1. Introduction
Antarctic sea ice is dominated by seasonal sea ice. Sea-ice extent in summer is only about 15% of that in winter (Reference Comiso and NishioComiso and Nishio, 2008). To understand the sea-ice mass balance, the seasonal variation of both sea-ice extent (area with concentration greater than, e.g., 15%) and thickness must be measured. Currently, sea-ice extent and concentration are monitored daily by passive-microwave satellite remote sensing (Reference Gloersen, Campbell, Cavalieri, Comiso, Parkinson and ZwallyGloersen and others, 1992; Reference Markus, Cavalieri and JeffriesMarkus and Cavalieri, 1998; Reference Comiso, Cavalieri and MarkusComiso and others, 2003). However, there are no corresponding basin-scale thickness observations.
In the past few decades, considerable efforts have been made to measure sea-ice freeboard and thickness in the Southern Ocean. Ship-based measurements (Reference AckleyAckley, 1979; Reference Wadhams, Lange and AckleyWadhams and others, 1987; Reference Lange and EickenLange and Eicken, 1991; Reference Worby, Geiger, Paget, Ackley and DeLibertyWorby and others, 2008b), airborne remote sensing (Reference LeuschenLeuschen and others, 2008; Reference Lieser, Massom, Worby and YiLieser and others, in press) and upward-looking sonar (ULS) (Reference Strass, Fahrbach and JeffriesStrass and Fahrbach, 1998; Reference Drinkwater, Liu and HarmsDrinkwater and others, 2001; Reference Harms, Fahrbach and StrassHarms and others, 2001; Reference Worby, Bush and AllisonWorby and others, 2001; Reference Renner and LytleRenner and Lytle, 2007) have covered various locations and different seasons in the Southern Ocean. These measurements are sparsely located and/or sparsely distributed in time, and the sampled areas were mostly at the margins of the Antarctic sea-ice pack that is accessible by ships. Therefore, available sea-ice freeboard and thickness estimates tend to be from the thin end of the thickness distribution.
The most comprehensive dataset of Antarctic sea-ice thickness to date is from the Antarctic Sea Ice Processes and Climate (ASPeCt) project summarized by Reference Worby, Geiger, Paget, Ackley and DeLibertyWorby and others (2008b). This is a compilation of 21 710 individual ship-based observations from 81 voyages and 1663 aircraft-based observations. the observations cover two and a half decades from 1981 to 2005. However, significant regional and seasonal gaps exist. the limitations of surface-based observations demonstrate that only satellite observations can provide the necessary spatial and temporal observation coverage to systematically study the sea ice in the Southern Ocean. Recent radar altimetry data have been used to study the sea-ice surface elevations (Reference Giles, Laxon and WorbyGiles and others, 2008), but the large footprint and the penetration effect of the radar altimetry data make it difficult to retrieve sea-ice freeboard or thickness in the Southern Ocean. Hopefully, the more sophisticated instrument design and retracking method of CryoSat2 will improve the performance of the radar altimeter in the Southern Ocean.
NASA’s Ice, Cloud and land Elevation Satellite (ICESat; 2003–09) has been used to measure sea-ice freeboard and thickness in both the Arctic (Reference Kwok, Zwally and YiKwok and others, 2004, Reference Kwok, Cunningham and Zwally2006, Reference Kwok, Cunningham, Zwally and Yi2007, Reference Kwok, Cunningham, Wensnahan, Rigor, Zwally and Yi2009; Reference Kwok and CunninghamKwok and Cunningham, 2008; Reference Farrell, Laxon, McAdoo, Yi and ZwallyFarrell and others, 2009; Reference Spreen, Kern, Stammer and HansenSpreen and others, 2009; Yi and Zwally, http:// earth.esa.int/cryosat2005/participants/69/pres_yi.pdf) and the Southern Ocean (Reference Zwally, Yi, Kwok and ZhaoZwally and others, 2008; Reference Lieser, Massom, Worby and YiLieser and others, in press; Reference XieXie and others, in press; Yi and Zwally, http://earth.esa.int/cryosat2005/participants/69/pres_yi.pdf).Zwally and others (2008) demonstrated that ICESat surface elevation profile can be used to retrieve sea-ice freeboard and can be combined with Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) snow depth to estimate thickness in the Weddell Sea, Antarctica. We apply a technique similar to that of Reference Zwally, Yi, Kwok and ZhaoZwally and others (2008) to derive sea-ice freeboard from ICESat elevation profiles and estimate sea-ice thickness over the Weddell Sea for 17 observation periods extending from February 2003 to April 2009. For the first time, the seasonal and interannual variations of basin-scale sea-ice freeboard and thickness in the Southern Ocean are observed during the 6 year ICESat observation period.
2. Data
In January 2003, NASA launched ICESat with a precision laser altimeter system for measuring surface elevations (Reference ZwallyZwally and others, 2002a; Reference Schutz, Zwally, Shuman, Hancock and DiMarzioSchutz and others, 2005). the precision of ICESat measurements of mean surface elevations of flat surfaces is 2 cm over 70 m laser footprints spaced at 172m (Reference Kwok, Zwally and YiKwok and others, 2004; Yi and Zwally, http://earth.esa.int/cryosat2005/participants/69/pres_yi.pdf), providing a powerful new tool for studying sea-ice freeboard and thickness. the ICESat orbit extends to polar latitudes of 86˚, and provides coverage of all sea ice in the Southern Ocean surrounding Antarctica and most of the sea ice in the Arctic Ocean. Due to lifetime limitations of ICESat’s three lasers, ICESat operated periodically from 2003 to 2009.
The operational periods are of 34–38 days, except for four periods when special events happened. (1) the September– November 2003 period has 57 days; during that period, ICESat operation changed from an 8 day calibration/validation orbit to a 91 day operation orbit. (2) In October 2008, ICESat laser 3 failed, limiting that operation period to 16 days; subsequently, (3) an extra 23 days of laser 2 operation was added to complete the ground track lost in October 2008 with an additional few days of orbit overlap. (4) the last campaign period lasted for 12 days; ICESat laser 2 failed on 11 October 2009, prematurely ending this campaign. Data from this short and final period are not used in this study. Table 1 lists the campaign periods, operating times, Antarctic seasons and repeat orbits of ICESat observations.
Table 1. ICESat campaign period, operating time, Antarctic season when measurements were made, repeat orbit period, and month–year label for each campaign. Seasons are: summer (JFM), fall (AMJ), winter (JAS) and spring (OND)
ICESat data products GLA05 and GLA06 from February 2003 to April 2009 are used in this study. We use data release 428 for data products from laser 1 to laser 3j, release 429 for laser 3k, release 530 for laser 2d, and release 531 for laser 2e. Similar to Reference Zwally, Yi, Kwok and ZhaoZwally and others (2008), the following conditions were adopted to filter out data contaminated by clouds, saturation and land/islands.
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1. Gain limit: an upper limit of detector gain is applied to filter out stronger atmospheric attenuated waveforms. For the high-energy campaign periods (laser 1, 2a, 2b, 3a and 3b), the gain limit is set at 50 counts. For the low-energy campaign periods (laser 2d and 2e), no gain limit is applied. For the mid-energy campaigns (laser 2c, 3j, 3k, and laser 3c, 3d, 3e, 3f, 3g, 3h, 3i) the gain limits are set at 120 and 80 counts respectively. Gain limit has to be empirically adjusted, since lower laser energy penetrates less cloud and gain associated with atmospheric forward-scattered waveforms increases while laser energy decreases.
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2. Pulse-broadening limit: we define a pulse-broadening parameter,
(1)
where σ R is the echo waveform 1σ pulse width, σ T is the transmitted waveform 1σ pulse width, and c is the speed of light. S measures the broadening of the transmitted pulse associated with surface topography and the undesirable effects of saturation and atmospheric forward scattering. Heavily saturated waveforms and forward-scattering waveforms have broadened pulse widths, so data with S > 0.8m are discarded.
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3. Reflectivity limit: heavily saturated waveforms also tend to have very high apparent reflectivity, and forward-scattering waveforms tend to have low reflectivity, so data with reflectivity smaller than 0.05 or larger than 0.9 are discarded.
Since ICESat elevation data do not distinguish surface types such as water, sea ice or land, AMSR-E ice concentration is used to separate sea ice from land and water. In this study, only areas with ice concentration more than 60% are considered.
The snow-depth and ice-concentration (NASA Team) data used in this study are from AMSR-E (Reference Markus, Cavalieri and JeffriesMarkus and Cavalieri, 1998; Reference Comiso, Cavalieri and MarkusComiso and others, 2003). For the study area, we used data in the Weddell Sea between the Antarctic Peninsula and 0˚ longitude.
3. Method
Details of the technique used to derive sea-ice freeboard from ICESat elevation profiles are provided by Reference Zwally, Yi, Kwok and ZhaoZwally and others (2008). In brief, the technique of deriving freeboards uses segments of open water and thin ice detected by the laser altimeter to determine the height of the along-track ocean surface, which is then used as the ocean reference level for the freeboard heights of the snow-covered sea ice. Freeboard is defined here as the total height of the snow cover and sea ice above the ocean (whereas it is sometimes used to refer to only the sea-ice portion, leading to the possibility of so-called negative freeboards).
After establishing the ocean reference level for each ICESat along-track elevation measurement, the freeboard height is determined relative to this reference level. the ICESat detection of open-water and thin-ice areas was demonstrated by Reference Kwok, Cunningham and ZwallyKwok and others (2006) and Reference Zwally, Yi, Kwok and ZhaoZwally and others (2008) in comparison with available Envisat synthetic aperture radar (SAR) images that show leads and polynyas with thin ice and open water. Estimation of sea-ice thickness from the freeboards requires additional information and a number of assumptions about the densities and thicknesses of the snow cover and the sea ice. the parameters required to retrieve sea-ice thickness here are similar to estimations of sea-ice thickness from radar altimetry (Reference Laxon, Peacock and SmithLaxon and others, 2003) and submarine sonar measurement of sea-ice drafts (Reference Rothrock, Yu and MaykutRothrock and others, 1999).
3.1. Elevation and relative elevation
The ICESat-measured surface elevation, H ie, is referenced to an Earth ellipsoid, as used by TOPEX/Poseidon and Jason-1. ICESat surface elevations have instrument corrections, dry and wet troposphere corrections and tidal corrections applied. We also applied saturation correction and inverse barometer correction (Reference Zwally, Yi, Kwok and ZhaoZwally and others, 2008). In the following analysis, we define the elevation, h, above the geoid as
where ΔH sat is the saturation correction and h g is the geoid height. Note that the influence of ΔH ib, ΔH sat and h g are removed from H ie, but other factors such as dynamic topography and the residuals in the static geoid still affect h.
Due to the limited accuracy of the geoids and ocean tide models, and limited knowledge of the dynamic topography, sea-ice surface elevation referenced to a geoid cannot be regarded as sea-ice freeboard. Computing sea-ice freeboard requires the elevation difference between the top of the snow surface on the sea ice and local ocean levels. If the elevation difference is known, even if the absolute elevations are biased, the sea-ice freeboard can still be determined. By determining local ocean level and using only the relative elevation, effects of the longer-wavelength (>20 km) factors, such as geoid error, long-wavelength laser pointing error and tidal error (which affect the absolute elevation), are removed from the freeboard calculation.
3.2. Freeboard calculation
Figure 1 shows an example of computed freeboard from an elevation profile over the Weddell Sea from October to November 2003. In Figure 1a, elevation, h, is referenced to the geoid. To remove the long-wavelength geoid error, tidal error and dynamic ocean topography, we compute a 20 km running mean, h m, of h, which is then used as a reference level (Fig. 1b) in the computation of relative elevations, h r (h – h m). In this study, leads (open water and thin ice) in the sea ice are considered to be at ocean level. Ocean level, h s, at any given point is determined by averaging the lowest 2% of the h r values within ±25 km of that point.
Fig. 1. An example of h m, h s, h r and F calculation. the profile is from October to November 2003. (a) Elevation, h, is referenced to the Earth Gravitational Model 1996 (EGM96) geoid. h m is the 20 km running mean of h. (b) Relative elevation, h r (=h – h m). Ocean level, h s, is determined by averaging the lowest 2% of the h r values within ±25km of a point. (c) Freeboard height, F = h r – h s.
Freeboard height, F, at a given point is defined as F = h r – h s. To have a valid F at a point, there must be enough valid elevation measurements available within ±25 km of that point. In this study, a point is discarded if <50% of the total 300 points are available. After freeboard at each point along an elevation profile is calculated, freeboards from ground tracks of each campaign period are gridded to 25 km×25km gridcells. the 2% value was selected empirically. It provides enough points in calculating mean sea level to reduce measurement noise, and minimizes the influence of thin ice in the calculation. In cases when open water is <2% within the 50km range, hs will measure the height of thin ice, thus underestimating freeboard. Figure 1c shows freeboard height F = h r – h s.
3.3. Thickness calculation
There are three typical states of sea ice in the Southern Ocean (Fig. 2). Figure 2a is the most common state, with a layer of snow on top of ice, and the snow/ice interface above sea level. This state is described by Reference Giles, Laxon and WorbyGiles and others (2008) and Reference Zwally, Yi, Kwok and ZhaoZwally and others (2008) over the Southern Ocean and by Reference Kwok, Cunningham, Wensnahan, Rigor, Zwally and YiKwok and others (2009) over the Arctic. Over the Southern Ocean, however, the snow/ice boundary frequently fell below sea level (Reference Lange, Schlosser, Ackley, Wadhams and DieckmannLange and others, 1990; Reference Lytle and AckleyLytle and Ackley, 1996) (Fig. 2b), mainly due to the accumulation of snow. the sea ice can stay in this state for an extended period; eventually sea water will penetrate the sea ice or flow from the sides to form slush and then refreeze in 2– 3 weeks (Reference Lytle and AckleyLytle and Ackley, 1996) (Fig. 2c). For the state in Figure 2a, sea-ice thickness, T I, is a function of freeboard height, F, snow depth, T S, snow density, ρ S, water density, ρ W, and sea-ice density, ρ I. According to Archimedes’ buoyancy principle,
Fig. 2. Three typical cases of sea ice in the Southern Ocean. (a) the most common state, with a layer of snow on top of ice, and the snow/ice interface above sea level. (b) Over the Southern Ocean, the snow/ice boundary frequently fell below sea level, mainly due to the accumulation of snow on the snow/air interface. the sea ice can stay in this state for an extended period; eventually sea water will penetrate the sea ice from below or flow from the sides to form slush and then refreeze as shown in (c).
In this study, constant densities of ρ S = 300 kgm–3, ρ W= 1023.9 kgm–3 and ρ I = 915.1 kgm–3 (Reference Laxon, Peacock and SmithLaxon and others, 2003) are used to calculate sea-ice thickness from the freeboard. T I can then be expressed as
For the state in Figure 2c, F = T s and, assuming ρ slush = ρ I, Equation (3) becomes
T I can then be expressed as
We recognize that ice thickness is sensitive to the local and regional variability of snow and ice densities. Since we have no detailed information about the errors in local densities, the error in T I is not calculated. In this study, the freeboard is always measured from snow/air or ice/air surface to sea level, hence it is always positive. If the snow depth is larger than freeboard, snow depth is set equal to the freeboard, as in Reference Zwally, Yi, Kwok and ZhaoZwally and others (2008). This treatment is equivalent to assuming the state in Figure 2b will turn into the state in Figure 2c and then the slush freezes. This will introduce an unknown error in thickness before the state in Figure 2b turns into the state in Figure 2c.
4. Results
Sea-ice freeboard heights for 17 ICESat campaign periods from March 2003 to April 2009 in the Weddell Sea were derived from ICESat laser altimeter measurements. Thickness is estimated by combining ICESat freeboard, AMSR-E snow depth and nominal densities of snow, water and sea ice. Sea-ice freeboard and thickness distributions show clear seasonal variations that reflect the yearly cycle of the growth and decay of the Weddell Sea pack ice.
4.1. Freeboard
Freeboard maps and distributions are shown in Figure 3. the seasonal sea-ice area variation is clearly presented here for every year of the observations from 2003 to 2009. the area minimum is in the February–March (summer) periods. For the five February–March periods, the mean freeboards are 0.35–0.46 m. Mean freeboards for the two March–April periods are 0.34 and 0.43 m. Large portions of thin ice formed in the May–June periods (fall). For the three fall periods, the mean freeboards vary from 0.26 to 0.29 m. Maximum areas are in the October–November periods (early spring); for the six early-spring periods, mean freeboards are 0.33–0.41 m. the mean freeboard and the standard deviation of the mean freeboard are listed in Table 2.
Fig. 3. Sea-ice freeboard for 17 campaign periods. the red lines are at the mean freeboards of the histograms. During the February–March periods, values of the modes and means are comparable and the histogram shapes are close to normal distribution. During the May–June periods, the histograms are heavily positively skewed, and the modes are much smaller than the means, reflecting the rapid growth of the newly formed thin ice. During the October–November periods, the histograms are less skewed, the means are larger than for the May–June period and the modes are closer to the means, reflecting the growth in thickness of the previously formed thin ice. Due to surface freeboard changes during a campaign period and multiple satellite measurement occurring at different times, some stripe-type features are visible, especially for the May–June periods, reflecting rapid growth in the fall season.
Table 2. Campaign periods, mean freeboard, standard deviation of mean freeboard, mean thickness (T), standard deviation of mean thickness, and flooding-related parameters
In general, the freeboard increases from east to west in the Weddell Sea for all seasons, with the maximum values along the east coast of the Antarctic Peninsula. the C-shaped patterns associated with the Weddell Gyre are notable in the fall and spring. While sea-ice area reaches minimums in February–March, the mean freeboards are comparable to the values of early spring, but remain larger than the fall values. This is due to the summer survival of thick sea ice and the melt of thin sea ice over the season. As might be expected, mean freeboards are larger in March–April than in May– June. the November–December period in 2008 shows the spring melting; the area is much smaller than in the October–November periods.
4.2. Thickness
Figure 4 shows the sea-ice thickness computed via Equations (4) and (6), based on ICESat freeboard and AMSR-E snow depth. Equation (4) is used for most of the gridcells. For areas with T S > F, we assume the areas will be flooded and then refreeze, and set snow depth, T S, equal to freeboard, F, in our calculation. This assumption will introduce errors in thickness before the sea ice is flooded and before the slush refreezes. However, for most of the T S > F case, the sea ice will be flooded and the slush will refreeze in 2–3 weeks (Reference Lange, Schlosser, Ackley, Wadhams and DieckmannLange and others, 1990; Reference Lytle and AckleyLytle and Ackley, 1996). the spatial distribution patterns in the thickness maps are similar to those in the freeboard maps. For the five February–March periods, the mean thicknesses, T I, range from 1.48 to 1.94 m. For the three fall periods, they range from 1.32 to 1.37 m. For the six October–November periods, they range from 2.10 to 2.59 m. the mean thickness and the standard deviation of the mean thickness are listed in Table 2.
Fig. 4. Sea-ice thickness for 17 campaign periods. the red lines are at the mean thickness of the histograms. During February–March periods, unlike for the freeboard, the histograms are not close to normal distribution, the small amount of thick ice increased the means and the modes are lower, ~1m. During the May–June periods, the newly formed thin ice reduces both means and modes compared to the February– March periods. During the October–November periods, both modes and means continue to grow compared to the May–June period, reflecting the growth in thickness of the previously formed thin ice.
In general, the thickness increases from the eastern to the western Weddell Sea for all seasons, with the maximum values along the east coast of the Antarctic Peninsula. A C-shaped pattern of the Weddell Gyre is also notable in the fall and spring seasons. the thickness distribution in October– November shows the largest annual variations: there is thick ice distributed along the northwest side of the Weddell Sea in 2003, 2004, 2005 and 2007, but not much thick ice in the area in 2006 and 2008; in 2006, there is more thick ice distributed in the central west Weddell Sea than in the other October–November periods.
An underestimate of snow depth will produce a positive bias of sea-ice thickness and vice versa. Reference Worby, Markus, Steel, Lytle and MassomWorby and others (2008a) found that AMSR-E snow depth over the Antarctic can underestimate snow depth by a factor of 2.3 for rough sea-ice regions; if proven, this would make the calculated thickness appear higher in this study. Reference XieXie and others (in press) compared ICESat freeboard and thickness with their in situ cruise measurement in the Bellingshausen–Amundsen Seas under ICESat ground track during October 2007. They concluded that the ICESat freeboard (0.42±0.24 m) and thickness (1.38±0.70 m) in the studied area agree with their in situ measurements (0.360.28m and 1.26±0.94 m, ±respectively) reasonably well. Reference Lieser, Massom, Worby and YiLieser and others (in press) compared an airborne laser altimetry and ICESat freeboard in East Antarctica, also during October 2007. the freeboard from the airborne laser was 0.59±0.52m and from ICESat was 0.41±1.26 m. the large differences may reflect the high drift rate of the ice (19kmd–1), which may produce large fluctuations in mean freeboard in the region. However, due to different sea-ice characteristics, results from the Bellingshausen–Amundsen Seas and East Antarctica may not be applicable to the Weddell Sea.
4.3. Flooding
In the Weddell Sea, the snow/ice boundary frequently falls below sea level and becomes flooded (T S > F). Reference Lytle and AckleyLytle and Ackley (1996) estimated that ~50% of the area was flooded in February–March in the west Weddell Sea during their 1992 field season. Table 2 lists the percentage of gridcells with T S > F and the mean of F – T S. In the five February–March periods, the number of TS > F cells ranges from 20.2% to 42.8%. the highest percentage in the three observed seasons, 42.8%, is comparable with Lytle and Ackley’s estimate. In the six October–November periods, the number of T S > F cells ranges from 0.1% to 8.5%, with three periods less than 1%. the three May–June periods have modest flooding percentages, 11.4–19.7%, smaller than the February–March ranges and larger than the October–November ranges. the mean F – T S values in Table 2 show small values range from 0.02 to 0.08m in the February–March periods, indicating the snow depth, T S, and freeboard, F, are very close when a large percentage of cells are flooded. on the other hand, when the percentage of T S > F are low in the October–November periods, the mean F – T S values are high, ranging from 0.14 to 0.22 m, and very few flooding events occur.
We evaluate the possible snow-depth error introduced by its uncertainty and flooding by assuming snow depth equals ICESat-measured freeboard; this is equivalent to using Figure 2c and Equation (6) to represent all situations. Although this is an oversimplification for most of the time, it provides an estimate of sea-ice thickness independent of any snow-depth data input.
Let T F represent the mean thickness calculated from Equation (6) only and T represent the mean T I for each period. the T F/T ratios for each campaign period are listed in Table 2. For the five February–March periods, the ratios are 56–70%. For the six October–November periods, they are 43–52%. the higher T F/T values for the February–March periods reflect the smaller differences of F and T S listed in Table 2, and the lower T F/T values for the October– November periods reflect the larger F and T S differences.
4.4. Geoid and dynamic ocean topography
After removing the geoid and inverted barometer effects, the elevation signal is still dominated by the unresolved geoid residuals and the dynamic ocean topography. Here we define the difference between ICESat-measured sea level (h s, referenced to h m) and the Earth Gravitational Model 1996 (EGM96) geoid (h g) as h d = h m + h s. In Figure 5 the consistent pattern of different campaign periods indicates that a major portion of h d is due to time-invariant factors, most likely uncertainties in the geoid and unmodeled dynamic ocean topography. the possible contributors to the time-variant portion of h d are ICESat laser-pointing errors, tidal errors and unmodeled dynamic ocean topography. We have calculated the mean h d grid of all 17 campaign periods in the sea-ice covered regions. the average h d grid can be treated as a new mean sea level of the studied region. This result demonstrates that ICESat data could be used to improve the geoid model in the Southern Ocean and mapping of dynamic ocean topography. Reference Forsberg and SkourupForsberg and Skourup (2005) used some early ICESat data and Gravity Recovery and Climate Experiment (GRACE) data to improve an Arctic geoid model.
Fig. 5. Mean sea level above EGM96 geoid (h d) for 17 periods and their average.
5. Discussion and Conclusions
We have derived sea-ice freeboard over the Weddell Sea, using ICESat-measured surface elevation. Combining ICESat freeboard with AMSR-E passive microwave snow depth and nominal densities of snow, sea ice and water, we estimated sea-ice thickness. the freeboard and thickness maps in the Weddell Sea for 17 campaign periods show seasonal and interannual variations.
We calculated sea-ice extent and volume for grids with AMSR-E ice concentration higher than 60% for each campaign period over the Weddell Sea. To derive the trends over the 6 years, a sinusoidal function with a yearly cycle and a linear trend is used to fit the sea-ice extent and
volume time series (Fig. 6). Although the observations are not continuous and not at exactly the same time of year, the multi-function fitting matches the observations well. the 6 year trends in sea-ice extent and volume are (0.023 ±0.051) ×106 km2 a–1 (0.45% a–1) and (0.007±0.092)×103 km3 a–1 (0.08% a–1), indicating small increases with time. However, the large standard deviations relative to the calculated trends indicate that these positive trends are not statistically significant. Future satellite laser altimeter missions (e.g. ICESat-2) will permit continued monitoring of freeboard, producing monthly average maps, and will refine observations of the seasonal cycles and longterm trends derived from ICESat for the 2003–09 period.
Fig. 6. Weddell Sea ice extent and volume from 2003 to 2009. A sinusoidal function with a yearly cycle and a linear trend, y = y 0 + at +A cos(ωt + φ), is used to fit both sea-ice extent and volume time series. During the 6 year period, the changing rate for extent is (0.023±×0.051)106 km2 a–1; the changing rate for volume is (0.007±0.092)×103 km3 a–1. the peak-to-peak amplitudes of the seasonal cycle are 3.6×106 km2 in extent and 7.0×103 km3 in volume.
The peak-to-peak amplitudes of the seasonal cycle are 3.6×106 km2 in extent and 7.0×103 km3 in volume. the extent trend, 4.5% (10 a)–1 is much larger than the 0.7% (10 a)–1 found by Reference Comiso and NishioComiso and Nishio (2008) for a much longer period (1979–2006). However, the standard deviation of the extent trend is large, and shorter-period subsets (~6 years) of Reference Zwally, Comiso, Parkinson, Cavalieri and GloersenZwally and others (2002b) and Reference Comiso and NishioComiso and Nishio (2008) showed both larger positive and negative trends.
ICESat-determined sea level can potentially be used to improve the geoid and dynamic ocean topography knowledge in the sea-ice covered regions. an improved geoid will help improve sea-level determination and therefore improve ICESat measured freeboard accuracy. A better geoid will also help resolve the gravity field and tectonic features of a region (Reference McAdoo, Farrell, Laxon, Zwally, Yi and RidoutMcAdoo and others, 2008). We will compare ICESat-determined sea level to a new geoid model, EGM08 (N.K. Pavlis and others, http://www.massentransporte.de/fileadmin/kolloquium_muc/2008-10-08/Bosch/EGM2008.pdf), in future studies.
Uncertainties in freeboard, snow depth, and densities of snow, water and ice introduce uncertainties in sea-ice thickness estimates. the precision of the AMSR-E snow depth is 5 cm (Reference Drinkwater, Liu and HarmsComiso and others, 2003), based on Equation (4); this will lead to an uncertainty of ~33cm in ice thickness. A similar study by Reference Kwok, Cunningham, Zwally and YiKwok and others (2007) on Arctic sea ice showed a freeboard uncertainty of ~5 cm. Based on Equation (4), this will lead to an uncertainty of ~47 cm in ice thickness. Discounting the error in the densities of snow, water and ice, the combined uncertainty due to ICESat freeboard and AMSR-E snow depth, based on Equation (4), is ~58 cm. We recognize that the uncertainty of the estimated sea-ice thickness is high. In future studies, better-calibrated snow depth and better-observed/-modeled densities of snow, water and sea ice are needed.
In situ measurements (e.g. sea-ice freeboard, thickness, snow depth and snow density) coincident with ICESat and AMSR-E measurements are necessary to further calibrate/ validate the snow-depth, freeboard and thickness results. the analysis of Sea Ice Mass Balance in the Antarctic (SIMBA) cruise data (Reference XieXie and others, in press) and ASPeCt cruise data (Reference Lieser, Massom, Worby and YiLieser and others, in press) show reasonable agreement between ICESat freeboard and thickness and in situ observations. Validation is difficult with point-wise measurements in the presence of ice drift, but the coordinated field experiments with both airborne and ground-based observations will make current and future satellite observations more credible as they can be more thoroughly compared with the in situ observations.
Acknowledgements
This work is supported by NASA’s funding of the ICESat Project Science. We thank A. Ivanoff, D. J. Cavalieri, T. Markus, and S. Fiegles for their help in providing the AMSR-E snow-depth and ice-concentration data. We thank both the Scientific Editor, S. Kern, and the two anonymous referees for their careful and helpful reviews.
