Mass changes of the Greenland and Antarctic ice sheets and ...Mass changes of the Greenland and Antarctic ice sheets and shelves and contributions to sea-level rise: 1992 2002 H. Jay

Mass changes of the Greenland and Antarctic ice sheets andshelves and contributions to sea-level rise 1992ndash2002

H Jay ZWALLY1 Mario B GIOVINETTO2 Jun LI2 Helen G CORNEJO2

Matthew A BECKLEY2 Anita C BRENNER3 Jack L SABA2 Donghui YI2

1Cryospheric Sciences Branch Code 6141 NASA Goddard Space Flight Center Greenbelt Maryland 20771 USAE-mail zwallyicesat2gsfcnasagov

2SGT Inc Code 6141 NASA Goddard Space Flight Center Greenbelt Maryland 20771 USA3Science Systems and Application Inc 10210 Greenbelt Road Suite 600 Lanham Maryland 20706 USA

ABSTRACT Changes in ice mass are estimated from elevation changes derived from 105 years(Greenland) and 9 years (Antarctica) of satellite radar altimetry data from the European Remote-sensingSatellites ERS-1 and -2 For the first time the dHdt values are adjusted for changes in surface elevationresulting from temperature-driven variations in the rate of firn compaction The Greenland ice sheet isthinning at the margins (ndash42 2Gt andash1 below the equilibrium-line altitude (ELA)) and growing inland(+53 2Gt andash1 above the ELA) with a small overall mass gain (+113Gt andash1 ndash003mmandash1 SLE (sea-levelequivalent)) The ice sheet inWest Antarctica (WA) is losing mass (ndash474Gt andash1) and the ice sheet in EastAntarctica (EA) shows a small mass gain (+1611Gt andash1) for a combined net change of ndash3112Gt andash1

(+008mmandash1 SLE) The contribution of the three ice sheets to sea level is +005 003mmandash1 TheAntarctic ice shelves show corresponding mass changes of ndash9511Gt andash1 in WA and +14210Gt andash1

in EA Thinning at the margins of the Greenland ice sheet and growth at higher elevations is an expectedresponse to increasing temperatures and precipitation in a warming climate The marked thinnings in thePine 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 shelvesThe ice growth in the southern Antarctic Peninsula and parts of EA may be due to increasing precipitationduring the last century

INTRODUCTION

The mass balances of the Greenland and Antarctic ice sheetsare of interest because of their complex linkage to climatevariability and their direct effects on sea-level change Inrecent decades the spatial distribution of mass input andoutput data has greatly improved as field observations havebeen complemented by advances in remote sensing anddynamic modeling Approximately 399Gt andash1 of ice isaccumulated on the Greenland ice sheet above the equi-librium line and approximately 1637Gt andash1 on the Antarcticice sheet (modified from Giovinetto and Zwally 2000Zwally and Giovinetto 2001) which is equivalent to theremoval of 56mmandash1 from the oceans The net massbalance is the difference between the mass input in the zoneof net accumulation and the sum of the net ablation at thesurface (including runoff) the direct discharge of ice intothe ocean and discharge of subglacial water across thegrounding line Uncertainties in previous mass-balanceestimates ( 530Gt andash1 for Greenland and 384Gt andash1 forAntarctica (Huybrechts and others 2001)) have been largelydue to the difficulty of accurately measuring all the massinput and output fluxes (eg Rignot and Thomas 2002)

Expected responses of the ice sheets to climate warmingare both growth in thickness of the inland ice areas due toincreasing precipitation and thinning near the margins dueto increasing surface melting (Huybrechts and others 2001)In addition dynamic ice thinning near the margins may beinduced by processes such as removal or thinning ofadjacent ice shelves or ice tongues (Thomas 2003 Rignotand others 2004 Scambos and others 2004) as well asenhanced basal sliding due to surface meltwater reaching

the icendashbedrock interface (Zwally and others 2002c) Alleyand others (2003) reviewed the state of knowledge of ice-sheet behavior from recent observational and modelingadvances and suggested that the ice sheets may have agreater sensitivity to climate warming than previouslyconsidered

Since the first results using altimeter surveys of ice-sheetelevation changes to estimate changes in ice volume andmass balance (Zwally 1989) there has been an increasinguse of altimetric measurements of elevation change (dHdt)to improve upon estimates from mass-flux studies Recentresults include the detection of significant thinning of themargins of the Greenland ice sheet which was attributed toincreases in both melting and dynamic thinning (Abdalatiand others 2001 Krabill and others 2004) thickening of theEA ice sheet attributed to increases in precipitation (Davisand others 2005) and growth of the interior of Greenland(Johannessen and others 2005) Nevertheless a comprehen-sive assessment of the current mass balance of the ice sheetshas not beenmade due in part to the limited performances ofsatellite radar altimeters over the steeper ice-sheet marginsand in part to limitations in the spatial and temporal coverageof airborne laser-altimeter surveys Elevation changes arealso caused by temporal variations in the rate of firncompaction (Zwally 1989 Braithwaite 1994 Arthern andWingham 1998 Zwally and Li 2002) but corrections forthis effect have not previously been made

In this study we extend the analysis of radar altimeterdata from the two European Remote-sensing Satellites (ERS-1 and -2) to 900 of the Greenland ice sheet 771 of theAntarctic ice sheet and 818 of the Antarctic ice shelves InGreenland we use results of Airborne Topographic Mapper

Journal of Glaciology Vol 51 No 175 2005 509

(ATM) laser-altimeter surveys to increase coverage of themargins We also use optimal-interpolation procedures toprovide nearly complete spatial coverage of the ice sheetsand shelves (Figs 1a and 2a) For the first time we use a firncompaction model with a 20 year record of satellite-basedsurface temperatures to calculate corrections for elevationchanges due to changes in the rate of firn compactioncaused by temporal variations in firn temperature and near-surface melting

OBSERVED AND INTERPOLATED ELEVATIONCHANGES (dHdt )Measurements of ice surface elevations (H) from ERS-1 and-2 radar altimeters are compiled as elevation time seriesH(t) from which elevation change (dHdt) values are derived(Fig 3) The ERS altimeters operated in either ocean modewith a resolution of 45 cm per range gate or ice mode with aresolution of 182 cm per range gate We use only ice modedata because of a spatially variant bias between the modesand the greater spatial and temporal coverage of the icemode data We applied our V4 range-retracking algorithmatmospheric range corrections instrument corrections slopecorrections and an adjustment for solid tides (Zwally andBrenner 2001) Instrument corrections include subtractionof a 409 cm bias from ERS-1 elevations to account for adifferent instrument parameter used for ERS-2 (Femenias1996) and corrections for drifts in the ultra-stable oscillatorand bias changes in the scanning point target response thatare obtained from the European Space Agency We use theDUT DGM-E04 orbits which have a radial orbit precision of5ndash6 cm (Scharroo and Visser 1998)

The time periods are from mid-April 1992 to mid-October2002 for Greenland and to mid-April 2001 for AntarcticaThe series are constructed for gridpoints nominally 50 kmapart from sets of elevation differences measured at orbitalcrossovers using time periods of 91 days Our methodsenable us to obtain useful H(t) series over more of the ice-sheet area than some other analyses have For mostgridpoints crossovers within a 100 km circle centered onthe gridpoint are used and within 200 km for a few pointsCrossover selection is also limited to elevations within250m of the elevation at the gridpoint center which forslopes gt1200 restricts the selected areas to bands alongelevation contours where the elevation changes tend to bespatially coherent The first sequence of elevation differencesat crossings between period T1 and all successive Ti iscombined with the second sequence of those for crossingsbetween T2 and all successive Ti and so forth for alladditional sequences which are then combined in one H(t)(Zwally and Brenner 2001) The resulting H(t) series use allindependent crossovers including inter-satellite crossoverswhich greatly increases the number of crossovers and theaccuracy of the results (more crossovers and longer timeintervals) as compared to using only the first sequence oronly intra-satellite crossovers For Greenland we have16106 crossovers from ERS-1ERS-1 52 106 from ERS-2ERS-2 and 59 106 from ERS-1ERS-2 For Antarctica wehave 157 106 crossovers from ERS-1ERS-1 276106 fromERS-2ERS-2 and 419 106 from ERS-1ERS-2 whereas onlycrossovers from ERS-1ERS-1 and ERS-2ERS-2 are used byDavis and others (2005)

We obtain dHdt values for 602 (90) of the 670gridpoints on Greenland ice and 4085 (79) of the 5175

Fig 1 Greenland (a) Distribution of surface elevation change data by source derived from ERS-1 and -2 radar altimetry ATM (closest-neighbor interpolation from airborne surveys) and obtained by optimal interpolation ice terminus of coterminous ice sheet (red)equilibrium line (black dashes) 2000m elevation contour (blue) drainage divides (black) drainage system designation (number in circles)and location of H(t) series depicted in Figure 3a (labeled blue full circles) (b) Distribution of elevation change (dHdt) (c) Distribution of ice-thickness change (dIdt)

Zwally and others Mass changes of Greenland and Antarctic ice sheets and shelves510

gridpoints on Antarctic ice ie 77 of the grounded pointsand 82 of the floating points (Table 1) The distancebetween points in our nominal 50 km grid which ismapped in a polar stereographic projection with planetangent at the pole ranges between 48784 km at 608 and52286 km at 908 In Greenland the coterminous ice-sheetarea is sampled by 670 gridpoints excluding islands andice caps not attached by ice (Fig 1b) The area ofAntarctica is sampled by 5238 gridpoints excluding islandsnot attached by ice (Fig 2b) The working grid is reducedto N frac14 5175 by excluding the relatively small areas ofgrounded ice in Graham Land and grounded and floatingice in eastern Palmer Land for which it is not possibleto assemble reliable H(t) series Of the 5175 gridpointsused 4606 are on grounded ice (coterminous ice sheetislands attached by ice and ice rises) and 569 are onfloating ice (ice shelves and ice tongues) East Antarctica(EA) and West Antarctica (WA) are divided on the basisof ice provenance (Fig 2) rather than the traditionalboundary along the Transantarctic Mountains (Zwally andothers 2002b)

Although the ERS-1 and -2 altimeters are nearly identicala significant inter-satellite elevation bias was measured overthe ice sheets during the 13months of simultaneousoperation from May 1995 through May 1996 The ERS-1ERS-2 bias does not occur over the oceans nor on some ofthe flat ice surfaces Although the bias tends to be correlatedwith each of three interrelated parameters (received back-scatter power surface slope and surface elevation) it wasnot possible to formulate the bias as a consistent function ofthese parameters over all of the ice sheet and ice shelvesTherefore for Antarctica we averaged the measured biasesat crossovers between ERS-1 and ERS-2 on a 50 km grid andsmoothed the averages over five gridpoints with a linearweighting with distance from the center For Greenland weaveraged the crossover differences on a 50 km grid usingcrossovers within 400 km and a restriction to elevationswithin 250m of the gridpoint giving a smoothing similarto that for Antarctica

The applied bias correction lowers the ERS-2 elevationsby an average of 307 cm with standard deviation (SD) frac14209 cm spatial variation over Greenland by 175 cm withSD frac14 133 cm over Antarctic grounded ice and by 120 cmwith SD frac14 96 cm over Antarctic floating ice Over Green-land the bias correction lowers the average dHdt byroughly 35 cmandash1 Over Antarctica the correction lowersthe average dHdt by 24 cmandash1 with SD frac14 17 cmandash1 ongrounded ice and by 16 cmandash1 with SD frac14 12 cmandash1 onfloating ice The effects of the bias correction on calculationsof mass change (dMdt) for the ERS gridpoints are roughlyndash50Gt andash1 for Greenland and ndash205Gt andash1 for Antarcticaindicating the importance of this correction For GreenlandJohannessen and others (2005) used a different method tocalculate the bias and state lsquothe calculated spatiallyaveraged ERS-1ERS-2 bias is 215 20 cmrsquo which may besmaller than our 307 cm because we include more lower-elevation gridpoints They also state the effect on dHdtvaries from typically 2 cmandash1 over the interior plateau toabout 20 cmandash1 over the margins (presumably negativevalues) which spans our average ndash35 cmandash1 Davis andothers (2005) in effect apply a bias correction by calculatingseparate H(t) series for ERS-1 and ERS-2 and adjusting themtogether during the 12month overlap period but do not statethe magnitude of their adjustments

Fig 2 Antarctica (a) Distribution of surface elevation change databy source derived from ERS-1 and -2 radar altimetry and obtainedby optimal interpolation coast and grounding line (black heavy)ice-shelf front (black dashes) drainage divides (black thin) of whichthe wider trace depicts the WAEA divide by ice provenancedrainage system designation (number in circles) and location ofH(t)series depicted in Figure 3b (labeled blue full circles) Excluded fromthis study whole area of system 25 grounded-ice area in 26 andgrounded- and floating-ice areas in 27 (b) Distribution of elevationchange (dHdt) (c) Distribution of ice-thickness change (dIdt)

Zwally and others Mass changes of Greenland and Antarctic ice sheets and shelves 511

Fig 3 H(t) series (black) and multi-parameter linearndashsinusoidalfunction (red) labeled same as locations shown in Figures 1a and2a and listing site elevation in meters and derived dHdts incmandash1 Crossovers within 100 km circle of location are used exceptwithin 50 km for PG2 (a) Greenland CW (central west) 3087+135 16 SW (southwest) 2456 +120 17 CE (central east)2700 +84 05 NC (north central) 2314 +52 05 NS (nearSummit) 3225 +30 08 JI (Jakobshavn Isbraelig) 1316 ndash74 54SE (southeast) 2173 ndash127 17 HG (Humboldt Glacier) 472ndash306 88 NM (north margin) 1365 ndash307 51 NI (lsquoNortheastGreenland Ice Streamrsquo) 614 ndash422 62 (b) Antarctica AP(Antarctic Peninsula) 1832 +357 39 UK (upper Kamb IceStream) 941 +259 11 CI (Carlson Inlet) 271 +230 25 AX(Alexander Island) 688 +212 30 AI (Amery Ice Shelf) 49+150 17WR (western Ross Ice Shelf) 52 +86 06WC (WestAntarctica ndash coastal) 1734 +68 13 RI (Ronne Ice Shelf) 54+53 27 VL (Victoria Land) 2297 +53 11 DM (DronningMaud Land) 3104 +39 07 BY (Byrd Station) 1524 ndash12 07GM (Gamburtsev Mountains) 3074 ndash41 07 MI (MacAyeal IceStream) 682 ndash72 11 CR (central Ross Ice Shelf) 52 ndash94 12UL (upper Lambert Glacier) 1068 ndash114 13 SH (ShiraseGlacier) 1160 ndash116 38 LC (Larsen C ice shelf) 42ndash179 18 LB (Larsen B ice shelf) 28 ndash204 20 DG (DenmanGlacier) 1161 ndash206 50 GI (George VI Ice Shelf) 51ndash210 16 WI (Wilkins Ice Shelf) 27 ndash245 27 WG (westGetz Ice Shelf) 45 ndash276 20 TF (Thwaites Glacier Tongue) 40ndash314 29 PF (Pine Island Glacier Tongue) 68 ndash353 23 TG(Thwaites Glacier) 774 ndash422 30 EG (east Getz Ice Shelf) 93ndash424 26 TN (Totten Glacier) 866 ndash448 48 SF (SmithGlacier Tongue) 52 ndash605 32 PG2 (Pine Island Glacier) 627ndash689 34 PG (Pine Island Glacier) 323 ndash879 57 SG (SmithGlacier) 407 ndash2618 75 (for this site only note factor of 3)


Another significant correction is applied for the depend-ence of the height measured by the altimeter on the receivedbackscatter power similar to those applied in precedingstudies (Wingham and others 1998 Davis and others 2005)We derive a spatially variant sensitivity (dHdG) of themeasured height (H) to changes in the measured back-scattered power using the value of the automatic gain control(AGC) as themeasure of the backscattered power (G)We firstconstruct G(t) time series at each gridpoint using the sameprocedure as for the H(t) series For each gridpoint wecorrelate theN values ofHi(ti) andGi(ti) and calculate a linearfit H frac14 H0 + (dHdG)G and the correlation coefficient (R)

The corrected elevation series is then Hci frac14 Hi ndash (dHdG)(Gi ndashG0) where G0 frac14 ndashH0(dHdG)ndash1 The sensitivityfactor (dHdG) of the elevation to the backscatter is correlatedwith R so for smaller values of R the magnitudes of thesensitivity and the correction decrease Where the absolutevalue of R is lt02 no backscatter correction is appliedbecause the correlation and sensitivity are both small WheredHdGltndash02mdBndash1 it is limited to ndash02mdBndash1 and wheredHdGgt07mdBndash1 it is limited to 07mdBndash1 to limit a fewoutlying values with poorer statistics

The average effect of the backscatter correction on dHdtis small but local corrections can be large For example at

Table 1 Mean values and errors of terms (dHdt dCdt dBdt dSdt) used in the estimate of ice-thickness change (dIdt) for areas ofGreenland and West and East Antarctica defined by ice provenance listing net mass balance (dFdt dMdt) and sea-level contribution (SLE)All values are listed as computed to allow tracing of estimates in other columns (some second and third decimals are not significant) smalldifferences are due to use of round-off values

Dataset gorf

Grid Area dHdtsect dCdt sect dBdt amp dSdtsect dIdt sect dFdt dMdt SLE

Re dFdt Re dMdt

N 106 km2 cmandash1 cmandash1 cmandash1 cmandash1 Gt andash1 Gt andash1 mmandash1 mmandash1

GreenlandERS only g 602 15678 900 +270 028 ndash167003 +005004 +431018 +60826 ndash01680007ERS + ATM closneigh

g 622 16191 930 +063 030 ndash161003 +005004 +219018 +31926 ndash00880007

ERS + ATM+ opt interp

g 670 17411 100 ndash075 035 ndash150002 +006004 +069016 ndash184 20 +10825 +0051 0006 ndash00300007

Greenland relative to ELAH ELA g 583 15189 872 +220 023 ndash171003 +006005 +385013 +23408 +52618 ndash0065 0002 ndash01450005G Hlt ELA g 87 02222 128 ndash2095 223 ndash009002 +004003 ndash2092 089 ndash418 18 ndash418 18 +0115 0005 +01150005

Greenland relative to 2000m contourH2000m g 401 10404 598 +477 014 ndash179003 +002001 +654007 +61206 ndash01690002Hlt2000m g 269 07007 402 ndash895 085 ndash106003 +016009 ndash799 039 ndash504 25 +01390007

AntarcticaERS only g 3613 95085 771 +014 011 ndash006

(6 10ndash3)+045

(7 10ndash3)(ndash610ndash4)011

(ndash5 10ndash2)94

(+1 10ndash5) 0026

ERS only f 472 12492 818 ndash113 018 ndash216005 +028004 +476089 +51797Subtotal gf 4085 107577ERS + opt interp g 4606 121930 989 +018 011 ndash008

(6 10ndash3)+054

(7 10ndash3)ndash028 011 ndash136 54 ndash303 121 +0038 0015 +00840033

ERS + opt interp f 569 15063 986 ndash136 017 ndash227005 +028004 +362113 +21266 +474148Total gf 5175 136993

West AntarcticaERS + opt interp g 748 19959 162 ndash292 024 ndash158003 +125003 ndash259 025 ndash207 20 ndash466 44 +0057 0006 +01290012ERS + opt interp f 295 07841 514 ndash471 024 ndash279008 +028004 ndash1385 167 ndash420 51 ndash945 114

East AntarcticaERS + opt interp g 3858 101971 827 +079 012 +021

(4 10ndash3)+040

(6 10ndash3)+018012 +7348 +163107 ndash0020 0013 ndash00450030

ERS + opt interp f 274 07222 473 +227 022 ndash170005 +028004 +2259152 +63043 +141996

All ice sheetsGrand total g 139341 990 (Sum of Greenland (g N frac14 670) amp Antarctica (g N frac14 4606) ndash320 58 ndash195 124 +0088 0016 +00540034

The coterminous ice sheet in Greenland is sampled by 670 gridpoints of which 583 lie above the equilibrium-line altitude (ELA) all gridpoints are consideredto sample grounded ice (g) Antarctica excluding islands not attached by ice is sampled by 5238 gridpoints of these DS25 (N frac14 14 (g)) DS26 (N frac14 19 (g))and DS27 (N frac14 30 (22 (g) 8 floating ice (f))) are excluded from the studyFor Antarctica the sampled area is relative to totals of sampled plus unsampled areas N frac14 5238 138603 106 km2 N frac14 4661 (g) 123332 106 km2N frac14 577 (f) 15270106 km2The dHdt error s statistic which includes the seasonal and annual variability of accumulation (see text)sectThe mean values of dHdt dCdt dBdt and dIdt are adjusted for area and the composite error includes those for dHdt (s) dCdt dBdt ((g) only) and sea-level rise (dSdt (f) only) estimates for floating ice are factored by the freeboard ratio (Fb mean value = 662 see text)Conversions to mass for dFdt use a factor of 04 for firn at 400 kgmndash3 except in the net ablation zone of Greenland (09 for ice at 900 kgmndash3) and for dMdtuse factors of 09 for (g) and 087 for (f) at 870 kgmndash3Sea-level equivalent of 362Gtmmndash1 (Gt frac14 km3water) allows for area of estuaries ice shelves and tidal marshes


Byrd Station (808 S 1208W) the dHdG is 040mdBndash1 R is090 and the range of G variation is 32 dB with a strongseasonal cycle The uncorrected dHdt is 54 13 cmandash1

with a seasonal amplitude of 64 cm peak-to-peak and thecorrected dHdt is ndash1207 cmandash1 with a smaller seasonalamplitude of 24 cm Generally the backscatter correctionappears to remove noise and significantly improve theregularity of the seasonal cycle In Greenland the meancorrection applied to dHdt is only ndash002 cmandash1 with a236 cmandash1 SD spatial variation In Antarctica the meancorrection is ndash034 cmandash1 with a 294 cmandash1 SD spatialvariation on grounded ice and ndash013 cm andash1 with a252 cmandash1 SD spatial variation on floating ice The approxi-mate effects on calculations of mass change (dMdt) for theERS gridpoints are ndash15Gt andash1 for Greenland and ndash32Gt andash1

for AntarcticaA multi-parameter linearndashsinusoidal function is fitted to

the H(t) series to obtain linear trends of dHdt whileaccounting for seasonal variations in the elevation measure-ment (Fig 3) The frequency of the sine function is fixed at1 year The fit calculates the slope (dHdt) intercept phase(eg the date of minimum) and the amplitude of the seasonalcycle with standard deviations of each parameter In mostH(t) series the linearndashsinusoidal model represents the datavery well The standard deviation (s) of the linear slope(dHdt) obtained from the multi-parameter fitting is used asthe estimate of the error in the derived dHdt trends The sare affected by departures of the slope from the modelrepresentation of a linear trend and a seasonal sinusoidalvariation as well as by the measurement errors in Hi(ti)Such departures may include unmodeled temporal varia-bility due to short-term variability of the accumulation rateor other factors Therefore the s provide estimates of theerrors that include effects of natural variability in theelevation which we carry through to estimates of the massbalance Alternatively Davis and others (2005) use anlsquoautoregressionrsquo technique (Ferguson and others 2004) tomatch non-linear variations of the seasonal cycle andinterannual variability which in general tends to reducethe s of the linear term We believe it is more appropriatefor the unmodeled variability to be represented in s givinga larger error estimate Also removing interannual varia-bility can lead to a linear trend that does not accuratelyrepresent the change during the period of the measurementsMaps of our s including an optimal interpolation of s witha factor that increases with the distance of interpolation areshown in the Appendix (Fig 7)

The dHdt at Byrd Station (BY in Figs 2a and 3b) forexample is ndash1207 cmandash1 which is comparable to aglobal positioning system-based measurement (Hamiltonand others 1998) of ndash0422 cmandash1 within the range oferrors Adjusting our dHdt for firn-compaction (dCdt frac14ndash07 cmandash1) and bedrock motion (dBdt frac14 +17 cm andash1)gives an ice thinning rate of 22 cmandash1 which compareswell with the thinning rate of 3 cmandash1 from field measure-ments of ice flow and mass-continuity calculations (Whil-lans 1977) In contrast a region about 175 km to thesouthwest and inland of Kamb Ice Stream has large elevationincreases (eg dHdt frac14 +259 11 cmandash1 at point UK inFigs 2a and 3b)

The distributions of dHdt are shown in Figures 1b and2b and descriptive statistics are listed in Table 1 We utilizeATM results (Abdalati and others 2001) from 1993 to 1999and closest-neighbor interpolation to obtain dHdt values for

an additional 3 of the area of Greenland We use theoptimal interpolation method of kriging with default optionsin the Golden Software Inc Surfer1 (version 70) computerprogram to provide nearly complete spatial coverage (100of the coterminous grounded-ice area of Greenland and99 of each of the grounded- and floating-ice areas ofAntarctica) The grounded and floating areas of Antarcticaare interpolated separately and merged Most of theinterpolated points are widely distributed over the steepercoastal areas of the ice sheets except for the area ofAntarctica south of 8158 S (Fig 2a and b) The observeddHdt along the 8158 S perimeter of the interpolated areaare mostly small (ie ndash5 to +5 cmandash1) except for the regionof large increases south of point UK in WA The averagedHdt on grounded ice in the area south of 8158 S is+16 cmandash1 and the calculated average ice thickness andmass changes are relatively small (dIdt frac14 +064 cmandash1 anddMdt frac14 +14Gt andash1)

CALCULATION OF ICE-THICKNESS CHANGES(dIdt )Deriving ice-thickness changes (dIdt) from dHdt valuesrequires correction for elevation changes (dCdt) induced bytemporal variations in the rate of firn compaction andadjustment for vertical motion of the underlying bedrock(dBdt) or sea level (dSdt) Over grounded ice the thicknesschange is

dIdt

gfrac14 dH

dt dC

dt dB

dt eth1THORN

We use the radial components (dBdt) of three models ofisostatic rebound (from Ivins and others 2001 Huybrechts2002 Peltier 2004) labeled (dBdt)IHP respectively inter-polated to our gridpoints The model of Ivins and others(2001) is global and covers Greenland although thereferenced work is limited to Antarctica The averages(Fig 8 in Appendix) are weighted to account for distributionsthat showed similar patterns ie for Greenland dBdt frac1414(dBdt)P + 14(dBdt)H + 12(dBdt)I and for AntarcticadBdt frac14 14(dBdt)I + 14(dBdt)P + 12(dBdt)H The dBdterrors are estimated at 12 of the range from the averageof the two results with similar patterns to the third modelresult

On floating ice the change in thickness is

dIdt

ffrac14 Fb

dHdt

dCdt

dSdt

eth2THORN

where Fb is the freeboard ratio of total thickness to freeboardheight (ice surface elevation above sea level) The Fb valuefor each gridpoint is determined from buoyancy usingFb frac14 w(w ndash if) where w frac14 10285 kgmndash3 is the densityof Antarctic Shelf Water (Whitworth and others 1998) andif is the mean density of the floating-ice column Weiteratively calculate ice thickness and if values for eachgridpoint to account for the dependence of if on thicknessThe resulting mean ice thickness of the Antarctic ice shelves(N frac14 569) is 488m (SD frac14 313m) the mean if is 870 kgm

ndash3

(SD frac14 28 kgmndash3) and the mean Fb is 662 (SD frac14 089) Weuse dSdt frac14 2804mmandash1 for contemporaneous sea-levelrise (Leuliette and others 2004)

The dCdt values (Fig 9 in Appendix) are calculated foreach gridpoint with an enhanced firn compaction modelthat is sensitive to variations in firn temperature and surface


melting obtained from a 20 year record of surfacetemperatures from satellite infrared observations The firncompaction model (Li and Zwally 2002 Zwally and Li2002) is augmented by inclusion of the effects of vaportransport in the firn (Li and Zwally 2004) and the effects ofnear-surface melting The model uses a temperature-dependent activation energy and has greater sensitivityand a more rapid compaction response to variations intemperature than other models (eg Arthern and Wingham1998) The model produces seasonal variations in therate of densification seasonal variations in density withdepth and seasonal changes in surface elevation thatare generally consistent with observations (Li and Zwally2002 2004 Zwally and Li 2002 Li and others 2003Dibb and Fahnestock 2004) Surface melting and refreez-ing is included by using an empirical meltingndashtemperaturemodel (Braithwaite and Zhang 2000) which gives melt-ing when the monthly average temperature is gtndash88C andthe corresponding changes in density are calculatedA similar treatment of the effect of melting on densificationis given in Reeh and others (in press) The mean accumu-lation rates are held constant with time in the model sincethe intent is to calculate temperature-dependent variationsin surface elevation and not variations caused by variabilityin accumulation rates which are discussed in the nextsection

The model is driven with the latest available data ofmonthly surface temperatures (Comiso 2003 Comiso andParkinson 2004) for 1982ndash2003 from satellite-borne Ad-vanced Very High Resolution Radiometers The temperaturedata for the Greenland ice sheet have been improved fromthe early version of the dataset by a recalibration usingmore ground-station data of surface temperature A steady-state 1 year monthly temperature cycle determined as theaverage of the first 3 years (1982ndash84) of temperature datawith constant accumulation (A) and surface firn density of03 is used to establish the initial steady-state densityprofile with depth The surface height variation C(t) iscalculated from 1982 to 2003 and dCdt is obtained by alinear fit to the C(t) for the time period of the H(t) andderived dHdt We use an error estimate of 30 on thecalculated dCdt which is approximately equivalent to therange of error that would be induced by 25 errors inthe temperature anomalies

In general warmer temperatures increase the rate ofcompaction and lower the surface elevation whereas coldertemperatures raise the surface elevation Near-surfacemelting and subsequent refreezing in the firn also lowersthe surface by changing firn to higher-density ice which inturn affects the rate of subsequent densification Althoughmuch of the densification in the upper firn layers occursduring the warmer summer months temperature anomaliesin winter also have a large impact on the rate ofdensification during summer because of their precondition-ing effect on the summer firn temperatures

In Greenland the calculated dCdt values are mostlynegative showing primarily the effect of a positive trend inwinter temperatures as well as the increase in summermelting during the 1990s The average dCdt over theaccumulation zone is ndash171 cmandash1 indicating an averagesurface lowering from an increased rate of compactionWithout adjustment for dCdt this surface lowering might beincorrectly interpreted as a mass loss of 234Gt andash1 (using anaverage column ice density of 09) In WA the average dCdt

for grounded ice is ndash158 cmandash1 (284Gt andash1 equivalent) andon the floating ice is ndash279 cmandash1 (130Gt andash1 equivalent)These surface lowerings in WA are caused by a regionalwarming trend including melting effects on the ice shelvesand in some coastal areas In EA the average dCdt on thegrounded ice is +021 cmandash1 (ndash193Gt andash1 equivalent) withthe largest increases around 1358 E within a few hundred kmof the coast The small increase in EA is due to the smallcooling trend over much of the region On the floating ice inEA the average dCdt is ndash170 cmandash1 (732Gt andash1 equiva-lent) which is due to warming and melting of the ice shelvesindicated by the temperature record

Our calculated dIdt for Greenland and Antarctic sub-regions are listed in Table 1 and shown in Figures 1c and 2cThe data are weighted for small differences in the area of thegrid squares in the polar stereographic map projectionValues for each drainage system (DS) are listed in Table 2and shown in Figure 4a

ESTIMATION OF MASS CHANGES (dMdt )The mass change (dMdt ) associated with dIdt depends onwhether the change in thickness of the firnice column iscaused by the ice dynamics not being in balance with thelong-term (multi-decadal) accumulation rate or is caused byshorter-term (decadal) variability in accumulation rate (A(t))Separating components of dIdt gives

dMdt

frac14 ice dIdt

NStS

thorn dIdt

StSthorn dI

dt

ln dI

dt

Out

Ar eth3THORN

where ice frac14 0917 is the density of ice (ie relative towater) and Ar is the area of the firnice column In the firstterm (dIdt)NStS is the change in thickness due to any non-steady-state (NStS) change in firn thickness from short-termchanges in A(t) andor temperature (T(t)) The factor canrange from about 033 to 1 if the rate of firn compaction isnot in steady state with the surface mass input The term icemay be considered as the effective density of the NStScomponent of the mass change In steady state the velocityof firn compaction is constant the density profile with depthis not changing and the flux of lower-density firn input at thesurface is equal to the downward flux of ice at depth ( frac14 1and (dIdt)NStS frac14 0) In the ablation zone the first term iszero neglecting the seasonal effect of winter snow coverThe second term in Equation (3) is due to the steady-state(StS) component of the mass added at the surface andice(dIdt)StS is equal to the long-term average accumulationrate (A) The third and fourth terms are due to the averagehorizontal ice flow into and out of the column during themeasurement period which may include short- as well aslong-term dynamic changes The sum of the last three termsdetermines the long-term mass balance

In general is a function of the time histories of A(t) andT(t) and the response time fc of the firn compactionprocess which is on the order of a few years to decadesOur calculations of dCdt remove the effect of T(t) for10 years prior to and including the measurement periodHowever because current knowledge of A(t) is limited the(dIdt)NStS term cannot be completely determined Fortu-nately several factors reduce the effect of variations of A(t)First short-term stochastic fluctuations in A cause bothpositive and negative (dIdt)NStS and therefore tend toaverage out in a 10 year period However such fluctuationsappropriately increase our estimated error (s) for dHdt


Table 2 Mean values and errors in the estimate of ice-thickness change (dIdt) and net mass balance (dFdt dMdt) for grounded-ice (g) andfloating-ice (f) areas of drainage systems (DS) in Greenland West Antarctica and East Antarctica listing sea-level contribution (SLE) and theratio of net mass balance to adjusted net accumulation at the surface (Ajj) for each All values are listed as computed to allow tracing ofestimates in other columns (some second and third decimals are not significant) small differences are due to use of round-off values

DS No-name gorf

Grid Area dIdt (dFdt) (dMdt) SLE Ajsect Ajj

(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt

106 km2 cmandash1 Gt andash1 Gt andash1 mmandash1 mmandash1 Gt andash1 Gt andash1

Greenland11-NWwKnRassL g 60 01608 +282 011 +129 007 +409 015 ndash0004 ndash0011 1612 1612 0080 025312-NWeKnRassL g 37 00998 ndash283 029 ndash182 012 ndash254 026 +0005 +0007 1652 1652 ndash0110 ndash015421-NEnKgFVIIsL g 55 01472 +249 007 +082 004 +330 010 ndash0002 ndash0009 756 756 0109 043622-NEcKgFVIIsL g 49 01299 +488 007 +285 004 +570 008 ndash0008 ndash0016 1132 1132 0252 050423-NEsKgFVIIsL g 18 00477 ndash043 009 ndash150 002 ndash019 004 +0004 +0001 ndash208 ndash208 0720 008931-CEKgCXsL g 60 01566 +707 126 +437 079 +997 178 ndash0012 ndash0028 2844 2844 0154 035032-CEBlossevKyst g 45 01151 ndash1434 082 ndash1054038 ndash1486085 +0029 +0041 1315 1315 ndash0802 ndash113041-SEKgCIXsL g 23 00582 +756 061 +125 014 +396 032 ndash0003 ndash0011 057 057 2185 693142-SEKgFVIsKyst g 35 00867 ndash1458 149 ndash777 052 ndash1137116 +0021 +0031 111 111 ndash6995 ndash1024343-SEKapFarvel g 14 00337 ndash2733 074 ndash656 010 ndash829 022 +0018 +0023 ndash202 ndash202 3427 410051-SWsDavisStrS g 30 00734 ndash013 109 ndash076 032 ndash008 072 +0002 +210ndash4 1412 1412 ndash0054 ndash000652-SWcDavisStrS g 58 01459 +252 015 ndash120 009 +331 019 +0003 ndash0009 ndash717 ndash717 0168 ndash046253-SWJakobshavn g 34 00872 +706 019 +186 007 +554015 ndash0005 ndash0015 1970 1970 0094 028154-SWnDavisStrS g 54 01400 +205 017 ndash275 009 +259 021 +0008 ndash0007 1336 1336 ndash0206 019460-CentralWest g 98 02588 +450 020 +198 020 +1047046 ndash0005 ndash0029 3747 3747 0053 0280

West Antarctica18-cRossIS g 73 01980 +402 017 +318 014 +717 031 ndash0009 ndash0020 2434 2434 0131 0295

f 64 01729 ndash2975 088 ndash1987059 ndash4476132 1930 1930 ndash1066 ndash231919-eRossIS g 165 04434 ndash072 011 ndash127 020 ndash287 045 +0004 +0008 6457 6372 ndash0020 ndash0045

f 33 00888 ndash1084 178 ndash372 061 ndash838 137 1402 1402 ndash0275 ndash059720-nMByrdL g 76 02015 +124 095 +100 076 +225 171 ndash0003 ndash0006 5756 5054 0020 0045

f 22 00582 ndash6132 496 ndash1379112 ndash3105251 2051 2051 ndash0696 ndash151421-SmiThwG g 83 02213 ndash2288 071 ndash2023063 ndash4557142 +0056 +126 7292 6922 ndash0293 ndash0658

f 3 00079 ndash2038 571 ndash622 174 ndash1401393 619 619 ndash1040 ndash226322-PineIslandG g 74 01966 ndash971 078 ndash763 061 ndash1719138 +0021 +0047 8300 8026 ndash0095 ndash0214

f 2 00053 ndash216 193 ndash444 396 ndash100 892 384 384 ndash1198 ndash260523-nEllsworthL g 34 00892 ndash332 131 ndash118 047 ndash267 105 +0003 +0007 7355 6358 ndash0019 ndash0042

f 15 00392 ndash876 498 ndash133 075 ndash299 170 3509 3509 ndash0039 ndash008524-wPalmerL g 66 01716 +297 192 +203 132 +458 297 ndash0006 ndash0013 10738 9321 0022 0049

f 22 00572 ndash5585 401 ndash1234089 ndash2780200 5034 5034 ndash0254 ndash05521-wFilch-RonIS g 177 04743 +180 033 +340 063 +767 142 ndash0009 ndash0021 11359 10658 0032 0072

f 108 02890 +2176 120 +2429 134 +5471301 5802 5802 0434 094326-LarsenIS f 26 00656 ndash1792 473 ndash454 120 ndash1023270 5855 5855 ndash0080 ndash0175

East Antarctica2-cFilch-RonIS g 328 08933 ndash012 007 ndash042 024 ndash094 054 +0001 +0003 7742 7485 ndash0006 ndash0013

f 42 01132 +1260 131 +551 057 +1241129 1888 1888 0302 06573-eFilch-RonIS g 564 15181 +082 005 +500 033 +1125074 ndash0014 ndash0031 7780 7654 0065 0147

f 18 00484 +920 178 +172 033 +387 075 838 838 0212 04624-CoatsL g 97 02563 +290 023 +298 024 +670 053 ndash0008 ndash0019 5201 4580 0065 0146

f 27 00709 +3146 429 +862 118 +1941265 2752 2752 0324 07055-wDMaudL g 79 02065 +742 101 +612 083 +1378187 ndash0017 ndash0038 3223 2823 0217 0488

f 18 00465 +5922 833 +1064 150 +2396337 1254 1254 0878 19116-eDMaudL g 231 06038 ndash032 021 ndash077 052 ndash173 116 +0002 +0005 6402 5680 ndash0014 ndash0030

f 30 00772 +2497 210 +745 063 +1677141 1951 1951 0395 08607-EnderbyL g 179 04624 ndash119 120 ndash220 222 ndash495 500 +0006 +0014 6117 5391 ndash0041 ndash0092

f 1 00026 +569 1765 +006 018 +013 040 089 089 0067 01458-KempL g 61 01554 ndash1451 273 ndash901 169 ndash2029381 +0025 +0056 2849 2340 ndash0385 ndash0867

f 1 00025 +1120 1711 +011 017 +024 037 089 089 0126 02749-wAmeryIS g 60 01550 +424 073 +263 045 +592 102 ndash0007 ndash0016 1469 1383 0190 0428

f 6 00154 +3478 530 +207 032 +466 071 364 364 0589 128010-cAmeryIS g 351 09336 ndash068 007 ndash255 028 ndash575 063 +0007 +0016 4774 4774 ndash0054 ndash0120

f 8 00206 +5511 536 +439 043 +988 096 404 404 1124 244511-eAmeryIS g 93 02435 ndash008 024 ndash008 024 ndash017 053 +2 10ndash4 +5 10ndash4 1836 1804 ndash0004 ndash0009

f 5 00129 +4296 427 +214 021 +482 048 289 289 0767 166812-DavisSeaS g 279 07163 +168 081 +482 233 +1086524 ndash0013 ndash0030 15304 14026 0034 0077

f 21 00527 +9150 1071 +1863 218 +4195491 2686 2686 0718 156213-WilkesL g 430 11114 ndash138 020 ndash615 090 ndash1385202 +0017 +0038 22663 20682 ndash0030 ndash0067

f 6 00151 +475 3831 +028 224 +062 503 820 820 0035 007614-TerreAdelie g 268 06910 ndash002 024 ndash007 067 ndash015 151 +2 10ndash4 +4 10ndash4 14757 13587 ndash0001 ndash0001

f 6 00152 ndash9032 2045 ndash530 120 ndash1194270 079 079 ndash6951 ndash1511915-nVictoriaL g 54 01405 ndash353 419 ndash198 236 ndash446 530 +0005 +0012 3052 2767 ndash0072 ndash0161

f 2 00052 ndash4796 2105 ndash096 042 ndash217 095 160 160 ndash0623 ndash135616-sVictoriaL g 99 02619 +225 034 +236 035 +530 079 ndash0007 ndash0015 2099 2063 0114 0257

f 1 00026 ndash8851287 ndash009 013 ndash020 029 013 013 ndash0708 ndash153917-wRossIS g 685 18481 +089 006 +656 042 +1477095 ndash0018 ndash0041 11485 11485 0057 0129

f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519

Footnotes on facing page


an example of which is discussed below for an apparentlynon-linear H(t) Second in integrals of dMdt over largeregions some of the (dIdt)NStS are likely to be positive andsome negative thereby also reducing their net effectTherefore we use the approximation

dMdt

frac14 adIdt

Ar eth4THORN

where a is the average density of the firnice column ie090 on grounded ice and 087 on floating ice and dIdt isthe observed thickness change We show dMdt for Green-land and Antarctic sub-regions and drainage systems in

Tables 1 and 2 and Figure 4b and discuss the results in thenext section

Our approximation is equivalent to assuming the dIdt aredistributed throughout the firnice column and that NStS firncompaction terms are on average small compared to thelonger-term balance terms As improved information on A(t)is acquired (eg Box and others in press Monaghan andothers in press) the effect on densification can be calculatedand (dIdt)NStS estimated Meanwhile we note that changesin A(t) tend to be positively correlated with T(t) with dataand models showing correlations ranging from about 5 to20 per kelvin (eg Zwally 1989 n 26 Kapsner and

Fig 4 Distribution of mean dIdt (a) and dMdt (b) for drainage systems of Greenland West Antarctica and East Antarctica (EA includes datafor DS1gampf and DS26f)

Table 2 FootnotesPrefixes n northern s southern w western c central e eastern Suffixes IS Ice Shelf L Land S sector G GlacierThe whole area of DS25 and 27 and the area of grounded ice in DS26 are excluded from the study (see Table 1 footnote )The net mass-balance computations (dFdt dMdt) use mean dIdt adjusted for area factored as described in Table 1 footnote sectsectSurface balance data for Greenland and Antarctica from Zwally and Giovinetto (2000) and Giovinetto and Zwally (2000) respectively data for DS26(f) fromVaughan and others (1999) and DG Vaughan (personal communication 1999)

Surface balance after deflation and ablation corrections have been applied (Antarctica grounded ice only modified from Giovinetto and Zwally 2000)


others 1995) Therefore where A(t) is correlated with T(t)our approximation will estimate greater mass gain or lessmass loss than is actually occurring in regions that arewarming and less mass gain or greater mass loss than isactually occurring in regions that are cooling The magni-tude of this effect depends on the timescale of the variationsin A(t) As noted sub-decadal variations tend to average outin a 10 year observation Decadal trends during only themeasurement period would have the most impact whiledecadal trends that are part of a longer-term trend wouldhave small impact because the non-steady-state densifica-tion term would be small

Alternatively choosing a smaller value of a would furtherreduce our estimates of overall mass imbalance which areshown to be small To increase our estimates of massimbalance or to change their sign would require selectiveapplication of values regionally andor assumptionsregarding the relative magnitude of the dynamic vs sur-face-balance terms in Equation (3) Previously a commonlyused a implicitly or explicitly was the 092 density of ice(eg Krabill and others 2000) Zwally (1989) used 05 and092 to give a range of mass estimates Davis and others(2005) used a frac14 035 to estimate dMdt based on a positivedHdt in EA However the surface density is close to 03 inmost locations and 035 is the typical density of the topannual layer or two Therefore using 035 is equivalent toassuming that a positive dHdt is continuously caused solelyby the addition of new firn with little subsequent compac-tion from year to year and that the long-term mass-balanceterms (accumulation plus dynamic) in Equation (3) are zeroIn that case Equation (3) would be

dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN

where all thickness changes are assumed to be caused by

short-term changes in accumulation and F is the change inmass of the firn To illustrate the effect of this assumption onestimates of the overall mass-balance values in Tables 1and 2 we also list dFdt values using frac14 044 or a frac14 04which is a typical mean density for the top strata corres-ponding to 10 years of accumulation as shown by wide-spread sampling of the ice sheets (eg Benson 1962Kojima 1964) The dFdt calculations include the dCdtcorrection for temperature effects on firn compaction

Finally we note that our dMdt estimates for the iceshelves include mass changes caused by thickening orthinning which may be affected by changes in the rate ofdischarge of grounded ice into the shelves However theestimates do not take into account mass changes resultingfrom possible systematic changes in the ice-shelf fronts dueto episodic calving events (eg Zwally and others 2002b) orice-shelf disintegration (eg Skvarca and others 1999)

DISCUSSION OF REGIONAL CHANGES INELEVATION THICKNESS AND MASSIn Greenland most dHdt values on the inland ice sheetabove 2000m are increasing in the range 0ndash15 cmandash1

(Fig 1b) with an average of 477014 cmandash1 (Table 1) Forexample dHdt for four inland locations at central west(CW 13516 cmandash1) southwest (SW 120 17 cmandash1)central east (CE 84 05 cmandash1) and north central (NC52 05 cm andash1) illustrate the mostly linear trends ofincreasing elevation However the region near the summit(NS 3008 cmandash1) which had an accumulation lowaround 199495 (McConnell and others 2001) had adecreasing dHdt for the first 3 years followed by anincrease

At elevations above 2000m our dHdt appear verysimilar in some regions to those from ATM surveys made

Fig 5 Comparison of dHdt distribution for Greenland (a) ERS only (b) same as in Figure 1b and (c) produced by interpolation andextrapolation of airborne laser altimeter and ATM surveys data collected in 1993ndash99 (Krabill and others 2000)


between 1993 and 1998 in the south and 1994 and 1999 inthe north (Krabill and others 2000) but are more uniformlypositive over the ice sheet (Fig 5) The principal region ofelevation decreases above 2000m in both datasets is in thesoutheast (DS41 and 42) where for example dHdt frac14ndash12717 cmandash1 at point SE at 2173m (Fig 3a) Our dHdtresults are compared with our calculation of the ATM databy elevation intervals in Table 3 Above 2000m our averagedHdt of +477 cmandash1 is larger than the +0505 cmandash1 forthe ATM data (Krabill and others 2000 Table 3) or the+1005 cmandash1 as given by Thomas and others (2001) andrevised to +14 05 cmandash1 (personal communication fromR Thomas 2005) These differences may be due to thelimited spatial and temporal sampling of the ATM data andto sensitivity to seasonal changes in elevation because theATM flights made around May and June occur at the time ofmaximum change in the rate of firn compaction (Zwally andLi 2002)

At Greenland elevations below 2000m the pattern ofdecreases in most areas is in good agreement with the ATM-based values (Fig 5) Some of the differences near themargins are probably due to the extrapolationinterpolationof ATM values to the ice margins using temperatures atcoastal weather stations (Krabill and others 2000) com-pared to our direct extrapolationinterpolation of ERS andATM data Our average dHdt below 2000m is ndash895085 cmandash1 which indicates more thinning than our calcu-lation of dHdt frac14 ndash65 cmandash1 for the ATM data (Table 3)Below 1200m which is the approximate equilibrium-linealtitude (ELA) the respective dHdt are ndash2388 182 cmandash1

for our results and ndash122 cmandash1 for the ATMIn general our dHdt show more thickening at higher

elevations and more thinning at lower elevations thanthe ATM data Krabill and others (2000) reported a net iceloss of 51 km3 andash1 (or 459Gt andash1 using frac14 09) but werelsquounable to assign errorsrsquo to their estimate They used avalue of dBdt frac14 05 cmandash1 in the north and 04 cmandash1 inthe south compared to our overall average of 006 cmandash1which would reduce their mass loss by 62Gt andash1 Apply-ing our firn compaction correction reduces their loss byanother 234Gt andash1 and applying their revised dHdt of

+1405 cmandash1 (from +05 05 cmandash1) above 2000mreduces it by another 84Gt andash1 to a net mass loss of only8Gt andash1 which is very close to balance

In contrast our dHdt agree within 1 cmandash1 with thosereported by Johannessen and others (2005) for elevationsabove 2500m (Table 4) At lower elevations their dHdt areincreasingly more positive than both our ERS-only resultsand our ERS + ATM + optimal interpolation results Residualdifferences at the higher elevations may be due to their notapplying a backscatter correction that they estimate to beapproximately ndash08 cmandash1 However our less positive dHdtbetween 1500 and 2500m and our more negative dHdtbelow 1500m are probably due to the greater coverage ofour values derived from ERS only (eg 92 vs 71 between1500 and 2000m) and our inclusion of values from ATMand optimal interpolation

Our dHdt at four sample locations (JI HG NM and NI)with elevations of 472ndash1365m have elevation decreases of74ndash422 cmandash1 The H(t) for the two locations below theELA Humboldt Glacier (HG) and lsquoNortheast Greenland IceStreamrsquo (NI) show clear seasonal cycles of several metersamplitude with minima on 24 and 6 August near the endof the summer ablation season These H(t) clearly illustratethe capability of our analysis techniques to derive realisticH(t) in some of the low-elevation margins of the ice sheetsThe two locations just above the ELA North Margin (NM)and Jakobshavn Isbraelig (JI) also have seasonal cycle minima(on 16 September and 15 August) due to the summermelting and firn compaction The distributions of dIdtvalues above and below the ELA and above and below2000m effectively show increases in the higher elevationsand decreases in the lower elevations with average valuesshown in Figure 6

Nine drainage systems distributed over the NW and NE(DS11 21 22) CE (DS31) SE (DS41) and the SW andCW (DS52ndash54 60) covering 74 of the area of the icesheet have dMdt increases that range between +26 02and +105 05Gt andash1 Five systems distributed over theNW (DS12) NE (DS23) CE (DS32) and SE (DS42 43)covering 22 of the ice sheet show dMdt decreasesbetween 019004 and 14909Gt andash1 The estimated

Table 3 Comparison of dHdt for Greenland from this study with ATM results of Krabill and others (2000) Values listed as computed (somesecond decimals are not significant)

Surface elevation zone This study (all data) Other study Diff in dHdt

N Area dHdt dHdt

km 106 km2 cmandash1 cmandash1 cmandash1

Overall 670 17411 ndash075035 ndash204 +12927ndash33 144 03740 +626014 +093 +53322ndash27 201 05203 +399025 +044 +35517ndash22 135 03526 +192067 ndash148 +34012ndash17 105 02728 ndash409136 ndash658 +24907ndash12 57 01486 ndash1702212 ndash1133 ndash56902ndash07 22 00576 ndash3385366 ndash1415 ndash197000ndash02 6 00152 ndash5322871 ndash1501 ndash3821gt20 401 10404 +477014 +045 +432lt20 269 07007 ndash895085 ndash651 ndash244gt12 585 15197 +262030 ndash100 ndash162lt12 85 02214 ndash2388182 ndash1216 ndash1172

Area-weighted mean valuesComputed from data from W Krabill (personal communication 2000)


change in the remaining system (DS51) is essentially zeroThe largest mass losses are from three systems in the SE(DS32 42 and 43) which have a total loss of ndash34515Gt andash1 System 53 which consists mainly of theJakobshavn Isbraelig drainage basin shows a net mass gaindue to growth in the interior that dominates the thinningnear the mouth (Figs 1c and 5a and b) where there is ampleevidence of recent rapid thinning (Abdalati and others2001) and reports of accelerated thinning particularly in thefloating section (Thomas and others 2003 Joughin andothers 2003)

The average dHdt over Greenland is ndash075 035 cmandash1After correction for surface lowering due to firn compaction(dCdt frac14 ndash150002 cmandash1) and isostatic uplift (dBdt frac14006 004 cmandash1) the average increase in ice thickness is069016 cmandash1 and the estimated dMdt is slightlypositive (+108 25Gt andash1)

In WA most of the eastern Ross Ice Shelf drainage system(DS19) extending from the ice divide north of Byrd Stationinto the ice shelf is thinning (average dIdt frac14ndash07 01 cmandash1) For example dHdt is ndash72 11 cmandash1

at MI at 682m just inland of MacAyeal Ice Stream In thecoastal zone from 458W to 908W the dHdt values aremostly positive on western Palmer Land (DS24) (eg+357 39 cm andash1 at AP) and south of the AntarcticPeninsula in the western FilchnerndashRonne Ice Shelf (DS1) inthe range 5ndash30 cmandash1 (eg +23025 cmandash1 at CI)

In the Pine Island (DS22) and SmithThwaites (DS21)systems significant thinning is observed as previously re-ported (Wingham and others 1998 Shepherd and others2002 Zwally and others 2002a) with respective mass lossesof 172 14 and 456 14Gt andash1 but not as large as the8415Gt andash1 negative mass-flux estimate by Thomas andothers (2004) At one location (PG2) at 627m elevation onPine Island Glacier where the average dHdt over the 9 yearsis ndash689 34 cmandash1 the H(t) shows a tripling of thinningrate from 27 cmandash1 for 1992 to March 1995 to 79 cmandash1 forMarch 1995 to 2001 (Fig 3b) This increase in thinning ratecould be consistent with the observed increase in thevelocity of Pine Island Glacier (Joughin and others 2003Rignot and others 2004) However other H(t) in that region(eg PG at 323m TG at 774m and SG at 407m in Fig 3b)

do not show changes in thinning rates during this period thatmight provide evidence of acceleration in discharge rates asimplied by Thomas and others (2004)

The floating ice in WA is thinning significantly withaverage dIdt ranging from ndash88 50 cmandash1 on northernEllsworth Land (DS23) and ndash108 18 cmandash1 on the easternRoss Ice Shelf (DS19) to ndash216193 cmandash1 on the PineIsland system (DS22) and ndash204 57 cmandash1 on the SmithThwaites system (DS21) Some thinning is observed on thesouthern part of the FilchnerndashRonne Ice Shelf but thicknessincreases in the 5ndash60 cmandash1 range are dominant for thecentral and northern parts of the western lobe of this iceshelf However although dHdt for the point near the RonneIce Shelf front is positive (RI +53 27 cmandash1) the first55 years show a decreasing elevation followed by a suddenincrease of nearly 1m after the summer of 1998 when avery large open-water anomaly formed in the sea ice in frontof the shelf The open water is a likely source for a regionalaccumulation increase and a short-term thickening of theshelf This large interannual variability is reflected in therelatively large s of 50 for this location

The dHdt value of ndash20420 cmandash1 on the Larsen B iceshelf (LB) indicates a thinning of about 135 cmandash1 prior tobreak-up The dHdt frac14 ndash17918 cmandash1 on the remainingLarsen C ice shelf (LC) indicates a somewhat smallerthinning of about 118 cmandash1 within the range of previousanalysis (Shepherd and others 2003) The ice shelves on thewestern side of the Peninsula are also thinning withdIdt frac14 ndash162 cmandash1 on the Wilkins Ice Shelf (WI) andndash139 cmandash1 on the George VI Ice Shelf (GI) The shelvesalong the coast of WA from 1108W to 1358W are alsothinning with dIdt frac14 ndash183 cmandash1 on the west Getz IceShelf (WG) and ndash281 cmandash1 on the east Getz Ice Shelf (EG)

In EA dHdt are mostly in the range 5 cmandash1 over theinterior with some larger values within a few hundredkilometers of the coast The patterns of thickening orthinning tend to be spatially coherent over distances on theorder of 500 km with a mixture of areas of thickening andthinning in contrast to the more uniform pattern ofthickening recently reported (Davis and others 2005)For example our H(t) at the upper Lambert Glacier (UL)has a uniform linear decrease (ndash114 13 cmandash1) and

Table 4 Comparison of dHdt for Greenland from this study for all data and for ERS data only with the ERS results of Johannessen and others(2005) Values listed as computed (some second decimals are not significant)

Surfaceelevationzone

This study (all data) This study (ERS only) Other study(ERS only)

Diff in dHdt

dHdt Area N dHdt Area N dHdt Area (2) minus (9) (5) minus (9)

km cmandash1 106 km2 cmandash1 106 km2 cmandash1 106 km2 cmandash1 cmandash1

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)Overall ndash075 035 17411 670 +270028 15678 90 602 +54 02 13807 79 ndash615 040 ndash270034gt30 +634020 01067 41 +634020 01067 100 41 +55 03 01403 131 +084036 +084 03625ndash30 +589019 04773 184 +594013 04747 99 183 +64 03 04583 96 ndash051 036 ndash04603620ndash25 +332024 04563 176 +335023 04513 99 174 +70 04 03989 87 ndash368 047 ndash36504615ndash20 +036096 03210 123 +187084 02960 92 113 +56 05 02282 71 ndash524 108 ndash373098gt15 ndash1681134 03797 146 ndash556142 02390 63 91 ndash2009 01551 41 ndash1481161 ndash356168

Area-weighted mean valuesArea is relative to our area for each zone value greater than 100 above 3 km is unexplained


many of the dHdt over the adjacent DS11g and 12g areslightly negative (Fig 2) compared to the significant dHdtincreases in figure 2 of Davis and others (2005) Othersample dHdt at interior points are ndash4107 cmandash1 overthe Gamburtsev Subglacial Mountains (GM) and+3907 cmandash1 in Dronning Maud Land (DM) In thecoastal zone from 458W to 1808 E the surface elevationsare mostly increasing in the range 5ndash20 cmandash1 withexceptions including the ndash11638 cmandash1 on ShiraseGlacier (SH) ndash206 50 cmandash1 on Denman Glacier (DG)and ndash448 48 cmandash1 on Totten Glacier (TG) Most of thefloating-ice areas of EA show increases in elevationincluding +15017 cmandash1 on the Amery Ice Shelf (AI)and +8606 cmandash1 on the western Ross Ice Shelf (WR)The pattern of changes on the Ross Ice Shelf is clearlydelineated by the drainage systems with marked thickeningof the ice flowing from EA and thinning of the ice from WA

Our average thickening for EA (dIdt frac14 +02 01 cmandash1)is smaller than the 18 03 cmandash1 rate reported in Davis andothers (2005) which would be 16 cmandash1 if adjusted for ourcalculated slowing of firn compaction (dCdt frac14 021 cmandash1)Although their dIdt is eight times as large their dMdtincrease is only three times as large due to their lowestimated density for the added mass as discussed aboveWhile some of the difference may be due to respectivemethods of constructing the H(t) time series or ourinterpolated gridpoints a more likely cause is difference inthe methods of time-series analysis to derive dHdt Webelieve our calculated dHdt more accurately represent thechanges in elevation during the measurement period thanthe results of the autoregression method (Ferguson andothers 2004) which may remove interannual variability andmisrepresent the actual change during the measurementperiod In this regard we note that the long-term change infigure 1 of Davis and others (2005) over the measurementperiod appears smaller than their derived linear trend

The average dHdt increase over the total Antarcticgrounded ice is only +018 011 cmandash1 After correctionfor the small surface lowering due to firn compaction(dCdt frac14 ndash008 0006 cm andash1) and isostatic uplift(dBdt frac14 0540007 cmandash1) the average decrease in icethickness is 028 011 cm andash1 The changes in WA

grounded ice are significantly larger (dIdt frac14 ndash2603 cmandash1 and dMdt frac14 ndash466 44Gt andash1) than those inEA (dIdt frac14 +02 01 cm andash1 and dMdt frac14 +163 107Gt andash1) and the overall balance of grounded ice isnegative (dMdt frac14 ndash303 121Gt andash1) The changes infloating ice are large in both WA (dIdt frac14 ndash13917 cmandash1 and dMdt frac14 ndash945 114Gt andash1) and EA (dIdt frac14+22615 cmandash1 and +142 10Gt andash1) with signs corres-ponding to the respective loss and gain of grounded ice

Although the overall average ice-thickness changes aresmall average dIdt in particular DS are large (Fig 4aTable 2) In Greenland average dIdt range from +7606 cmandash1 in DS41 in the southeast and +7102 cmandash1 inJakobshavn DS53 in the southwest to ndash14615 cmandash1 inDS42 and ndash27307 cmandash1 in DS43 in the southeastIn WA average dIdt on grounded ice range from+4002 cmandash1 in the central Ross Ice Shelf DS18 tondash22907 cmandash1 in the Smith and Thwaites DS21 In EAaverage dIdt on grounded ice range from +74 10 cmandash1

in west Dronning Maud Land DS5 to ndash14527 cmandash1 inKemp Land DS8 In WA average dIdt on floating ice rangefrom +21812 cmandash1 on the FilchnerndashRonne Ice ShelfDS1 to ndash204 57 cmandash1 in the Smith and Thwaites DS21and ndash216 193 cmandash1 in the Pine Island DS22 In EAaverage dIdt on floating ice range from +915 107 cmandash1

in the Davis Sea DS12 +592 83 cmandash1 on the westDronning Maud Land DS5 and +55154 cmandash1 on thecentral Amery Ice Shelf DS10 to ndash903 205 cmandash1 in TerreAdelie DS14 The dominance of negative balances on bothfloating and grounded ice in WA and the dominance ofpositive balances on both floating and grounded ice in EAare illustrated in Figure 4

DISCUSSION OF OVERALL MASS CHANGES ANDEFFECT ON SEA LEVELOf the three ice sheets WA shows the largest imbalance(dMdt frac14 ndash47 4Gt andash1) which is partially offset by apositive balance in EA (+1611Gt andash1) for a net loss ofgrounded ice from Antarctica (ndash3112Gt andash1) contributing+008003mmandash1 to sea-level change The loss fromAntarctica is partially compensated by a small gain in

Fig 6 Histograms of dIdt for Greenland (a) above and below the ELA and (b) above and below the 2000m surface elevation contour


Greenland (+113Gt andash1) contributing ndash003 001mmandash1

to sea-level change for net mass loss of 2012Gt andash1 and acombined sea-level contribution from the three ice sheets of+005003mmandash1 The small mass gain in Greenland iscontrary to the widely held view that Greenland is losingsignificant mass during approximately the same period but isconsistent (within the range of errors) with our reinterpreta-tion of the ATM-based results that indicate the ice sheet wasclose to balance (ndash8Gt andash1) The loss fromWA and the gain inEA are remarkably consistent with the respective values ofndash48 14 and +2223Gt andash1 from mass-flux analysis of onlyabout 50 of the Antarctic outlet glaciers under theassumption of only a 5 uncertainty in accumulation rates(Rignot and Thomas 2002)

The contribution to sea-level change is small relative tothe potential contribution from ice sheets not only inrelation to the bulk of grounded ice that lies above sea levelbut also in relation to the mass flux across the icendashairinterface The loss in Antarctica and the gain in Greenlandare each less than about 3 of the respective surfacebalance estimates or together less than 1 of the total massinput The uncertainties are also significantly less than thosenoted in Huybrechts and others (2001) The contribution ofthe ice sheets is also small compared to the most recentestimate of current sea-level rise of 28 04mmandash1 fromsatellite altimetry (Leuliette and others 2004) which furtherconfounds possible explanations of the causes of con-temporary sea-level rise

We include estimates of dFdt (Table 1) for the end-pointassumption that the observed dIdt are occurring only in thefirn due to short-term changes in precipitation and that thedynamic balance terms are zero except in the ablation zoneof Greenland where firn compaction is neglected Whilethere is evidence for decadal changes in precipitation suchas the 4 per decade increase in Greenland shown by Boxand others (in press) and the long-term trends in Antarcticaccumulation mentioned below we believe evidence ofshort-term changes over the ice sheets to support thisassumption is lacking Nevertheless under this assumptionthe small mass gain of 11 3Gt andash1 in Greenland would bechanged to a small mass loss of 182Gt andash1 because theassumption reduces the estimated gain above the ELA butdoes not change the loss below the ELA In Antarctica theassumption would reduce the mass loss from 31 12Gt andash1

to 14 5Gt andash1 The resulting net loss from the three icesheets would be increased from 2012Gt andash1 to 326Gt andash1 giving a slightly larger combined sea-level contri-bution of +009002mmandash1

The small positive dIdt averaged over EA is consistentwith evidence of multi-decadal increasing trends in accu-mulation from ice cores (Mosley-Thompson and others1999 Wen and others 2001 Goodwin and others 2003)and modeling estimates of long-term trends in Antarcticprecipitation (Smith and others 1998) In particular icegrowth in the region of the Antarctic Peninsula may also bedue to increasing precipitation during the last century (Smithand others 1998) The marked thinnings in the Pine Islandand Thwaites Glacier basins of WA and the Totten Glacierbasin in EA are probably ice-dynamic responses to long-termclimate change and perhaps past removal of adjacent iceshelves The correlation between the mass changes ofgrounded and floating ice in EA and WA may suggest acoherent response of grounded and floating ice to atmos-pheric and oceanic forcings The thinning of ice shelves in

WA may be fostering increased outflow and the thickeningof ice shelves in EA may be contributing to reduced outflow

In Greenland most drainage systems have small massgains or losses with the largest mass losses from threesystems in the southeast The most significant division indMdt values is between the accumulation zone with a gainof 526 18Gt andash1 above the ELA and the ablation zonewith a loss of 41818Gt andash1 below the ELA (Fig 5) Thegain above 2000m elevation is 61206Gt andash1 and the lossbelow 2000m is 50425Gt andash1 These changes indicate agradual steepening of the ice sheet as expected with climatewarming at a greater rate than previously indicated by theATM results

Although the finding of near balance in Greenland mightbe interpreted to mitigate concern about the futurecontributions of the ice sheets to sea-level rise the findingsindicate that significant climate-induced changes are takingplace Furthermore recent ATM surveys indicate a recentincrease in coastal thinning (Krabill and others 2004) butadditional attention needs to be given to effects of increasingprecipitation both inland and in coastal regions (Bromwichand others 2001 Hanna and others 2001 Box and othersin press) The extent to which the competing processes ofinland growth will continue to balance coastal shrinkageuntil shrinkage under the predicted climate warmingbecomes dominant (Huybrechts and others 2004) will beseen as observations continue and model predictions arevalidated or improved

While the overall net mass changes are small thechanges are generally much larger in particular drainagesystems (Table 2 Fig 4b) Moreover the ratio of net masschanges to surface balance estimates in many drainagesystems (Figs 10 and 12 in Appendix) are up to three ordersof magnitude larger than the overall ice-sheet ratios of masschange to mass input (Table 2 (dMdt)Ajj Fig 12) Forexample DS5 in west Dronning Maud Land and DS9 to thewest of the Amery Ice Shelf in EA have positive massbalances of 49 and 43 respectively over their massinputs In contrast DS21 (Smith and Thwaites Glaciers) andDS22 (Pine Island Glacier) in WA have negative massbalances of 66 and 21 respectively over their massinputs In Greenland DS41 in the southeast has a positivebalance of 690 suggesting a large underestimate of theaccumulation rate in that system whereas the adjacentDS32 to the north has a negative balance of 110 and theadjacent DS42 to the south has a negative balance of over1000 This wide disparity in regional mass balancesclearly illustrates the risks of sampling strategies based onstudying only the places where the largest changes aretaking place

Overall our results describe the ice-sheet mass balanceduring essentially the last decade of the 20th century andthus provide a baseline for evaluating future changesAlthough non-linear variations in H(t) for periods of3ndash5 years are evident in some regions we believe the linearcharacter of most of the dHdt trends suggests a dominanceof multi-decadal mass-balance processes during this periodClearly these factors are expected to change (Huybrechtsand others 2004) perhaps at a greater rate than has beenpredicted as recent measurements of increased outflow andincreasing precipitation in Greenland may be indicating(Alley and others 2003) Therefore continued comprehen-sive monitoring of ice elevations is essential to determine inparticular the relative importance of increasing summer


temperatures on both ice melting and dynamic thinningcompared to the effect of increasing precipitation on bothinland growth and reduction of ablation at lower elevations

ACKNOWLEDGEMENTSWe thank the European Space Agency for our selection asERS investigators and for providing the radar altimeter dataand technical information Data processing and analysis wassupported by NASArsquos Cryospheric Sciences Program and byICESat Project Science We appreciate comments andsuggestions from reviewer RB Alley and from RJ Braith-waite We thank P Huybrechts E Ivins and R Peltier fordigital copies of their bedrock motion data W Krabill for adigital copy of the ATM-based dHdt map J Comiso forthe digital temperature data D Vaughan for digital surfacebalance data for the Larsen Ice Shelf and I Allison for hissuggestion to account for sea-level rise in calculation of ice-shelf thickness changes

REFERENCESAbdalati W and 9 others 2001 Outlet glacier and margin

elevation changes near-coastal thinning of the Greenland icesheet J Geophys Res 106(D24) 33729ndash33742

Alley RB and 10 others 2003 Abrupt climate change Science299(5615) 2005ndash2010

Arthern RJ and DJ Wingham 1998 The natural fluctuations offirn densification and their effect on the geodetic determinationof ice sheet mass balance Climatic Change 40(4) 605ndash624

Benson CS 1962 Stratigraphic studies in the snow and firn of theGreenland ice sheet SIPRE Res Rep 70

Box JE and 8 others In press Greenland ice sheet surface massbalance variability (1988ndash2004) from calibrated polar MM5output J Climate

Braithwaite RJ 1994 Thoughts on monitoring the effects ofclimate change on the surface elevation of the Greenland icesheet Global Planet Change 9(3ndash4) 251ndash261

Braithwaite RJ and Y Zhang 2000 Sensitivity of mass balance offive Swiss glaciers to temperature changes assessed by tuning adegree-day model J Glaciol 46(152) 7ndash14

Bromwich DH QS Chen LS Bai EN Cassano and Y Li 2001Modeled precipitation variability over the Greenland ice sheetJ Geophys Res 106(D24) 33891ndash33908

Comiso JC 2003 Warming trends in the Arctic from clear satelliteobservations J Climate 16(21) 3498ndash3510

Comiso JC and CL Parkinson 2004 Satellite-observed changesin the Arctic Phys Today 57(8) 38ndash44

Davis CH Y Li JR McConnell MM Frey and E Hanna 2005Snowfall-driven growth in East Antarctic ice sheet mitigatesrecent sea-level rise Science 308(5730) 1898ndash1901

Dibb JE and M Fahnestock 2004 Snow accumulation surfaceheight change and firn densification at Summit Greenlandinsights from 2 years of in situ observation J Geophys Res109(D24) D24113 (1010292003JD004300)

Femenias P 1996 ERS QLOPR and OPR range processing ESAESRIN Tech Note ER-TN-RS-RA-0022 Frascati European SpaceAgencyEuropean Space Research Institute

Ferguson AC CH Davis and JE Cavanaugh 2004 Anautoregressive model for analysis of ice sheet elevationchange time series IEEE Trans Geosci Remote Sens 42(11)2426ndash2436

Giovinetto MB and HJ Zwally 2000 Spatial distribution of netsurface accumulation on the Antarctic ice sheet Ann Glaciol31 171ndash178

Goodwin I H De Angelis M Pook and NW Young 2003 Snowaccumulation variability in Wilkes Land East Antarctica and therelationship to atmospheric ridging in the 1308ndash1708 E region

since 1930 J Geophys Res 108(D21) 4673 (1010292002JD002995)

Hamilton GS IM Whillans and PJ Morgan 1998 First pointmeasurements of ice-sheet thickness change in Antarctica AnnGlaciol 27 125ndash129

Hanna E P Valdes and J McConnell 2001 Patterns andvariations of snow accumulation over Greenland 1979ndash98from ECMWF analyses and their verification J Climate 14(17)3521ndash3535

Huybrechts P 2002 Sea-level changes at the LGM from ice-dynamic reconstructions of the Greenland and Antarctic icesheets during the glacial cycles Quat Sci Rev 21(1ndash3)203ndash231

Huybrechts P M Kuhn K Lambeck MT Nhuan D Qinand PL Woodworth 2001 Changes in sea level InHoughton JT and 7 others eds Climate change 2001 thescientific basis Contribution of Working Group I to theThird Assessment Report of the Intergovernmental Panel onClimate Change Cambridge Cambridge University Press639ndash694

Huybrechts P J Gregory I Janssens and M Wild 2004Modelling Antarctic and Greenland volume changes duringthe 20th and 21st centuries forced by GCM time sliceintegrations Global Planet Change 42(1ndash4) 83ndash105

Ivins ER X Wu CA Raymond CF Yoder and TS James 2001Temporal geoid of a rebounding Antarctica and potentialmeasurement by the GRACE and GOCE satellites In SiderisMG ed Gravity Geoid and Geodynamics 2000 GGG2000IAG International Symposium Banff Alberta Canada July 31ndashAugust 4 2000 Berlin Springer 361ndash366 (InternationalAssociation of Geodesy Symposia 123)

Johannessen OM K Khvorostovsky MW Miles and LP Bobylev2005 Recent ice-sheet growth in the interior of GreenlandScience 310(5750) 1013ndash1016

Joughin I E Rignot CE Rosanova BK Lucchitta andJ Bohlander 2003 Timing of recent accelerations of Pine IslandGlacier Antarctica Geophys Res Lett 30(13) 1706 (1010292003GL017609)

Joughin I W Abdalati and M Fahenstock 2004 Large fluctua-tions in speed on Greenlandrsquos Jakobshavn Isbrae glacier Nature432 608ndash610

Kapsner WR RB Alley CA Shuman S Anandakrishnan andPM Grootes 1995 Dominant influence of atmosphericcirculation on snow accumulation in Greenland over the past18000 years Nature 373(6509) 52ndash54

Kojima K 1964 Densification of snow in Antarctica InMellor Med Antarctic snow and ice studies Washington DC AmericanGeophysical Union 157ndash218 (Antarctic Research Series 2)

Krabill WB and 9 others 2000 Greenland ice sheet high-elevation balance and peripheral thinning Science 289(5478)428ndash430

Krabill W and 12 others 2004 Greenland Ice Sheet increasedcoastal thinning Geophys Res Lett 31(24) L24402 (1010292004GL021533)

Leuliette EW RS Nerem and GT Mitchum 2004 Calibration ofTOPEXPoseidon and Jason altimeter data to construct acontinuous record of mean sea level change Marine Geodesy27(1ndash2) 79ndash94

Li J and HJ Zwally 2002 Modeled seasonal variations of firndensity induced by steady-state surface air-temperature cycleAnn Glaciol 34 299ndash302

Li J and HJ Zwally 2004 Modeling the density variation inshallow firn layer Ann Glaciol 38 309ndash313

Li J HJ Zwally H Cornejo and D Yi 2003 Seasonal variationof snow-surface elevation in North Greenland as modeledand detected by satellite radar altimetry Ann Glaciol 37233ndash238

McConnell JR and 6 others 2001 Annual net snow accumulationover southern Greenland from 1975 to 1998 J Geophys Res106(D24) 33827ndash33838


Monaghan AJ DH Bromwich and S-H Wang In press Recenttrends in Antarctic snow accumulation from Polar MM5 PhilosTrans Royal Soc A

Mosley-Thompson E JF Paskievitch AJ Gow and LG Thomp-son 1999 Late 20th century increase in South Pole snowaccumulation J Geophys Res 104(D4) 3877ndash3886

Peltier WR 2004 Global glacial isostatic adjustment and thesurface of the ice-age Earth the ICE-5G(VM2) model andGRACE Annu Rev Earth Planet Sci 32 111ndash149

Reeh N DA Fisher RM Koerner and HB Clausen In press Anempirical firn-densification model comprising ice lenses AnnGlaciol

Rignot E and RH Thomas 2002 Mass balance of polar icesheets Science 297(5586) 1502ndash1506

Rignot E G Casassa P Gogineni W Krabill A Rivera andR Thomas 2004 Accelerated ice discharge from the AntarcticPeninsula following the collapse of Larsen B ice shelf GeophysRes Lett 31(18) L18401 (1010292004GL020697)

Scambos TA JA Bohlander CA Shuman and P Skvarca 2004Glacier acceleration and thinning after ice shelf collapse in theLarsen B embayment Antarctica Geophys Res Lett 31(18)L18402 (1010292004GL020670)

Scharroo R and P Visser 1998 Precise orbit determination andgravity field improvement for the ERS satellites J Geophys Res103(C4) 8113ndash8127

Shepherd A D Wingham and JA Mansley 2002 Inland thinningof the Amundsen Sea sector West Antarctica Geophys ResLett 29(10) 1364 (1010292001GL014183)

Shepherd A DWingham T Payne and P Skvarca 2003 Larsen iceshelf has progressively thinned Science 302 (5646) 856ndash859

Skvarca P W Rack H Rott and T Donangelo 1999 Climatictrend and the retreat and disintegration of ice shelves on theAntarctic Peninsula an overview Polar Res 18(2) 151ndash157

Smith IN WF Budd and P Reid 1998 Model estimates ofAntarctic accumulation rates and their relationship to tempera-ture changes Ann Glaciol 27 246ndash250

Thomas RH 2003 Force-perturbation analysis of recent thinningand acceleration of Jakobshavn Isbraelig Greenland J Glaciol50(168) 57ndash66

Thomas R and 7 others 2001 Mass balance of higher-elevationparts of the Greenland ice sheet J Geophys Res 106(D24)33707ndash33716

Thomas RH W Abdalati E Frederick WB Krabill S Manizadeand K Steffen 2003 Investigation of surface melting anddynamic thinning on Jakobshavn Isbraelig Greenland J Glaciol49(165) 231ndash239

Thomas R and 17 others 2004 Accelerated sea level rise fromWest Antarctica Science 306 (5694) 255ndash258

Vaughan DG JL Bamber MB Giovinetto J Russell andAPR Cooper 1999 Reassessment of net surface mass balancein Antarctica J Climate 12(4) 933ndash946

Wen J and 6 others 2001 Snow density and stratigraphy at DT001in Princess Elizabeth Land East Antarctica Polar MeteorolGlaciol 15(43) 43ndash54

Whillans IM 1977 The equation of continuity and its applicationto the ice sheet near lsquoByrdrsquo Station Antarctica J Glaciol18(80) 359ndash371

Whitworth T III AH Orsi SJ Kim and WD Nowlin Jr 1998Water masses and mixing near the Antarctic Slope front InJacobs SS and RF Weiss eds Ocean ice and atmosphereinteractions at the Antarctic continental margin WashingtonDC American Geophysical Union 1ndash27 (Antarctic ResearchSeries 75)

Wingham DJ AL Ridout R Scharroo RJ Arthern andCK Shum 1998 Antarctic elevation change 1992 to 1996Science 282(5388) 456ndash458

Zwally HJ 1989 Growth of Greenland ice sheet interpretationScience 246(4937) 1589ndash1591

Zwally HJ and AC Brenner 2001 Ice sheet dynamics and massbalance In Fu L-L and A Cazanave eds Satellite altimetryand earth sciences New York Academic Press Inc 351ndash369(International Geophysical Series 69)

Zwally HJ and MB Giovinetto 2000 Spatial distribution ofnet surface mass balance on Greenland Ann Glaciol 31126ndash132

Zwally HJ and MB Giovinetto 2001 Balance mass fluxand ice velocity across the equilibrium line in drainagesystems of Greenland J Geophys Res 106(D24) 33717ndash33728

Zwally HJ and J Li 2002 Seasonal and interannual variations offirn densification and ice-sheet surface elevation at Greenlandsummit J Glaciol 48(161) 199ndash207

Zwally HJ and 15 others 2002a ICESatrsquos laser measurements ofpolar ice atmosphere ocean and land J Geodyn 34(3ndash4)405ndash445

Zwally HJ MA Beckley AC Brenner and MB Giovinetto2002b Motion of major ice-shelf fronts in Antarctica from slant-range analysis of radar altimeter data 1978ndash98 Ann Glaciol34 255ndash262

Zwally HJ W Abdalati T Herring K Larson J Saba andK Steffen 2002c Surface melt-induced acceleration of Green-land ice-sheet flow Science 297(5579) 218ndash222


APPENDIX

Fig 7 Distribution of s of the derived dHdt from ERS data for Greenland (a) and Antarctica (b) as described in the text

Fig 8 Distribution of dBdt for Greenland (a) and Antarctica (b) as described in the text


Fig 9 Distribution of dCdt in Greenland (a) and Antarctica (b) calculated with a temperature-driven firn compaction model as described inthe text The firn compaction reduces the surface elevation over the Greenland accumulation zone by 171 cmandash1 as the result of climatewarming during the measurement period In WA the lowering on grounded ice is 158 cmandash1 and the lowering on floating ice is 279 cmandash1also due to regional warming as is the 170 cmandash1 lowering on EA floating ice In EA grounded ice a small 021 cmandash1 surface rise is causedby a small cooling over the inland ice The dCdt are computed for all points where A is gt25 kgmndash2 andash1 which in Greenland excluded121 gridpoints mostly located in the ablation zone and in Antarctica excluded 92 gridpoints mostly located in the interior of EA whereaccumulation is small

Fig 10 Distribution of net accumulation at the surface based on compiled data (a) Surface balance rate on Greenland determined forgridpoints (i) by analysis of firn emissivity in the area above the intra-percolation line compared with pit and core data at stations and alongtraverse routes bulk corresponding to strata accumulated 1950ndash80 and (ii) by accumulationablation models output below the intra-percolation line (Zwally and Giovinetto 2000 2001) (b) Isopleths map of surface balance for Antarctica (in 100 kgmndash2 andash1) drawn on thebasis of field data from pits cores and stake networks at stations and along traverse routes bulk corresponding to strata accumulated1950ndash2000 (Giovinetto and Zwally 2000 updated)


Fig 11 Distribution of net accumulation at the surface interpolated from compilations of field data and models output (a) Isopleths map ofsurface balance on Greenland (in 100 kgmndash2 andash1) drawn on the basis of the grid values shown in Figure 10a (Zwally and Giovinetto 2001modified) (b) Surface balance rate on Antarctica determined for gridpoints by interpolation from the isopleths pattern shown in Figure 10b(Giovinetto and Zwally 2000 updated)

Fig 12 Distribution of the ratio between net mass budget and net surface accumulation in the grounded-ice and floating-ice areas of eachdrainage system of Antarctica and Greenland as listed in Table 2 (column (dMdt)Ajj) In Antarctica the estimated gains and losses aresmaller than 50 of the accumulation in 22 of the grounded-ice entities of the 24 systems included in the study or 97 of their total areaand smaller than 100 in 13 of the floating-ice entities of the 25 systems included in the study or 58 of their total area In Greenland thegains and losses are smaller than 50 of the accumulation in 11 of the 15 systems included in the study or 83 of their total area

MS received 24 November 2005 and accepted 30 December 2005


(ATM) laser-altimeter surveys to increase coverage of themargins We also use optimal-interpolation procedures toprovide nearly complete spatial coverage of the ice sheetsand shelves (Figs 1a and 2a) For the first time we use a firncompaction model with a 20 year record of satellite-basedsurface temperatures to calculate corrections for elevationchanges due to changes in the rate of firn compactioncaused by temporal variations in firn temperature and near-surface melting

OBSERVED AND INTERPOLATED ELEVATIONCHANGES (dHdt )Measurements of ice surface elevations (H) from ERS-1 and-2 radar altimeters are compiled as elevation time seriesH(t) from which elevation change (dHdt) values are derived(Fig 3) The ERS altimeters operated in either ocean modewith a resolution of 45 cm per range gate or ice mode with aresolution of 182 cm per range gate We use only ice modedata because of a spatially variant bias between the modesand the greater spatial and temporal coverage of the icemode data We applied our V4 range-retracking algorithmatmospheric range corrections instrument corrections slopecorrections and an adjustment for solid tides (Zwally andBrenner 2001) Instrument corrections include subtractionof a 409 cm bias from ERS-1 elevations to account for adifferent instrument parameter used for ERS-2 (Femenias1996) and corrections for drifts in the ultra-stable oscillatorand bias changes in the scanning point target response thatare obtained from the European Space Agency We use theDUT DGM-E04 orbits which have a radial orbit precision of5ndash6 cm (Scharroo and Visser 1998)

The time periods are from mid-April 1992 to mid-October2002 for Greenland and to mid-April 2001 for AntarcticaThe series are constructed for gridpoints nominally 50 kmapart from sets of elevation differences measured at orbitalcrossovers using time periods of 91 days Our methodsenable us to obtain useful H(t) series over more of the ice-sheet area than some other analyses have For mostgridpoints crossovers within a 100 km circle centered onthe gridpoint are used and within 200 km for a few pointsCrossover selection is also limited to elevations within250m of the elevation at the gridpoint center which forslopes gt1200 restricts the selected areas to bands alongelevation contours where the elevation changes tend to bespatially coherent The first sequence of elevation differencesat crossings between period T1 and all successive Ti iscombined with the second sequence of those for crossingsbetween T2 and all successive Ti and so forth for alladditional sequences which are then combined in one H(t)(Zwally and Brenner 2001) The resulting H(t) series use allindependent crossovers including inter-satellite crossoverswhich greatly increases the number of crossovers and theaccuracy of the results (more crossovers and longer timeintervals) as compared to using only the first sequence oronly intra-satellite crossovers For Greenland we have16106 crossovers from ERS-1ERS-1 52 106 from ERS-2ERS-2 and 59 106 from ERS-1ERS-2 For Antarctica wehave 157 106 crossovers from ERS-1ERS-1 276106 fromERS-2ERS-2 and 419 106 from ERS-1ERS-2 whereas onlycrossovers from ERS-1ERS-1 and ERS-2ERS-2 are used byDavis and others (2005)

We obtain dHdt values for 602 (90) of the 670gridpoints on Greenland ice and 4085 (79) of the 5175

Fig 1 Greenland (a) Distribution of surface elevation change data by source derived from ERS-1 and -2 radar altimetry ATM (closest-neighbor interpolation from airborne surveys) and obtained by optimal interpolation ice terminus of coterminous ice sheet (red)equilibrium line (black dashes) 2000m elevation contour (blue) drainage divides (black) drainage system designation (number in circles)and location of H(t) series depicted in Figure 3a (labeled blue full circles) (b) Distribution of elevation change (dHdt) (c) Distribution of ice-thickness change (dIdt)













Dataset gorf


Re dFdt Re dMdt



g 622 16191 930 +063 030 ndash161003 +005004 +219018 +31926 ndash00880007






(6 10ndash3)+045


(ndash5 10ndash2)94

(+1 10ndash5) 0026


(6 10ndash3)+054





(4 10ndash3)+040














dIdt

gfrac14 dH

dt dC

dt dB

dt eth1THORN



dIdt

ffrac14 Fb

dHdt

dCdt

dSdt

eth2THORN


ndash3











dMdt

frac14 ice dIdt

NStS

thorn dIdt

StSthorn dI

dt

ln dI

dt

Out

Ar eth3THORN





DS No-name gorf


(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt




























f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519




dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX






















Dataset gorf


Re dFdt Re dMdt



g 622 16191 930 +063 030 ndash161003 +005004 +219018 +31926 ndash00880007






(6 10ndash3)+045


(ndash5 10ndash2)94

(+1 10ndash5) 0026


(6 10ndash3)+054





(4 10ndash3)+040














dIdt

gfrac14 dH

dt dC

dt dB

dt eth1THORN



dIdt

ffrac14 Fb

dHdt

dCdt

dSdt

eth2THORN


ndash3











dMdt

frac14 ice dIdt

NStS

thorn dIdt

StSthorn dI

dt

ln dI

dt

Out

Ar eth3THORN





DS No-name gorf


(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt




























f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519




dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX

















Dataset gorf


Re dFdt Re dMdt



g 622 16191 930 +063 030 ndash161003 +005004 +219018 +31926 ndash00880007






(6 10ndash3)+045


(ndash5 10ndash2)94

(+1 10ndash5) 0026


(6 10ndash3)+054





(4 10ndash3)+040














dIdt

gfrac14 dH

dt dC

dt dB

dt eth1THORN



dIdt

ffrac14 Fb

dHdt

dCdt

dSdt

eth2THORN


ndash3











dMdt

frac14 ice dIdt

NStS

thorn dIdt

StSthorn dI

dt

ln dI

dt

Out

Ar eth3THORN





DS No-name gorf


(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt




























f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519




dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX















Dataset gorf


Re dFdt Re dMdt



g 622 16191 930 +063 030 ndash161003 +005004 +219018 +31926 ndash00880007






(6 10ndash3)+045


(ndash5 10ndash2)94

(+1 10ndash5) 0026


(6 10ndash3)+054





(4 10ndash3)+040














dIdt

gfrac14 dH

dt dC

dt dB

dt eth1THORN



dIdt

ffrac14 Fb

dHdt

dCdt

dSdt

eth2THORN


ndash3











dMdt

frac14 ice dIdt

NStS

thorn dIdt

StSthorn dI

dt

ln dI

dt

Out

Ar eth3THORN





DS No-name gorf


(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt




























f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519




dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX



















dIdt

gfrac14 dH

dt dC

dt dB

dt eth1THORN



dIdt

ffrac14 Fb

dHdt

dCdt

dSdt

eth2THORN


ndash3











dMdt

frac14 ice dIdt

NStS

thorn dIdt

StSthorn dI

dt

ln dI

dt

Out

Ar eth3THORN





DS No-name gorf


(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt




























f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519




dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX


















dMdt

frac14 ice dIdt

NStS

thorn dIdt

StSthorn dI

dt

ln dI

dt

Out

Ar eth3THORN





DS No-name gorf


(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt




























f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519




dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX












DS No-name gorf


(dFdt)Ajj

(dMdt)Ajj

Re dFdt Re dMdt




























f 82 02212 +910 081 +777 069 +1751156 3372 3372 0239 0519




dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX












dMdt

frac14 adIdt

Ar eth4THORN










dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX













dFdt

frac14 ice dIdt

NStS

thorn 0

Ar eth5THORN



















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX





















N Area dHdt dHdt

















Diff in dHdt

































































































APPENDIX























Diff in dHdt

































































































APPENDIX






































































































APPENDIX




























































































APPENDIX
















































































APPENDIX









































APPENDIX











APPENDIX






















Documents

Mass changes of the Greenland and Antarctic ice sheets and ...Mass changes of the Greenland and Antarctic ice sheets and shelves and contributions to sea-level rise: 1992 2002 H. Jay