2.1 ICESat-2 (IS-2) freeboards

The Advanced Topographic Laser Altimeter System (ATLAS) on board ICESat-2 uses three beam pairs to profile the surface. The pairs are separated by about 3.3 km cross track. Each pair consists of a strong and a weak beam with an inter-beam spacing of 90 m. The pulse energies of the strong beams are ∼ 4 times that of the weak. Each beam profiles the surface at a pulse repetition rate of 10 kHz and footprints of ∼ 14 m (Neumann et al., 2019). Along-track freeboards are from the ICESat-2 ATL10 products (Release 002) from the National Snow and Ice Data Center (Kwok et al., 2019b). The ATL10 product provides sea ice freeboard estimates – with a variable along-track resolutions (∼ 27 to 200 m) – in 10 km segments that contain a sea surface reference. Local sea surface references (h_ref) (i.e., the estimated local sea level) are from available sea ice leads within a 10 km segment. Freeboard heights (h_f) are the differences between surface heights (h_s) and the local sea surface reference (i.e., $h_{\text{f}}=h_{\text{s}}-h_{\text{ref}}$). For individual beams, freeboard profiles are calculated with sea surface references from that beam with no dependence on estimates from other beams. In ATL10, freeboards are calculated only where the ice concentration is > 50 % and where the height samples are at least 25 km away from the coast (to avoid uncertainties in coastal tide corrections). Details of the sea ice algorithms can be found in Kwok et al. (2019a) and an early assessment of surface heights can be found in Kwok et al. (2019c). Only the freeboards from the strong beams are used in the following analyses, and cloud-contaminated retrievals are also not used. We note that, in the IS-2 data set used here, there is a 1-month gap in coverage (July) indicated in the figures due to a spacecraft anomaly and that data are only available for the first 2 weeks of November 2019 in this release of the IS-2 data set. Uncertainty in IS-2 freeboard retrievals is ∼ 2–4 cm based on assessment in Kwok et al. (2019c).

2.2 CS-2 radar freeboards

Along-track CS-2 freeboards are derived using the procedure in Kwok and Cunningham (2015), which contains a detailed description of the retrievals and an assessment of these freeboard estimates in the Arctic. The pulse-limited footprint of the CryoSat-2 synthetic aperture radar altimeter is approximately 0.31 km by 1.67 km along- and across-track. Freeboards are retrieved for individual returns but the derived CS-2 freeboards used here have been averaged to 25 km resolution and weighted by AMSR-derived ice concentration. As there are no large-scale assessments of these freeboard estimates, only comparisons with available ice thickness measurements from variety of sensors (e.g., upward-looking sonars, airborne lidars, and airborne electromagnetic profilers) provide an indirect measure of quality. Noting that freeboard is approximately one-ninth of ice thickness (due to the density contrast between, ice and seawater) differences between CS-2 and various thickness measurements in the Arctic in Kwok and Cunningham (2015) are as follows: 0.06 ± 0.29 m (ice draft from moorings), 0.07 ± 0.44 m (submarine ice draft), 0.12 ± 0.82 m (airborne electromagnetic profiles), and −0.16 ± 0.87 m (Operation IceBridge).

Figure 1Naming of the sea ice sectors used in the paper.

3.1 Interpretation of time-varying IS-2 and CS-2 freeboards

Since this is the first large-scale examination of the combined IS-2 and CS-2 freeboards of the Antarctic ice cover, it is worthwhile reviewing the key processes that contribute to regional-scale freeboard changes. This will aid in the interpretation of the observations. As a reminder, the changes in total freeboard (Δh_f) are the sum of the changes in thickness of the snow layer (Δh_fs) and changes in ice freeboard (Δh_i), i.e., $\mathrm{\Delta }{h}_{\text{f}}\left(t\right)=\mathrm{\Delta }{h}_{\text{fs}}\left(t\right)+\mathrm{\Delta }{h}_{\text{i}}\left(t\right)$ (Fig. 2). In the winter Arctic, there are three key processes that contribute to the changes in total freeboard: basal growth, ice deformation, and snow accumulation and redistribution. Since the Arctic Basin exports only ∼ 10 % of its area annually (mainly through the Fram Strait; Kwok et al., 2013), there is relatively little melt in winter away from the ice margins. Therefore, it is simpler to observe a coherent seasonal cycle of freeboard growth over a fixed region of the Arctic Basin (i.e., the correlated increases in both the IS-2 and CS-2 freeboards seen in Kwok et al., 2020). In the Antarctic, however, the heavier snowfall (Massom et al., 1997), ice production in large coastal polynyas (Drucker et al., 2011), formation of snow ice (Jeffries et al., 2001; Maksym and Markus, 2008), larger ice divergence (i.e., production of areas of open water) than the Arctic, wind-blown redistribution of the snow cover including losses into leads (Andreas and Claffey, 1995; Massom et al., 1997, 1998), and the continuous large-scale export of sea ice towards the ice margins (where the ice melts) (Kwok et al., 2017) add complexity to the interpretation of the seasonal evolution of freeboards.

Below, we briefly summarize five key processes that contribute to the modification of the total freeboard (h_f) of a drifting ice parcel during the Antarctic winter. Separating the contributions from the snow (h_fs) and ice layers (h_fi), we write

α and β are scale factors, and signs indicate the addition or removal of height from these layers. The δh values are described below.

1. Snowfall (δh_snow). Precipitation minus evaporation (P-E) adds to the snow layer and the loading depresses the ice freeboard by −αδh_snow. α is a fractional value, and in this case it is dependent on the densities of ice, snow, and seawater.

2. Spatial redistribution of snow including loss into leads (δh_ϕ). Snow is redistributed due to wind stress and is sometimes lost into open leads (δh_ϕ); the ice freeboard adjusts hydrostatically by −αδh_ϕ.

3. Snow ice formation. When sea water infiltrates the snow layer during flooding, the refrozen ice layer becomes part of the ice freeboard and results in a loss of δh_sti from the snow layer (i.e., the snow pack settles when flooded) and a gain of βδh_sti by the ice freeboard. β represents the fraction of the snow thickness that is converted to ice freeboard after the transformation process.

4. Ice deformation (convergence and divergence of the ice cover). Mechanical redistribution due to convergence and divergence of the ice cover tends to increase and decrease, respectively, the area-averaged thickness of the snow layer ($\mathit{\delta }{h}_{\text{def}}^{\text{s}}$) and ice freeboard ($\mathit{\delta }{h}_{\text{def}}^{\text{i}}$). The relationship between $\mathit{\delta }{h}_{\text{def}}^{\text{s}}$ and $\mathit{\delta }{h}_{\text{def}}^{\text{i}}$ may be more complicated and is hence written separately.

5. Basal ice growth and melt (δh_gm). The growth and melt of sea ice adds and removes from the ice freeboard and increases and decreases the total freeboard, respectively.

This brief summary is a simplification, as there are higher-order processes such as changes due to snow metamorphism, but their area-averaged contributions to freeboard changes are likely to be small. Another factor (noted above) to bear in mind in the interpretation of regional variability of freeboard (below) is the advective change and sea ice melt at the margins.

Figure 3Monthly composites of IS-2 freeboard (h_f), CS-2 freeboard $\left(h_{\text{fi}}^{\text{CS2}}\right)$, and derived snow depth $\left(h_{\text{fs}}^{\mathrm{\Delta }f}\right)$ for the period between April and November 2019 (25 km grid; in cm).

3.2 Monthly composites IS-2 and CS-2 freeboards

Figure 3 shows the monthly composites of IS-2 and CS-2 freeboards for April through November 2019. The associated freeboard distributions are shown in Fig. 4. The numerical values and sample statistics of the monthly distributions are in Table 2. We examine freeboard distributions of the seven sectors in the following order: Amundsen–Bellingshausen (A-B), coastal Amundsen–Bellingshausen (CoA-B), East Weddell and West Weddell (E-Wedd, W-Wedd), Ross, Pacific Ocean, and Indian Ocean.

3.2.1 Amundsen and Bellingshausen seas sectors (A-B and CoA-B)

The freeboard distributions of the Amundsen and Bellingshausen seas between the Antarctic Peninsula and 140^∘ W are constructed with samples from two sectors (Fig. 4a and b): one lies between coastal Antarctica and 70^∘ S (referred to as the CoA-B sector) and the other has an open boundary to include the seaward extent of the advancing winter ice edge (A-B sector).

For the 8 winter months, the highest variability (amongst the seven sectors) is seen in the CoA-B sector, where the area-averaged IS-2 and CS-2 freeboards range from 29.2 ± 16.6 (min) to 54.0 ± 32.5 (max) cm and 11.2 ± 6.03 to 15.6 ± 6.83 cm, respectively. The squared correlation (ρ²) between the two freeboards of 0.90 (Fig. 4c) – the highest of all seven sectors – indicates that the co-variability may be attributable to responses to the same forcing. Indeed, examination of the monthly maps of ice drift (Fig. 5) suggests that the correlated increases in the two freeboards is likely due to the persistent wind-driven convergence of sea ice against the Antarctic coast (west of 90^∘ W). The resulting ridging in the coastal Amundsen Sea ice cover resulted in a redistribution of the thinner ice into thicker categories. This simultaneously increases both the lidar and radar freeboards. The anomalous on-shore ice drift in 2019 (Fig. 5b) can be contrasted to the mean ice drift pattern for the period 2012–2019 (Fig. 5a). The large-scale atmospheric pattern in 2019 shows the location and depth of the Amundsen Sea Low (ASL) centered in the northeast Ross Sea (Fig. 5b). The atmospheric pattern in 2019 is such that on-shore wind is nearly perpendicular to the coast and the depth of the ASL can be seen in the density of the isobars. The longer tails of the freeboard distributions seen after May are also signatures of ice convergence, where snow accumulation would be unlikely to affect the tails of both distributions, i.e., ice freeboard tends to be anti-correlated to snow accumulation. Hence, the freeboard variability here seems to be dominated by wind-driven ice deformation, which masked the signal of other processes.

For the A-B sector (which includes the CoA-B sector), the seasonal signal is more muted. The IS-2 and CS-2 freeboards range from 25.3 ± 17.8 to 38.2 ± 25.0 cm and 9.53 ± 5.78 to 11.1 ± 6.26 cm and are lower because of the thinner seasonal ice cover away from the coastal zone (CoA-B). The squared correlation (ρ²) between the two freeboards of 0.43 (Fig. 4c) is also likely connected to the large signal in the CoA-B sector in the south. In November, the increase in the IS-2 freeboard not seen in the CS-2 freeboard is potentially due the limited 2-week IS-2 coverage.

Figure 4Monthly distributions of (a) IS-2 (h_f) and (b) CS-2 $\left(h_{\text{fi}}^{\text{CS2}}\right)$ freeboards for the period between April and November 2019. Their monthly means are compared in (c). Numerical values in the line plots show the squared correlation between the two freeboards (distributions are normalized).

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3.2.3 Ross Sea sector

Significant ice production occurs in this sector (between 140^∘ W and 160^∘ E). New ice production in the Ross Sea is located primarily in the Ross Shelf Polynya and the Terra Nova Bay (TNB) and McMurdo Sound polynyas. Annual ice production here (south of the 1000 m isobaths) is higher than that in the Weddell Sea (Drucker et al., 2011). The average annual ice area export in a 34-year record is 0.75×10⁶ km² (at a flux gate along the 1000 m isobaths that parallels the ice front of the Ross Sea Ice Shelf). The ∼ 1400 km flux gate encloses an area of $\sim \mathrm{490}\times {\mathrm{10}}^{\mathrm{3}}$ km² to the south. On average, the southern Ross Sea exports more than its area of sea ice that is largely produced in the polynyas.

In all months of 2019, the signature of thinner sea ice with lower freeboards exported from the polynyas can be seen as a distinct tongue that extends seaward then westward beyond the Ross embayment in both the IS-2 and CS-2 freeboards composites (Fig. 3). The spatial features are consistent with the cyclonic (clockwise) drift pattern, centered over the northeastern Ross Sea associated with the ASL, in all months between June and September (Fig. 5b). The drift pattern shows a coastal inflow of thicker sea ice into the Ross Sea from the Amundsen Sea in the east that is distinctly thicker than the outflow of thinner ice from the southern Ross Sea. North of Cape Adare in the northwestern corner of the Ross Sea, the northward drift splits into two branches, with one that moves westward into the Somov Sea and another that moves northeastward before it gets entrained in the Antarctic Circumpolar Current (ACC).

Table 1Dependence of number of retrievals on space–time separation. November is not included here because the IS-2 data (Release 002) covered only half the month.

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The IS-2 and CS-2 freeboards range from 13.8 ± 6.45 to 23.0 ± 13.6 cm and 6.78 ± 2.81 to 9.35 ± 4.00 cm, respectively (Fig. 4c, Table 1). Both freeboards show a gradual increase, with a peak in the IS-2 freeboard during August, likely due to overlapping coverage of the ice convergence events by the A-B (discussed above) and Ross sectors and due to inflow of the thicker deformed ice from the A-B sector. The squared correlation (ρ²) between the two freeboards of 0.88 (Fig. 4c), comparable to that in the CoA-B sector, is likely due to the continual production of thin ice in the polynyas, the growth of the thin ice as it is advected northward, and the northward drift and growth of the sea ice from the A-B sector.

3.2.4 Pacific Ocean and Indian Ocean sectors

The Pacific Ocean and Indian Ocean sectors are located between 90^∘ E and 160^∘ W and 15 and 90^∘ E, respectively. Except for the larger extent of the ice cover in the Indian Ocean sector (around 15 and 40^∘ E), where the winter edge extends into the South Atlantic and Indian Oceans, the ice cover occupies a very narrow band that extends only ∼ 400 km seaward at its maximum extent. In 2019, associated with the location of the Davis Strait Low (DSL) pressure pattern (Kwok et al., 2017), there is an average westward ice drift in both sectors in all months that is consistent with that seen in the mean 2012–2019 drift patterns (Fig. 5a). The Pacific Ocean sector ice cover is composed of mainly seasonal ice formed locally and fed by coastal polynyas and outflows from the Ross Sea. Similarly, the Indian Ocean sector is largely seasonal ice grown locally and in coastal polynyas and coming from the Pacific Ocean sector.

Figure 5Monthly mean (April through November) ice drift in the Southern Ocean for (a) 2012–2019 and (b) 2019.

The behavior of the freeboards in both sectors is similar (except for in magnitude) (Fig. 4). The higher IS-2 and CS-2 freeboards (though less pronounced in the CS-2 freeboards) in April–May are from a small population of sea ice adjacent to the coast (see Fig. 3). Broadly, we find it difficult to explain the source of higher freeboard sea ice in both sectors early in the growth season. The behavior of higher freeboards of both the IS-2 and CS-2 freeboards are consistent – the squared correlations (ρ²) between them are 0.55 and 0.64 in the Pacific Ocean and Indian Ocean sectors, respectively. From a retrieval perspective, we also note that the heights of the local sea surface estimates near the ice edge are affected by sea state, likely due to scattering from the troughs of waves propagating into the ice cover. This effect is predominant in the Pacific and Indian Ocean sectors because of the smaller sea ice extent. The consequence is surface heights that may be tens of centimeters below the local mean sea level, resulting in higher freeboards. We have filtered most of these anomalous freeboards (visually) in the IS-2 and CS-2 processing, but some are still present.

In general, the behavior of the sea ice cover in the Pacific Ocean and Indian Ocean sectors resembles that of the E-Wedd sector, with the lowest end-of-season IS-2 and CS-2 freeboards. The thinner seasonal ice dominates the behavior of the mean freeboards in all months (Fig. 3). The lowest CS-2 freeboards are found in the Indian Ocean sector in November (5.77 ± 2.88 cm). The CS-2 freeboards remained within a narrow range after May, the lowering of the IS-2 freeboards over the winter months suggests a balance of the different processes discussed above. Again, it is difficult to resolve these processes at the regional scale that the data is being examined at in this paper.

4.1 Snow depth from freeboard differences

We follow the procedure detailed in Kwok et al. (2020) (henceforth K20) using a layered geometry depicted in Fig. 2. A layer of snow ice, an important component of the Southern Ocean ice cover, is included and assumed to have the same bulk density as sea ice. In our simplification, the snow ice layer is considered to be part of ice layer (h_i) and indistinguishable from sea ice insofar as mechanical loading or hydrostatic equilibrium is concerned; this is necessitated by our lack of knowledge on how to effectively model the snow ice formation process. The snow depth (h_fs) can thus be expressed as the difference between the total freeboard (h_f) from IS-2 estimates and sea ice freeboard (h_fi):

The snow depth $\left(h_{\text{fs}}^{\mathrm{\Delta }f}\right)$ is then given by

assuming that the scattering from the snow ice interface dominates the returns at K_u-band wavelengths (CS-2 altimeter). With one free parameter, η_s, this equation relates snow depth to the IS-2 and CS-2 freeboard differences (i.e., the two observables here): η_s is the refractive index at K_u-band, ${\mathit{\eta }}_{\text{s}}=c/c_{\text{s}}\left({\mathit{\rho }}_{\text{s}}\right)$ (Ulaby et al., 1986); c is the speed of light in free space; and ρ_s is the bulk snow density. Equation (3) accounts for the reduced propagation speed of the radar wave (c_s) in a snow layer with bulk density ρ_s. At temperatures below freezing, the lidar and radar returns can be assumed to be from the air–snow and snow–ice interfaces, respectively, and thus they provide observations of total and ice freeboards. The validity and shortcomings of this assumption and its implications are discussed in Sect. 6. A bulk snow density of 320 kg m⁻³ is used in all our calculations. There is no generally accepted value for the bulk density of snow in the Antarctic. Massom et al. (2001) suggest 200–300 kg m⁻³ under cold and dry conditions and higher density (320–500 kg m⁻³) for warm and windy conditions, which is not unlike the Arctic. Below, we elected to use an average winter bulk density of 320 kg m⁻³ (like that of the Arctic) but with a higher variability of 70 kg m⁻³ to cover the range of conditions.

4.1.3 Ice deformation

The episodic and localized nature of ice deformation and the impact of this process on differencing freeboards separated in time are discussed in K20. Here, we provide a brief summary. The time order of freeboard sampling has an asymmetric effect; i.e., the impact of a convergence or divergence event separating the freeboard samples would be different. If the selected CS-2 freeboard precedes an IS-2 freeboard in time, the snow depth would be overestimated (underestimated) if a convergence (divergence) event occurred in the interim. If the selected CS-2 freeboard is from a later time and a convergence (divergence) event occurred in between, the snow depths would be underestimated (overestimated). Also note is that the loss of snow during a convergence event may have a confounding effect. Here, the selected CS-2 freeboards are centered on the time of the IS-2 samples; hence, random events around that center time would increase the snow depth variance but would have a small impact on the average monthly snow depth. These results, discussed in the previous section, suggest that the effect of sea ice deformation in biasing the snow depth estimates may be small. For the six combinations of space–time sampling of the two freeboards, the variability in retrieved snow depths was less than a centimeter.

Table 2Monthly mean (standard deviation) of IS-2 freeboard (h_f), CS-2 freeboard $\left(h_{\text{fi}}^{\text{CS2}}\right)$, and derived snow depth $\left(h_{\text{fs}}^{\mathrm{\Delta }f}\right)$.

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4.2 Snow depth estimates in 2019

The monthly snow depth composites and their distributions are shown in Figs. 3 and 6a, respectively. Table 2 shows the numerical values. Due to the low variability of the CS-2 freeboards, the spatial pattern of the snow depth estimates and the IS-2 freeboards are highly correlated in all the sectors (ρ>0.95 – see Fig. 7). Here, we summarize the spatial features of note. A more in-depth discussion of the relationship between snow depth and freeboard can be found in the next section, and an assessment of the quality of the snow depth estimates (whether they are biased) is given in the following section and Sect. 5, where these estimates were used to calculate ice thickness.

The thickest snow is seen in the W-Wedd sector (sector mean of 22.8 ± 12.4 cm in May) and the CoA-B sectors (31.4 ± 23.1 cm in September). With the multiyear sea ice cover in the W-Wedd sector, thicker snow is expected. The thinnest snow is found in the Ross (7.35 ± 4.30 cm in April) and E-Wedd (8.21 ± 5.81 cm in June) sectors. The thinner snow depth in the Ross sector is likely due to the extensive coverage by thin and young ice exported from the active Ross Sea polynyas, and in the E-Wedd sector this is likely due to the large seasonal ice cover. Lower snowfall rates may also contribute to these results (Cullather et al., 1998; Toyota et al., 2016). The spatial patterns show consistent thinning of the snow cover towards the ice margins almost everywhere and in all months; we see no spatial anomalies in snow depth near the ice edge that are expected of higher precipitation. Except for coastal zones with active polynyas (e.g., southern Ross and Weddell seas), snow depth is generally higher in coastal zones.

Figure 6Monthly distributions of (a) derived snow depth $\left(h_{\text{fs}}^{\mathrm{\Delta }f}\right)$ and (b) ice thickness (h_i) for the period between April and November 2019 (distributions are normalized).

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Figure 7Monthly relationship between snow depth and freeboard. Parameters from the regression analysis (slope, intercept, correlation coefficient, and standard error) are shown in the top-left corner of each panel.

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Seasonal increases in the monthly mean snow depth are seen only in the A-B and CoA-B sectors. In the CoA-B sector, the increase is ∼ 13 cm (approximately half that of the IS-2 freeboard increase) over the 8 months. This is likely due to precipitation delivered by the on-shore wind pattern linked to the location and depth of the Amundsen Sea Low (ASL) discussed earlier. In all other sectors, we find slowly varying snow covers between April and November, similar to the observed behavior of IS-2 and CS-2 freeboards. This is quite remarkable and suggests the processes that remove snow from the surface (e.g., snow ice transformation, loss into leads, divergence) must be significant and overwhelm all precipitation signals in all months. Consequently, an in-depth study of these processes will be important for understanding of the behavior of the Antarctic snow cover.

4.3 Relationship between freeboard and snow depth

K20 examined the relationship between freeboard and retrieved snow depth for the Arctic ice cover. This is of geophysical interest as the connection could be potentially utilized to provide rough estimates of snow depths where there are gaps in CS-2 observation. Figure 7 shows the monthly scatterplots of $h_{\text{fs}}^{\mathrm{\Delta }f}$ and Antarctic IS-2 freeboard for the 8 months between April and November. At the length scale of 25 km, the regression analysis (slope, intercept, and standard error in each plot) of the monthly fields shows that the two values are highly correlated (with the freeboard explaining > 90 % of the variance in snow depth); this is not entirely surprising as snow depth is derived from IS-2 freeboard. The regression slopes vary between 0.66 and 0.70 between April and November. For this Antarctic winter at least, the results suggest that between 66 and 70 % of the IS-2 freeboard is snow. This can be contrasted with the 2019 Arctic winter (K20) where snow occupies a lower fraction or ∼ 50 %–55 % of the IS-2 freeboard.

The negative intercepts of between −3.4 and −4.5 cm are worth noting, as one should expect (by definition) zero snow depth at near-zero IS-2 freeboard. The consistent values of the monthly intercepts suggest that one of the estimates may be biased. Here, we write

where ${\widehat{h}}_{\text{fs}}$ is the snow depth estimate and α and β are the regression slope and intercept. If zero snow depth is expected at zero total freeboard, then an unbiased estimate of snow depth (h_fs) can be written as

where δ is the bias. To obtain the true unbiased estimate of snow depth (h_fs), an adjustment of ${\widehat{h}}_{\text{fs}}$ by δ (or −β) is needed. The negative intercepts observed in the scatterplots imply that ${\widehat{h}}_{\text{fs}}$ is overestimated by +3.4 to +4.5 cm.

One likely source of these biases is the displacement of retracking point (RP) of the radar altimeter (CS-2) away from the snow–ice interface, resulting in higher CS-2 freeboards (Kwok, 2014). At K_u-band frequencies (CS-2), the RPs are displaced from the true ice surface when elevated snow salinities (due to brine-wicking, flooding) are found near the snow–ice interface or because of changes in scattering in the presence of moisture in the snow layer when air temperature warms (Winebrenner et al., 1994). For Antarctic sea ice in particular, the salinity of snow layer was characterized by Massom et al. (1997) to include two components: (1) a “background” salinity < 1 in the upper part of the snow column, likely contributed by blowing snow due to wicked salt, aerosol, or sea spray transported during strong winds over adjacent leads and polynyas, and (2) a high-salinity (> 10) basal component (0–3 cm), which is sometimes damp due to brine-wicking when the snow is thin or associated with flooding of the snow interface. It is the basal-layer salinity that has a large impact on CS-2 freeboards. Massom et al. (1997) also noted that basal salinities exceeding 10 commonly occur under relatively thin snow covers when brine is available at their surface for vertical uptake into an accumulating snow layer.

The displacement of the RPs above the snow-ice interface from radar penetration experiments in the field has been reported in a number of publications (Willatt et al., 2010, 2011). Using salinity profiles from snow pits (collected in the Canadian Arctic Archipelago) to drive a scattering model, Nandan et al. (2017, 2020) prescribed a nominal adjustment (δ) of ∼ 7 cm of the RP from first-year ice throughout most of the year. Kwok and Kacimi (2018), in an analysis of data from CS-2 and OIB, also reported consistently higher CS-2 radar freeboards along an airborne transect of the Weddell Sea.

K20 showed that an adjustment of the snow depth (δ), due to the displacement of the scattering surface, would decrease the ice thickness estimates by

A 7 cm adjustment results in a reduction in the estimated ice thickness of −0.37 m. The physical basis of a displacement of the RP due to brine wicking is sound, but a better understanding of the time evolution of these processes and the magnitude of this adjustment is needed if these corrections are to be applied to individual freeboard estimates. This will be addressed in more detail in the discussion of thickness calculations in the next section.

5.1 Ice thickness and sector volume

We calculate two ice thicknesses: (1) h_i, using snow depth from altimeter freeboards, and (2) $h_{\text{i}}^{\mathrm{0}}$, by setting snow depth equal to the total freeboard

In the first equation, we assume that the radar-derived surface is from the snow–ice interface. The ice thickness, $h_{\text{i}}^{\mathrm{0}}$, in the second equation sets a lower bound on the thickness estimates for a given total freeboard of h_f, with assumed densities of water, snow, and ice (ρ_w=1024 kg m⁻³, ρ_s=320 kg m⁻³, ρ_i=917 kg m⁻³). When flooding and snow ice formation occur and the ice freeboard is zero, an estimate of total freeboard (i.e., snow depth) can be used to estimate ice thickness (given reasonable values for snow and ice densities).

Ice volume for each Antarctic sector is simply the product of the average thickness ${\stackrel{\mathrm{‾}}{h}}_{\text{i}}$ and area A_sec of each sector,

To examine the potential impact on ice volume due to biases in CS-2 freeboards due to salinity effects, we write

where δ is the adjustment factor that accounts for the displacement of the CS-2 freeboard above the snow–ice interface discussed in Sect. 4.3.

Figure 8Monthly composites of calculated ice thicknesses: (a) h_i, using snow depth from freeboard differences $\left(h_{\text{fs}}^{\mathrm{\Delta }f}\right)$, and (b) $h_{\text{i}}^{\mathrm{0}}$, assuming zero ice freeboard, i.e., h_fs=h_f, for the period between April and November 2019. (25 km grid; in meters).

Figure 9Monthly distributions of calculated ice thicknesses: (a) h_i, using snow depth from freeboard differences $\left(h_{\text{fs}}^{\mathrm{\Delta }f}\right)$, and (b) $h_{\text{i}}^{\mathrm{0}}$, assuming zero ice freeboard, i.e., h_fs=h_f, for the period between April and November 2019. Their monthly means are compared in (c) (distributions are normalized).

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5.2 Monthly ice thickness (April–November)

The monthly thickness composites (h_i and $h_{\text{i}}^{\mathrm{0}}$) and their distributions are shown in Figs. 8 and 9, respectively, and the numerical averages are in Table 2. Again, the spatial patterns of the thickness composites are very similar to that of the freeboards and snow depth, and so here we note only the features and differences.

As expected, the thickest ice is found in the W-Wedd sector (mean 2.50 ± 1.08 m in May) and the CoA-B sector (3.25 ± 1.71 m in September). These are also sectors where the highest snow depths are found. The thinnest ice is in the Ross (0.90 ± 0.41 m in April) and E-Wedd (< 1.5 m for all months) sectors. The tongue of lower ice thickness in the Ross sector (Fig. 8) is a clear signature of the outflow of thin and young ice produced in the Ross Sea polynyas. Similarly, for the E-Wedd sector, the large expanse of thinner seasonal ice is also evident. Consistent thinning towards the ice margins is seen almost everywhere and in all months.

The seasonal cycle of ice thickness is surprisingly weak. Seasonal increases in the monthly mean ice thickness are only evident in the A-B and CoA-B sectors. Notably, in the CoA-B sector, the increase in ∼ 1 m (from 1.85 ± 1.11 m in April to 2.94 ± 1.43 m in November) over the 8 months discussed earlier, is connected to coastal ice convergence (the mechanical redistribution of thin to thicker ice) associated with persistent on-shore wind pattern in 2019. In all other sectors, we find either decreases or relatively unchanging thicknesses (i.e., weak seasonality) from April to November.

Figure 10Comparison of seasonal ice thickness calculated with δ=0, 3 and 6 cm, and assuming zero ice freeboard (i.e., h_fs=h_f) with shipborne measurements in Worby et al. (2008).

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Figure 11Evolution of the volume and area of the Antarctic sea ice cover between April and October 2019.

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There are no seasonally and regionally diverse data sets from field observations that could be used to assess the large-scale satellite retrievals. Field observations of ice thickness are from two main sources: shipborne observations and mechanical drilling profiles. The most extensive compilation of Antarctic ice thickness is from the ASPeCt database reported in Worby et al. (2008), it contains data from 83 voyages and 2 helicopter flights for the period 1980–2005. Figure 10 compares our thickness estimates with the ASPeCt data summarized in Worby et al. (2008). For all seasons and sectors, the overall ice thickness in the ASPeCt data (circles in Fig. 10) is less than half the mean thickness in our estimates (solid blue line). There are two reasons these data sets are not comparable: (1) the ASPeCt data are biased towards thin and level ice types and (2) few of the ASPeCt data have been collected at a similar time and location; indeed, ASPeCt observations of the coastal southern Bellingshausen and Amundsen seas in spring are not available. Underway shipboard observations made while traversing the pack ice (in ASPeCt database) favor sampling the thinner end of the thickness distribution due to physical, navigational, and logistical constraints. Hence, the sample population in the ASPeCt database is not likely to represent the regional statistics needed for assessment of the satellite retrievals. Drilling data may be more comparable, as they provide a better sampling of the thickness distribution and of ice thick enough to stand on, but this limits the sampling of very thin ice. However, almost all drilling data to date are from thinner floes (Ozsoy-Cicek et al., 2013) and the thickest ice is often avoided. Even though drilling measurements have provided locations on where one should expect thicker ice (e.g., Williams et al., 2015; Lange and Eicken, 1991; Massom et al., 2001), they rarely provide averages at spatial scales compatible with satellite averages.

Ice thickness estimates from Operation IceBridge provide averages at a larger scale, but they are still limited in terms of seasonal coverage. In an examination of 3 years of OIB ice thickness, Kwok and Kacimi (2018) report October ice thicknesses that range from 2.40 to 2.60 m over a transect across the Weddell Sea (from the tip of the Antarctic Peninsula to Cape Norvegia). This is more compatible with the averages in the W-Wedd sector in Fig. 10a (solid blue line). In a north–south OIB transect of the Ross Sea in November, Tian et al. (2020) found ice thicknesses between 0.48 and 0.99 m, again more compatible with that seen in Fig. 10d (solid blue line). In any case, a more exhaustive evaluation of the present data set remains a challenge.

Table 3Monthly mean (standard deviation) of estimated ice thickness: (1) h_i, with derived snow depth (h_i); (2) $h_{\text{i}}^{\mathrm{0}}$, assuming h_fs=h_f; (3) $h_{\text{i}}^{\mathrm{3}}$, with δ=3 cm; and (4) $h_{\text{i}}^{\mathrm{6}}$, with δ=6 cm.

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5.3 Are the thickness estimates high?

In sectors where there is predominantly seasonal ice (Ross, Pacific, Indian, E-Wedd) the ice thickness in the early winter months of April and May, at close to ∼ 1.5 m, seems to be too high. In these sectors, the growth of 1 m of sea ice in the 1–2 months between freeze-up (in February, March) and April–May is unlikely. With ice drift that is largely seaward and divergent during these months (Fig. 5), the only two processes that contribute significantly to increases in thickness are basal growth and snow ice formation. In the short 1–2 months from freeze-up, basal thermodynamic growth of 1 m is unlikely given the oceanic conditions (ocean heat flux in a weakly stratified ocean compared to the Arctic). Additionally, it would require high snowfall rates to create a significant thickness of snow ice in that amount of time. Thus, this points strongly to biases in the CS-2 freeboards, as the estimated thicknesses are highly sensitive to these biases (due to large 3 : 1 contrast between ice and snow densities in Eq. 11).

Clearly, if ice freeboard were zero everywhere, then $h_{\text{i}}^{\mathrm{0}}$ (Eq. 12) would be the best estimate of ice thickness given measurements of total freeboard. However, this is unlikely to be the case, especially in the W-Wedd and CoA-B sectors where thicker ice is known to be present (see the discussion above). If there were a large-scale bias in the CS-2 freeboards (assuming the processes that contribute to the radar biases are the same everywhere) then areas with the lowest CS-2 freeboards provide a rough guidance on the magnitude of that bias. In the four sectors of largely seasonal ice (Ross, Pacific, Indian, E-Wedd), the sector-averaged CS-2 freeboards have the lowest values and low seasonal variability that ranges from 5.86 ± 2.50 cm (minimum) to 10.3 ± 3.67 cm for all months. This suggests a bias (δ) of ∼ 6 cm if we assumed that early season ice freeboards have to be near zero. This value can be compared to reported biases from different studies; some examples are listed below.

• The thickness of the high-salinity basal layer of 0–3 cm (> 10) reported by Massom et al. (1997).

• Suggested adjustment (δ) of ∼ 7 cm on first-year ice in the Arctic based on a scattering study using profiles of basal salinities (Nandan et al., 2017, 2020).

• Observed CS-2 biases of up to 8 cm in the Weddell Sea in an assessment of the IceBridge- and CS-2-derived ice thicknesses (Kwok and Kacimi, 2018).

• The 3.4–4.5 cm bias from the linear regressions estimated in Sect. 4.3.

In the following section, we examine the sensitivity of thickness and volume if these biases were generally representative over the entire ice cover.

5.4 Thickness and volume estimates with and without adjustments

As discussed above, sea ice would be too thick using the CS-2 freeboards directly and too thin if ice freeboard were assumed to be zero everywhere. Guided by the potential range of CS-2 freeboard biases above, we calculate the regional thickness and volume of the Antarctic ice cover with adjustments (δ) of 3 and 6 cm (Eq. 13) to assess the variability of sector ice volume between the two extremes of thicknesses (i.e., h_i and $h_{\text{i}}^{\mathrm{0}}$) over the winter of 2019. The monthly $h_{\text{i}}^{\mathrm{0}}$ composites and the sector thicknesses (with δ=0, 3, 6 cm) can be seen in Fig. 10 and Table 3, and the monthly ice volumes are shown in Fig. 11.

The adjustments to CS-2 freeboards, as expected, lower the thickness (5 cm per 1 cm of adjustment, based on Eq. 10); at δ=6 cm the sector mean would be reduced by 0.32 m. The impact is higher, in terms of fractional change in total thickness, in sectors with thinner ice (e.g., E-Wedd). The range of thicknesses in Fig. 10 gives us at least an indication of the potential range of variability between assuming zero ice freeboard and the rough estimates of δ (applied as a sector-wide bias). Even though current knowledge does not allow us to adjust individual thickness retrievals, these large-scale adjustments likely provide a better estimate than those calculated using h_i or $h_{\text{i}}^{\mathrm{0}}$ .

The end-of-season ice volume in each sector is proportional to the area production (Fig. 11h) with the largest ice volume in the E-Wedd sector. This, of course, is not the ice volume production in a particular sector. In order to calculate seasonal ice production, one has to account for volume exchanges at the sector boundaries and volume lost to melt at the ice edge. Of interest here is the ice volume and its sensitivity to δ. At the end of the season, the difference in total Antarctic ice volume between assuming δ=0 and h_fs=h_f is ∼ 10 000 km³, or one-third of the total volume. Adjustments with δ=3 and δ=6 cm reduce the differences by ∼ 2000 and 4000 km³, respectively. As with ice thickness, in sectors where the ice is thicker (W-Wedd, Fig. 10), the fractional changes are smaller. An adjustment of 6 cm gives a circumpolar ice volume of 15 600 km³ in October, for an average thickness of ∼ 1.13 m.

These volume estimates can be compared to volume estimates from ICESat freeboards. Using AMSR snow depths, Zwally et al. (2008) estimated the average October–November (2004 and 2005) Weddell Sea ice volume to be ∼ 8750 km³, comparable to our 2019 estimate of 7264 km³ (without any adjustments). Here, differences are expected as the efficacy of the AMSR snow depths has yet to be demonstrated.

Assuming snow depth to be the total freeboard (i.e., zero ice freeboard), Kurtz and Markus (2012) estimated an average circumpolar ice volume of 11 111 km³ in the spring (2003 through 2008) with an average thickness of 0.83 m; this can be compared to our October estimate of 10 062 km³ and 0.72 m using the same assumption. Our lower volume estimates may be partly attributable to the retreat in Antarctic ice coverage (Parkinson, 2019) since the ICESat mission of > 10⁶ km². With the same assumption of zero ice freeboard, the change of 0.11 m between ICESat and IS-2 in 2019 may be of interest, but this is more of an indication of decrease in total freeboard rather than an actual change in ice thickness.