Several techniques are used to measure the mass balance of large ice masses. The mass budget approach compares input from snow accumulation with output from ice flow and melt water runoff. Repeated altimetry measures surface elevation changes. Temporal variations in gravity over the ice sheets reveal mass changes. Changes in day length and in the direction of the Earth’s rotation axis also reveal mass redistribution.
18.104.22.168.1 Mass budget
Snow accumulation is often estimated from annual layering in ice cores, with interpolation between core sites using satellite microwave measurements or radar sounding (Jacka et al., 2004). Increasingly, atmospheric modelling techniques are also applied (e.g., Monaghan et al., 2006). Ice discharge is calculated from radar or seismic measurements of ice thickness, and from in situ or remote measurements of ice velocity, usually where the ice begins to float and velocity is nearly depth-independent. A major advance since IPCC (2001) has been widespread application of Interferometric Synthetic Aperture Radar (InSAR) techniques from satellites to measure ice velocity over very large areas of the ice sheets (e.g., Rignot et al., 2005). Calculation of mass discharge also requires estimates for runoff of surface melt water, which is large for low-elevation regions of Greenland and parts of the Antarctic Peninsula but small or zero elsewhere on the ice sheets. Surface melt amounts usually are estimated from modelling driven by atmospheric reanalyses, global models or climatology, and often calibrated against surface observations where available (e.g., Hanna et al., 2005; Box et al., 2006). The typically small mass loss by melting beneath grounded ice is usually estimated from models. Mass loss from melting beneath ice shelves can be large, and is difficult to measure; it is generally calculated as the remainder after accounting for other mass inputs and outputs.
Ice sheet mass inputs and outputs are difficult to estimate with high accuracy. For example, van de Berg et al. (2006) summarised six estimates of net accumulation on the grounded section of Antarctica published between 1999 and 2006, which ranged from 1,811 to 2,076 Gt yr–1 or ±7% about the midpoint. Transfer of 360 Gt of grounded (non-floating) ice to the ocean would raise sea level about 1 mm. Uncertainty in the Greenland accumulation rate is probably about 5% (Hanna et al., 2005; Box et al., 2006). Although broad InSAR coverage and progressively improving estimates of grounding-line ice thickness have substantially improved ice discharge estimates, incomplete data coverage implies uncertainties in discharge estimates of a few percent. Uncorrelated errors of 5% on input and output would imply mass budget uncertainties of about 40 Gt yr–1 for Greenland and 140 Gt yr–1 for Antarctica. Large interannual variability and trends also complicate interpretation. Box et al. (2006) estimated average accumulation on the Greenland Ice Sheet of 543 Gt yr–1 from 1988 to 2004, but with an annual minimum of 482 Gt yr–1, a maximum of 613 Gt yr–1 and a best-fit linear trend yielding an increase of 68 Gt yr–1 during the period. Glacier velocities can change substantially, sometimes in months or years, adding to the overall uncertainty of mass budget calculations.
22.214.171.124.2 Repeated altimetry
Surface elevation changes reveal ice sheet mass changes after correction for changes in depth-density profiles and in bedrock elevation, or for hydrostatic equilibrium if the ice is floating. Satellite radar altimetry (SRALT) has been widely used to estimate elevation changes (Shepherd et al., 2002; Davis et al., 2005; Johannessen et al., 2005; Zwally et al., 2006), together with laser altimetry from airplanes (Krabill et al., 2004) and from the Ice, Cloud and land Elevation Satellite (ICESat; Thomas et al., 2006). Modelled corrections for isostatic changes in bedrock elevation are small (a few millimetres per year), but with uncertainties nearly as large as the corrections in some cases (Zwally et al., 2006). Corrections for near-surface firn density changes are larger (>10 mm yr–1; Cuffey, 2001) and also uncertain.
Radar altimetry has provided long-term and widespread coverage for more than a decade, but with important challenges (described by Legresy et al., 2006). The available SRALT data are from altimeters with a beam width of 20 km or more, designed and demonstrated to make accurate measurements over the almost flat, horizontal ocean. Data interpretation is more complex over sloping, undulating ice sheet surfaces with spatially and temporally varying dielectric properties and thus penetration into near-surface firn. Empirical corrections are applied for some of these effects, and for inter-satellite biases. The correction for the offset between the European Remote Sensing Satellite (ERS-1 and ERS-2) altimeters is reported by Zwally et al. (2006) to affect mass change estimates for the interval 1992 to 2002 by about 50 Gt yr–1 for Greenland, and to differ from the corresponding correction of Johannessen et al. (2005) by about 20 Gt yr–1, although some of this difference may reflect differences in spatial coverage of the studies combined with spatial dependence of the correction. Changes in surface dielectric properties affect the returned waveform and thus the measured range, so a correction is made for elevation changes correlated to returned-power changes. This effect is small averaged over an ice sheet but often of the same magnitude as the remaining signal at a point, and could remove part or all of the signal if climate change affected both elevation and surface character, hence returned power.
The SRALT tracking algorithms use leading edges of reflected radar waveforms, thus primarily sampling higher-elevation parts of the large footprint. This probably introduces only small errors over most of an ice sheet, where surfaces are nearly flat. However, glaciers and ice streams often flow in surface depressions that can be narrower than the radar footprint, so that SRALT-derived elevation changes are weighted towards slower-moving ice at the glacier sides (Thomas et al., 2006). This is of most concern in Greenland, where other studies show thinning along outlet glaciers just a few kilometres wide (Abdalati et al., 2001). Elevation-change estimates from SRALT have not been validated against independent data except at higher elevations, where surfaces are nearly flat and horizontal and dielectric properties nearly unchanging (Thomas et al., 2001). Although SRALT coverage is lacking within 900 km of the poles, and some data are lost in steep regions, coverage has now been achieved for about 90% of the Greenland Ice Sheet and 80% of the Antarctic Ice Sheet (Zwally et al., 2006) (Figure 4.19).
Laser altimeters reduce some of the difficulties with SRALT by having negligible penetration of near-surface layers and a smaller footprint (about 1 m for airborne laser, and 60 m for ICESat). However, clouds limit data acquisition, and accuracy is affected by atmospheric conditions and particularly by laser pointing errors. Airborne surveys over Greenland in 1993/1994 and 1998/1999 yielded estimates of elevation change accurate to ±14 mm yr–1 along survey tracks (Krabill et al., 2002). However, the large gaps between flight lines must be filled, often by simple interpolation in regions of weak variability or by interpolation using physical models in more complex regions (Krabill et al., 2004; Figure 4.17).
126.96.36.199.3 Geodetic measurements, including measurement of temporal variations in Earth gravity
Since 2002, the Gravity Recovery and Climate Experiment (GRACE) satellite mission has been providing routine measurement of the Earth’s gravity field and its temporal variability. After removing the effects of tides, atmospheric loading, etc., high-latitude data contain information on temporal changes in the mass distribution of the ice sheets and underlying rock (Velicogna and Wahr, 2005). Estimates of ice sheet mass balance are sensitive to modelled estimates of bedrock vertical motion, primarily arising from response to changes in mass loading from the end of the last ice age. Velicogna and Wahr (2005) estimated a correction for Greenland Ice Sheet mass balance of 5 ± 17 Gt yr–1 for the bedrock motion, with an equivalent value of 177 ± 73 Gt yr–1 for Antarctica (Velicogna and Wahr, 2006). (Note that stated uncertainties for ice sheet mass balances referenced to published papers are given here as published. Some papers include error terms that were estimated without formal statistical derivations, and other papers note omission of estimates for certain possible systematic errors, so that these as-published errors generally cannot be interpreted as representing any specific confidence interval such as 5 to 95%.)
Other geodetic data provide constraints on mass changes at high latitudes. These data include the history of changing length of day from eclipse records, the related ongoing changes in the spherical-harmonic coefficients of the geopotential, and true polar wander (changes in the planet’s rotation vector; Peltier, 1998; Munk, 2002; Mitrovica et al., 2006). At present, unique solutions are not possible from these techniques, but hypothesised histories of ice sheet changes can be tested against the data for consistency, and progress is rapidly being made.