeCt results [Worby et al., 2008a]. 2. Data Sets 2.1. ICESat Freeboards [7] NASA s ICESat mission launched in January 2003 has been the only laser altimeter used for mapping and monitoring the Earth s land and ice surface elevations [Zwally et al., 2002]. The altimeter gives ~2 cm in elevation precision over flat/smooth ice surfaces within 70 m footprints spaced 172 m along track [Zwally et al., 2008; Kwok et al., 2006]. The confirmed, preflight 2 cm range precision of ICESat over flat ice sheet surfaces and polynyas [Zwally et al., 2008, Kwok et al., 2004], enables observation of the ice thickness variations both within a year and between different years, when these variations are ~20 cm or greater and, therefore, exceed the variation induced by ICESat range precision errors [Kwok et al., 2004]. ICESat (release 531) GLA05 (waveform-based range corrections data) and GLA06 (elevation data) datasets from the National Snow and Ice Center ( icesat) between 2003 and 2009 are used in this paper to derive snow freeboard and then sea ice thickness. [8] Three main methodologies have been used for determining a local reference for sea level to correctly derive freeboards from ICESat measurements. The first uses coincident synthetic aperture radar (SAR) imagery for detection of new lead openings [Kwok et al., 2004, 2006, 2007]; the second uses ICESat reflectivities and the standard deviation of reflectivity measurements to identify leads instead [Kwok et al., 2006, 2007]; the third one uses the mean of the lowest 2% of ICESat elevation values within 25 km of each side of any given footprint along an ICESat track to compute a local reference sea level [Zwally et al., 2008]. As indicated by Kwok 2439

3 Table 1. Campaign Periods and the Statistical Properties of ICESat Derived Freeboards (m) Grouped Into Three Austral Seasons: Summer (top), Autumn (middle), and Spring (bottom) for the Bellingshausen and Amundsen Seas Sector a Period ID %-F Mean S.D. Mode Median Max CV M-M Number FM ,437 FM 04 2b ,058 FM 05 3b ,087 FM 06 3e ,492 MA 07 3h ,286 FM 08 3j ,800 MA 09 2e ,518 Mean in Summer ,240 MJ 04 2c ,146 MJ 05 3c ,895 MJ 06 3f ,099 Mean in Autumn ,713 SON 03 2a ,081 ON 04 3a ,636 ON 05 3d ,863 ON 06 3g ,418 ON 07 3i ,223 O 08 3k ,647 ND 08 2d ,725 O 09 2f ,880 Mean in Spring ,934 a Note: Period shows the months of operation, followed by the year of operation, with FM as February and March, MA as March and April, MJ as May and June, SON as September, October, and November, ON as October and November, O as October, and ND as November and December; ID denotes laser identification; %-F denotes the percentage of negative freeboard; S.D. denotes the standard deviation; CV denotes the correlation of variance and equals to mean/s.d.; M-M denotes mean minus median; and Number is the effective ICESat footprints used. and Cunningham [2008], the first method provides the best accuracy. The advantage of using the second and third methods is that they are independent of SAR imagery requirements, since SAR imagery is not available everywhere at the same time as the altimeter measurements. The third method, also referred to as the along track filtering approach [Zwally et al., 2008], is more robust and always calculates a freeboard with properly filtered ICESat elevation data. As indicated in their paper, to avoid spurious elevations due to saturation and forward scattering effects, data of heavily saturated waveforms with reflectivity larger than 0.9 and pulse broadening parameter (S) larger than 0.8, and data of forward scattering waveforms with reflectivity less than 0.05 and S larger than 0.8 are not used in their calculations. In this paper, this method is used to derive snow freeboard. [9] Table 1 shows the statistics of ICESat derived snow freeboards for each campaign period from 2003 to 2009, grouped according to austral seasons of data acquisition. There are seven campaigns in the summer season or transition from summer to autumn (five from February to March and two from March to April), three campaigns in autumn season (from May to June), and eight campaigns in the spring season (from October to November, with the laser 2a starting in late September and laser 2d extending to middle of December). The percentage of negative ICESat freeboard is usually less than 1%, but with two out of 18 campaigns (both in spring) having over 1% (1.19% and 1.43%) negative freeboards. This is in agreement with 1% assumption of negative freeboard in Zwally et al. [2008]. Fractional freeboard values over 1 m and over 2 m are examined for each campaign and are found to vary from 1.9 to 10.8% (mean 5.6%) for freeboard values over 1 m and 0.1 to 0.6% (mean 0.3%) for freeboard values over 2 m. Therefore, in this paper, we use a 2 m cutoff to separate sea ice from icebergs, i.e., fraction of icebergs varies from 0.1 to 0.6%, instead of the higher assumed iceberg percentages using the 1 m cutoff as in Zwally et al. [2008]. In Zwally et al. [2008], there was no rationale provided for the use of the 1 m cutoff value. Based on field experiences, the areal fraction of icebergs is not likely to be as high as 2%, although, there is as yet no published result to support this statement. Based on NASA ICEBridge s Digital Mapping System (DMS) and Airborne Topographic Mapper (ATM) data for the 2009, 2010, and 2011 flights over the BA sea sector, we find that icebergs appeared on less than 5% of the DMS images (and were a small fraction of the area within any image) and 90% of the iceberg elevations (above local sea level) were higher than 5 m (unpublished results). Therefore, this analysis (publication being prepared) shows the fraction of icebergs over sea ice should be much less than 1% (freeboards over 2 m), with 99% freeboards higher than 2 m. For further processing and analysis in this paper, we thus assign those negative freeboard values as zero and also exclude those freeboard values greater than 2 m, treated as icebergs. The statistical properties of each campaign shown in Table 1 are values after these two considerations, i.e., the minimum value for each campaign is zero, and maximum values are no more than 2 m. The numbers of effective footprints are overall much less in the summer season as compared with those from the autumn or spring seasons, since the sea ice coverage reaches its minimum in the summer season AMSR-E Snow Depth [10] In order to utilize the buoyancy equation to compute sea ice thicknesses from freeboard values, information such as snow depth, as well as a number of assumptions about the densities of snow cover, sea ice, and sea water are required [Zwally et al., 2008]. To date, satellite remote sensing has provided the only operationally routine way to measure the snow depth over the Southern Ocean that is nearly coincident temporally with altimeter measurements of snow freeboard. 2440

4 AMSR-E aboard the Aqua satellite was a microwave radiometer and provides daily brightness temperature, sea ice concentration, and snow depth polar grids data (AE_SI12) with a grid resolution of 12.5 km by 12.5 km [Comiso et al., 2003]. Even though the data set is daily, the snow depth values are provided as a 5-day running mean with an upper limit of 60 cm due to the limited penetration depths of the frequencies used, and values are applicable for dry snow conditions only [Cavalieri et al., 2004]. Within these limitations, AMSR-E provides an operational snow depth dataset on sea ice of the polar regions. In this study, the AMSR-E snow depth products (version 11) for the method comparison period, October and November of 2007, are used in the buoyancy equation to compute ice thickness National Ice Center Weekly Concentration and Ice Edge [11] National Ice Center (NIC) produces ice charts and ice concentration maps manually using all available satellite imagery, including but are not limited to ENVISAT, DMSP OLS, AVHRR, RADARSAT, and QuikSCAT, and supplemental information such as climatology, drifting buoys, and ship reports [ Ozsoy-Cicek et al., 2009]. We use weekly NIC ice concentration maps (available biweekly) to derive weekly ice edges that include the traces of sea ice for the week. There are usually two such ice edges maps in the period of one ICESat campaign (around one month). The maximum ice edge of each ICESat campaign is then used in this study to define the ice extent of each campaign. 3. Sea Ice Thickness Estimation Methods [12] Two different approaches, buoyancy equation and empirical equation, are used to compute sea ice thicknesses based on ICESat freeboard and other parameters, at two different horizontal scales: high resolution at the ICESat footprint scale (i.e., 70 m) and coarse resolution at the AMSR-E snow depth data scale (i.e., 12.5 km). The ICESat ON07 campaign period is chosen to compare these computations with extensive surface validation measurements made in October 2007 during the ship-based experiment in the Bellingshausen Sea, Sea Ice Mass Balance in the Antarctic (SIMBA) [Xie et al., 2011; Lewis et al., 2011; Weissling et al., 2011; Weissling and Ackley, 2011; Ozsoy-Cicek et al., 2011] Buoyancy Principle [13] Using buoyancy or hydrostatic balance, sea ice thickness (T i ) is calculated using equation (1) [Zwally et al., 2008; Yi et al., 2011]. T i ¼ F sn r w T sn ðr w r s Þ (1) r w r i where T sn (m) is snow depth; F sn (m) is the snow freeboard derived from the ICESat altimetry data; and r s, r w,andr i indicate snow, water, and ice densities. Taking snow density kg/m 3 from field measurements during the SIMBA 2007 experiment [Lewis et al., 2011] and sea water and ice densities, 1027 and 920 kg/m 3 based on literature, equation (1) is reduced as; T i ¼ 9:60 F sn 6:46 T sn (2) [14] Based on field measurements for Antarctic sea ice, snow depth in this region is actually very close to snow freeboard [Xie et al., 2011; B. Ozsoy-Cicek et al., submitted manuscript, 2013]. If the snow depth is equal to the snow freeboard, there is no sea ice above sea level. This is also referred to as zero ice freeboard. Therefore, the buoyancy equation (2) can also be simplified as equation (3), by replacing the snow depth T sn with the snow freeboard F sn in equation (2). T i ¼ 3:14 F sn (3) [15] There are different types of errors related to the buoyancy equations. A major source of error is related to the assumed densities of snow, seawater, and ice, since all can vary based on location, season, and year. Another error source is in the estimation of snow depth, since there are limitations on the use of the snow depth product for Antarctic sea ice. The AMSR-E snow depth was used in Zwally et al. [2008]; however, as stated in the paper, AMSR-E has an upper limit of 0.6 m for dry snow and even less for wet snow. A study performed by Worby et al. [2008b] in East Antarctica showed that snow depth over sea ice was underestimated by a factor of 2.3 using the AMSR-E snow depth product. Underestimating the snow cover would result in an overestimate of ice thickness [Zwally et al., 2008], as further discussed below. Another source of error is from the snow freeboard derived from ICESat. Kurtz and Markus [2012] indicated the uncertainty of ICESat freeboard (2 cm) caused uncertainty of ice thickness estimation of 0.23 m for a 25 km pixel scale. In the case of a dense slush layer developed at the snowice interface, an additional term should be added to the buoyancy (equation (1)), or the sea ice thickness would be underestimated from 0.66% for 0.5 m ice to 28.8% for 4.5 m ice [Weissling et al., 2011]. Since the slush layer is actually very common [Lytle and Ackley, 1996; Hosseinmostafa et al., 1995; Jeffries et al., 1995; Jeffries, 1998] in Antarctic sea ice, the underestimation due to ignoring the slush layer in equation (1) might cancel out some overestimation error resulted from the use of AMSR-E snow depth. It is, therefore, rather complex to assess the overall errors from equation (1) for estimating ice thickness of Antarctic sea ice. Kurtz and Markus [2012] estimated an overall ice thickness error of 0.37 m for the bouyancy equation and 0.23 m for the bouyancy equation under the zero ice freeboard assumption Empirical Equation at ICESat Resolution [16] The empirical relation (equation (4)) used for this study was derived by linear regression from field measurements of coincident pairs of snow freeboard and sea ice thickness averaged over individual transects over the Bellingshausen- Amundsen Seas region from 1993 to 2007 [Ozsoy-Cicek, 2010; B. Ozsoy-Cicek et al., submitted manuscript, 2013]. A total of 53 ice drilling transects of 50 m to 100 m in length taken at 1 m intervals available from the four cruises, Palmer 1993 (27 transects, August-September), GLOBEC 2001 (11 transects, July-August) and 2002 (12 transects, August- September), and SIMBA 2007 (5 transects, September- October) for the region, are used for the regression to derive equation (4) [Ozsoy-Cicek, 2010]. The equation has a correlation coefficient (R 2 ) value of 0.84, as compared with a value of 0.73 for a similar equation, published in Xie et al. [2011]but 2441

5 Table 2. Sea Ice Thickness (m) Statistics at the AMSR-E Pixel Scale (a) and ICESat Footprint Scale (b) During the Spring 2007 Season (ON07) for the Bellingshausen and Amundsen Seas Sector a (a) AMSR-E pixel scale Method Min Max Mean Mode Median S.D. Buoyancy equation (2) (+96) 2.18 (+61) 0.64 ( 29) 1.41 (+26) 1.84 (+116) (b) ICESat footprint scale Method Min Max Mean Mode Median S.D. Buoyancy equation (2) Constant SD (+209) 2.36 (+75) 0.72 ( 20) 1.26 (+13) 2.58 (+204) Variable SD (+192) 2.20 (+63) 0.72 ( 20) 1.36 (+21) 2.21 (+160) Simplified buoyancy equation (3) (+6) 1.33 ( 1) 0.80 ( 11) 1.07 ( 4) 0.96 (+13) Empirical equation (4) a Note that numbers in parentheses are the percentage differences (%) from the corresponding numbers derived from the empirical equation (4). SD denotes snow depth. derived only from the SIMBA 2007 data. Using the equation from Xie et al. [2011] would result in slightly larger sea ice thickness (~5%) as compared with using equation (4). T i ¼ 2:7877 F sn þ 0:1688 (4) [17] Comparing equation (3) with equation (4), it is easily found that, when F sn is less than or equal to m, the ice thickness from equation (3) is less than or equal to that from equation (4); otherwise, the inverse is true. Based on Table 1, the majority of the F sn values are less than m. This indicates ice thickness derived from equation (3) (the zero sea ice freeboard model) would be slightly less than that from equation (4) (the empirical approach based on field measurements), as shown in Table 2 where the mean, modal, and median ice thicknesses resulting from equation (3) are all slightly less than those from equation (4). [18] Errors using equation (4) are based in the field measurements of snow freeboard and ice thickness that were used to derive the equation and with the ICESat altimetry data used to estimate the snow freeboard. Considering these errors together, the Xie et al. [2011] showed an overall ice thickness error of 0.49 m [Xie et al., 2011], while equation (4) can explain 84% of ice thickness variation (B. Ozsoy-Cicek et al., submitted manuscript, 2013) Coarse Resolution (12.5 km Cell Size) Sea Ice Thickness Computation [19] At the 12.5 km resolution scale, the buoyancy equation (equation (2)) is used to derive the ice thickness. Similar to other studies [Zwally et al., 2008; Yi et al., 2011], we upscale the ICESat freeboard measurements to the AMSR-E snow depth resolution scale by averaging all freeboard values up to the 12.5 km 12.5 km AMSR-E pixel scale rather than the 50 km 50 km grid cell used in these other studies. Where the AMSR-E snow depth exceeded the corresponding averaged ICESat freeboard value, the AMSR-E snow depth is replaced by the averaged freeboard value as done previously [Zwally et al., 2008; Yi et al., 2011]. Based on the upscaled freeboard and the AMSR-E snow depth, equation (2) is then used to compute the ice thickness for each grid cell. We note here, however, that this scaling procedure alone can lose essential information on the ice thickness distribution. From field observations within one 12.5 km by 12.5 km area, there can be a large variety of thin and thick ice types and even larger variation of snow depth, even within a single ice type [e.g., Lytle and Ackley, 1996; Lewis et al., 2011]. By averaging all freeboards and using one snow depth for this area, only a mean thickness can be computed. Therefore, no information is provided on the distribution of ice thicknesses, including the mode values (level ice), or the percentage of ice formed by deformation processes, or the percentage of thin ice types, that may otherwise be available using the full high-resolution ICESat freeboard measurements for thickness calculations through other techniques described below. Methods that use the full resolution of the ICESat altimetry to provide complete information on the ice thickness distribution, not just an areally averaged mean thickness estimate for a 12.5 km by 12.5 km area, are, therefore, more advantageous. Since there is no real field data in such a 12.5 km scale to assess the error in ice thickness estimation using equation (1), the possible error sources are discussed in section High-Resolution (70 m Footprint) Sea Ice Thickness Computations [20] At the ICESat footprint scale, we test both methods (buoyancy principle and empirical relation) to derive the ice thickness. For the empirical relation (equation (4)) and simplified buoyancy relation (equation (3)), the only input is the ICESatderived snow freeboard values. For the buoyancy principle (equation (2)), the AMSR-E snow depth are used at the ICESat footprint scale, with two different considerations: a constant AMSR-E snow depth and a variable AMSR-E snow depth AMSR-E Constant Snow Depth at ICESat Resolution (70 m) [21] For each ICESat measurement, we take the snow depth information from the respective AMSR-E cell in which that ICESat footprint falls and compute ice thickness using equation (2). Some AMSR-E snow depth values are determined to be larger than their corresponding ICESat freeboard values. However, in summer, autumn, or spring season when ICESat data are taken, the warm ice conditions allow flooding as soon as the snow-ice interface is depressed below sea level. Snow depths greater than snow freeboard are, therefore, typically physically unrealizable as snow depth estimated from AMSR-E has to be always less than or at most equal to snow freeboard (when it is flooded). For these values, we adjust the computation, by replacing those unrealizable snow depths with each ICESat freeboard as previously done, for cell averaged values at the coarse resolution scale [Zwally et al., 2008; Yi et al., 2011]. 2442

6 AMSR-E Variable Snow Depth at ICESat Resolution (70 m) [22] Since the algorithm used in snow depth determination using AMSR-E data is applicable only to dry snow conditions and has an upper limit of 60 cm snow depth [Cavalieri et al., 2004], and the AMSR-E data has a much coarser resolution than the ICESat data, a method, applied to Arctic sea ice, has been used to obtain snow depth values at the ICESat freeboard scale and then used to derive ice thickness at the ICESat footprint scale [Kurtz et al., 2009]. In this regard, Kurtz et al. [2009] used the relation between the snow depth and ICESat freeboard values as a proxy for the snow depth variation over first year Arctic sea ice regions and thereby downscaled AMSR-E snow depth measurements to the ICESat footprint resolution for Arctic sea ice. [23] Linear correlation between snow depth and snow freeboard values for Antarctic sea ice is also found (R 2 > 0.9) not only for first year ice but also for multi-year ice [Xie et al., 2011; Ozsoy-Cicek, 2010; B. Ozsoy-Cicek et al., submitted manuscript, 2013]. Therefore, as in the Kurtz et al. [2009] approach, using the AMSR-E snow depth value as a constraint for the ICESat measurements in that pixel, we downscale AMSR-E snow depth values to ICESat resolution using equation (5) [Kurtz et al., 2009]: T sn j ¼ F sn j T sn AMSR E N X N j¼1 F sn j (5) where T sn_j is the snow depth for the ICEsat footprint j; F sn_j is the corresponding freeboard value for the footprint j; T sn_amsr-e is the snow depth value obtained from the corresponding AMSR-E pixel; N is the total number of ICESat measurements in the AMSR-E pixel. [24] Similar to the constant snow depth case above, some of the downscaled snow depths are still greater than the corresponding snow freeboard values. We, therefore, follow the previous approach, setting the downscaled snow depth equal to the ICESat-derived freeboard value and using equation (2) to compute ice thickness. [25] Based on Kurtz et al. [2009] for Arctic sea ice, using the constant snow depth for each footprint (equation (2)) resulted in overestimation of thin ice (less than 2 m), while for thick ice over 2 m, the difference between the calculated and measured ice thickness was small. Using variable snow depth (equation (5)), the difference between the calculated (using equation (2)) and measured ice thickness was around 1% [Kurtz et al., 2009]. 4. Results and Discussion 4.1. Model Intercomparisons to Compute Ice Thickness [26] Using the spring 2007 (ON07) ICESat data as an example, ice thicknesses are calculated under both coarse and high-resolution scales for comparisons (Table 2). It is important to note that at the coarse resolution scale, averaging over many ice freeboards in a 12.5 km by 12.5 km area will provide only a mean thickness and no modal value for the pixel area, as many ridges and different ice types are found at scales much less than 12.5 km. We, therefore, only use this result (Table 2a) for mean thickness value comparisons with high-resolution methods. [27] It is found that the two different considerations of snow depth: constant or variable, for the buoyancy equation (equation (2)), do not show much difference in terms of maximum, mean, mode, median, and standard deviation of ice thickness. However, they are much different from the results using the empirical equation (equation (4)) and simplified buoyancy equation (3) with ICESat freeboard replacing snow depth (Table 2b). As compared with the empirical equation, the buoyancy equation (equation (2)) overestimates maximum ice thickness (~ m vs ~5.73 m, i.e., %), mean ice thickness (~ m vs ~1.35 m, i.e., %), median thickness (~ m vs ~1.12 m, i.e., %), and slightly underestimates modal thickness (~0.72 m vs ~0.9 m, i.e., 20%). The standard deviation of ice thickness from the buoyancy equation is also much larger than that from the empirical equation (~ m vs 0.85 m). [28] All statistics at the AMSR-E pixel scale (Table 2a) are close to those in the ICESat footprint scale (Table 2b) when the buoyancy equation (equation (2)) is used with the downscaled AMSR-E snow depth. This confirms the overall overestimation of using the buoyancy equation, no matter whether at coarse or high-resolution scale, in terms of maximum, mean, and standard deviation. The overestimation is reduced at the AMSR-E pixel scale as compared to the ICESat footprint scale, due to the averaging at the coarse resolution scale Reason of Ice Thickness Overestimation Based on the Buoyancy Principle for Antarctic Sea Ice [29] Figure 1 shows the scatter plots of the AMSR-E snow depth and ICESat freeboard for the ON07 season for all cases discussed above. The maximum snow depth of 0.6 m from AMSR-E is actually much less than the maximums from field based observations and measurements [Worby et al., 2008a; Lewis et al., 2011] and also differs from the fact that snow depth is actually very close to snow freeboard in the Antarctic, i.e., a nearly 1:1 linear relationship (R 2 > 0.91), based on field measurements [Xie et al., 2011; B. Ozsoy-Cicek et al., submitted manuscript, 2013], unlike the high variability shown in scatter plots of AMSR-E snow depth and ICESat freeboards (Figures 1a and 1c). Due to this underestimation of snow depth from AMSR-E, the ice freeboard is overestimated when snow depth is subtracted from the ICESat snow freeboard and the buoyancy equation (equation (2)) thus estimates a much higher sea ice thickness, in terms of maximum, mean, and standard deviation (Table 2). Using the Kurtz et al. [2009] approach to redistribute AMSR-E snow depth into each ICESat footprint scale (equation (5)), the computed snow depths (Figure 1b) can be much larger than the original values (maximum 0.6 m at the 12.5 km scale), while it is still in most cases smaller than the snow freeboard from ICESat. This underestimated snow depth still remains the main reason contributing to the overestimation of ice thickness using buoyancy equation (2), despite the slightly reduced overestimation (2.20 m vs 2.36 m) as compared with that when the original/ constant AMSR-E snow depth is used (Table 2b). The maximum values of snow depth and freeboard (Figure 1, B1 and B2) are slightly larger than the SIMBA field measurements during the similar period (Figure 2). The main reason is that the ICESat and corresponding AMSR-E data covered a large area and included thick and ridged multi-year ice. The 2443

7 Figure 1. Scatter plots of AMSR-E snow depth and ICESat freeboard values for the ON07 season for the Bellingshausen and Amundsen Seas sector for all data pairs (left) and all data pairs with snow depth set equal to freeboard when snow depth freeboard (right). Panels from top to bottom are, respectively, original/constant AMSR-E snow depth at the ICESat footprint scale (A1, A2), computed AMSR-E snow depth using equation (5) at the ICESat footprint scale (B1, B2), and original AMSR-E snow depths and averaged ICESat freeboard at the AMSR-E pixel scale (C1, C2). upscaled ICESat freeboards at the AMSR-E pixel scale are less than 1.5 m (Figure 1, C1 and C2), which is less than the maximum 2 m of the individual ICESat footprints used in this study (Figures 1a and 1b). This contributes to the overall smaller maximum (11.23 m), mean (2.18 m), and standard deviation (1.84 m) of ice thickness at the AMSR-E pixel scale as compared with those from the ICESat footprint scale (Table 2a). By simply replacing the AMSR-E snow depth with the ICESat snow freeboard, the estimation of ice thickness is much reduced and very close to the empirical equation (equation (4)) based estimation (Table 2b). Therefore, the underestimation of snow depth from AMSR-E is indeed the primary reason for the overestimation of ice thickness based on the buoyancy equation. [30] Table 3 shows the statistical results for all ICESat campaigns by using the empirical equation (4) and the simplified buoyancy equation (3). The averaged seasonal mean, mode, and median from equation (3) are very close to but slightly lower than those from equation (4), by 0.02 m (or percentage difference of 1.8%), 0.09 m (or 10.9%), and.05 m (or.4%), while the seasonal maximum and standard deviation are slightly higher, by 0.53 m (or 9.3%) and 0.10 m (or 13.1%), respectively. The minimum value zero (from equation (3)), which differs from the 0.17 m from 2444

8 Figure 2. Frequency distributions of Snow freeboard and snow depth (left) and ice thickness (right) from the 163 in situ measurements at the five stations and sites during SIBMA 2007 [Source: Xie et al., 2011]. equation (4) (Tables 2b and 3), is due to those zero freeboards that were set from the ~1% of negative freeboard values, resulting from the along-track filtering approach [Zwally et al., 2008], while the empirical equation can still give a reasonable minimum ice thickness of 0.17 m. This clearly indicates both the empirical equation and the simplified buoyancy equation are compatible and give reasonable estimations of ice thickness. The empirical equation reflects the field conditions where, for the most part, either a high percentage of snow/ice interface is flooded or has a small positive freeboard [Lewis et al., 2011; Weissling et al., 2011; Jeffries et al., 2001], that is, close, but not exactly equal, to the zero ice freeboard assumption. The empirical equation (4) derived thicknesses can actually explain ~84% of the ice thickness variation [Ozsoy-Cicek, 2010; B. Ozsoy-Cicek et al., submitted manuscript, 2013] from field measurements. [31] Replacing the AMSR-E snow depth with the ICESat freeboard for the buoyancy equation gives reasonable ice thickness estimations for all seasons and all ICESat data for the region. These ice thicknesses and snow depths for the ON07 season are also compatible with measurements from the SIMBA experiments (Figure 2) [Xie et al., 2011], with slightly lower values from SIMBA due to the fact that the ICESat covered a large area and included more thick and ridged multi-year ices. This further indicates the concept that underestimation of snow depth by AMSR-E on Antarctic sea ice is indeed the major reason for the overestimation of ice thickness based on the buoyancy equation. Further comparison of the differences between using equations (3) and (4) (Table 3), it is found that the spring season has the smallest difference or percentage difference, while the autumn season has the largest percentage difference, in terms of mean, mode, and median, i.e., 1.0% (for spring) vs 4.0% (for autumn), 10.0% vs 14.3%, and 3.0% vs 7.6%, respectively (not shown). This seasonal difference may come from two factors. First, when the zero freeboard assumption is applied in equation (3), with thin snow cover over newer thin ice in autumn, there may be proportionally more ice with positive freeboard, which the empirical equation (4) takes into account. The zero freeboard assumption (equation (3)), however, applies to ice of all thicknesses and snow covers which may be less applicable for low snow depths on ice formed in autumn. Second, equation (3) is a simplified version of equation (2) where the densities of snow, ice, and water are all based on the field measurements in the spring season (SIMBA 2007). These density values may be different from those in summer, and possibly a larger difference from those in the autumn seasons Table 3. Statistics of Sea Ice Thicknesses (m) Computed Using the Simplified Buoyancy Equation (Equation (3)) and Empirical Equation (equation (4)) for the Bellingshausen and Amundsen Seas Sector for All ICESat Campaigns a Simplified Buoyancy Equation (3) Empirical Equation (4) Period ID Min Max Mean Mode Median S.D. Min Max Mean Mode Median S.D. FM FM 04 2b FM 05 3b FM 06 3e MA 07 3h FM 08 3j MA 09 2e Mean in Summer MJ 04 2c MJ 05 3c MJ 06 3f Mean in Autumn SON 03 2a ON 04 3a ON 05 3d ON 06 3g ON 07 3i OND08 3k,2d O 09 2f Mean in Spring a Note that the Period and ID are the same as in Table

9 Figure 3. Seasonal cycle of mean (1std) and modal ice thicknesses from empirical equation (equation (4)) for the Bellingshausen and Amundsen Seas sector, with ice areas derived from NIC (National Ice Center) ice concentration maps (top curve) for spring seasons only. Black for the summer seasons, red for the autumn seasons, and green for the spring seasons. Green lines are for the spring thickness mean and ice area. Blue dashed line is the trend line for all thicknesses. 03SU, 03A, 03W, and 03SP are, respectively, summer, autumn, winter, and spring 2003 seasons. The same naming conventions apply to other years. when new snow and ice are forming. However, based on the above numbers, zero ice freeboard assumption and density differences together only account for less than 5% of seasonal mean ice thickness difference, while the inaccuracy incurred by using an independent snow depth derived from AMSR-E accounts for the remaining 95% or more mean sea ice thickness overestimation. In Kurtz and Markus [2012], they used different densities of snow and ice for different seasons for equation (1) to derive equations (2) and (3) Best Practice Method to Compute Ice Thickness Distributions [32] Based on the above results, it is clear that the empirical equation (equation (4)) is the preferable method to compute ice thickness at the ICESat footprint scale and accounts for 84% ice thickness variation for the study region. [33] Figure 3 shows the seasonal pattern of mean and modal thicknesses (from Table 3). There is an overall similar tendency of increase, decrease, and increase for either summer or spring mean ice thickness, with maximum values in spring 2005 and summer 2006 and minimum values in spring 2003 and summer The modal values have less variation, with maximum in spring 2008, possibly due to the December data being included. Minimum modal values are in autumn seasons (red squares), as well as the summers of 2007 and 2008 (black squares). Although there is no winter data available from ICESat data, based on Figure 3 and Table 3, we can see the pattern of thickness mean and mode most likely increase from autumn to spring and decrease from spring to the following autumn, with exceptions that a slight increase in summer 2004 and 2006 occurred from the previous spring. Considering all thickness values together, there is a slightly overall increasing trend (+0.03 m/year) of mean ice thickness from 2003 to 2009 (Figure 3), although it is insignificant (p = 0.11) at the 95% level. For summer or spring seasons alone, there is also a slight increasing trend, 0.01 m/year (p = 0.72) for summer seasons and 0.03 m/year (p = 0.41) for spring seasons. For autumn seasons, since there are only 3 values, it is not appropriate to discuss their trend, although the thickness shows increase from 2004 to The slight increasing trend is consistent with those reported in Kurtz and Markus [2012], although their values, 0.07 m/year for summer and 0.05 m/year for spring, are slightly larger than ours. Noting that in their paper, the BA sector is the only one showing ice thickness increase in both seasons, with the Indian Ocean sector showing 0.01 m/year increase in spring seasons; all other sectors in their paper show thickness decrease. It is worthy to mention that, most of those trends (increase or decrease) in this paper and in Kurtz and Markus [2012] are very small and statistically insignificant. In contrast, both thinning of sea ice and declining ice extent in the Arctic are very large and are statistically significant [Kwok et al., 2009; Perovich, 2011]. [34] Maximum ice extent/area for Bellingshausen- Amundsen region during each spring season is also included in Figure 3. Although the spring mean ice thicknesses do not show much difference as compared to their standard deviation, the corresponding ice area varied considerably, ranging from 1.62 (spring 2006) to 2.75 (spring 2004) million km 2.Unlike in the Arctic, there appears to be little coherence between ice area and ice thickness variability, in that the highest mean thicknesses are slightly tending toward the summer minimum areas in the Bellingshausen and Amundsen Seas region. This may indicate that some of the reduction in ice area may be also due to compaction events that slightly increase the mean ice thickness for those years. However, comparing year to year for ice volume (the product of area and mean thickness, not shown in the figure) suggests that overall mass balance is more governed by the higher variability in ice area (up to 60%) compared to ice thickness variability (up to 35%). The spring ice volume shows variability year to year but is primarily dominated by ice extent variability, with no increasing or decreasing trend over this record length. The dependence of the volume on the ice extent primarily suggests that ice thickness changes have also not covaried with the ice extent losses seen over the satellite record in this region, unlike the Arctic. These properties reflect the interactive processes of ice advection, thermodynamic growth, and ice deformation, all which 2446

10 Figure 4. Frequency distribution of the computed sea ice thicknesses using empirical equation (4) for (a) summer, (b) autumn, and (c) spring seasons for the Bellingshausen and Amundsen Seas sector. Basic statistics (from Table 3) are also included in the figure for ease of reading. S.D. denotes standard deviation. substantially influence ice mass balance in the Bellingshausen- Amundsen Seas region. The spatial details of how the increase in area occurs, whether at the ice edge or by expansion of the ice pack away from the coast in coastal polynyas, require closer examination. Based on Figure 3 and Table 3, the modal thickness does not vary much, suggesting the thermodynamic condition may not change much from year to year. With up to 25% of the ice thickness in this region, however, formed by the flooding and refreezing of snow into snow-ice [Jeffries et al., 1995], the thermodynamic growth condition is complex and most certainly affected by annual differences in temperature and precipitation. In spite of this complexity, Ackley et al. [1991] suggested that ice thickness alone, without structural determination, could have some equivalence between that seen in cold (but dry) conditions and warm (but wet) conditions due to varying amounts of snow ice formation. The mean ice thickness, reflecting the ice dynamics (ridging and rafting), does, however, vary considerably and changes from year to year, meaning more or less wind force has impacted the ice [Weeks, 2010; Ackley, 1996] in different years. [35] Although the mode peaks at lower values than the mean and long tails extend 2 to 5 times the mode value (Figure 4), both the mode and mean show similar seasonal variation (Figure 3). Mean and mode values with wider differences suggest a higher contribution of deformation in particular years. Relatively high mode values in spring may be characteristic of the deep snow cover and thick level ice formed thermodynamically during the previous autumn and winter. Mean ice thicknesses in spring are more variable, suggesting greater variations in ice dynamics or deformation from year to year (causing greater ice thickness variations) than thermodynamics that causes modal thickness variation [Weeks, 2010; Ackley, 1996]. With these seasonal and interannual variations, it appears, therefore, that both mean and mode values are needed to describe the average properties of the ice pack [Zwally et al., 2008], and to relate the coupled parameters to the respective contributions of deformation and thermal (including precipitation) forcing in any given year. [36] Table 3 shows seasonal median values ranging from 0.8 to 1.4 m over the period that are always larger than the corresponding modal values ( m) and lower than the mean values ( m), with standard deviation of m. Starting from autumn, a general picture of seasonal mean, modal, and median ice thickness increases progressively from autumn, to winter, and to 2447

11 Figure 5. ICESat-derived sea ice thickness means by using empirical equation (equation (4)) for each season and for all seasons, (a) summer, (b) autumn, and (c) spring, averaged in 12.5 km by 12.5 km grid cell for visualization purpose. Gray outlines are the maximum ice extents derived from NIC ice concentration datasets for corresponding seasons, with bold numbers as the corresponding sea ice areas (million km 2 ). spring, then decreases from spring through summer, and back to the annual minimum values in autumn, when new thin ice dominates the ice thickness distribution. The asymmetric shape of the thickness distribution (Figure 4) reflects the key role of ice deformation processes in the evolution of the thickness distribution. The statistical properties of the thickness distribution interannually (high range of mean thickness and standard deviation) indicate the variability of deformation processes. [37] Figure 5 shows the spatial distribution of mean sea ice thickness variations for each season and for all seasons for the Bellingshausen and Amundsen Seas of west Antarctica, with minimum ice extent/area in summer seasons (Figure 5a), overall largest ice extent/area in the spring seasons (Figure 5c), and moderate ice extent/area in the autumn seasons (Figure 5b). Thicker ice is generally distributed nearer coastal regions, although in many cases, thicker ice also appeared at the ice edge for both autumn and spring seasons. This was actually the case in the SIMBA period, the ON07 season. This suggests some thicker first year or multi-year ice drifts north towards the ice edge due to wind storms and ocean currents. A major mechanism for the melting of sea ice in spring and summer seasons is drift to warmer ocean water at the ice edge [Lewis et al., 2011; Ozsoy-Cicek et al., 2011]. The remaining thicker ice in summer seasons is mostly seen in the central Amundsen Sea and near the Antarctic peninsula, 2448

12 Figure 5. (continued) 2449

13 Figure 6. Seasonal mean ice thickness distributions from ICESat ( ) by using empirical equation (equation (4)): (a) summer, (b) autumn, and (c) spring at both ICESat footprint scale and upscaled (averaged) 12.5 km scale (AMSR-E pixel size). while thinner ice is seen in the Bellingshausen Sea and some near the coastal region of the Amundsen Sea. [38] Figure 6 shows the seasonal mean ice thickness distributions of at both ICESat footprint scale and upscaled 12.5 km scale (AMSR-E pixel size), with average 118 (summer), 78 (autumn), 73 (spring) ICESat footprints in one 12.5 km AMSR-E pixel. The thickness in the ICESat footprint scale is more widely spread from the low end to the high end of the thickness distribution, particularly the maximum ice thickness that is much larger in the ICESat footprint scale than that in the averaged scale. The variability of ice thickness is also shown in the standard deviation. Although mean ice thickness at both scales has only slight difference, i.e., 6 cm for summer, 0 cm for autumn, and 2 cm for spring, the difference in standard deviation is much larger, i.e., 33 cm for summer, 23 cm for autumn, and 28 cm for spring. Overall, the mean (modal) thicknesses in the ICESat footprint scale are equal to or slightly higher (lower) than those averaged in the 12.5 km grid, while ICESat footprints capture a broader range of the ice thickness distribution, which implies wide range of precision Comparison With Other Studies [39] Ship-based ASPeCt observations provide the only available/published field-based Antarctic sea ice thickness and snow depth datasets [Worby et al., 2008a], with Bellingshausen and Amundsen Seas sector having the largest data gaps in all seasons. For example, only 138 ASPeCt observations from December 1993 February 1994 (Akademik Fedorov)forsummer, 485 ASPeCt observations from both September October 1994 (NB Palmer) and August September 1995 (NB Palmer) for spring, 495 ASPeCt observations from July August 2001 (LM Gould and NB Palmer) for winter, and not enough data for autumn to establish statistics. Therefore, both the numbers of observation data and their spatial distributions [Figure 1 of Worby et al., 2008a] are very limited for the BA sector. For instance, the 138 summer observations were only in the easternmost Amundsen Sea near the Ross Sea sector and coastal region. This resulted in overall high values of mean ice thickness (2.14 m) and mean snow depth (0.5 m) as compared to this paper, 1.3 m (Table 3) and 0.4 m (Table 1, snow freeboard as a proxy of snow depth), respectively. However, if we compare them in the same location (easternmost Amundsen Sea near the Ross Sea sector and coastal region) in Figure 5a (summer mean), the ice thickness that ranges from 1.3 to 2.5 m is much closer to the mean 2.14 m of ASPeCt. The 485 spring ASPeCt observations had wide longitude distribution but mostly in lower latitudes (lower than 70ºS), with mean ice thickness and snow depth 0.79 m and 0.13 m, which are lower than those from this paper, 1.36 m (Table 3) and 0.45 m (Table 1), respectively. However, if we compare the distribution of ASPeCt observations with the same locations: the 2450