Altimetry

Altimetry is conducted from aircraft using laser ranging (Reference KrabillKrabill and others, 2004; Reference Thomas, Frederick, Krabill, Manizade and MartinThomas and others, 2006), and from satellite using laser (Reference Thomas, Frederick, Krabill, Manizade and MartinThomas and others, 2006) or radar (Reference ZwallyZwally and others, 2005) sensors. The narrow laser footprint requires interpolation, and reflections from clouds complicate interpretation especially for the satellite-borne lasers (Reference ShumanShuman and others, 2006), as does the so-far limited lifetime of those lasers.

Radar samples larger areas, has operated reliably for longer times, and penetrates cloud cover. Radar also penetrates the snow surface to a varying depth (e.g. Rémy and others, 2001). Radar altimeters were designed to operate over the nearly planar ocean, and the sloping flanks of ice sheets cause difficulties with off-nadir reflections. As discussed by, for example, Reference Jezek and AlleyJezek and Alley (1988), Reference Arthern, Wingham and RidoutArthern and others (2001) and Rémy and others (2001), change in surface roughness or in near-surface layering or density can affect the waveform shape returned to the satellite and thus the computed range, even if the range is not changing.

Commonly, power returned to the satellite from the surface is found to correlate with estimated range (distance), when radar returns from a given point on the surface are compared over time (e.g. Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others, 1998). It is reasonable to expect that changing surface character will change both the returned power and the single range number that is calculated from the information in the returned waveform. Workers typically remove range changes correlated with returned-power changes, presuming those range changes are artifacts. Reference ZwallyZwally and others (2005), for example, removed all range variation that correlated with returned-power variation with a correlation coefficient of 0.2 or higher, but limited corrections to between –0.2 and 0.7 mdB^–1 to avoid outliers. (We found the paper of Reference ZwallyZwally and others (2005) especially helpful in detailing the corrections used, their magnitudes and signs and the effects of alternate assumptions on the analysis.)

Reference ZwallyZwally and others (2005) found the total range-power correction averaged over an ice sheet to be small (–0.02cm a^–1 for changes in the surface elevation of Greenland, –0.34cm a^–1 for grounded ice in Antarctica) but with a fairly large spatial variability (standard deviations of 2.36 cma^–1 for Greenland and 2.94 cma^–1 for Antarctica). Single-site corrections are of the same magnitude as remaining signals. Zwally and others noted that for Byrd Station, West Antarctica, this correction shifts an apparent thickening of 5.4±1.3cm a^–1 to a thinning of 1.2 ±0.7 cm a^–1, and the corrected value is consistent with independent evidence from surface global positioning system (GPS) measurements but the uncorrected value is not. Similarly, Reference Wingham, Ridout, Scharroo, Arthern and ShumWingham and others (1998), for 1˚×1˚ regions in inland Antarctica, obtained a mean correction of 1.1 cma^–1, a standard deviation of 6.1 cm a^–1 and a correction ranging from –25.7 to 38.8 cma^–1, based on applying a range-power correlation from June 1993 to December 1994 to a 5 year window. Reference Davis and FergusonDavis and Ferguson (2004) provided additional insight to the range-power correction, seasonal vs interannual changes, spatial distribution in Antarctica, and more.

We believe, however, that it is virtually unavoidable that some climate changes affecting actual range (through increased or decreased snowfall, or increased or decreased temperature affecting the rate of expulsion of air during density increase) will also affect the surface character (through effects on density, layering, melt-layer formation and burial, and surface roughness). Hence, the range-power correction is highly likely to remove signal in at least some places, and the regional nature of some climate changes and some trends means that a near-zero ice-sheet average could mask important signals. Despite a literature much richer than can be cited in a short paper, comprehensive treatments synthesizing ‘ground-truth’ measurements of roughness, surface snow characteristics, radar-derived and independently derived (e.g. by GPS surveying on the surface) elevation changes are generally not available. Even the sign of any induced error is not obvious for this correction.

Long-term monitoring of elevation changes requires accurate intercomparison of datasets collected at different times, a problem that is considered carefully in aerogeo-physics, that will be important if another laser-altimetry satellite is launched, and that has mattered in radar altimetry. Reference ZwallyZwally and others (2005) used an empirical correction to relate datasets from the European Remote-sensing Satellites ERS-1 and ERS-2, which for Greenland required lowering ERS-2 data by 30.7 cm. Reference Johannessen, Khvorostovsky, Miles and BobylevJohannessen and others (2005), using a different empirical technique, obtained a corresponding value of 21.5 cm, although differences in area of coverage in the two studies may explain some or all of this difference in correction. Note that the effect of the Zwally and others correction is larger than the remaining signal, and the difference between the Johannessen and others and Zwally and others corrections (if arising from a true difference and not an area-of-coverage effect) is about as large as the signal, highlighting the importance of the correction. (Work by Reference Davis, Li, McConnell, Frey and HannaDavis and others (2005), Reference Johannessen, Khvorostovsky, Miles and BobylevJohannessen and others (2005), Reference ZwallyZwally and others (2005) and Reference Wingham, Shepherd, Muir and MarshallWingham and others (2006) based on ERS-1 and ERS-2 typically spans 1992–2002, or similar time intervals.)

Changes in air storage in the near-surface layers are important: an estimated rate of ice-sheet thickness change may represent ice, or as much as two-thirds air and only one-third ice, with a corresponding uncertainty in effect on sea level (e.g. Reference WinghamWingham, 2000; Reference CuffeyCuffey, 2001). Using a firn densification model, Reference Arthern and WinghamArthern and Wingham (1998) estimated that for conditions corresponding to Site 2, Greenland, a 1˚C warming would cause an equilibrium thinning of the firn (expulsion of air) of 0.53 m, with half of the change completed over 45 years. In comparison, a 10% increase in accumulation rate would increase air storage in the firn by 0.46 m, with half of the change completed in only 6 years (yielding an average thickening rate over the first 6 years following the perturbation of almost ˚ cma^–1, vs thinning of just over 1 cma^–1 averaged over the first 45 years for the temperature response). Accumulation probably increases somewhat less than 10% ˚C^–1 (e.g. Reference Kapsner, Alley, Shuman, Anandakrishnan and GrootesKapsner and others, 1995), but any increase in excess of 1–2% ˚C^–1 would cause the accumulation-rate changes to initially dominate, according to the Reference Arthern and WinghamArthern and Wingham (1998) model. The model of Reference Zwally and LiZwally and Li (2002) is somewhat more temperature-sensitive. Analyses by Reference McConnellMcConnell and others (2000) suggested that elevation changes in central Greenland were primarily controlled by changes in accumulation rate, although without separating the effects of variations in mass accumulation from variations in the density of that accumulation.

Reference ZwallyZwally and others (2005) used estimated temperatures from satellite data and a firn densification model to correct elevation changes for the effect of temperature on the rate of densification. Warming in Greenland drove a calculated surface lowering of 1.7 cm a^–1 in Greenland (23 Gt a^–1 of ice equivalent), with a surface lowering of 1.6 cma^–1 for the West Antarctic ice sheet (28 Gt a^–1) and a rise in the East Antarctic ice sheet of 0.2 cma^–1 (19 Gt a^–1). Zwally and others did not make a corresponding correction for accumulation-rate effects on near-surface density. Hence, as discussed by Zwally and others, if temperature and accumulation rate rose recently at a site where no thickness change was measured, the authors would calculate that the surface should be dropping in response to the warming, and would infer that the lack of elevation change demonstrated increase of ice thickness at that site over that time interval.

However, in recognition of the possible effects of accumulation rate on near-surface density, Zwally and others also reported the mass balance assuming that the inland changes in Greenland, and the changes in Antarctica, were firn rather than ice. The effect was to shift Greenland from growing by 10.8±2.6 Gt a^–1 to shrinking by 18.4±2.0 Gt a^–1, and to shift Antarctica from shrinking by 30.3±12 Gt a^–1 to shrinking by 13.6±5.4 Gt a^–1 for firn of 400 kgm^–3. Note that there is only a small effect on the combined mass balance of the ice sheets if both firn numbers (combined shrinkage of 32 ±6Gt a^–1) or both ice numbers (combined shrinkage of 19±12 Gt a^–1) are used. However, as discussed below, the strong evidence for recent increase in accumulation rate in inland Greenland, but lack of strong evidence for a corresponding increase in Antarctica, argues that something closer to the firn number for Greenland and to the ice number for Antarctica may be more appropriate; simply using those numbers would give a combined mass balance over the 1992–2002 interval of shrinkage by 49±12 Gt a^–1. In the Zwally and others study, the uncertainty related to near-surface density change thus is as large as about 30 Gt a^–1 for the ice sheets.

Reference Thomas, Frederick, Krabill, Manizade and MartinThomas and others (2006) assumed a uniform surface lowering for Greenland of 1 cma^–1 in response to warming-induced densification, and then assigned measured ice-sheet thickening inland a density of 600 kgm^–3 to allow for increased air storage near the surface in response to increased accumulation rate, and 900 kgm^–3 near the coast where ablation removes all of the seasonal snow. To the best of our knowledge, no one has yet conducted a full model-driven correction for temperature and accumulation-rate effects.

Isostatic corrections can affect altimetry as well. Discussion is included in the next subsection.

Gravimetry

The GRACE (Gravity Recovery and Climate Experiment, managed jointly by NASA and the German Aerospace Research Center (DLR)), was launched in March 2002 (Reference Tapley, Bettardpur, Watkins and ReigberTapley and others, 2004), and offers a great opportunity for an independent measure of ice-sheet mass balance. A breakaway group in a bicycle race will, on cresting a steep climb and starting the descent, move away from the still-climbing peloton, but the peloton will close the gap when the breakaway begins the next climb. A record of the positions of the breakaway and the peloton would reveal the locations of the mountains to an attentive observer. In the same way, the changing positions of the GRACE satellites reveal subtle features of the Earth’s gravity field reflecting mass differences, and time evolution can reveal changes in mass storage.

Errors arise from numerous sources, many of which are considered by Reference Wahr, Swenson and VelicognaWahr and others (2006). The GRACE ‘footprint’ is perhaps 1000 km across, so changes well beyond the region of interest can be important. Different techniques exist for making this correction and have been used by the different groups working on the ice-sheet mass balance. Inspection of the four GRACE-based estimates in Figure 1 highlights the magnitudes of some of the remaining difficulties. The short time over which the satellites have been operating (since 2002) is of considerable concern as well.

Changes in bedrock elevation, primarily arising from isostatic response to past changes in mass loading, play a larger role in gravimetry than in altimetry. Because flowing mantle rocks have density ~3300 kgm^–3 vs ~910 kgm^–3 for ice, a given elevation change will affect the gravitational field ~3.6 times more if caused by isostasy than if caused by change in ice thickness.

For Greenland, Reference ZwallyZwally and others (2005) combined results from three isostatic treatments to estimate ongoing isostatic uplift of 0.6±0.4mma^–1, with faster uplift of 5.4±0.07mma^–1 for Antarctica. Assuming the Antarctic value is accurate, failure to have included it would have biased mass balance of Antarctica estimated from altimetry by ~60 Gt a^–1, but mass balance estimated from gravimetry by almost 220 Gt a^–1. As noted by Reference Chen, Wilson, Blankenship and TapleyChen and others (2006a), ‘estimates of Antarctic snow/ice mass rates from GRACE data are completely dependent on the adopted PGR [postglacial rebound] model, with uncertainties that might be on the order of 100%’. Using GRACE data, Chen and others found a region of rapid mass loss in West Antarctica, and a region of rapid mass gain in East Antarctica, with a net near zero; however, the authors argued that independent glaciological and meteorological data point to the West Antarctic anomaly as being a feature of ice-mass loss, and the East Antarctic anomaly as being an error in the isostatic adjustment modeling.

Note that even for altimetry, the uncertainties in isostatic behavior are important. Reference ZwallyZwally and others (2005) estimated an isostatic uplift rate for the region covered by ERS radar altimetry of 4.5 mma^–1 (and a slightly larger rate of 5.4 mma^–1 for the entire grounded ice sheet) vs the value of 1.7 mma^–1 for the ERS-covered region adopted by Reference Wingham, Shepherd, Muir and MarshallWingham and others (2006). The areas of ERS data coverage in the two studies were not identical although quite similar, so these numbers are not exactly comparable. Nonetheless, had the Zwally and others isostatic adjustment been adopted by Wingham and others, their central estimate of ice-sheet growth would have been reduced by more than half.

Other geodetic constraints

Reference MunkMunk (2002) noted that joint analysis of the history of changing length of day from eclipse records, the related ongoing changes in the spherical harmonic coefficients of the geopotential, and changes in the rotation vector of the planet (true polar wander) apparently ruled out the possibility of a large mass flux from the ice sheets to the oceans. (Motion of mass from the near-polar ice sheets to the more equatorial oceans slows the Earth’s rotation like a spinning ice skater extending her arms; the motion of mass associated with ongoing isostatic response to the end of the last ice age partially offsets this; and the off-spin-axis changes in mass flux excite true polar wander.) However, Reference Mitrovica, Wahr, Matsuyama, Paulson and Tami-sieaMitrovica and others (2006) argued that use of measured rather than calculated shape of the planet in the calculations (including ‘bulging’ of the Earth at the equator from non-rotational causes such as mantle convection) weakens the Munk triple constraint, allowing (but not necessarily requiring) accelerated late-20th-century contribution to sea-level rise from melting of land ice up to ~360 Gt a^–1 (~1mma^–1 of sea-level equivalent).

Input–output

Rapid improvements in atmospheric analyses are narrowing uncertainties on surface-balance terms, matching improvements in ice-flow measurements, and rapidly reducing errors that once seemed almost insurmountable.

For Greenland, the recent analyses of Reference Hanna, Huybrechts, Janssens, Cappelen, Steffen and StephensHanna and others (2005) and Reference BoxBox and others (2006) used European Centre for Medium-range Weather Forecasts (ECMWF) operational and re-analysis products. Reference Hanna, Huybrechts, Janssens, Cappelen, Steffen and StephensHanna and others (2005) downscaled the global fields to Greenland surface observations using fuzzy interpolation, and Reference BoxBox and others (2006) embedded the mesoscale model PolarMM5 in the global fields and adjusted to match surface observations. Complete surface mass-balance calculations were made (snowfall, sublimation, meltwater generation, runoff and refreezing, etc.). Large interannual variability complicates interpretation of trends, and important baseline differences still exist (see Fig. 1).

For Antarctica, similar efforts are less accurate owing to the larger size of the ice sheet, greater uncertainties in the atmospheric products, and fewer and shorter ground-truth records. Studies using US National Centers for Environmental Prediction (NCEP), ECMWF and Japanese re-analysis products, and two different mesoscale models driven by ECMWF re-analysis and one by NCEP re-analysis, found no strong trends in Antarctic accumulation from 1980 to 2004 (Reference Van de Berg, van den Broeke, Reijmer and van MeijgaardVan de Berg and others, 2006) or for 1985–2001 (Reference Monaghan, Bromwich and WangMonaghan and others, 2006), although the uncertainties remain large.

Ice-flow output must be added to surface fluxes. This requires knowledge of ice velocity and thickness, collected where flotation begins. Surface velocities may be obtained in many ways, but satellite data are especially useful, including synthetic aperture radar (SAR) interferometry, speckle tracking and feature tracking. Thicknesses are from ice-penetrating radar. Uncertainties are noted in Reference ThomasThomas and others (2004) and Reference Rignot and KanagaratnamRignot and Kanagaratnam (2006), among others. These uncertainties include the difficulty of obtaining thickness data encircling an ice sheet at the grounding line at the same time as velocity measurements are made; depth variation of velocity, especially where surveys are not exactly at the grounding line; and questions about seasonal variations, near-surface density variations, etc.

Synopsis

There exists no optimal technique to measure ice-sheet mass balance. Important errors are associated with all of the available techniques. For some, the sign of a bias can be estimated: for example, a study relying only on radar altimetry, with its large footprint and difficulty of measuring steep surfaces, is likely to underestimate thinning localized in narrow troughs draining steep coastal regions (Reference Thomas, Frederick, Krabill, Manizade and MartinThomas and others, 2006). In other cases, even the sign of the bias is not clear.

The commonality of signal detected by different techniques seems important. The techniques are mostly independent. (Altimetry and gravimetry do share dependence on isostatic calculations, but the different sensitivities partially alleviate this problem.) From inspection of Figure 1, it is difficult to avoid the conclusion that the Greenland ice sheet was losing mass at an accelerating rate over the last decade or longer. This conclusion is strengthened if one remembers that the H and B records in the figure (Reference Hanna, Huybrechts, Janssens, Cappelen, Steffen and StephensHanna and others, 2005; Reference BoxBox and others, 2006) do not include the known ice-flow accelerations (hence, arrows are added to those balance indications in the figure). Also, the known increase in accumulation rate in high-elevation regions leads one to expect that air storage in the near-surface layers has increased there, so that changes in elevation there are occurring at lower density than ice, favoring the shrinking-ice-sheet rather than growing-ice-sheet side of the Z box. Remembering that 360 Gt is ~1mm of sea-level equivalent, it appears that uncertainties have not yet been reduced to 0.1 mma^–1 of sea-level change.

The situation in Antarctica is less clear. Because no strong trend in accumulation rate has been detected, the lower end of the Z box (elevation changes are ice) may be preferred. The different times of collection of some of the datasets may be biasing the results. We believe that the favored interpretation (>50% confidence) includes a recent shift to or acceleration in net mass loss, but we believe that the level of confidence is not especially high.

Greenland

In Greenland, the atmospheric and surface mass-balance calculations indicate an increase in melt-season temperature, occurring with increasing area of melting, increasing meltwater runoff, increasing snow accumulation rate and decreasing surface mass balance (Reference Hanna, Huybrechts, Janssens, Cappelen, Steffen and StephensHanna and others, 2005; Reference BoxBox and others, 2006; also see Reference Hall, Williams and CaseyHall and others, 2006). Interannual variability is high, so the confidence in some of these trends is not especially high, but these results are at least more likely than not in all cases. A link between the warming and the shift to negative surface mass balance appears strong.

Cause and effect is somewhat harder to demonstrate for the accelerations in ice-flow velocity, although effects of warming appear to be the most likely explanation. Reference ThomasThomas and others (2004) showed mostly by a process of elimination that the large thinning of the floating tongue of Jakobshavns Isbræ, Greenland, preceding its break-up was linked to increased basal melting, suggesting the influence of warmer waters, with increased flow velocity and thinning following. Reference Luckman, Murray, de Lange and HannaLuckman and others (2006) noted the similar behavior of Helheim and Kangerdlugssuaq glaciers on the east coast of Greenland: ‘The period of continued warming and thinning appears to have primed these glaciers for a step-change in dynamics not included in current models. We should expect further Greenland outlet glaciers to follow suit’ (abstract). The increased meltwater runoff from the surface also is probably contributing to increased ice-flow velocity through increased basal lubrication following drainage through moulins in at least some places (Reference Zwally, Abdalati, Herring, Larson, Saba and SteffenZwally and others, 2002).

Please note that we have made no attempt to attribute the warming to human forcing vs natural variations, nor have we addressed the issue of whether past natural warming has caused past ice-sheet mass loss. We have not tried to separate ‘fluctuation’ from ‘trend’. We simply note that the evidence favors the interpretation that the Greenland ice sheet has experienced a recent acceleration of mass loss in response to the effects of recent environmental warming, with melt-season air temperatures and associated effects on energy balance probably contributing, along with ocean temperatures.

Antarctica

For Antarctica, strong regional temperature trends, large variability but weak continent-wide temperature trends are indicated (e.g. Reference Thompson and SolomonThompson and Solomon, 2002; Reference SchneiderSchneider and others, 2006). (Large fluctuations are also observed in Greenland records.) Because of the restricted nature of Antarctic surface melting and the small runoff, any continent-wide temperature change is not especially important in mass-balance modeling. Little trend is observed in accumulation rates, but with much uncertainty (Reference Monaghan, Bromwich and WangMonaghan and others, 2006).

Strong warming has been observed in the Antarctic Peninsula region, contributing to the break-up of the Larsen B and Wordie ice shelves and associated ice-flow acceleration (e.g. Reference Morris, Vaughan, Domack, Leventer, Burnett, Bindschadler, Convey and KirbyMorris and Vaughan, 2003; Reference Scambos, Bohlander, Shuman and SkvarcaScambos and others, 2004). Enhanced basal melting, probably from warmer waters but possibly from changes in oceanic circulation, appears to have contributed to loss of the Larsen B and to thinning of ice shelves in the Pine Island Bay region (Reference Shepherd, Wingham, Payne and SkvarcaShepherd and others, 2003, Reference Shepherd, Wingham and Rignot2004), allowing ice-flow speed-up (e.g. Reference Dupont and AlleyDupont and Alley, 2005).

Reference HuybrechtsHuybrechts (2002) found a long-term trend of ice-sheet shrinkage (by about 90 Gt a^–1, a notable amount relative to the imbalances suggested in Figure 2) in most of his modeling sensitivity studies; however, the trend was estimated to end within the next millennium, and timing of deglacial forcing is probably not known to better than a millennium (such that the trend might be larger, or might be nearly finished; notes about model behavior, below, are at least suggestive that the real ice sheet may change more rapidly than the model one, favoring completion of the trend already).

Given the large remaining uncertainties in mass balance, accumulation-rate changes and long-term trend, one might still argue that increasing accumulation rate in response to warming is increasing ice-sheet mass more than accelerated coastal flow is decreasing that mass, and that any shrinkage is a result of the long-term trend. However, with a central estimate of little accumulation-rate change to date, a central estimate of recently increased mass loss, and the evidence that warming contributed to this recent increase, it appears to us to be at least more likely than not that the ice sheet has responded to recent near-coastal warming by losing mass.