Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences


    We present our estimates of the thickness and volume of the Arctic Ocean ice cover from CryoSat-2 data acquired between October 2010 and May 2014. Average ice thickness and draft differences are within 0.16 m of measurements from other sources (moorings, submarine, electromagnetic sensors, IceBridge). The choice of parameters that affect the conversion of ice freeboard to thickness is discussed. Estimates between 2011 and 2013 suggest moderate decreases in volume followed by a notable increase of more than 2500 km3 (or 0.34 m of thickness over the basin) in 2014, which could be attributed to not only a cooler summer in 2013 but also to large-scale ice convergence just west of the Canadian Arctic Archipelago due to wind-driven onshore drift. Variability of volume and thickness in the multiyear ice zone underscores the importance of dynamics in maintaining the thickness of the Arctic ice cover. Volume estimates are compared with those from ICESat as well as the trends in ice thickness derived from submarine ice draft between 1980 and 2004. The combined ICESat and CryoSat-2 record yields reduced trends in volume loss compared with the 5 year ICESat record, which was weighted by the record-setting ice extent after the summer of 2007.

    1. Introduction

    In the recent IPCC Assessment Report-AR5 [1], observations from multiple sources (submarine, electro-magnetic (EM) probes and satellite altimetry) supported high confidence statements pertaining to the thinning of the ice cover in the central Arctic since the 1980s. And for the first time, basin-wide decreases in Arctic sea ice volume from satellite measurements made in the period 2003–2008 (ICESat) [2] and 2010–2012 (CryoSat-2) [3] have contributed to this assessment of recent changes in Arctic sea ice conditions. The combination of ice extent, thickness and volume now provides a more comprehensive picture of the integrated behaviour of the Arctic ice cover in a changing climate.

    With the completion of NASA’s ICESat mission in 2009, CryoSat-2 (launched in 2010) is now the only in-orbit mission with an inclination (92°) that allows near-complete altimetric mapping of the Arctic Ocean ice cover [4]. Laxon et al. [3] processed and provided a first assessment of Arctic ice volume based on 2 years (2011–2012) of CS-2 acquisitions. Numerous studies that addressed remaining issues in retracking methodology, interpretation of the surface returns and the conversion of sea ice freeboard to thickness have followed (e.g. [58]). At this writing, more than 4 years of CS-2 data are now available to the science community.

    While ICESat offered only two to three 34-day mapping campaigns annually during its mission life, the monthly maps of the Arctic Ocean from CS-2 provide more frequent temporal mappings for resolving basin-scale processes and responses of the ice cover to thermodynamic and especially shorter time-scale dynamic forcing. The objective of this paper is to provide a closer examination of the seasonal and interannual variability of the ice cover, and to review the longer term Arctic record (including submarine and ICESat) of sea ice thickness and volume with the addition of 4 years of CS-2 data between October 2010 and May 2014.

    The paper is organized as follows. The following section describes the datasets used in our analyses. The methodologies and choice of parameters used to derive surface elevation, and estimate sea ice freeboard and thickness from the CS-2 data are summarized in §3. In §4, we compare the derived results with available measurements from moorings, submarines, airborne EM (AEM) probes and the IceBridge campaigns. In §5, the variability of the Arctic Ocean thickness, and volume from the CS-2 record (between 2010 and 2014), and impact of the anomalous atmospheric circulation during the summer of 2013 are discussed. Uncertainties in the ice volume estimates are examined. The basin-scale CS-2 ice thickness and volumes are discussed in the context of ICESat and earlier submarine records in §6. The last section concludes the paper.

    2. Data description

    (a) CryoSat-2 data

    Altimeter data used here are acquired by the synthetic aperture radar (SAR)/Interferometric Radar Altimeter (SIRAL) instrument on CryoSat-2 (CS-2). These data are available at a repository within the ESA data portal ( The pulse-limited footprint of the synthetic aperture radar altimeter is approximately 0.31 km by 1.67 km along- and across-track, and multiple-looks of each point on the surface are used to reduce noise caused by radar speckle [9]. The recorded altimetric waveforms (both SAR and SARIn modes) and the required parameters for the analysis in this paper are from the Level 1B and Level 2 CS-2 data products. The interferometeric mode of SIRAL (SARIn) was operated over parts of the Arctic between 2011 and 2014, but only the altimetric waveforms from the SARIn mode of these acquisitions used in the present analysis.

    (b) Other datasets

    (i) Ice draft from BGEP mooring sites (2010–2013)

    Ice draft measurements are from three moored upward looking sonars (ULS) deployed as part of the Beaufort Gyre Exploration Project (; [10]). The instruments are typically at a water depth of 50 and 85 m and provide ranges to the bottom surface of the sea ice every 2 s with a footprint of about 2 m. Ice draft is determined from the corrected range minus the pressure of the transducer (corrected for atmospheric pressure variations), after taking into account instrument tilt, sound speed and density variations in the seawater. Individual ice drafts are typically accurate to within ±0.1 m (95% confidence limits) [11].

    (ii) Submarine ice draft (2011)

    Submarine ice drafts are from two cruises (USS Connecticut and USS New Hampshire) in April 2011. Released draft data are archived at the National Snow and Ice Data Center [12]. Mean drafts are provided for segments of the cruise varying from 5 to 10 km in length. The draft data are expected to be biased with respect to actual draft due to the first return nature of the estimate by approximately +29 cm with a variability of approximately 25 cm [13]. This expected bias is removed before use.

    (iii) Snow and ice thickness from AEM (2011 and 2012)

    Snow+ice thickness is from an airborne EM instrument towed by a DC-3 aircraft known as the Polar-5. Ten surveys, with lengths ranging between 65 and 350 km, flown in April 2011 and 2012, provided measurements over both first-year ice (FYI) and multiyear ice (MYI) in the Western Arctic. While the accuracy of AEM data over level ice is 0.1 m, the uncertainty may be larger when ridged ice is present [14].

    (iv) Ice thickness from Operation IceBridge (2011 and 2012)

    Ice thickness from Operation IceBridge (OIB) [15] is derived from total freeboard (ice plus snow) acquired by a lidar, and snow depth measurements from an ultrawideband snow radar [16]. The data from the two OIB campaigns used here span a period between 10 March and 9 April 2011 and between 16 and 28 March 2012 [16]. These campaigns provide long transects (sometimes more than 3000 km) that survey the ice cover of the western Arctic between Alaska and Greenland. Uncertainties computed within individual 40 m retrievals are variable and are dependent on available sea surface reference and quality of snow depth estimates [17].

    (v) Ancillary data

    Gridded fields of MYI fraction are from ASCAT data processed using the approach in [18]. ASCAT is a moderate resolution wide-swath C-band scatterometer that provides daily coverage of the Arctic Ocean. Uncertainty in the classification is ±10% in areas with near even mixtures of MYI and seasonal ice, and lower in areas with nearly pure ice types. Daily ice motion fields are the sequential fields of passive microwave observations using the procedures by Kwok et al. [19] and Kwok [20].

    3. Estimates of ice thickness

    With surface elevations (ho) from CS-2 waveforms and assuming isostatic equilibrium, ice thickness (hi) is calculated with the following equation:

    Display Formula
    where hfi and hfs are sea ice freeboard and snow depth, and ρw, ρi and ρs are the bulk densities of water, ice and snow. Below, we describe the procedures used to obtain sea ice freeboard (hfi) from CS-2 L1B data, and discuss the choice of parameters (in equation (3.1)) used to convert hfi to hi.

    (a) Surface elevation, sea ice freeboard (hfi) and ice/water discrimination

    The first step determines the surface elevation (ho)—relative to the WGS-84 ellipsoid—from each CS-2 waveform. Different CS-2 retracking techniques over sea ice (e.g. [36]) have been suggested and devised, and sensitivities of specific techniques analysed [6]. Accurate assessments of retracking techniques through comparisons of derived thickness estimates with in situ or airborne datasets are often limited by disparities in spatial resolution, the lack of space–time coincidence, and the inherent uncertainties in the available in situ measurements. To date, it has been difficult to determine an optimal retracking approach (that unambiguously locates the ice surface in the return waveform) for estimation of hi due to the variability, uncertainty and competing effects of the different parameters (e.g. ice densities, snow depth, etc.) used in equation (3.1).

    One issue of particular concern is the response of retrackers in the presence of a variable snow layer [21,22]. Laxon et al. [3] cautioned that radar penetration into the overlying snow layer remains a subject of investigation and may introduce errors into the thickness calculations. In one study with simulated data, Kwok [7] noted that, with the CS-2 range-resolution of approximately 47 cm, scattering from the air–snow interface/snow layer may broaden the response of the snow–ice interface, effectively displacing the scattering surface towards the altimeter. This effect is largest when the strength of returns from the two interfaces are comparable and when snow thicknesses are more than 20 cm. Compared to using leading edge location to define the range to the surface, the simulation results [7] also suggest that the centroid location of the leading return of the first peak is less sensitive to scattering from the air–snow interface and snow layer.

    Here, we take the retracking point (RP) defined by the centroid of the waveform area (in the interval between the range location of the selected peak and 1.5 times the range to the half-power point on the leading edge of that peak) as the range to the ice surface. Specifically, we select the first unambiguous peak (more than 15 dBf; dBf is dB-femtowatts) in the oversampled (frequency-domain 16 times) altimeter waveform as the return from the surface. The power of the CS-2 peaks ranges up to greater than 70 dBf (see distribution in figure 1 and discussion below), and we find 15 dBf to be an effective threshold for avoiding noisy portions of the waveform. An unambiguous peak is one in which the leading edge of that peak is clearly defined, i.e. without any local minima in the range interval between its half- and maximum power points. The power of the peak (Pc) and the width of the centroid relative to the range location of the peak (Wc) are used for ice/water discrimination.

    Figure 1.

    Figure 1. Retracking and ice/water discrimination. (a,b) Distributions of the centroid width (Wc) and power of the peaks (Pc) selected as surface returns (colours show normalized population density: red is high and blue is low) for January–April and September–December (2011–2013). Means/s.d. of Wc and Pc at the mode of the distribution (top right corner) with the fraction of the population designated as sea surface returns (centre). Sea surface returns are those samples with Pc>40 dB-fW (above dashed while line) and widths to the left of the black and slanted red lines. (c) Average surface tilt (absolute value) in the sea surface for all winter months (October–May) between 2011 and 2013. The means and s.d. (signed slope) of the field are in the bottom right. (d) Shaded surface relief of the EGM2008 geoid. (e) SSH (left) and tilt (right) for individual 25 km segments of region shown in (d) in 2012; local relief in SSH and tilts are associated bathymetric features (e.g. deep ocean ridges). (f) ±RMS (grey area) and mean (black line) of detilted sea surface height in 25 km segments for the 3 years.

    The second step in the processing identifies returns from open water leads; this relies on specular reflections from leads at near-nadir incidence compared to diffuse reflections from ice floes [23,24]. For surface type (ice, water) discrimination in CS-2 data, Laxon et al. [3] used a pulse peakiness (PP) parameter and a stack standard deviation (SSD) parameter that provides a measure of the variation in surface backscatter with incidence angle [4]. Ricker et al. [6] used a modified version of the PP that considers the neighbourhood of the peak of the surface return. Both PP-based parameters are relative measures of peak signal strength compared to strength of the entire waveform. Instead of using PP and SSD, we introduce an approach that uses Pc and Wc, which are specific and local attributes of the selected RP. For specular returns, we expect high Pc’s and narrow Wc’s that are close to the expected half-width of the centroid of the range impulse response of the altimeter. The locations of the specular or quasi-specular returns are clearly seen in the distinct and localized concentration of high Pc and narrow Wc population in the top left corner of the joint distributions of the two parameters (figure 1). In the 3 years of CS-2 data, variability of the mode is small Wmodec=∼13.0−13.5 cm and Pmodec=43.7−45.8 dBf. The observed Wmodec can be compared to the centroid (Wc) of the modelled range impulse response of the SIRAL radar [25] of 12 cm. Here, we find those samples with Pc>40 dBf and those returns with Wc to the left of the slanted red line (in the distribution plots) to be specular returns to be suitable for use as sea surface reference (hSSH) for freeboard calculations. All these samples are used (i.e. none discarded) in future calculations. We illustrate the effectiveness of this approach below.

    A mean sea surface height (Inline Formula) is calculated for each 25 km segment (along-track) with at least three open water samples (hSSH); on average, between October and May (2011–2014), approximately 43% of the segments meet this criterion. We also compute the linear slope (tilt) in segments where the available samples span more than half the length (12.5 km) of the segment. The tilt of the sea surface (figure 1b), for the 3 years of CS-2 data, shows generally low surface slopes (less than 2 cm/10 km) over most of the Arctic. We also note that the observed surface tilts are sensitive to those areas with surface relief due to unmodelled geoid heights associated with deep ocean ridges (figure 1d). Figure 1e shows the consistency in Inline Formula and surface tilts of individual 25 km segments within a region in the central Arctic. Over three winters (2011–2013), the distributions of detilted ±RMS scatter of hSSH from all the 25 km segments in the monthly fields (figure 1f) show consistent values with a mean of approximately 2.5 cm. This provides a measure of the noise in the hSSH estimates. For those segments that do not meet the detilting requisites, Inline Formula is taken as the average of the available samples and segments with large surface tilts (more than 7 cm/10 km) are discarded.

    Sea ice freeboard (hfi), in the 25 km along-track segments, is determined as follows:

    Display Formula
    Display Formula
    where cs/c is the ratio of speed of light in snow and free space, and the dependence of this ratio on ρs is provided by equation (3.3) [26]. In the absence of a snow layer, the difference between the height of scattering surface ho and the local Inline Formula in equation (3.2) provides an estimate of hfi. With a snow layer of thickness hfs, however, two adjustments are needed to account for the displacement of the scattering surface away from the ice surface. δhp is the adjustment for scattering from the air–snow interface and the snow layer and is always negative as the scattering due to the air–snow interface/snow layer displaces the scattering centre towards the radar. δhd, due to the reduced propagation speed in the snow layer, adds to ho. We do not have any estimates of δhp for individual returns, and as simulations [7] suggest that the centroid retracker is less sensitive to snow layer effects, we take this parameter to be zero. That is, we take the RP to be the height of the sea ice surface. The thickness and bulk density of snow, in equations (3.2) and (3.3), are discussed next.

    (b) Snow depth and density

    Snow depth (hfs) and density (ρs) in equation (3.1) are computed as follows:

    Display Formula
    Display Formula
    We use the time- and space-varying snow depth and density, hWfs(X,t), from Warren et al. [27] but follow the approach by Laxon et al. [3] where they used a fraction (α) of the climatological snow depth to represent the reduced snow accumulation over FYI as suggested by available snow depth retrievals from OIB [28]. Here, hfs is dependent on the fractional coverage of FYI (fFY) from analysed fields of ASCAT data. Although Laxon et al. [3] used a fixed value of α=0.5, we use α=0.5 and α=0.7 in our analysis to examine the variability of our CS-2 thickness estimates when compared with other datasets. Snow density follows their monthly averages, Inline Formula, prescribed by Warren et al. [27].

    (c) Bulk density of sea ice

    The bulk density of sea ice (ρi) varies with ice type and thickness [29]. In FYI, the decrease is associated with brine drainage and growth rate processes, which reduce the volume fraction of the heavier brine entrained within the ice. Lower densities in MYI ice are due to the inclusion of proportionally less brine and more gas in subsequent summers, especially in the freeboard portion that is nearly low-density fresh ice. In the conversion to ice freeboard, the uncertainty in bulk density is a source of error and is introduced through the multiplier ρw/(ρwρi) in the first term of equation (3.1) (see different parametrizations in figure 2), which accounts for the larger fraction of the resulting ice thickness. Using the thickness-dependent density parametrization in Kovacs et al. [29] Inline Formula, Kwok & Cunningham [32] found a variability of 10 kg m−3 in ρi accounts for only approximately 10% of the variability in ice thickness. A recent investigation by Alexandrov et al. [31], however, found that uncertainty in ρi could be a more significant error source in the estimate of hi due to large expected difference in ρi between FYI and MYI. Based on measurements from the Sever Expedition prior to 1993, they suggest that the densities of FYI and MYI should be more appropriately: Inline Formula and Inline Formula. For the same freeboard, reducing ρi by 35 kg m−3 decreases the calculated ice thickness by more than 25%. Earlier studies [30] using AIDJEX measurements (1971–1972) also point to a stronger dependence of bulk density on thickness (compared to Kovacs [29]), and suggests a parametrization of the following form: ρi(hf)=−194hf+974, where Inline Formula.

    Figure 2.

    Figure 2. Dependence of ρw/(ρwρi) in equation (3.1) on the ice thickness using ice densities from Ackley et al. [30], Kovacs [29] and Alexandrov et al. [31].

    While it is clear that there should a dependence of ρi on thickness and ice type, it is difficult to reconcile the differences in ρw/(ρwρi) in the three parametrizations mentioned above (figure 2): the dependence of ρi on the actual age of the sea ice seems lacking. With the younger MY ice cover (less than 3 years) found in the Arctic in recent years [33], the mean Inline Formula may perhaps be different from that obtained from older MY ice from earlier decades. With that proviso and in order to assess the impact of different ice densities, we calculate our CS-2 ice thickness with one (i.e. Inline Formula) and with two bulk sea ice densities (Inline Formula and Inline Formula). For examination of variability, the one-density case will provide upper bounds while the two-density case the lower bounds in the estimated thickness and volume estimates. As with hfs, the bulk density is calculated using the fractional coverage of FY ice (fFY) from analysed fields of ASCAT data:

    Display Formula

    4. Assessment of CS-2 estimates

    As discussed in the previous section, the CS-2 surface elevations (between October 2010 and May 2014) are converted into four separate sets of thickness estimates using combinations of α(=0.5 and 0.7) and bulk sea ice densities (single and two). In subsequent calculations, we take ρw=1025 kg m−3. This section examines the differences between these four sets of CS-2 thickness estimates and available measurements from four sources: ice drafts from moored and submarine ULS, snow and ice thickness from AEM and sea ice thickness from NASA’s OIB. The locations of the in situ and airborne measurements are shown in figure 3a,b. The scatterplots, in figure 3cf, show comparisons with estimates from only one set of parameters (i.e. single density and α=0.7) as the visual differences between the scatterplots are minor. Table 1 summarizes the four comparisons as well as the results from Laxon et al. [3].

    Figure 3.

    Figure 3. Assessment of our CS-2 thickness estimates. Coverage of the in situ datasets in (a) 2011 and (b) 2012. Comparison of estimates with: (c) monthly average ice draft from four BGEP ULS moorings in the October–May periods between 2010 through 2013; (d) ice draft from the USS Connecticut (open circles) and USS New Hampshire (filled circles) in 2011; (e) AEM snow plus ice thickness from April 2011 (open) and 2012 (filled); (f) ice thickness from the OIB campaigns in March and April of 2011 (open) and 2012 (filled). Monthly BGEP ice drafts are compared with CS-2 estimates inside 200 km boxes centred at the location of each mooring. Gridded submarine, EM, and OIB measurements are compared with monthly CS-2 estimates on a common 25 km polar stereographic grid.

    Table 1.Differences (mean and s.d. in metres) and correlations between our CS-2 analysis and ice thickness/draft from four different sources. Scatterplots of the comparisons in bold are shown in figure 3.

    snow depth in seasonal ice
    ice density (kg m−3) source α=0.5 α=0.7 Laxon et al. [3]
    ρi=917 BGEP moorings—draft −0.14±0.29 (0.76) 0.06±0.29(0.79)
    submarine draft −0.14±0.47 (0.62) 0.07±0.44(0.62)
    EM (snow+ice) 0.00±0.88 (0.68) 0.12±0.82(0.67)
    IceBridge thickness −0.29±0.86 (0.56) −0.16±0.87(0.53)
    Inline Formula BGEP moorings—draft −0.19±0.29 (0.76) −0.00±0.28 (0.79) 0.08±0.24 (0.89)
    submarine draft −0.23±0.40 (0.60) −0.03±0.39 (0.59) n.a.
    EM (snow+ice) −0.64±0.71 (0.66) −0.53±0.71(0.64) 0.070.62 (0.70)
    IceBridge thicknessa n.a. n.a. 0.05±0.72 (0.61)

    aIceBridge data were processed with a constant ice density of 915 kg m−3.

    (a) Ice draft from BGEP mooring sites (October–May 2010 through 2013)

    Monthly BGEP ice drafts are compared with CS-2 estimates inside 200 km boxes centred at the location of each mooring (figure 3c). The BGEP time series, covering three different growth seasons (October–May), represents the most temporally extensive record for assessing the quality of CS-2 estimates. Comparisons with available data from 3 years yield comparable correlations (0.76 versus 0.79) but lower mean ice draft (−0.14/−0.19 m versus −0.06/−0.00 m) when α=0.5 instead of α=0.7 is used (table 1). As the moorings are located in a region of the Beaufort with predominantly FYI, differences are largely due to α which controls snow loading on FYI, and less to bulk ice density (approx. 0.06 m). Differences in the scatter (s.d.: 0.28 versus 0.29 m) are negligible. Overall, the agreement between the mooring and CS-2 ice drafts is better when α=0.7 is used. In this and following comparisons, we also note that a fraction of the scatter in the comparison is due to ice drift and to variability of ice thickness within the defined region of averaging.

    (b) Submarine ice draft (2011)

    Gridded submarine ice drafts are compared with monthly CS-2 estimates on a common 25 km polar stereographic grid (figure 3d). Ice drafts are from two cruises (USS Connecticut and USS New Hampshire) in March/April 2011. The correlations are comparable (0.59–0.62) but average ice drafts are biased (−0.14/−0.23 m versus 0.07/−0.03 m) when α=0.5 (versus 0.7) is used (table 1). These average differences are consistent and comparable with the moorings. This is not surprising as both submarine tracks were in areas of mostly FYI, with only a short segment of the USS New Hampshire track in a region of mixed FYI and MYI. The scatter of the differences is higher (ranges from 0.39 to 0.44 m) than in the comparison with the BGEP record. As above, use of α=0.7 yields better overall agreements between the submarine and CS-2 ice drafts.

    (c) Snow and ice thickness from AEM profiling (2011–2012)

    As with the submarine data, EM data (snow+ice thickness) are gridded before comparison with monthly CS-2 estimates (figure 3e). Ten surveys, with lengths ranging between 65 and 350 km, flown in April 2011 and 2012, provided measurements of combined snow+ice thickness over both FYI and MYI. With correlations of 0.64–0.68, the comparisons show a larger contrast in the average differences (0.00/0.12 versus −0.64/−0.53 m) between the estimates processed with one and two densities (table 1). Underestimation of the ice thickness in the two-density case is surprising, as we expected our estimates of ice thickness processed with two densities to be more comparable to in situ measurements that contain MYI samples. We also note that the spread in the differences are lower when two densities are used. Still, use of α=0.7 yielded better overall agreements in these comparisons.

    (d) Ice thickness from Operation IceBridge (2011–2012)

    The data from two OIB campaigns were acquired in two periods: 10 March–09 April 2011 and 16–28 March 2011 (figure 3f). Similar to the comparisons with the submarine and EM measurements, OIB thicknesses are gridded before comparisons with monthly CS-2 estimates. Since OIB data were processed with one density, we compare only the one-density estimates with each other (see tables 1 and 2). The correlations are lower (0.56/0.53) than the comparisons with other in situ measurements with the mean difference −0.29±0.86 m (α=0.5) and −0.16±0.87 (α=0.7). The increased scatter in the differences relative to the mooring, submarine and EM measurements, also noted by Laxon et al. [3], are unclear and a subject of future investigations.

    Table 2.Arctic Ocean sea ice thickness, volume and area in Oct (2010–2013) and May (2011–2014) calculated using one- and two-densities (Cases 1 and 2).

    Arctic basin
    Case 1 Case 2 Case 1 Case 2 Case 1 Case 1
    thickness (m)
    Oct 2010 1.26 1.06 0.91 0.84 1.91 1.47
    Oct 2011 1.16 0.99 1.02 0.93 1.43 1.10
    Oct 2012 1.28 1.07 0.96 0.90 1.79 1.36
    Oct 2013 1.40 1.14 0.91 0.84 2.18 1.63
    mean 1.27 1.07 0.95 0.88 1.83 1.39
    May 2011 2.34 2.13 2.19 2.05 3.82 2.95
    May 2012 2.23 2.07 2.14 2.02 3.48 2.69
    May 2013 2.23 2.05 2.07 1.97 3.60 2.79
    May 2014 2.46 2.20 2.20 2.06 4.02 3.03
    mean 2.32 2.11 2.15 2.02 3.73 2.86
    volume (km3)
    Oct 2010 6981 5846 3273 3000 3708 2846
    Oct 2011 5962 5094 3461 3172 2501 1922
    Oct 2012 5873 4932 2697 2522 3177 2410
    Oct 2013 8458 6911 3380 3103 5078 3809
    mean 6819 5696 3203 2949 3616 2747
    May 2011 16 432 14 997 13 923 13 060 2509 1937
    May 2012 15 842 14 664 14 066 13 294 1776 1371
    May 2013 15 810 14 537 13 156 12 485 2654 2052
    May 2014 17 499 15 594 13 364 12 477 4135 3117
    mean 16 396 14 948 13 627 12 829 2769 2119
    Ice Area (106 km2)
    Oct 2010 5.47 3.26 2.21
    Oct 2011 5.16 3.07 2.09
    Oct 2012 4.62 2.73 1.90
    Oct 2013 6.03 3.32 2.71
    mean 5.32 3.10 2.23
    May 2011 7.10 5.90 1.20
    May 2012 7.03 6.08 0.95
    May 2013 7.02 5.97 1.05
    May 2014 7.05 5.38 1.67
    mean 7.05 5.83 1.22

    5. Arctic Ocean CS-2 ice thickness/volume

    In this section, we examine the seasonal behaviour of Arctic Ocean sea ice thickness and volume in the present CS-2 record (2010–2014). Henceforth, we restrict our attention to the two sets of estimates processed with α=0.7/one-density (case 1) and α=0.7/two-density (case 2) because the above comparisons show that, for the choice of parameters used here, they yield better agreements with measurements. Even though the better overall agreement is obtained with one ice density, the two-density results serve to provide lower bound estimates recognizing that uncertainties in MYI density remain an issue in the calculation of thickness.

    In the following, we refer to the Arctic Ocean as that area bounded by the gateways into the Pacific (Bering Strait), the Canadian Arctic Archipelago (CAA), and the Greenland (Fram Strait) and Barents Seas (figure 4a, left panel). Within these boundaries, the Arctic Ocean covers a fixed area of approximately 7.23×106 km2. The spatial patterns of ice thickness and their distributions, and ice volumes for the eight months between October and May are summarized in figures 4 and 5. The 25 km gridded ice thickness fields (figure 4) represent the mean thickness of CS-2 retrievals that fall inside individual grid boundaries. Data gaps including the data hole around the North Pole are filled (following the interpolation procedure outlined in [4]). We also separate thickness and volumes into regions with predominantly MYI (MYI fraction>0.7) and FYI (MYI fraction<0.7); this provides contrast in the seasonal/interannual behaviour of sea ice in the MYZ (multiyear ice zone) and FYZ (first-year ice zone). The fields of MYI fractions (shown in figure 5a) used in these calculations are derived from ASCAT backscatter [18].

    Figure 4.

    Figure 4. Gridded 2 month sea ice thickness fields and their distributions. (a) 2010–2011, (b) 2011–2012, (c) 2012–2013 and (d) 2013–2014. Multiyear (MY) and first-year (FY) areas are delineated using the 70% MY concentration isopleth, and distributions are within the Arctic basin defined by the boundaries in top left panel. These fields are processed with: α=0.7 and single density.

    Figure 5.

    Figure 5. Seasonal (October–May) behaviour of ice thickness and volume in 2010–2014 computed using single and dual densities. (a) Multiyear sea ice fraction and (b) basin coverage from ASCAT. (c) Total and multiyear sea ice volumes within the Arctic basin. (d) Differences in total and multiyear sea ice volumes when ice thicknesses are computed using single and dual densities. (e) Changes in mean, MY and FY sea ice thickness between October and May. Arctic basin volume and thickness are computed within the boundaries in figure 4. See §5e for remarks on uncertainty in volume estimates.

    Below, we first discuss the variability seen in the one-density case (case 1) before addressing the differences between the two cases.

    (a) Seasonal and interannual variability

    As seen in the fields (figure 4), the spatial gradients in thickness follow a distinctive pattern across the Arctic basin with the thickest ice next to Ellesmere Island and the Greenland Coast, followed by a gradual thinning towards the central Arctic and coast of Siberia. Seasonal increases in thickness can be seen in the 4 year CS-2 fields and thickness distributions. The 4 year monthly mean ice thickness ranges from 1.27 m in October to 2.32 m in May (table 2). Over the same period in the 4 year record, the average seasonal thickness increases from 0.95 to 2.15 m in the FYZ, and from 1.83 to 3.73 m in the MYZ. The end of season (May) thickness of approximately 2 m in the FYZ is consistent with that seen in the BGEP mooring record [34]. However, the larger thickness increases (also approx. 2 m) in the MYZ (versus the FYZ) is somewhat of a surprise since the expected basal growth of thicker ice should be less than that over seasonal ice. We return to this in the next subsection. We also note the longer tails in the thickness distributions from the MYZ that are from higher freeboards due to thicker and rougher surfaces on the ice cover.

    Ice volume within a grid cell is the product (hcA) of the mean cell thickness (hc) and cell area (A) and the total volume is the volume sum of all grid cells within the Arctic Ocean. In the 4 year record, the mean Arctic Ocean ice volume is 6819 km3 in October and 16 369 km3 in May. For the FYZ, the average seasonal growth in volume is from 3203 to 13 627 km3. By contrast, a decrease from 3616 to 2769 km3 is observed in the MYZ. The mean monthly ice volume in the FYZ in May, 13 627 km3, is nearly five times the mean volume 2769 km3 stored in the MYZ. Mean ice production in the Arctic, minus ice export during the approximately eight months of the winter is 9577 km3, or equivalently approx. 1.33 m of sea ice growth over the Arctic Ocean. While there is an increase in FYI volume due to seasonal growth and deformation, there is a decrease in MYI volume of 847 km3. The decrease suggests that even though expected mean thickness in the MYI should increase as a result ice growth and deformation, volume loss due to sea ice outflow at the Fram Strait and other Arctic passages reduces this total volume present in the Arctic [4]. In the 4 year record, the seasonal decreases suggest that volume export exceeds ice volume production (i.e. growth) in the MYZ within the Arctic Ocean; this was also evident in the ICESat record [4].

    (b) Thickness and volume in multiyear ice zone

    In interpreting these thickness estimates, it should be recognized that they represent the mean of the large-scale thickness distributions, and thus the observed changes include contributions from both thermodynamics (ice growth) and dynamics (mechanical redistribution, i.e. rafting/ridging). In every year of the CS-2 record, a decrease in ice volume (October–May) in the MYZ is seen to accompany an increase in ice thickness. Since this increase in ice thickness could only be explained by convergence (rafting/ridging), a decrease in area of the MYZ area inside the Arctic should be evident. Indeed, examination of the MYZ area (from ASCAT) in the Arctic Ocean shows an average October–May loss of close to approx. 1.0×106 km2 (figure 5 and table 2). This can be seen in the compression of the MYZ north of the Greenland Coast and the CAA in all 4 years, and especially in the motion of the edge of the MYZ in 2011 and 2014 (figure 5a,b). Of course, only a fraction of the approximately 106 km2 is lost to compression; a larger fraction of MYI is exported every year in the outflow at the Fram Strait [35]. Average ice outflow at the Fram Strait between October and May is approximately 0.7×106 km2 (a fraction of which is MYI) [35]. Assuming 70% of the area exported is MYI (i.e. approx. 0.49×106 km2) and that the remainder of the total loss in MYI area (approx. 0.51×106 km2) is lost to the rafting/ridging of an MYI cover with an area of approximately 1.73×106 km2 (average of mean October and May coverage: table 2), the resulting MYI thickness would increase by approximately 41% (=β/(1−β), where βA/Ao). Thus, if we started with an initial ice thickness of 2 m, the resulting thickness would be approximately 2.82 m (=1.41×2 m) after convergence. Adding in approximately 1 m of expected basal growth in MYI [36], the end of the season thickness of approximately 3.82 m is close to what was observed (table 2). This is a rather rough calculation, but it nevertheless illustrates the effect of convergence observed ice thickness. Large convergence of the ice cover north of the Greenland Coast and CAA over a few short months after the summer of 2007 has been reported elsewhere [37], but this longer 4 year CS-2 record underscores the importance of ice deformation in maintaining the thick ice cover in the Arctic.

    (c) Two-density results

    As mentioned earlier, the two-density results were retained to provide lower bound estimates recognizing that uncertainties in MYI ice density remain an issue in the calculation of MYI thickness. As expected, the impact of using a fixed density for MYI is to lower ice thickness and volume for MYI (figure 5 and table 2). Overall, MYI thickness is reduced by approximately 0.25 m in October and by approximately 0.5 m in May. The effect on ice volume is proportional to MYI area coverage. For the three CS-2 years, the total volume is lowered by 1000–2000 km3 if a fixed MYI density were used.

    (d) Ice volume/thickness in autumn 2013

    The ice cover in 2013/2014 stands out in the mean CS-2 thickness fields (figures 4 and 5). The record of ice thickness and volume shows clearly that the ice cover in October of 2013 is higher than the previous 3 years and approximately 2500 km3 higher than that of the previous October. Certainly, the summer was cooler compared with the other years in the CS-2 record as seen in the anomalies in melting degree days (MDD); MDD is the cumulative sum of the mean daily 2 m air temperatures above freezing (figure 6a). Here, we also note the contribution of the convergence of the ice cover due to the unusual circulation pattern in the summer of 2013.

    Figure 6.

    Figure 6. Sea ice conditions during the summer of 2013. (a) Anomalies in melting degree days for (June–August) 2011, 2012 and 2013. (b) Mean (June–August) ice motion fields: decadal average (2004–2013), 2011, 2012 and 2013. (c) Ice area flux through gate (red) shown in (b). (d) Convergence of ice cover between June and August by back-propagation of boundaries of polygon (dashed line show net flux across the gate).

    Ice convergence associated with the atmospheric forcing in June–August 2013 (as indicated by SLP distribution) was remarkable (figure 6b). Compared to large-scale advection of sea ice towards the CAA in June–August of 2013, the average summer ice motion and sea-level pressure (SLP) distribution of the last decade and the previous 3 years show ice drift that is more moderate and parallel to the coast. In 2013, there was no turning of the ice away from the coast due to the relative location of the high- and low- pressure centres over the Arctic Ocean.

    As a measure of the large-scale advection of sea ice towards the CAA, we calculate the ice area advected across a flux gate that is nearly parallel to the coast of the CAA (figure 6b). Results for the three summers (in figure 6c) show that while the area flux across that gate were small for the summers (June–August) of 2011 and 2012, the total area advected towards the CAA in 2013 was more than 0.45×106 km2, with the largest contribution in June.

    In more detail, we examine the deformation of an area (Ao defined by the dashed line in figure 6d) next to the CAA. By back-propagation of the boundaries of that area using daily ice drift, we trace the boundaries to their locations (in June) and thus their coverage at an earlier time. The results (coloured regions) from tracing the dashed boundaries from the end of August back to the beginning of June show significant convergence in 2013 consistent with the area flux calculated at the gate (described above). In 2013, there was a 23.5% decrease in the area of the ice cover as it converged on the CAA coast. This suggests that the longer tail and thicker ice in the MYI thickness distribution in October 2013 (figure 4) are due to convergence as well as reduced melt in a cooler summer. Again, this underscores the importance of ice deformation in maintaining the thick ice cover in the Arctic, especially in the convergence region north of the Greenland coast.

    (e) Uncertainty in volume estimates

    Uncertainties in volume estimates stem from errors in thickness estimates. The error in an individual thickness estimate Inline Formula can be written as the sum of a bias term Inline Formula and a random term Inline Formula. Kwok et al. [2] noted that if the errors of individual thickness estimates (from 25 km segments) are uncorrelated and unbiased (i.e. Inline Formula, then the many thousands of retrievals that comprise a monthly volume estimate of the entire Arctic Ocean would result in very small uncertainties indeed. However, they also note that these assumptions are likely unrealistic as the space–time variability and the potential biases of the competing ice parameters used in the retrievals (e.g. snow depth, snow and ice density, etc.) have not been sufficiently quantified for analysis of the uncertainties in volume calculations using error propagation methodologies. Inline Formula is more complex and should be more appropriately be written with space–time dependence (i.e. Inline Formula); thus filling the gaps in our knowledge of the error characteristics of the parameters that contribute to this term is a challenge. For example, we have highlighted the differences in the volume estimates calculated using different densities of sea ice but the correct way to use the limited data on ice density remains an issue to be resolved. And, in this paper, we have elected to show the results using both the one- and two-density approaches as bounds in our volume calculations.

    An approach, the one taken here (§3), has been to use comparisons of the retrieved ice thickness with available measurements from aircraft and in situ campaigns to provide assessments of the bias Inline Formula and random (eh) terms. If we treated the sample mean and the standard deviation (σh) of the differences (in table 1) as the bias and random terms in the thickness error, we can compute volume errors Inline Formula as

    Display Formula
    where A=625 km2 and N=11 000 are the area and number of grid elements covering the Arctic Ocean. Taking the α=0.7/one-density case (table 1), Inline Formula ranges from −1100±57 km3 (OIB estimates) to 412±19 km3 (BGEP moorings). In these calculations, we have assumed that errors in the airborne and field measurements are small and so all the errors are attributed to the CS-2 retrievals. While this analysis is far from having Inline Formula, this provides a more realistic indication of the potential range of uncertainties of the estimates derived from available measurements, especially if the measurements represent samplings from diverse seasons and locales.

    6. Longer term records

    To place our CS-2 estimates in the context of longer term records of thickness and volume, we first compare the record of volume estimates from CS-2 and ICESat, and then the thickness estimates of the two satellite records with submarine analyses.

    (a) ICESat and CS-2 records (2003–2012)

    Ice volumes from ICESat reported in [4] and our CS-2 records, as well as the ice volumes reported by Laxon et al. [3] are shown in figure 7. Since the ICESat thickness estimates in Kwok et al. [4] were processed with a single ice density, we included the two-density estimates to show the lower bound in volume estimates if a lower MYI density were used.

    Figure 7.

    Figure 7. Arctic sea ice volume from ICESat and CS-2. Arctic sea ice volume is computed within the boundaries in figure 4. One-density (filled symbols) and two-density (open symbols) volume estimates and their trends are shown. See §5e for remarks on uncertainty in volume estimates.

    Prior to examining the two records, it is necessary to consider potential inter-satellite biases. One way to assess inter-satellite biases is to compare with consistent measurements that span both records. The best available time series is the ULS measurements from the BGEP moorings (table 1). Assessment of ICESat and our CS-2 estimates of ice draft from these moorings yield biases of 0.1 m [4] and 0.06 m (table 1), respectively. Laxon et al. [3] also considered inter-satellite biases between ICESat data (used here) and their CS-2 volume estimates by comparisons with common in situ datasets (table 1): they found a bias of 0.08 m when their CS-2 estimates were compared with those from the BGEP moorings. However, they are different for other in situ measurements. They conclude, and we agree, that present understanding of both the satellite and in situ data, each with their own potential biases and error characteristics, is insufficient to resolve any inter-satellite bias to a higher degree of certainty than what could be gleaned from these comparisons (e.g. table 1). We also note, as Laxon et al. [3] had, that if differences of approximately 0.1 m were representative and statistically homogeneous over the basin, then it would introduce a volume bias of approximately 700 km3 in our overall Arctic Ocean volume estimates.

    Except for the notable increase in volume in 2013, the short 4 years of CS-2 data do not show any particular trend (figure 7). The decline in ice volume between the two satellite periods is higher during the autumn (October–November). Taken together, this near decadal record (from ICESat-2 and CS-2) depicts losses in Arctic Ocean ice volume of 4170 km3/decade and 7760 km3/decade in winter (February–March) and autumn (October–November); these are more moderate trends compared with the steeper losses of 8620 km3/decade (February–March) and 12 370 km3/decade (October–November) in the ICESat record. Trends computed using the two-density estimates are 10–13% lower (figure 7).

    (b) Submarine, ICESat, and CS-2 records in the DRA (1980–2012)

    The combined submarine, ICESat and CS-2 data, within the data release area (DRA) of declassified submarine measurements (covering approx. 38% of the Arctic Ocean), are shown in figure 8. When Kwok & Rothrock [38] concatenated the ICESat thickness in the DRA with the regression of the submarine sonar data presented in Rothrock et al. [36], they found a decline in the winter thickness of 1.75 m from 3.64 m in 1980 to 1.89 m during the last winter of the ICESat record. In that record, the steepest thinning rate is −0.08 m yr−1 in 1990 compared to a slightly higher winter/summer rate of −0.10/−0.20 m yr−1 in the 5-year ICESat record (2003–2008). The two records show a long-term trend of sea ice thinning in the DRA.

    Figure 8.

    Figure 8. Average winter (February–March) and autumn (October–November) ice thickness in the DRA from regression of submarine data, ICESat, CS-2 estimates. (a) Coverage of the central Arctic by the DRA. (b) Decline in ice thickness between 1980 and 2014. Shaded areas show residuals in the regression and quality of the submarine data. One-density (filled symbols) and two-density (open symbols) thicknesses are shown.

    With our CS-2 record, the increase in ice thickness in the DRA during the 2013/2014 season is again notable. The overall thinning in ice thickness since the peak in the results of the submarine regression has not changed significantly during the winter (February–March); the mean ice thickness is close to 2 m. In autumn (October–November), the mean thickness seems to have increased from less than 1 m after the record minimum in ice coverage at the end of the summer of 2007. Still, the largest contrast is between the thickness in the 1980s and that observed during the latter half of the last decade.

    7. Conclusion

    We examined the variability in Arctic Ocean ice thickness and volume observed in our estimates of these parameters from 4 years of CS-2 data, and summarized their decadal-scale behaviour within the context of ICESat and earlier submarine records. In this section, we revisit the salient points in this paper.

    With the choice of parameters used in processing the CS-2 data, our best estimates of the mean ice thickness and draft are within 0.16 m of in situ and airborne measurements (fixed moorings, submarine, EM sensors, IceBridge). We showed the sensitivity of our estimates to ice density and to the assumed snow depth on FYI. The impact of MYI density is recognized. However, our reservations with using a fixed MYI density remains in that the younger MYI cover (less than 3 years) found in the Arctic in recent years [33] may perhaps be different from older MYI from earlier decades (in which the lower MYI density was based), and that the density of MYI may be more variable than expected. Further, there are unresolved issues in the estimation of thickness and volume from CS-2 data discussed in §3.

    In terms of sea ice processes, the importance of ice deformation (dynamics) in maintaining the thick ice cover in the Arctic Ocean is clearly seen in the monthly fields. In the four CS-2 seasons (October–May), the signature of ice deformation is evident in the simultaneous increases in MYI thickness, and decreases in the areal coverage and volume of MYI. In addition to a cooler summer, atmospheric circulation and ice drift in the summer of 2013 suggest that ice deformation also played a role in creating the notably thicker ice cover (volume higher by approx. 2500 km3) found in the following October. The large-scale advection of sea ice towards the Canadian Arctic Archipelago and the large regional convergence during the summer seen in the ice drift, indicate significant deformation (rafting/ridging) that is evident in the tail of the thickness distribution in October of 2013.

    Except for the notable increase in volume in 2013, the short 4 years of CS-2 data do not show any observable trend. Together with the ICESat retrievals, the CS-2 record to-date depicts losses in Arctic Ocean ice volume of 4170 km3/decade and 7760 km3/decade in winter (February–March) and autumn (October–November). These are more moderate trends compared with the steeper losses of 8620 km3/decade (February–Mar) and 12 370 km3/decade (October–November) from ICESat [4], which are weighted by the record-setting ice extent after the summer of 2007 near the end of the ICESat record.

    In the DRA of declassified submarine measurements, the overall thinning of sea ice since the 1980s has not changed significantly during the winter (February–March). In autumn (October–November), the mean thickness seem to have increased from the less than 1 m at the end of the summer of 2007. No particular trend can be inferred from the short CS-2 record.


    R.K. and G.F.C. carried out this work at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


    One contribution of 9 to a discussion meeting issue ‘Arctic sea ice reduction: the evidence, models and impacts (part 1)’.