The U.S. <strong>Climate</strong> <strong>Change</strong> <strong>Science</strong> <strong>Program</strong> Chapter 2improved ice-discharge estimates, yet incompletedata coverage and residual errors implyerrors on total discharge of 2% (Rignot et al.,2008). Consequently, assuming these errors inboth snow accumulation and ice losses, currentmass-budget uncertainty is ~ ± 92 Gt a –1(Rignot et al., 2008) for Antarctica and ± 35 Gta –1 for Greenland. Moreover, additional errorsmay result from accumulation estimates beingbased on data from the past few decades; atleast in Greenland, we know that snowfall isincreasing with time. Similarly, it is becomingclear that glacier velocities can change substantiallyover quite short time periods (Rignotand Kanagaratnam, 2006), and the time periodinvestigated (last decade) showed an increasein ice velocities, so these error estimates mightwell be lower limits.3.1.2 Repeated AltimetryRates of surface-elevation change with time(dS/dt) reveal changes in ice-sheet mass aftercorrection for changes in depth/density profilesand bedrock elevation, or for hydrostaticequilibrium if the ice is floating. Satellite radaraltimetry (SRALT) has been widely used (e.g.,Shepherd et al., 2002; Davis et al., 2005; Johannessenet al., 2005; Zwally et al., 2005), togetherwith laser altimetry from airplanes (Arendtet al., 2002; Krabill et al., 2000), and fromNASA’s ICESat (Zwally et al., 2002a; Thomaset al., 2006). Modeled corrections for isostaticchanges in bedrock elevation (e.g., Peltier, 2004)are small (a few millimeters per year) but witherrors comparable to the correction. Those fornear-surface snow density changes (Arthern andWingham, 1998; Li and Zwally, 2004) are larger(1 or 2 cm a –1 ) and also uncertain.Wingham et al., 2006) that are smaller than thedifferences between different interpretations ofessentially the same SRALT data (Johannessenet al., 2005; Zwally et al., 2005). In addition toprocessing errors, uncertainties result from thepossibility that SRALT estimates are biased bythe effects of local terrain or by surface snowcharacteristics, such as wetness (Thomas et al.,2008). Observations by other techniques revealextremely rapid thinning along Greenlandglaciers that flow along depressions where dS/dtcannot be inferred from SRALT data, and collectivelythese glaciers are responsible for mostof the mass loss from the ice sheet (Rignot andKanagaratnam, 2006), implying that SRALTdata underestimate near-coastal thinning ratessignificantly. Moreover, the zone of summermelting in Greenland progressively increasedbetween the early 1990s and 2005 (Box et al.,2006), probably raising the radar reflectionhorizon within near-surface snow by a meter ormore over a significant fraction of the ice-sheetpercolation facies (Jezek et al., 1994). Comparisonbetween SRALT and laser estimates ofdS/dt over Greenland shows differences that areequivalent to the total mass balance of the icesheet (Thomas et al., 2008).3.1.2.2 Aircraft and SatelliteLaser AltimetryLaser altimeters provide data that are easierto validate and interpret: footprints are small(about 1 m for airborne laser, and 60 m forICESat), and there is negligible laser penetrationinto the ice. However, clouds limit data acquisi-3.1.2.1 Satellite Radar AltimetryAvailable SRALT data are from altimeters witha beam width of 20 km or more, designed anddemonstrated to make accurate measurementsover the almost flat, horizontal ocean. Datainterpretation is more complex over sloping andundulating ice-sheet surfaces with spatially andtemporally varying dielectric properties. Errorsin SRALT-derived values of dS/dt are typicallydetermined from the internal consistency of themeasurements, often after iterative removal ofdS/dt values that exceed some multiple of the localvalue of their standard deviation. This resultsin small error estimates (e.g., Zwally et al., 2005;42
Abrupt <strong>Climate</strong> <strong>Change</strong>tion, and accuracy is affected by atmosphericconditions and particularly by laser-pointingerrors. The strongest limitation by far is thatexisting laser data are sparse compared toSRALT data.Airborne laser surveys over Greenland in1993–94 and 1998–89 yield elevation estimatesaccurate to ~10 cm along survey tracks (Krabillet al., 2002), but with large gaps between flightlines and an incomplete coverage of the glaciers.ICESat orbit-track separation is also quite largecompared to the size of a large glacier, particularlyin southern Greenland and the AntarcticPeninsula where rapid changes are occurring,and elevation errors along individual orbittracks can be large (many tens of centimeters)over sloping ice. Progressive improvement inICESat data processing is reducing these errorsand, for both airborne and ICESat surveys,most errors are independent for each flight lineor orbit track, so that estimates of dS/dt averagedover large areas containing many surveytracks are affected most by systematic ranging,pointing, or platform-position errors, totalingprobably less than 5 cm. In Greenland, suchconditions typically apply at elevations above1,500–2,000 m. dS/dt errors decrease with increasingtime interval between surveys. Nearerthe coast there are large gaps in both ICESatand airborne coverage, requiring dS/dt valuesto be supplemented by degree-day estimates ofanomalous melting (Krabill et al., 2000, 2004).This supplementation increases overall errorsand almost certainly underestimates total lossesbecause it does not take full account of dynamicthinning of unsurveyed outlet glaciers.In summary, dS/dt errors cannot be preciselyquantified for either SRALT data, because ofthe broad radar beam, limitations with surfacetopography at the coast, and time-variablepenetration, or laser data, because of sparsecoverage. The SRALT limitations discussedabove will be difficult to resolve. Laser limitationsresult primarily from poor coverage andcan be partially resolved by increasing spatialresolution.All altimetry mass-balance estimates includeadditional uncertainties in:1. The density (rho) assumed to convertthickness changes to mass changes. If changesare caused by recent changes in snowfall, theappropriate density may be as low as 300 kilogramsper cubic meter (kg m –3 ); for long-termchanges, it may be as high as 900 kg m –3 . This isof most concern for high-elevation regions withsmall dS/dt, where the simplest assumption isrho = 600 ± 300 kg m –3 . For a 1-cm a –1 thicknesschange over the million square kilometers ofGreenland above 2,000 m, uncertainty wouldbe ± 3 Gt a –1 . Rapid, sustained changes, commonlyfound near the coast, are almost certainlycaused by changes in melt rates or glacier dynamics,and for which rho is ~900 kg m –3 .2. Possible changes in near-surface snowdensity. Densification rates are sensitive tosnow temperature and wetness. Warm conditionsfavor more rapid densification (Arthernand Wingham, 1998; Li and Zwally, 2004), andmelting is likely to be followed by refreezing asice. Consequently, recent Greenland warmingprobably caused surface lowering simply fromthis effect. Corrections are inferred from largelyunvalidated models and are typically