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Taking stock of our losses Earth's ice sheets are melting and sea levels are rising, so it behooves us to understand better which climate processes are responsible for how much of the mass loss. Smith et al. estimated grounded and floating ice mass change for the Greenland and Antarctic ice sheets from 2003 to 2019 using satellite laser altimetry data from NASA's ICESat and ICESat-2 satellites. They show how changing ice flow, melting, and precipitation affect different regions of ice and estimate that grounded-ice loss averaged close to 320 gigatons per year over that period and contributed 14 millimeters to sea level rise. Science , this issue p. 1239

Conversion of altimetry-derived ice-sheet volume change to mass requires an understanding of the evolution of the combined ice and air content within the firn column. In the absence of suitable techniques to observe the changes to the firn column across the entirety of an ice sheet, the firn column processes are typically modelled. Here, we present new 40-year simulations of firn processes over the Greenland and Antarctic Ice Sheets using the Community Firn Model and atmospheric reanalysis variables. A dataset of more than 250 measured depth-density profiles from both ice sheets provides the basis of the calibration of the dry-snow densification scheme. The resulting scheme results in a reduction in the rate of densification, relative to a commonly used semi-empirical model, through a decreased dependence on the accumulation rate, a proxy for overburden stress. The modelled firn column runoff, when combined with atmospheric variables from MERRA-2, generates realistic mean integrated surface mass balance values for the Greenland (+361 Gt yr−1) and Antarctic (+2623 Gt yr−1) ice sheets when compared to published model-ensemble means. We find that seasonal volume changes associated with firn air content are approximately 3 times larger than those associated with surface mass balance; however, when averaged over multiple years, ice and air-volume fluctuations within the firn column are of comparable magnitudes. Between 1996 and 2019, the Greenland Ice Sheet lost more than 5 % of its firn air content indicating a reduction in the total meltwater retention capability. Nearly all (>98 %) of the meltwater produced over the Antarctic Ice Sheet is retained within the firn column through infiltration and refreezing.

Mass changes of the Antarctic ice sheet impact sea-level rise as climate changes, but recent rates have been uncertain. Ice, Cloud and land Elevation Satellite (ICESat) data (2003–08) show mass gains from snow accumulation exceeded discharge losses by 82 ± 25 Gt a−1, reducing global sea-level rise by 0.23 mm a−1. European Remote-sensing Satellite (ERS) data (1992–2001) give a similar gain of 112 61 Gt a−1. Gains of 136 Gt a−1 in East Antarctica (EA) and 72 Gt a−1 in four drainage systems (WA2) in West Antarctic (WA) exceed losses of 97 Gt a−1 from three coastal drainage systems (WA1) and 29 Gt a−1 from the Antarctic Peninsula (AP). EA dynamic thickening of 147 Gt a−1 is a continuing response to increased accumulation (>50%) since the early Holocene. Recent accumulation loss of 11 Gt a−1 in EA indicates thickening is not from contemporaneous snowfall increases. Similarly, the WA2 gain is mainly (60 Gt a−1) dynamic thickening. In WA1 and the AP, increased losses of 66 ± 16 Gt a−1 from increased dynamic thinning from accelerating glaciers are 50% offset by greater WA snowfall. The decadal increase in dynamic thinning in WA1 and the AP is approximately one-third of the long-term dynamic thickening in EA and WA2, which should buffer additional dynamic thinning for decades.

Variations in accumulation rate As(t) and temperature Ts(t) at the surface of firn cause changes in the rate of firn compaction (FC) and surface height H(t) that do not involve changes in mass, and therefore need to be accounted for in deriving mass changes from measured H(t). As the effects of changes in As(t) and Ts(t) propagate into the firn, the FC rate is affected with a highly variable and complex response time. The H(t) during measurement periods depend on the history of As(t) and Ts(t) prior to the measurements. Consequently, knowledge of firn response times to climate perturbations is important to estimate the required length of the time series of As(t) and Ts(t) used in FC models. We use our numerical FC model, which is time-dependent on both temperature and accumulation rate, to examine the response times of both H(t) and the rates of change dH(t)/dt to variations in As(t) and Ts(t) using sample perturbations and climate data for selected sites in Antarctica. Our results show that the response times for dH(t)/dt, which are of particular interest, are much shorter than the responses of H(t). Typical response times of dH(t)/dt are from several years to Ts(t) from satellite observations since 1982 and As(t) from meteorological data since 1979 are essentially of sufficient length to correct for FC height changes for measurements beginning in 1992.

[1] Sea ice thicknesses derived from NASA's Ice, Cloud, and Land Elevation Satellite (ICESat) altimetry data are examined using two different approaches, buoyancy and empirical equations, and at two spatial scales—ICESat footprint size (70 m diameter spot) and Advanced Microwave Scanning Radiometer (AMSR-E) pixel size (12.5 km by 12.5 km) for the Bellingshausen and Amundsen Seas of west Antarctica. Ice thickness from the empirical equation shows reasonable spatial and temporal distribution of ice thickness from 2003 to 2009. Ice thickness from the buoyancy equation, however, additionally needing snow depth information derived from the AMSR-E, shows an overestimation in terms of maximum, mean (+63% to 75%), and standard deviation while underestimation in modal thickness (−20%) as compared with those from the empirical equation approach. When ICESat snow freeboard is used as the snow depth in the buoyancy equation, i.e., the zero ice freeboard assumption, the derived ice thicknesses match well with those from the empirical equation approach, within 5% overall. The AMSR-E, therefore, may underestimate snow depth and accounts for ~95% of the ice thickness overestimation as compared with the buoyancy approach. The empirical equation derived ice thickness shows a consistent asymmetrical distribution with a long tail to high values, and seasonal median values ranging from 0.8 to 1.4 m over the 2003–2009 period that are always larger than the corresponding modal values (0.6–1.1 m) and lower than the mean values (1.0–1.6 m), with standard deviation of 0.6–1.0 m. An overall increasing trend of 0.03 m/year of mean ice thickness is found from 2003 to 2009, although statistically insignificant (p = 0.11) at the 95% confidence level. Starting from autumn, a general picture of seasonal mean, modal, and median ice thickness increases progressively from autumn to spring and decreases from spring to the following autumn, when new thin ice dominates the ice thickness distribution. The asymmetric shape of the thickness distribution reflects the key role of ice deformation processes in the evolution of the thickness distribution. The statistical properties of the thickness distribution interannually (high range of mean thickness and standard deviation) indicate the variability of deformation processes. However, spring ice volume, the product of ice mean thickness and areal extent computed for the spring maximum, shows variability year to year but is primarily dominated by ice extent variability, with no increasing or decreasing trend over this record length. The dependence of the volume on the ice extent primarily suggests that ice thickness changes have also not covaried with the ice extent losses seen over the satellite record in this region, unlike the Arctic. These properties reflect the interactive processes of ice advection, thermodynamic growth and ice deformation that all substantially influence ice mass balance in the Bellingshausen-Amundsen Seas region.

We calculated Antarctic sea-ice freeboard and thickness for ICESat and ATM campaigns. A Gridded ATM freeboard map of nine IceBridge campaigns in October 2009, 2010, and 2011 is shown in Figure 1.

Ice velocities observed in 2005/06 at three GPS stations along the Sermeq Avannarleq flowline, West Greenland, are used to characterize an observed annual velocity cycle. We attempt to reproduce this annual ice velocity cycle using a 1-D ice-flow model with longitudinal stresses coupled to a 1-D hydrology model that governs an empirical basal sliding rule. Seasonal basal sliding velocity is parameterized as a perturbation of prescribed winter sliding velocity that is proportional to the rate of change of glacier water storage. The coupled model reproduces the broad features of the annual basal sliding cycle observed along this flowline, namely a summer speed-up event followed by a fall slowdown event. We also evaluate the hypothesis that the observed annual velocity cycle is due to the annual calving cycle at the terminus. We demonstrate that the ice acceleration due to a catastrophic calving event takes an order of magnitude longer to reach CU/ETH (‘Swiss’) Camp (46 km upstream of the terminus) than is observed. The seasonal acceleration observed at Swiss Camp is therefore unlikely to be the result of velocity perturbations propagated upstream via longitudinal coupling. Instead we interpret this velocity cycle to reflect the local history of glacier water balance.

Mass-balance analysis of the Greenland ice sheet based on surface elevation changes observed by the European Remote-sensing Satellite (ERS) (1992-2002) and Ice, Cloud and land Elevation Satellite (ICESat) (2003-07) indicates that the strongly increased mass loss at lower elevations (

Changes in ice-sheet surface elevation are caused by a combination of ice-dynamic imbalance, ablation, temporal variations in accumulation rate, firn compaction and underlying bedrock motion. Thus, deriving the rate of ice-sheet mass change from measured surface elevation change requires information on the rate of firn compaction and bedrock motion, which do not involve changes in mass, and requires an appropriate firn density to associate with elevation changes induced by recent accumulation rate variability. We use a 25 year record of surface temperature and a parameterization for accumulation change as a function of temperature to drive a firn compaction model. We apply this formulation to ICESat measurements of surface elevation change at three locations on the Greenland ice sheet in order to separate the accumulation-driven changes from the ice-dynamic/ablation-driven changes, and thus to derive the corresponding mass change. Our calculated densities for the accumulation-driven changes range from 410 to 610 kgm–3, which along with 900 kgm–3 for the dynamic/ablation-driven changes gives average densities ranging from 680 to 790 kgm–3. We show that using an average (or ‘effective’) density to convert elevation change to mass change is not valid where the accumulation and the dynamic elevation changes are of opposite sign.

Sea-ice freeboard heights for 17 ICESat campaign periods from 2003 to 2009 are derived from ICESat data. Freeboard is combined with snow depth from Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) data and nominal densities of snow, water and sea ice, to estimate sea-ice thickness. Sea-ice freeboard and thickness distributions show clear seasonal variations that reflect the yearly cycle of growth and decay of the Weddell Sea (Antarctica) pack ice. During October–November, sea ice grows to its seasonal maximum both in area and thickness; the mean freeboards are 0.33–0.41m and the mean thicknesses are 2.10–2.59 m. During February–March, thinner sea ice melts away and the sea-ice pack is mainly distributed in the west Weddell Sea; the mean freeboards are 0.35–0.46m and the mean thicknesses are 1.48–1.94 m. During May–June, the mean freeboards and thicknesses are 0.26–0.29m and 1.32–1.37 m, respectively. 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); however, the large standard deviations indicate that these positive trends are not statistically significant.

We derive mass changes of the Greenland ice sheet (GIS) for 2003–07 from ICESat laser altimetry and compare them with results for 1992–2002 from ERS radar and airborne laser altimetry. The GIS continued to grow inland and thin at the margins during 2003–07, but surface melting and accelerated flow significantly increased the marginal thinning compared with the 1990s. The net balance changed from a small loss of 7 ± 3 Gt a−1 in the 1990s to 171 ± 4 Gt a−1 for 2003–07, contributing 0.5 mm a−1 to recent global sea-level rise. We divide the derived mass changes into two components: (1) from changes in melting and ice dynamics and (2) from changes in precipitation and accumulation rate. We use our firn compaction model to calculate the elevation changes driven by changes in both temperature and accumulation rate and to calculate the appropriate density to convert the accumulation-driven changes to mass changes. Increased losses from melting and ice dynamics (17–206 Gt a−1) are over seven times larger than increased gains from precipitation (10–35 Gt a−1) during a warming period of ∼2 K (10 a)−1 over the GIS. Above 2000 m elevation, the rate of gain decreased from 44 to 28 Gt a−1, while below 2000 m the rate of loss increased from 51 to 198 Gt a−1. Enhanced thinning below the equilibrium line on outlet glaciers indicates that increased melting has a significant impact on outlet glaciers, as well as accelerating ice flow. Increased thinning at higher elevations appears to be induced by dynamic coupling to thinning at the margins on decadal timescales.

The Geoscience Laser Altimeter System (GLAS) aboard ICESat, launched in January 2003, has been designed to detect and monitor changes in the cryosphere. The first objective of this paper is to present high-resolution ice-surface elevation maps derived from GLAS data, using geostatistical analysis. In a regional study of Walgreen Coast and Northern Ellsworth Land, West Antarctica, differences in the representation of geographic and morphologic features in maps based on ERS-1 radar altimeter data and on GLAS data are investigated, with the result that in particular in topographically complex coastal areas and the margin of the ice sheet the improvement in precision and accuracy of the laser altimeter is significant. A second, applied objective is to map elevation changes in Pine Island Glacier, a glacier that plays a key role in the question of stability of the West Antarctic Ice Sheet and has been changing rapidly in recent years. Results of elevation differencing of 2003-GLAS-data and 1995-ERS-1-radar-altimeter-data DEMs (1) show that thinning rates have been increasing and (2) are applied to attribute the observed changes in Pine Island Glacier to internal processes in the glacier, related to dynamic thinning. More generally, this application serves to demonstrate that GLAS data facilitate study of cryospheric change.

Sea ice surviving the summer melt season to become multi-year ice in the Arctic Ocean is of interest because multi-year ice significantly affects the ice-thickness distribution and the dynamics and thermodynamics of the ice pack in subsequent seasons. However, the amount of ice surviving summer melting has not been well determined because the time of the minimum ice area varies from region to region. A concept of local temporal minimum (LTM) accounts for non-simultaneity of the melt–freeze transition by determining the minima ice concentrations (CLTM) on local spatial scales. CLTM are calculated for 25 km gridcells using 24 years (1979–2002) of satellite passive-microwave data. The total area of ice surviving the summer melt (ALTM) is given by spatial integration of CLTM. Over 24 years, the average ALTM is 2.6 × 106 km2 (excluding ∼0.7 × 105 km2 above 84° N). In contrast, the average area (3.8 × 106 km2) of all ice types (ASM), measured when the total (simultaneous) ice cover is a minimum in daily maps in mid-September, is an often-used estimate of ice surviving the summer melting that is ∼45% too large. Over 24 years, the ALTM decreased by 9.5 ± 2.2% (10 a)−1 (0.27 ± 0.06 × 106 km2 (10 a)−1), which is similar to the rate of decline of ASM and about three times the rate of the annual average. The time-of-occurrence of the LTM averaged over the perennial ice pack increased by 8 days from around 11 to 19 August, indicating a later ending of the melt season by about 3 days (10 a)−1 as the summer pack declines. Estimates of multi-year ice in midwinter from passive microwave observations are ∼17% smaller than ALTM, suggesting that the microwave algorithm does not measure all the multi-year ice.

Changes in the surface elevation of the Greenland and Antarctic ice sheets and ice shelves caused by variations in the rate of firn compaction are calculated with a time-dependent firn densification model driven by two decades (1982–2003) of satellite-observed monthly surface temperatures. The model includes the effects of melting and refreezing, both the direct changes in density and the subsequent effects on the densification rate. As previously shown, the temperature-dependent rate of densification is largest in summer, but changes in winter temperatures also have a significant effect. Over the last decade, climate warming has enhanced the rate of compaction and lowered the average surface elevation of Greenland by 1.8 cma-1 and most of West Antarctica by 1.9 cma–1. In East Antarctica, a small cooling raised the average surface elevation by 0.14 cma–1.

Changes in ice mass are estimated from elevation changes derived from 10.5 years (Greenland) and 9 years (Antarctica) of satellite radar altimetry data from the European Remote-sensing Satellites ERS-1 and -2. For the first time, the dH/dt values are adjusted for changes in surface elevation resulting from temperature-driven variations in the rate of firn compaction. The Greenland ice sheet is thinning at the margins (–42 ± 2Gta¯1 below the equilibrium-line altitude (ELA)) and growing inland (+53 ± 2Gta-1 above the ELA) with a small overall mass gain (+11 ± 3Gta–1; –0.03 mma–1 SLE (sea-level equivalent)). The ice sheet in West Antarctica (WA) is losing mass (–47 ± 4Gta–1) and the ice sheet in East Antarctica (EA) shows a small mass gain (+16 ± 11 Gta–1) for a combined net change of –31 ± 12 Gta–1 (+0.08mma–1 SLE). The contribution of the three ice sheets to sea level is +0.05±0.03mma–1. The Antarctic ice shelves show corresponding mass changes of –95 ± 11 Gta–1 in WA and +142 ± 10Gta–1 in EA. Thinning at the margins of the Greenland ice sheet and growth at higher elevations is an expected response to increasing temperatures and precipitation in a warming climate. The marked thinnings in the Pine Island and Thwaites Glacier basins of WA and the Totten Glacier basin in EA are probably ice- dynamic responses to long-term climate change and perhaps past removal of their adjacent ice shelves. The ice growth in the southern Antarctic Peninsula and parts of EA may be due to increasing precipitation during the last century.

The Ice, Cloud and land Elevation Satellite (ICESat) in its 8 day repeat orbit mode provided data not only on the along-track surface slope, but also on the cross-track surface slope from adjacent repeat ground tracks. During the first 36 days of operation, four to five such repeat orbits occurred within 1 km in the cross-track direction. This provided an opportunity to use ICESat data to measure surface slope in the cross-track direction at 1 km scale. An algorithm was developed to calculate the cross-track surface slope. Combining the slopes in the cross-track and along-track directions gives a three-dimensional surface slope at 1 km scale. The along-track surface slope and surface roughness at 10km scale are also calculated. A comparison between ICESat surface elevation and a European Remote-sensing Satellite (ERS-1) 5 km digital elevation model shows a difference of 1–2 m in central Greenland where the surface slope is small, and >20m at the edge of Greenland where the surface slope is large. The large elevation difference at the edge is most likely due to the slope-induced error in radar altimeter measurement. Accurate surface slope data from ICESat will help to correct the slope-induced error of radar altimeter missions such as Geosat, ERS-1 and ERS-2.

Vapor-transfer theory is incorporated into a previous firn-densification model to investigate the effect of vapor-transfer processes on densification in firn within 10 m of the surface. The densification rate in the model is governed by the change of overburden pressure (determined by the accumulation rate), the firn temperature, and the temperature gradient. The time of exposure to temperature gradients at shallow depths is a critical factor determining the importance of vapor-transfer processes. In high-accumulation and high-temperature conditions such as for the Greenland ice sheet, the temperature gradient and vapor transfer are less important due to the shorter exposure times. The high summer temperatures dominate the rate of densification and annual variations in density. In low-accumulation and low-temperature conditions, such as for inland Antarctica, the vapor transfer driven by the temperature gradient has a stronger effect on the densification rate, and temperature-driven processes are less important. These factors determine both the rate of density increase with depth and the amplitudes of annual variations in density with depth.

Comparison of the distribution of seasonal variations in surface elevation derived from a firn-densification–elevation model with observed variations derived from ERS-1/-2 satellite radar altimetry shows close similarity in the patterns of the amplitude of the variations over the North Greenland ice sheet. The amplitudes of the seasonal variations decrease from west to east and from south to north, determined by the accumulation rate and the surface-temperature distribution pattern. Several methods of estimating the amplitude of the seasonal variation in the observations are compared, including the use of a three-frequency sinusoidal function derived from the modeled seasonal variation that is asymmetric. The resulting correlation coefficient between the observed amplitude, estimated with the three-frequency function, and the modeled amplitude is 0.66 and the slope is 0.7. Residual differences may be caused by interannual variability in accumulation and temperature and other approximations in the model.

An ice-sheet flowline model is used to simulate the flow of ice along two particle paths toward the onset to Ice Stream D, West Antarctica. One path is near the centre line of the main tributary to the ice stream, while the second passes by the Byrd Station borehole site. In this paper, we analyze the flow of the moderately fast-flowing tributaries in terms of ice-fabric anisotropy and estimate the steady-state ice-flow regions with the compatible developed crystal orientation fabrics along two particle paths. Comparison between modelled isochrones and internal layers detected from radio-echo sounding surveys in the area is used to suggest that flow upstream of the onset to Ice Stream D appears to have been stable since at least the Last Glacial Maximum.

Ice flow at a location in the equilibrium zone of the west-central Greenland Ice Sheet accelerates above the midwinter average rate during periods of summer melting. The near coincidence of the ice acceleration with the duration of surface melting, followed by deceleration after the melting ceases, indicates that glacial sliding is enhanced by rapid migration of surface meltwater to the ice-bedrock interface. Interannual variations in the ice acceleration are correlated with variations in the intensity of the surface melting, with larger increases accompanying higher amounts of summer melting. The indicated coupling between surface melting and ice-sheet flow provides a mechanism for rapid, large-scale, dynamic responses of ice sheets to climate warming.

Seasonal variations of firn density in ice-sheet firn layers have been attributed to variations in deposition processes or other processes within the upper firn. A recent high-resolution (mm-scale) density profile, measured along a 181 m core from Antarctica, showed small-scale density variations with a clear seasonal cycle that apparently was not related to seasonal variations in deposition or known near-surface processes (Gerland and others, 1999). A recent model of surface elevation changes (Zwally and Li, in press) produced a seasonal variation in firn densification, and explained the seasonal surface elevation changes observed by satellite radar altimeters. In this study, we apply our one-dimensional time-dependent numerical model of firn densification that includes a temperature-dependent formulation of firn densification based on laboratory measurements of grain growth. The model is driven by a steady-state seasonal surface temperature and a constant accumulation rate appropriate for the measured Antarctic ice core. The modeled seasonal variations in firn density show that the layers of snow deposited during spring to mid-summer that have the highest temperature history compress to the highest density, and the layers deposited during later summer to autumn that have the lowest temperature history compress to the lowest density. The initial amplitude of the seasonal difference of about 0.13 reduces to about 0.09 in 5 years and asymptotically to 0.0 at greater depth, which is consistent with the core measurements.

Seasonal and interannual variations in surface elevation at the Greenland summit are modeled using a new temperature-dependent formulation of firn densification and are compared with elevations from European Remote-sensing Satellite (ERS-1/-2) radar altimetry. The rate constant and activation energy, usually set as constants in the Arrhenius-type relation, are strongly temperature-dependent, based on measurements of crystal-growth rates. A multiplicative factor in the densification rate accounts for differences between densification and grain-growth rates and is chosen to match the modeled and measured density profiles from 0 to 40 m. The stronger temperature dependence produces a significant seasonal cycle in the densification rate in the upper firn. Much of the densification and consequent surface lowering occur within 3 months in late spring/early summer, followed by a build-up from accumulation. Modeled elevation changes, using automatic weather station measurements of temperature and accumulation and modeled precipitation, agree well with observations. The respective seasonal amplitudes are 18 and 25 cm peak-to-peak with minima in mid-summer. The minimum elevation in 1995 is driven mainly by a temporary accumulation decrease and secondarily by warmer temperatures. Increased compaction driven by a summer warming trend decreases the modeled elevation (1992–99) by 20 cm, but accumulation increases in latter years dominate the overall 4.2 cm a−1 trend.

Estimates of balance mass flux and the depth-averaged ice velocity through the cross-section aligned with the equilibrium line are produced for each of six drainage systems in Greenland. (The equilibrium line, which lies at approximately 1200 m elevation on the ice sheet, is the boundary between the area of net snow accumulation at higher elevations and the areas of net melting at lower elevations around the ice sheet.) Ice drainage divides and six major drainage systems are delineated using surface topography from ERS (European Remote Sensing) radar altimeter data. The net accumulation rate in the accumulation zone bounded by the equilibrium line is 399 Gt/yr and net ablation rate in the remaining area is 231 Gt/yr. (1 GigaTon of ice is 1090 kM(exp 3). The mean balance mass flux and depth-averaged ice velocity at the cross-section aligned with the modeled equilibrium line are 0.1011 Gt kM(exp -2)/yr and 0.111 km/yr, respectively, with little variation in these values from system to system. The ratio of the ice mass above the equilibrium line to the rate of mass output implies an effective exchange time of approximately 6000 years for total mass exchange. The range of exchange times, from a low of 3 ka in the SE drainage system to 14 ka in the NE, suggests a rank as to which regions of the ice sheet may respond more rapidly to climate fluctuations.

As the planet's principal cold traps, the martian polar regions have accumulated extensive mantles of ice and dust that cover individual areas of approximately 10(6) km2 and total as much as 3-4 km thick. From the scarcity of superposed craters on their surface, these layered deposits are thought to be comparatively young--preserving a record of the seasonal and climatic cycling of atmospheric CO2, H2O, and dust over the past approximately 10(5)-10(8) years. For this reason, the martian polar deposits may serve as a Rosetta Stone for understanding the geologic and climatic history of the planet--documenting variations in insolation (due to quasiperiodic oscillations in the planet's obliquity and orbital elements), volatile mass balance, atmospheric composition, dust storm activity, volcanic eruptions, large impacts, catastrophic floods, solar luminosity, supernovae, and perhaps even a record of microbial life. Beyond their scientific value, the polar regions may soon prove important for another reason--providing a valuable and accessible reservoir of water to support the long-term human exploration of Mars. In this paper we assess the current state of Mars polar research, identify the key questions that motivate the exploration of the polar regions, discuss the extent to which current missions will address these questions, and speculate about what additional capabilities and investigations may be required to address the issues that remain outstanding.

Satellite passive-microwave data for November 1978 through December 1996 reveal marked seasonal, regional, and interannual variabilities, with an overall decreasing trend of −34,300±3700 km2/yr (−2.8%/decade) in Arctic sea ice extents over the 18.2-year period. Decreases occur in all seasons and on a yearly average basis, although they are largest in spring and smallest in autumn. Regionally, the Kara and Barents Seas have the largest decreases, at −15,200±1900 km2/yr (−10.5%/decade), followed by the Seas of Okhotsk and Japan, the Arctic Ocean, Greenland Sea, Hudson Bay, and Canadian Archipelago. The yearly average trends for the total, the Kara and Barents Seas, and the Seas of Okhotsk and Japan all have high statistical significance, with the null hypothesis of a 0 slope being rejected at a 99% confidence level. Regions showing increasing yearly average ice extents are Baffin Bay/Labrador Sea, the Gulf of St. Lawrence, and the Bering Sea, with only the increases in the Gulf of St. Lawrence being statistically significant at the 99% level. Hemispheric results for sea ice areas exhibit the same −2.8%/decade decrease as for ice extents and hence a lower absolute decrease (−29,500±3800 km2/yr), with the ice-free area within the ice pack correspondingly decreasing at −4800±1600 km2/yr. Confidence levels for the trends in ice areas and ice-free water areas exceed 99% and 95%, respectively. Nonetheless, interannual variability is high, and, for instance, the Arctic Ocean ice extents have a positive trend 1990–1996, in spite of their negative trend for the time period as a whole.

Elevations measured by the Mars Orbiter Laser Altimeter have yielded a high-accuracy global map of the topography of Mars. Dominant features include the low northern hemisphere, the Tharsis province, and the Hellas impact basin. The northern hemisphere depression is primarily a long-wavelength effect that has been shaped by an internal mechanism. The topography of Tharsis consists of two broad rises. Material excavated from Hellas contributes to the high elevation of the southern hemisphere and to the scarp along the hemispheric boundary. The present topography has three major drainage centers, with the northern lowlands being the largest. The two polar cap volumes yield an upper limit of the present surface water inventory of 3.2 to 4.7 million cubic kilometers.

Elevations from the Mars Orbiter Laser Altimeter (MOLA) have been used to construct a precise topographic map of the martian north polar region. The northern ice cap has a maximum elevation of 3 kilometers above its surroundings but lies within a 5-kilometer-deep hemispheric depression that is contiguous with the area into which most outflow channels emptied. Polar cap topography displays evidence of modification by ablation, flow, and wind and is consistent with a primarily H 2 O composition. Correlation of topography with images suggests that the cap was more spatially extensive in the past. The cap volume of 1.2 × 10 6 to 1.7 × 10 6 cubic kilometers is about half that of the Greenland ice cap. Clouds observed over the polar cap are likely composed of CO 2 that condensed out of the atmosphere during northern hemisphere winter. Many clouds exhibit dynamical structure likely caused by the interaction of propagating wave fronts with surface topography.

An updated compilation of oxygen-isotope ratio data for 562 sites in Antarctica shows a significant increase in the number of sites and an improvement in the representation of the coastal zone oyer previous versions. The data hase consists of ratio values (δ18O; multi-year mean 18O/16O relative to Standard Mean Ocean Water, in ‰) compiled as the dependent variable, together with data for the so-called independent variables: latitude, surface elevation, mean annual surface temperature and mean annual shortest distance to open ocean denoted by the 20% sea-ice concentration boundary. The problem of covariation between so-called independent variables is minimized using stepwise regression analyses. A general model is described using all the field data, and the regional variation at drainage-system scale is assessed by contrasting models for two physiographically distinct regions. in addition, entity-specific models are determined using data subsets for the conterminous grounded-ice and ice-shelf areas. Inversions of the specific models are applied to a 100 km grid data base to produce two contoured distributions of the ratio, one based on field data, and the other on remotely sensed data. The difference between these produces residuals that, relative to the summation of standard errors of the models, are small in most of the interior area of the ice sheet, and large in several areas of mountain and coastal regions, where interpolation and extrapolation of field data are particularly unreliable. Remotely sensed data generally produce ratio values which are isotopically cooler.

A compilation of mean values of the oxygen-isotope ratio relative 10 Standard mean ocean waterfor 22 siIes representative of conditions in northeastern Canada is complemented with data on mean annual surface temperature, latitude, surface elevation, and mean annual shortest distance to open ocean denoted by the 10% sea-ice concentration boundary. Stepwise regression analysis is used to develop a multivariate model suitable to inter the distribution ofin an area of complex topography and possibly mixed sourcing of advected water vapor. The best model is produced by a run in the backward mode at the 95% confidence level in which only temperature, latitude and distance to the open ocean remain in the model (the correlation coefficient is 0.915, the adjusted coefficient of determination is 0.809, the root mean square residual is 1.62). This model is similar to the bestpredictive model derived elsewhere for Greenland, suggesting a common principal source of advected moisture.

Mean oxygen-isotope ratio values relative to standard mean ocean water (δ18 O, in ‰) reported for 406 sites in Antarctica are compiled together with data on mean annual surface temperature, latitude, surface elevation, and mean annual shortest distance to open ocean denoted by the 20% sea-ice concentration boundary. Stepwise regression analyses with δ18O as the dependent variable are used as a model-building procedure based on statistical, rather than physical, criteria. Multivariate models sensitive to covariation between independent variables are defined using the whole dataset (N406 where N denotes the number of sites), as well as sub-sets for areas of conterminous grounded ice (N206) and ice shell (N110). The models show improvement over bivariate regression models. Distance to the open ocean enters all models at the second step. Inversions of the set and sub-set models applied to a database for 1351 gridpoint locations 100 km apart (it excludes the regions of Graham Land and eastern Palmer Land) are used to produce contoured distributions of δ18O. These may be used to assess the effects of atmospheric advection, as well as derive ice-flow adjustments for δ18O series obtained from deep-core or ablation-zone samples. Suggestions are made to improve model reliability.

Since the 2007 Intergovernmental Panel on Climate Change Fourth Assessment Report, new observations of ice-sheet mass balance and improved computer simulations of ice-sheet response to continuing climate change have been published. Whereas Greenland is losing ice mass at an increasing pace, current Antarctic ice loss is likely to be less than some recently published estimates. It remains unclear whether East Antarctica has been gaining or losing ice mass over the past 20 years, and uncertainties in ice-mass change for West Antarctica and the Antarctic Peninsula remain large. We discuss the past six years of progress and examine the key problems that remain.

The annual rate of net mass accumulation at the surface in the Antarctic and Greenland ice sheets is determined from firn emissivity based on Nimbus-5 ESMR and Nimbus-7 THIR data. In this study the determinations are limited to the areas of dry-snow facies and are based on a hyperbolic function of emissivity. Two coefficients of the function are selected for particular regions of each ice sheet after a comparison with field data selected for their reliability (82 stations in East Antarctica, 69 stations in West Antarctica and 89 stations in Greenland). Derived accumulation values are produced for grid-point locations 100 km apart which cover 56–94% of the dry-snow areas and 32–58% of the accumulation areas of each ice sheet. These values are compared with interpolated values obtained from the latest contoured compilations of field data. The means of derived values for East and West Antarctica are 12% and 39% larger, respectively, than the mean obtained from interpolated values, suggesting that the isopleth patterns as drawn in the compilation of field data lead to underestimates. The mean of derived values for Greenland is 5% smaller than the mean obtained from interpolated values, suggesting that the compilation of field data may lead to small overestimates that are within the error of determination and the variability of accumulation. Improving facies zonation and the determination of coefficients for the areas of upper percolation facies should improve these preliminary assessments.

Warming and Melting Mass loss from the ice sheets of Greenland and Antarctica account for a large fraction of global sea-level rise. Part of this loss is because of the effects of warmer air temperatures, and another because of the rising ocean temperatures to which they are being exposed. Joughin et al. (p. 1172 ) review how ocean-ice interactions are impacting ice sheets and discuss the possible ways that exposure of floating ice shelves and grounded ice margins are subject to the influences of warming ocean currents. Estimates of the mass balance of the ice sheets of Greenland and Antarctica have differed greatly—in some cases, not even agreeing about whether there is a net loss or a net gain—making it more difficult to project accurately future sea-level change. Shepherd et al. (p. 1183 ) combined data sets produced by satellite altimetry, interferometry, and gravimetry to construct a more robust ice-sheet mass balance for the period between 1992 and 2011. All major regions of the two ice sheets appear to be losing mass, except for East Antarctica. All told, mass loss from the polar ice sheets is contributing about 0.6 millimeters per year (roughly 20% of the total) to the current rate of global sea-level rise.

ICESat and Envisat altimetry data provide measurements of the instantaneous sea surface height (SSH) across the Arctic Ocean, using lead and open water elevation within the sea ice pack. First, these data were used to derive two independent mean sea surface (MSS) models by stacking and averaging along-track SSH profiles gathered between 2003 and 2009. The ICESat and Envisat MSS data were combined to construct the high-resolution ICEn MSS. Second, we estimate the 5.5-year mean dynamic topography (MDT) of the Arctic Ocean by differencing the ICEn MSS with the new GOCO02S geoid model, derived from GRACE and GOCE gravity. Using these satellite-only data we map the major features of Arctic Ocean dynamical height that are consistent with in situ observations, including the topographical highs and lows of the Beaufort and Greenland Gyres, respectively. Smaller-scale MDT structures remain largely unresolved due to uncertainties in the geoid at short wavelengths.

The mean rate-of-change of the surface elevation on lower Lambert Glacier is measured with satellite-radar altimetry from the Geosat Exact Repeat Mission (ERM) (1987 89) and Seasat (1978), using orbit cross-over analysis. The measurement region extends 190km in the along-flow direction from 72.1° to 70.4° S, an area that includes the grounding zone of Lambert Glacier. The Geosat ERM and Seasat altimetry are referenced to GEM T2 orbits. The random-noise levels in the data are reduced by low-pass filtering. The orbit bias between the two satellites is estimated from cross-over differences over sea ice seaward of the calving front of the Amery Ice Shelf. The results show a mean rate of increase of the surface height on lower Lambert Glacier of 31±10 mm year-1 during the decade from 1978 to 1987–89. The computation is also carried out independently using data not low-pass filtered but with orbit bias minimized by adjusting the Seasat and Geosat ERM orbits into a common ocean surface. The latter analysis shows a mean rate of increase of the surface height of 83 ± 9 mm year-1 during the same time period. Cross-over analyses carried out using altimetry not low-pass filtered and with orbits not adjusted into a common ocean surface yield intermediate results. Taken together, the cross-over analyses show that the surface height on lower Lambert Glacier increased at a mean rate within the range 20–90 mm year-1 during the decade 1978 to 1987–89.

The extent and duration of surface melting on the Antarctic ice shelves and margins of the Antarctic ice sheet are derived from satellite passive-microwave data for 1978–87. The occurrence of surface melting in daily maps of Tb is indicated by a marked increase in microwave brightness temperature (Tb), which is caused by moisture in the near-surface firn. Tb increases of more than 30 deg above the annual-mean Tb are chosen to indicate melting. Most Antarctic surface melting occurs during December and January. The observed melting is correlated with regional air temperatures, but some melt patterns also appear to be related to katabatic-wind effects. The correlations suggest that the surface melting in Antarctica increases about 3.5 × 106 d km2 per degree of summer temperature increase. The surface-melt index (duration times area of melting) calculated for Antarctica is 24 × 106 d km2, averaged over nine summers. The observed inter-annual and regional variability is large. Surface melting was most extensive during the 1982/83 summer (36 × 106 d km2) and least extensive during the 1985/86 summer (15 × 106d km2). The data indicate a decline in surface melting over the 9 years, but meaningful inferences regarding trends in surface melting are precluded by the large inter-annual variability.

Firn-temperature profiles are calculated in a thermal model using continuous surface temperatures derived from automatic weather station data and passive-microwave data in the Greenland summit region during the period 1987–99. the results show that significant interannual variations of mean summer (June–August) and annual temperatures occur in the top 15 m, in addition to the normal seasonal cycle of firn temperature. At 5 m depth, the seasonal cycle is damped to 13% of the surface seasonal range, but even at 15m about 1% or 0.6˚C of the seasonal cycle persists. Both summer and mean annual temperatures decrease from 1987 to 1992, followed by a general increasing trend. Interannual variability is 5˚C at the surface, but is dampened to 3.2˚C at 5 m depth and 0.7˚C at 15 m depth. Dampening of the interannual variability with depth is slower than dampening of the seasonal cycle, because of the longer time constant of the interannual variation. the warmer spring and summer temperatures experienced in the top 5 m, due to both the seasonal cycle and interannual variations, affect the rate of firn densification, which is non-linearly dependent on temperature. During the 12 year period 1987–99, the annual mean surface temperature is –29.2˚C, and the annual mean 15 m temperature is –30.1˚C, which is >1˚C warmer than a 15 mborehole temperature representing the period around 1959 and warmer than the best-fit temperature history by Alley and Koci (1990) back to AD 1500.