LETTER doi:10.1038/nature10847 Recent contributions of glaciers and ice caps to sea level rise Thomas Jacob',John Wahr',W.Tad Pfeffer2.3&Sean Swenson4 Glaciers and ice caps(GICs)are important contributors to present- hydrology and for glacial isostatic adjustment(GIA)computed using day global mean sea level rise-4.Most previous global mass balance the ICE-5G deglaciation model.We use 94 monthly GRACE solutions estimates for GICs rely on extrapolation of sparse mass balance from the University of Texas Center for Space Research,spanning measurements'24 representing only a small fraction of the GIC January 2003 to December 2010.The GIA corrections do not include area,leaving their overall contribution to sea level rise unclear. the effects of post-Little Ice Age (LIA)isostatic rebound,which we Here we show that GICs,excluding the Greenland and Antarctic separately evaluate and remove.All above contributions and their peripheral GICs,lost mass at a rate of 148+30Gtyr from effects on the GRACE solutions are discussed in Supplementary January 2003 to December 2010,contributing 0.410.08 mm yr Information. to sea level rise.Our results are based on a global,simultaneous Figure 1 shows mascons for all ice-covered regions,constructed inversion of monthly GRACE-derived satellite gravity fields,from from the Digital Chart of the World and the Circum-Arctic Map which we calculate the mass change over all ice-covered regions of Permafrost and Ground-Ice Conditions18.Each ice-covered region greater in area than 100 km2.The GIC rate for 2003-2010 is about is chosen as a single mascon,or as the union of several non-overlapping 30 per cent smaller than the previous mass balance estimate that mascons.We group 175 mascons into 20 regions.Geographically iso- most closely matches our study period.The high mountains of lated regions with glacierized areas less than 100km in area are Asia,in particular,show a mass loss of only 4+20 Gtyr for excluded.Because GRACE detects total mass change,its results for 2003-2010,compared with 47-55 Gt yr in previously published an ice-covered region are independent of the glacierized surface area estimates25.For completeness,we also estimate that the Greenland (Supplementary Information). and Antarctic ice sheets,including their peripheral GICs,con- Mass balance rates for each region are shown in Table 1 (see tributed 1.06+0.19 mm yr to sea level rise over the same time Supplementary Information for details on the computation of the rates period.The total contribution to sea level rise from all ice-covered and uncertainties).We note that Table 1 includes a few positive rates, regions is thus 1.48+0.26 mm yr-,which agrees well with inde- but none are significantly different from zero.We also performed an pendent estimates of sea level rise originating from land iceloss and inversion with GRACE fields from the GFZ German Research Centre other terrestrial sources. for Geosciences and obtained results that agreed with those from the Interpolation of sparse mass balance measurements on selected Center for Space Research(Table 1)to within 5%for each region. glaciers is usually used to estimate global GIC mass balance.24 The results in Table 1 are in general agreement with previous GRACE Models are also used37,but these depend on the quality of input studies for the large mass loss regions of the Canadian Arctic'and climate data and include simplified glacial processes.Excluding Patagonia",as well as for the Greenland and Antarctic ice sheets with Greenland and Antarctic peripheral GICs (PGICs),GICs have variously been reported to have contributed 0.43-0.51 mmyr to sea level rise (SLR)during 1961-200437,0.77mmyrduring 2001-2004,1.12 mm yr during 2001-2005'and 0.95 mmyr during 2002-20062 The Gravity Recovery and Climate Experiment(GRACE)satellite mission'has provided monthly,global gravity field solutions since 2002,allowing users to calculate mass variations at the Earth's sur- face'.GRACE has been used to monitor the mass balance of selected GIC regions4that show large ice mass loss,as well as of Antarctica and Greenland'. Here we present a GRACE solution that details individual mass balance results for every region of Earth with large ice-covered areas. The main focus of this paper is on GICs,excluding Antarctic and Greenland PGICs.For completeness,however,we also include results for the Antarctic and Greenland ice sheets with their PGICs.GRACE does not have the resolution to separate the Greenland and Antarctic ice sheets from their PGICs.All results are computed for the same 8-yr time period(2003-2010). To determine losses of individual GIC regions,we cover each region Figure 1 Mascons for the ice-covered regions considered here.Each with one or more 'mascons'(small,arbitrarily defined regions of coloured region represents a single mascon.Numbers correspond to regions Earth)and fit mass values for each mascon(ref.16 and Supplemen- shown in Table 1.Regions containing more than one mascon are outlined with tary Information)to the GRACE gravity fields,after correcting for a dashed line. Department of Physics and Cooperative Institute for Environmental Studies,University of Colorado at Boulder,Boulder,Colorado 80309,USAInstitute of Arctic and Alpine Research,University of Colorado at Boulder,Boulder,Colorado 80309,USA.Departmentof Civil,Environmental,and Architectural Engineering.University of Coloradoat Boulder,Boulder,Colorado80309,USA"National Center for Atmospheric Research,Boulder,Colorado 80305,USA.tPresent address:Bureau de Recherches Geologiques et Minieres,Orleans 45060,France. 514 NATURE VOL 48223 FEBRUARY 2012 2012 Macmillan Publishers Limited.All rights reserved
LETTER doi:10.1038/nature10847 Recent contributions of glaciers and ice caps to sea level rise Thomas Jacob1 {, John Wahr1 , W. Tad Pfeffer2,3 & Sean Swenson4 Glaciers and ice caps (GICs) are important contributors to presentday global mean sea level rise1–4. Most previous global mass balance estimates for GICs rely on extrapolation of sparse mass balance measurements1,2,4 representing only a small fraction of the GIC area, leaving their overall contribution to sea level rise unclear. Here we show that GICs, excluding the Greenland and Antarctic peripheral GICs, lost mass at a rate of 148 6 30 Gt yr21 from January 2003 to December 2010, contributing 0.41 6 0.08 mm yr21 to sea level rise. Our results are based on a global, simultaneous inversion of monthly GRACE-derived satellite gravity fields, from which we calculate the mass change over all ice-covered regions greater in area than 100 km2 . The GIC rate for 2003–2010 is about 30 per cent smaller than the previous mass balance estimate that most closely matches our study period2 . The high mountains of Asia, in particular, show a mass loss of only 4 6 20 Gt yr21 for 2003–2010, compared with 47–55 Gt yr21 in previously published estimates2,5. For completeness, we also estimate that the Greenland and Antarctic ice sheets, including their peripheral GICs, contributed 1.06 6 0.19 mm yr21 to sea level rise over the same time period. The total contribution to sea level rise from all ice-covered regions is thus 1.48 6 0.26 mm yr21 , which agrees well with independent estimates of sea level rise originating from land ice loss and other terrestrial sources6 . Interpolation of sparse mass balance measurements on selected glaciers is usually used to estimate global GIC mass balance1,2,4. Models are also used3,7, but these depend on the quality of input climate data and include simplified glacial processes. Excluding Greenland and Antarctic peripheral GICs (PGICs), GICs have variously been reported to have contributed 0.43–0.51 mm yr21 to sea level rise (SLR) during 1961–20043,7,8, 0.77 mm yr21 during 2001–20048 , 1.12 mm yr21 during 2001–20051 and 0.95 mm yr21 during 2002–20062 . The Gravity Recovery and Climate Experiment (GRACE) satellite mission9 has provided monthly, global gravity field solutions since 2002, allowing users to calculate mass variations at the Earth’s surface10. GRACE has been used to monitor the mass balance of selected GIC regions11–14 that show large ice mass loss, as well as of Antarctica and Greenland15. Here we present a GRACE solution that details individual mass balance results for every region of Earth with large ice-covered areas. The main focus of this paper is on GICs, excluding Antarctic and Greenland PGICs. For completeness, however, we also include results for the Antarctic and Greenland ice sheets with their PGICs. GRACE does not have the resolution to separate the Greenland and Antarctic ice sheets from their PGICs. All results are computed for the same 8-yr time period (2003–2010). To determine losses of individual GIC regions, we cover each region with one or more ‘mascons’ (small, arbitrarily defined regions of Earth) and fit mass values for each mascon (ref. 16 and Supplementary Information) to the GRACE gravity fields, after correcting for hydrology and for glacial isostatic adjustment (GIA) computed using the ICE-5G deglaciation model. We use 94 monthly GRACE solutions from the University of Texas Center for Space Research, spanning January 2003 to December 2010. The GIA corrections do not include the effects of post-Little Ice Age (LIA) isostatic rebound, which we separately evaluate and remove. All above contributions and their effects on the GRACE solutions are discussed in Supplementary Information. Figure 1 shows mascons for all ice-covered regions, constructed from the Digital Chart of the World17 and the Circum-Arctic Map of Permafrost and Ground-Ice Conditions18. Each ice-covered region is chosen as a single mascon, or as the union of several non-overlapping mascons. We group 175 mascons into 20 regions. Geographically isolated regions with glacierized areas less than 100 km2 in area are excluded. Because GRACE detects total mass change, its results for an ice-covered region are independent of the glacierized surface area (Supplementary Information). Mass balance rates for each region are shown in Table 1 (see Supplementary Information for details on the computation of the rates and uncertainties). We note that Table 1 includes a few positive rates, but none are significantly different from zero. We also performed an inversion with GRACE fields from the GFZ German Research Centre for Geosciences and obtained results that agreed with those from the Center for Space Research (Table 1) to within 5% for each region. The results in Table 1 are in general agreement with previous GRACE studies for the large mass loss regions of the Canadian Arctic12 and Patagonia11, as well as for the Greenland and Antarctic ice sheets with 1 Department of Physics and Cooperative Institute for Environmental Studies, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 2 Institute of Arctic and Alpine Research, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 3 Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 4 National Center for Atmospheric Research, Boulder, Colorado 80305, USA. {Present address: Bureau de Recherches Ge´ologiques et Minie`res, Orle´ans 45060, France. 12 13 16 17 14 15 19 1 2 11 3 4 5 6 7 8 9 10 18 20 Figure 1 | Mascons for the ice-covered regions considered here. Each coloured region represents a single mascon. Numbers correspond to regions shown in Table 1. Regions containing more than one mascon are outlined with a dashed line. 514 | NATURE | VOL 482 | 23 FEBRUARY 2012 ©2012 Macmillan Publishers Limited. All rights reserved
LETTER RESEARCH Table 1|Inverted 2003-2010 mass balance rates Region Rate(Gtyr) 1.Iceland -11±2 2.Svalbard -3±2 3.Franz Josef Land 0±2 4.Novaya Zemlya -4±2 5.Severnaya Zemlya -1±2 6.Siberia and Kamchatka 2±10 7.Altai 3±6 8.High Mountain Asia -4±20 8a.Tianshan -5±6 8b.Pamirs and Kunlun Shan -1±5 8c.Himalaya and Karakoram -5±6 8d.Tibet and Qilian Shan 7±7 Franz Joseph Land 9.Caucasus 1±3 10.Alps -2±3 6.Siberia and Kam 11.Scandinavia 3±5 12.Alaska -46±7 13.Northwest America excl.Alaska 5±8 14.Baffin Island -33±5 15.Ellesmere,Axel Heiberg and Devon Islands -34±6 16.South America excl.Patagonia -6±12 17.Patagonia -23±9 18.New Zealand 2±3 19.Greenland ice sheet PGICs -222±9 20.Antarctica ice sheet PGICs -165±72 Total -536±93 GICs excl.Greenland and Antarctica PGICs -148±30 Antarctica Greenland ice sheet and PGICs -384±71 Total contribution to SLR 1.48±0.26mmyr1 SLR due to GICs excl.Greenland and Antarctica PGICs 0.41±0.08mmyr SLR due to Antarctica+Greenland ice sheet and PGICs 1.06+0.19 mm yr-1 Uncertainties are given at the95%(2)confidence level. their PGICs'.Our results for Alaska also show considerable mass loss, although our mass loss rate is smaller than some previously published GRACE-derived rates that used shorter and earlier GRACE data spans (Supplementary Information).The global GIC mass balance,exclud- erica excl.Patagonia ing Greenland and Antarctic PGICs,is -148+30Gtyr,con- tributing 0.410.08 mm yr'to SLR. Mass balance time series for all GIC regions are shown in Fig.2.The seasonal and interannual variabilities evident in these time series have contributions from ice and snow variability on the glaciers,as well as from imperfectly modelled hydrological signals in adjacent regions and from random GRACE observational errors.Interannual variability can affect rates determined over short time intervals.Figure 2 and Supplementary Table 2 show that there was considerable interannual variability during 2003-2010 for some of the regions,especially High Mountain Asia(HMA).The HMA results in Supplementary Table 2 show that this variability induces large swings in the trend solutions when it is fitted to subsets of the entire time period.These results suggest that care should be taken in extending the 2003-2010 results presented in this paper to longer time periods. For comparison with studies in which PGICs are included with GICs,we upscale our GIC-alone rate to obtain a GIC rate that includes PGIC,based on ref.3(Supplementary Information).The result is that GICs including PGICs lost mass at a rate of 229+82 Gtyr (0.63+0.23 mm yr SLR),and that the combined ice sheets without their PGICs lost mass at 303100 Gtyr(0.84+0.28mm yr SLR).Although no other study encompasses the same time span, published non-GRACE estimates for GICs plus PGICs are larger: 0.98±0.19mmyr1over2001-2004,1.41±0.20mmr-1 over 2001-2005'and 0.765mm yr(no uncertainty given)over 2006- 20102.These differences could be due to the small number of mass 200320042005200620072008200920102011 balance measurements those estimates must rely on,combined with Year uncertain regional glacier extents.In addition,there are indications Figure 2 Mass change during 2003-2010 for all GIC regions shown in from more recent non-GRACE measurements that the GIC mass loss Fig.I and Table 1.The black horizontal lines run through the averages of the rate decreased markedly beginning in 200520 time series.The grey lines represent 13-month-window,low-pass-filtered Our results for HMA disagree significantly with previous studies. versions of the data.Time series are shifted for legibility.Modelled A recent GRACE-based studys over 2002-2009 yields significantly contributions from GIA,LIA and hydrology have been removed 23 FEBRUARY 2012 VOL 482 NATURE 515 2012 Macmillan Publishers Limited.All rights reserved
their PGICs19. Our results for Alaska also show considerable mass loss, although our mass loss rate is smaller than some previously published GRACE-derived rates that used shorter and earlier GRACE data spans (Supplementary Information). The global GIC mass balance, excluding Greenland and Antarctic PGICs, is 2148 6 30 Gt yr21 , contributing 0.41 6 0.08 mm yr21 to SLR. Mass balance time series for all GIC regions are shown in Fig. 2. The seasonal and interannual variabilities evident in these time series have contributions from ice and snow variability on the glaciers, as well as from imperfectly modelled hydrological signals in adjacent regions and from random GRACE observational errors. Interannual variability can affect rates determined over short time intervals. Figure 2 and Supplementary Table 2 show that there was considerable interannual variability during 2003–2010 for some of the regions, especially High Mountain Asia (HMA). The HMA results in Supplementary Table 2 show that this variability induces large swings in the trend solutions when it isfitted to subsets of the entire time period. These results suggest that care should be taken in extending the 2003–2010 results presented in this paper to longer time periods. For comparison with studies in which PGICs are included with GICs, we upscale our GIC-alone rate to obtain a GIC rate that includes PGIC, based on ref. 3 (Supplementary Information). The result is that GICs including PGICs lost mass at a rate of 229 6 82 Gt yr21 (0.63 6 0.23 mm yr21 SLR), and that the combined ice sheets without their PGICs lost mass at 303 6 100 Gt yr21 (0.84 6 0.28 mm yr21 SLR). Although no other study encompasses the same time span, published non-GRACE estimates for GICs plus PGICs are larger: 0.98 6 0.19 mm yr21 over 2001–20048 , 1.41 6 0.20 mm yr21 over 2001–20051 and 0.765 mm yr21 (no uncertainty given) over 2006– 201020. These differences could be due to the small number of mass balance measurements those estimates must rely on, combined with uncertain regional glacier extents. In addition, there are indications from more recent non-GRACE measurements that the GIC mass loss rate decreased markedly beginning in 200520. Our results for HMA disagree significantly with previous studies. A recent GRACE-based study5 over 2002–2009 yields significantly Table 1 | Inverted 2003–2010 mass balance rates Region Rate (Gt yr21 ) 1. Iceland 211 6 2 2. Svalbard 23 6 2 3. Franz Josef Land 0 6 2 4. Novaya Zemlya 24 6 2 5. Severnaya Zemlya 21 6 2 6. Siberia and Kamchatka 2 6 10 7. Altai 3 6 6 8. High Mountain Asia 24 6 20 8a. Tianshan 25 6 6 8b. Pamirs and Kunlun Shan 21 6 5 8c. Himalaya and Karakoram 25 6 6 8d. Tibet and Qilian Shan 7 6 7 9. Caucasus 1 6 3 10. Alps 22 6 3 11. Scandinavia 3 6 5 12. Alaska 246 6 7 13. Northwest America excl. Alaska 5 6 8 14. Baffin Island 233 6 5 15. Ellesmere, Axel Heiberg and Devon Islands 234 6 6 16. South America excl. Patagonia 26 6 12 17. Patagonia 223 6 9 18. New Zealand 2 6 3 19. Greenland ice sheet 1 PGICs 2222 6 9 20. Antarctica ice sheet 1 PGICs 2165 6 72 Total 2536 6 93 GICs excl. Greenland and Antarctica PGICs 2148 6 30 Antarctica 1 Greenland ice sheet and PGICs 2384 6 71 Total contribution to SLR 1.48 6 0.26 mm yr21 SLR due to GICs excl. Greenland and Antarctica PGICs 0.41 6 0.08 mm yr21 SLR due to Antarctica 1 Greenland ice sheet and PGICs 1.06 6 0.19 mm yr21 Uncertainties are given at the 95% (2s) confidence level. 2003 2004 2005 2006 Year 2007 2008 2009 2010 2011 Mass (Gt) 100 Gt 1. Iceland 2. Svalbard 3. Franz Joseph Land 4. Novaya Zemlya 5. Severnaya Zemlya 6. Siberia and Kamchatka 7. Altai 8. High Mountain Asia 9. Caucasus 10. Alps 11. Scandinavia 12. Alaska 13. North America excl. Alaska 14. Baffin Island 15. Ellesmere, Axel Heiberg and Devon Islands 16. South America excl. Patagonia 17. Patagonia 18. New Zealand Figure 2 | Mass change during 2003–2010 for all GIC regions shown in Fig. 1 and Table 1. The black horizontal lines run through the averages of the time series. The grey lines represent 13-month-window, low-pass-filtered versions of the data. Time series are shifted for legibility. Modelled contributions from GIA, LIA and hydrology have been removed. LETTER RESEARCH 23 FEBRUARY 2012 | VOL 482 | NATURE | 515 ©2012 Macmillan Publishers Limited. All rights reserved
RESEARCH LETTER larger mass loss for HMA than does ours;we explain why the result of look like in the GRACE results.We use those rates to construct ref.5 may be flawed in Supplementary Information.Conventional synthetic gravity fields and process them using the same methods mass balance methods have been used to estimate a 2002-2006 rate applied to the GRACE data,to generate the trend map shown in of-55 Gtyr for this entire region',with-29 Gt yr-1 over the Fig.3c.It is apparent that an ice loss of this order would appear in eastern Himalayas alone,by contrast with our HMA estimate,of the GRACE map as a large mass loss signal centred over the eastern -4+20 Gtyr(Table 1).We show results for the four subregions Himalayas,far larger in amplitude and extent than the GRACE results of HMA (Fig.3)in Table 1. in that region(compare Fig.3b with Fig.3c). This difference prompts us to examine this region in more detail. It is reasonable to wonder whether a tectonic process could be GRACE mass trends show considerable mass loss across the plains of causing a positive signal in the glacierized region that offsets a large northern India,Pakistan and Bangladesh,centred south of the glaciers negative glacier signal in HMA.To see what this positive rate would have and at low elevations(Fig.3a,b).Some of the edges of this mass loss to look like,we remove the simulated gravity field(based on ref.2)from region seem to extend over adjacent mountainous areas to the north, the GRACE data and show the resulting difference map in Fig.3d.If the but much of that,particularly above north-central India,is leakage of ice loss estimate were correct,the tectonic process would be causing an the plains signal caused by the 350-km Gaussian smoothing function anomalous mass increase over the Himalayas of~3 cm yrequivalent used to generate the figure.The plains signal has previously been water thickness,equivalent to~1cmyr of uncompensated crustal identified as groundwater loss.To minimize leakage in the HMA uplift.Although we cannot categorically rule out such a possibility,it GIC estimates,additional mascons are chosen to cover the plains seems unlikely.Global Positioning System and levelling observations in (Fig.3a),the sum of which gives an average 2003-2010 water loss rate this region indicate long-term uplift rates as large as 0.5-0.7 cm yr in of 35 Gt yr.Our plains results are consistent with the results of refs some places222.But it is highly probable that any broad-scale tectonic 16 and 21,which span shorter time periods. uplift would be isostatically compensated by an increasing mass The lack of notable mass loss over glacierized regions is consistent deficiency at depth,with little net effect on gravityand,consequently, with our HMA mascon solutions that indicate relatively modest losses no significant contribution to the GRACE results.The effects of com- (Table 1).We simulate what the ice loss rates predicted by ref.2 would pensation are evident in the static gravity field.Supplementary Fig.4 40 30 30 20 20 60 70 100° 80 90 70 80 90 Longitude east -4.000 -2.000 0 2.000 4.000 6.000 -2.4=1.8-1.2-0.600.6121.82.4 Elevation(m) GRACE trend(cm w.e.yr-1) 盟可 0 30 20 20 60 70 90 100 100 80 80 90 Longitude east -2.4-1.8-12-0.600.6121.82.4 3 -2.4-1.8-12-0.600.61.21.82.43 Synthetic trend(cm w.e.yr-1) GRACE trend-synthetic trend(cm w.e.yr-1) Figure 3 HMA mass balance determination.a,Topographic map overlaid smoothing function,overlaid with the HMA mascons.w.e.,water equivalent. with the HMA mascons (crosses)and India plain mascons(dots);the dashed c,Synthetic GRACE rates that would be causedby a total mass loss of55Gt yr- lines delimit the four HMA subregions(labelled as in Table 1).b,GRACE mass over HMA mascons,with 29 Gtyr over the eastern Himalayas,after ref.2. rate corrected for hydrology and GIA and smoothed with a 350-km Gaussian d.The difference between b and c. 516 NATURE VOL FEBRUARY 2012 2012 Macmillan Publishers Limited.All rights reserved
larger mass loss for HMA than does ours; we explain why the result of ref. 5 may be flawed in Supplementary Information. Conventional mass balance methods have been used to estimate a 2002–2006 rate of 255 Gt yr21 for this entire region2 , with 229 Gt yr21 over the eastern Himalayas alone, by contrast with our HMA estimate, of 24 6 20 Gt yr21 (Table 1). We show results for the four subregions of HMA (Fig. 3) in Table 1. This difference prompts us to examine this region in more detail. GRACE mass trends show considerable mass loss across the plains of northern India, Pakistan and Bangladesh, centred south of the glaciers and at low elevations (Fig. 3a, b). Some of the edges of this mass loss region seem to extend over adjacent mountainous areas to the north, but much of that, particularly above north-central India, is leakage of the plains signal caused by the 350-km Gaussian smoothing function used to generate the figure. The plains signal has previously been identified as groundwater loss16,21. To minimize leakage in the HMA GIC estimates, additional mascons are chosen to cover the plains (Fig. 3a), the sum of which gives an average 2003–2010 water loss rate of 35 Gt yr21 . Our plains results are consistent with the results of refs 16 and 21, which span shorter time periods. The lack of notable mass loss over glacierized regions is consistent with our HMA mascon solutions that indicate relatively modest losses (Table 1). We simulate what the ice loss rates predicted by ref. 2 would look like in the GRACE results. We use those rates to construct synthetic gravity fields and process them using the same methods applied to the GRACE data, to generate the trend map shown in Fig. 3c. It is apparent that an ice loss of this order would appear in the GRACE map as a large mass loss signal centred over the eastern Himalayas, far larger in amplitude and extent than the GRACE results in that region (compare Fig. 3b with Fig. 3c). It is reasonable to wonder whether a tectonic process could be causing a positive signal in the glacierized region that offsets a large negative glacier signal in HMA. To see what this positive rate would have to look like, we remove the simulated gravity field (based on ref. 2) from the GRACE data and show the resulting difference map in Fig. 3d. If the ice loss estimate were correct, the tectonic process would be causing an anomalous mass increase over the Himalayas of ,3 cm yr21 equivalent water thickness, equivalent to ,1 cm yr21 of uncompensated crustal uplift. Although we cannot categorically rule out such a possibility, it seems unlikely. Global Positioning System and levelling observations in this region indicate long-term uplift rates as large as 0.5–0.7 cm yr21 in some places22,23. But it is highly probable that any broad-scale tectonic uplift would be isostatically compensated by an increasing mass deficiency at depth, with little net effect on gravity24 and, consequently, no significant contribution to the GRACE results. The effects of compensation are evident in the static gravity field. Supplementary Fig. 4 −3 −2.4 −1.8 −1.2 −0.6 0 0.6 1.2 1.8 2.4 3 −3 −2.4 −1.8 −1.2 −0.6 0 0.6 1.2 1.8 2.4 3 80˚ −4,000 −2,000 0 2,000 4,000 6,000 −3 −2.4 −1.8 −1.2 −0.6 0 0.6 1.2 1.8 2.4 3 Elevation (m) a b GRACE trend (cm w.e. yr−1) GRACE trend – synthetic trend (cm w.e. yr−1) Longitude east Longitude east Latitude north Latitude north Synthetic trend (cm w.e. yr−1) c d 0.6 0.6 0.6 0.6 0.6 0.6 −0.6 −0.6 −0.6 −0.6 −1.2 −1.2 −1.2 −1.2 −2.4 −3.0 −1.8 −0.6 −0.6 −0.6 −2.4 −1.2 −1.8 −3.0 2.4 1.8 1.2 0.6 0.6 0.6 0.6 0.6 0.6 0.6 −0.6 −1.2 −1.2 −1.8 −2.4 8a 8b 8c 8d 8a 8b 8c 8d 8a 8b 8c 8d 8a 8b 8c 8d 40˚ 30˚ 20˚ 60˚ 70˚ 80˚ 90˚ 100˚ 40˚ 30˚ 20˚ 60˚ 70˚ 90˚ 100˚ 40˚ 30˚ 20˚ 60˚ 70˚ 80˚ 90˚ 100˚ 40˚ 30˚ 20˚ 60˚ 70˚ 80˚ 90˚ 100˚ Figure 3 | HMA mass balance determination. a, Topographic map overlaid with the HMA mascons (crosses) and India plain mascons (dots); the dashed lines delimit the four HMA subregions (labelled as in Table 1). b, GRACE mass rate corrected for hydrology and GIA and smoothed with a 350-km Gaussian smoothing function, overlaid with the HMA mascons. w.e., water equivalent. c, Synthetic GRACE rates that would be caused by a total mass loss of 55 Gt yr21 over HMA mascons, with 29 Gt yr21 over the eastern Himalayas, after ref. 2. d, The difference between b and c. RESEARCH LETTER 516 | NATURE | VOL 482 | 23 FEBRUARY 2012 ©2012 Macmillan Publishers Limited. All rights reserved
ETTER RESEARCH shows the free-air gravity field,computed using a 350-km Gaussian The average of two land surface models is used to correct for hydrology,and the smoothing function(used to generate Fig.3)applied to the EGM96 model differences are used to estimate uncertainties(Supplementary Information) mean global gravity field.The topography leaves no apparent sig- LIA loading corrections have been previously derived for Alaska!s and nature on the static gravity field at these scales,indicating near-perfect Patagonia,and equal 7 and 9 Gt yr,respectively.These numbers are subtracted from our Alaska and Patagonia inversions.For other GIC regions,where LIA compensation. characteristics are not well known,we estimate an upper bound for the correction For a solid-Earth process to affect GRACE significantly,it must be by constructing a GIA model that tends to maximize the positive LIA gravity largely isostatically uncompensated,which for these broad spatial trend.Ofall the additional GIC regions,only HMA has a predicted LIA correction scales would require characteristic timescales of the same order or less that reaches 1Gtyr-.There,the model suggests we remove 5Gt yr from our than the mantle's viscoelastic relaxation times (several hundred to a inverted result.But because the LIA correction in this region is likely to be an few thousand years).One possible such process might be the ongoing overestimate(Supplementary Information),our preferred result splits the differ- viscoelastic response of the Earth to past glacial unloading.We have ence (Supplementary Table 1),and we use that difference to augment the total investigated this effect,as well as possible contributions from erosion, HMA uncertainty. and find that neither is likely to be important (Supplementary Received 28 July 2011:accepted 9 January 2012. Information). Published online 8 February 2012. Another possible explanation for the lack of a large GRACE HMA signal is that most of the glacier melt water might be sinking into the 1. Cogley,J.G.Geodetic and direct mass-balance measurements:comparison and joint analysis.Ann.Glaciol.50,96-100(2009). ground before it has a chance to leave the glaciated region,thus causing Dyurgerov.M.B.Reanalysis of glacier changes:from the IGY to the IPY,1960- GRACE to show little net mass change.Some groundwater recharge 2008.Data Glaciol..Stud.108,1-116(2010) undoubtedly does occur,but it seems unlikely that such cancellation 3 Hock,R.,de Woul,M..Radic,V.Dyurgerov,M.Mountain glaciers and ice caps would be this complete.Much of HMA,for example,is permafrost,so around Antarctica make a large sea-level rise contribution.Geophys.Res.Lett36, L07501(2009). local storage capacity is small (see the Circum-Arctic Map of 4 Meier,M.F.etal.Glaciers dominate eustatic sea-level rise in the 21st century Permafrost and Ground-Ice Conditions;http://nsidc.org/fgdc/maps/ Science317,1064-1067(2007). Matsuo,K.Heki,K.Time-variable ice loss in Asian high mountains from satellite ipa browse.html).Therefore,although there would be surface melt, gravimetry.Earth Planet Sci.Lett 290,30-36(2010). the frozen ground would inhibit local recharge and there would be Willis,J.K.,Chambers,D.P.Kuo,C.Y.Shum,C.K.Global sea level rise,recent little ability to store the melt water locally.How far the water might challenges for the decade to come.Oceanographyash D23. have to travel before finding recharge pathways,we do not know.It is Hirabayashi,Y,Doll,P.&Kanae,S.Global-scale modelingofglacier mass balance true that some rivers originating in portions of HMA do not reach the for water resources assessments:glacier mass changes between 1948 and 2006. sea.Most notable are the Amu Darya and Syr Darya,which historically 1.Hydrol..(Amst)390,245-256(2010). feed the Aral Sea but have been diverted for irrigation.Any fraction of Kaser,G.Cogley,J.G.Dyurgerov,M.B.,Meier,M.F.Ohmura,A Mass balance of glaciers and ice caps:consensus estimates for 1961-2004.Geophys.Res.Lett.33, that diverted water that ends up recharging aquifers will not directly L19501(2006). contribute to SLR.However,the irrigation areas lie well outside our 9 Tapley,B.D.Bettadpur,S.,Watkins,M.Reigber,C.The gravity recovery and HMA mascons,and so even if there is notable recharge it is unlikely to climate experiment:mission overview and early results.Geophys.Res.Lett 31 L09607(2004). affect the HMA mascon solutions significantly 10.Wahr,J.Swenson,S,Zlotnicki,V.Velicogna,L Time-variable gravity from GRACE Our emphasis here is on GICs;the Greenland and Antarctic ice first results.Geophys.Res.Lett 31,L11501 (2004). sheets have previously been well studied with GRACEs.But for com- 11. Chen,J.L,Wilson,C.R,Tapley,B.D.Blankenship,D.D.lvins,E.R.Patago icefield melting observed by gravity recovery and climate experiment(GRACE). parison with non-GRACE global estimates,we combine our GIC results Geophys.Res.Lett.34,L22501(2007). with our estimates for Greenland plus Antarctica to obtain a total SLR 12.Gardner,A.S.et al.Sharply increased mass loss from glaciers and ice caps in the contribution from all ice-covered regions of 1.480.26 mm yr Canadian Arctic Archipelago.Nature 473,357-360(2011). 13.Luthcke.S.B.Arendt,A.A,Rowlands,D.D.,McCarthy,J.J.Larsen,C.F.Recent during 2003-2010.Within the uncertainties,this value compares glacier mass changes in the Gulf of Alaska region from GRACE mascon solutions. favourably with the estimate of 1.8+0.5 mm yr for 2006 from G1ac1ol.54,767-777(2008. ref 4.However,there are regional differences between these and prior 14.Riva,R.E.M.,Bamber.J.L Lavallee,D.A.Wouters,B.Sea-level fingerprint of continental water and ice mass change from GRACE.Geophys.Res.Lett 37, results,which need further study and reconciliation. L19605(2010) SLR from the addition of new water can be determined from 15.Rignot,E,Velicogna,L,van den Broeke,M.R,Monaghan,A.Lenaerts,J. GRACE alone as well as by subtracting Argo steric heights from Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise.Geophys.Res.Lett 38,L05503(2011). altimetric SLR measurements5.The most recent new-water SLR 16. Tiwari,V.M.,Wahr,J.Swenson,S.Dwindling groundwater resources in northern estimate,comparing the two methods,is 1.3+0.6mmyr for India,from satellite gravity observations.Geophys.Res.Lett 36,L18401 (2009). 2005-2010,which agrees with our total ice-covered SLR value to 17.Raup,B.H.,Kieffer,H.H.Hare,J.M.Kargel,J.S.Generation of data acquisition requests for the ASTER satellite instrument for monitoring a globally distributed within the uncertainties.The difference,0.2+0.6 mm yr,could rep- arget:glaciers.IEEE Trans.Geosci.Remote Sens 38,1105-1112(2000). resent an increase in land water storage outside ice-covered regions, 18.Brown,J.,Ferrians,O.J.Heginbottom,J.A.Melnikov,E.S.Circum-Arctic Map of but we note that it is not significantly different from zero. Permafrost and Ground-Ice Conditions.National Snow and Ice Data Center/World Data Center for Glaciology(19.revised,February 2001). 19.Velicogna,I.Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE Geophys.Res.Lett 36,L19503(2009). METHODS SUMMARY 20.Cogley,J.G.in Future Climates of the World (eds Henderson-Sellers,A.McGuffie. GRACE solutions consist of spherical harmonic(Stokes)coefficients and are used K189-214(Elsevier,2012). to determine month-to-month variations in Earth's mass distribution0.We use 21.Rodell,M.,Velicogna,L&Famiglietti,J.S.Satellite-based estimates of groundwater depletion in India.Nature 460,999-1002(2009). monthly values of C2o(the zonal,degree-2 spherical harmonic coefficient of the 22.Bettinelli,P.et al.Plate motion of India and interseismic strain in the Nepal geopotential)from satellite laser ranging,and include degree-one terms Himalaya from GPS and DORIS measurements.J.Geod.80,567-589(2006) To determine mass variability for each mascon,we find the set of Stokes coeffi- 23.Jackson,M.Bilham,R.Constraints on Himalayan deformation inferred from cients produced by a unit mass distributed uniformly across that mascon.We fit vertical velocity-fields in Nepal and Tibet.J.Geophys.Res.Solid Earth 99, 13897-13912(1994) these sets of Stokes coefficients,simultaneously,to the GRACE Stokes coefficients, 24.Zhong,S.J.Zuber,M.T.Crustal compensation during mountain-building. to obtain monthly mass values for each mascon.This method is similar to prev- Geophys..Res.Let27,3009-3012(2000). iously published mascon methods",though here we fit to Stokes coefficients 25.Lemoine,F.et al.The Development of the Joint NASA GSFC and NIMA Geopotential rather than to raw satellite measurements and we do not impose smoothness Mode/EGM96.NASA Goddard Space Flight Center (1998). constraints.To determine the optimal shape and number of mascons in a region, 26.Cheng,M.K.Tapley,B.D.Variations in the Earth's oblateness during the past 28 we construct a sensitivity kernel for several possible configurations,and choose the vears.J.Geophys.Res.109,B09402(2004). 27.Swenson,S.,Chambers,D.Wahr,J.Estimating geocenter variations from a configuration that optimizes that kernel and minimizes the GRACE trend residuals combination of GRACE and ocean model output.J.Geophys.Res.Solid Earth 113, (Supplementary Fig.1c). B08410(2008) 23 FEBRUARY 2012 VOL 482 NATURE 517 2012 Macmillan Publishers Limited.All rights reserved
shows the free-air gravity field, computed using a 350-km Gaussian smoothing function (used to generate Fig. 3) applied to the EGM96 mean global gravity field25. The topography leaves no apparent signature on the static gravity field at these scales, indicating near-perfect compensation. For a solid-Earth process to affect GRACE significantly, it must be largely isostatically uncompensated, which for these broad spatial scales would require characteristic timescales of the same order or less than the mantle’s viscoelastic relaxation times (several hundred to a few thousand years). One possible such process might be the ongoing viscoelastic response of the Earth to past glacial unloading. We have investigated this effect, as well as possible contributions from erosion, and find that neither is likely to be important (Supplementary Information). Another possible explanation for the lack of a large GRACE HMA signal is that most of the glacier melt water might be sinking into the ground before it has a chance to leave the glaciated region, thus causing GRACE to show little net mass change. Some groundwater recharge undoubtedly does occur, but it seems unlikely that such cancellation would be this complete. Much of HMA, for example, is permafrost, so local storage capacity is small (see the Circum-Arctic Map of Permafrost and Ground-Ice Conditions; http://nsidc.org/fgdc/maps/ ipa_browse.html). Therefore, although there would be surface melt, the frozen ground would inhibit local recharge and there would be little ability to store the melt water locally. How far the water might have to travel before finding recharge pathways, we do not know. It is true that some rivers originating in portions of HMA do not reach the sea. Most notable are the Amu Darya and Syr Darya, which historically feed the Aral Sea but have been diverted for irrigation. Any fraction of that diverted water that ends up recharging aquifers will not directly contribute to SLR. However, the irrigation areas lie well outside our HMA mascons, and so even if there is notable recharge it is unlikely to affect the HMA mascon solutions significantly. Our emphasis here is on GICs; the Greenland and Antarctic ice sheets have previously been well studied with GRACE15. But for comparison with non-GRACE global estimates, we combine our GIC results with our estimates for Greenland plus Antarctica to obtain a total SLR contribution from all ice-covered regions of 1.486 0.26 mm yr21 during 2003–2010. Within the uncertainties, this value compares favourably with the estimate of 1.8 6 0.5 mm yr21 for 2006 from ref 4. However, there are regional differences between these and prior results, which need further study and reconciliation. SLR from the addition of new water can be determined from GRACE alone as well as by subtracting Argo steric heights from altimetric SLR measurements6 . The most recent new-water SLR estimate, comparing the two methods, is 1.3 6 0.6 mm yr21 for 2005–20106 , which agrees with our total ice-covered SLR value to within the uncertainties. The difference, 0.2 6 0.6 mm yr21 , could represent an increase in land water storage outside ice-covered regions, but we note that it is not significantly different from zero. METHODS SUMMARY GRACE solutions consist of spherical harmonic (Stokes) coefficients and are used to determine month-to-month variations in Earth’s mass distribution9,10. We use monthly values of C20 (the zonal, degree-2 spherical harmonic coefficient of the geopotential) from satellite laser ranging26, and include degree-one terms27. To determine mass variability for each mascon, we find the set of Stokes coefficients produced by a unit mass distributed uniformly across that mascon. We fit these sets of Stokes coefficients, simultaneously, to the GRACE Stokes coefficients, to obtain monthly mass values for each mascon. This method is similar to previously published mascon methods28, though here we fit to Stokes coefficients rather than to raw satellite measurements and we do not impose smoothness constraints. To determine the optimal shape and number of mascons in a region, we construct a sensitivity kernel for several possible configurations, and choose the configuration that optimizes that kernel and minimizes the GRACE trend residuals (Supplementary Fig. 1c). The average of two land surface models is used to correct for hydrology, and the model differences are used to estimate uncertainties (Supplementary Information). LIA loading corrections have been previously derived for Alaska13 and Patagonia29, and equal 7 and 9 Gt yr21 , respectively. These numbers are subtracted from our Alaska and Patagonia inversions. For other GIC regions, where LIA characteristics are not well known, we estimate an upper bound for the correction by constructing a GIA model that tends to maximize the positive LIA gravity trend. Of all the additional GIC regions, only HMA has a predicted LIA correction that reaches 1 Gt yr21 . There, the model suggests we remove 5 Gt yr21 from our inverted result. But because the LIA correction in this region is likely to be an overestimate (Supplementary Information), our preferred result splits the difference (Supplementary Table 1), and we use that difference to augment the total HMA uncertainty. Received 28 July 2011; accepted 9 January 2012. Published online 8 February 2012. 1. Cogley, J. G. Geodetic and direct mass-balance measurements: comparison and joint analysis. Ann. Glaciol. 50, 96–100 (2009). 2. Dyurgerov, M. B. Reanalysis of glacier changes: from the IGY to the IPY, 1960– 2008. Data Glaciol. Stud. 108, 1–116 (2010). 3. Hock, R., de Woul, M., Radic, V. & Dyurgerov, M. Mountain glaciers and ice caps around Antarctica make a large sea-level rise contribution. Geophys. Res. Lett. 36, L07501 (2009). 4. Meier, M. F. et al. Glaciers dominate eustatic sea-level rise in the 21st century. Science 317, 1064–1067 (2007). 5. Matsuo, K. & Heki, K. Time-variable ice loss in Asian high mountains from satellite gravimetry. Earth Planet. Sci. Lett. 290, 30–36 (2010). 6. Willis, J. K., Chambers, D. P., Kuo, C. Y. & Shum, C. K. Global sea level rise, recent progress and challenges for the decade to come. Oceanography (Wash. DC) 23, 26–35 (2010). 7. Hirabayashi, Y., Doll, P. & Kanae, S. Global-scale modeling of glaciermass balances for water resources assessments: glacier mass changes between 1948 and 2006. J. Hydrol. (Amst.) 390, 245–256 (2010). 8. Kaser, G., Cogley, J. G., Dyurgerov, M. B., Meier, M. F. & Ohmura, A. Mass balance of glaciers and ice caps: consensus estimates for 1961–2004. Geophys. Res. Lett. 33, L19501 (2006). 9. Tapley, B. D., Bettadpur, S., Watkins, M. & Reigber, C. The gravity recovery and climate experiment: mission overview and early results. Geophys. Res. Lett. 31, L09607 (2004). 10. Wahr, J., Swenson, S., Zlotnicki, V. & Velicogna, I. Time-variable gravity from GRACE: first results. Geophys. Res. Lett. 31, L11501 (2004). 11. Chen, J. L., Wilson, C. R., Tapley, B. D., Blankenship, D. D. & Ivins, E. R. Patagonia icefield melting observed by gravity recovery and climate experiment (GRACE). Geophys. Res. Lett. 34, L22501 (2007). 12. Gardner, A. S. et al. Sharply increased mass loss from glaciers and ice caps in the Canadian Arctic Archipelago. Nature 473, 357–360 (2011). 13. Luthcke, S. B., Arendt, A. A., Rowlands, D. D., McCarthy, J. J. & Larsen, C. F. Recent glacier mass changes in the Gulf of Alaska region from GRACE mascon solutions. J. Glaciol. 54, 767–777 (2008). 14. Riva, R. E. M., Bamber, J. L., Lavallee, D. A. & Wouters, B. Sea-level fingerprint of continental water and ice mass change from GRACE. Geophys. Res. Lett. 37, L19605 (2010). 15. Rignot, E., Velicogna, I., van den Broeke, M. R., Monaghan, A. & Lenaerts, J. Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophys. Res. Lett. 38, L05503 (2011). 16. Tiwari, V. M., Wahr, J. & Swenson, S. Dwindling groundwater resources in northern India, from satellite gravity observations. Geophys. Res. Lett. 36, L18401 (2009). 17. Raup, B. H., Kieffer, H. H., Hare, J. M. & Kargel, J. S. Generation of data acquisition requests for the ASTER satellite instrument for monitoring a globally distributed target: glaciers. IEEE Trans. Geosci. Remote Sens. 38, 1105–1112 (2000). 18. Brown, J., Ferrians, O. J., Heginbottom, J. A. & Melnikov, E. S. Circum-Arctic Map of Permafrost and Ground-Ice Conditions. National Snow and Ice Data Center/World Data Center for Glaciology (1998, revised, February 2001). 19. Velicogna, I. Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE. Geophys. Res. Lett. 36, L19503 (2009). 20. Cogley, J. G. in Future Climates of the World (eds Henderson-Sellers, A. & McGuffie, K.) 189–214 (Elsevier, 2012). 21. Rodell, M., Velicogna, I. & Famiglietti, J. S. Satellite-based estimates of groundwater depletion in India. Nature 460, 999–1002 (2009). 22. Bettinelli, P. et al. Plate motion of India and interseismic strain in the Nepal Himalaya from GPS and DORIS measurements. J. Geod. 80, 567–589 (2006). 23. Jackson, M. & Bilham, R. Constraints on Himalayan deformation inferred from vertical velocity-fields in Nepal and Tibet. J. Geophys. Res. Solid Earth 99, 13897–13912 (1994). 24. Zhong, S. J. & Zuber, M. T. Crustal compensation during mountain-building. Geophys. Res. Lett. 27, 3009–3012 (2000). 25. Lemoine, F. et al. The Development of the Joint NASA GSFC and NIMA Geopotential Model EGM96. NASA Goddard Space Flight Center (1998). 26. Cheng, M. K. & Tapley, B. D. Variations in the Earth’s oblateness during the past 28 years. J. Geophys. Res. 109, B09402 (2004). 27. Swenson, S., Chambers, D. & Wahr, J. Estimating geocenter variations from a combination of GRACE and ocean model output. J. Geophys. Res. Solid Earth 113, B08410 (2008). LETTER RESEARCH 23 FEBRUARY 2012 | VOL 482 | NATURE | 517 ©2012 Macmillan Publishers Limited. All rights reserved
RESEARCH LETTER 28.Rowlands,D.D.et al Resolving mass flux at high spatial and temporal resolution and by NASA's'Making Earth Science Data Records for Use in Research Environments using GRACE intersatellite measurements.Geophys.Res.Lett 32,L04310(2005) (MEaSUREs)Program' 29.Ivins,E.R.James,T.S.Bedrock response to Llanquihue Holocene and present- day glaciation in southernmost South America.Geophys.Res.Lett 31,L24613 Author Contributions T.J.andJ.W.developed the study and wrote the paper.W.T.P.and (2004). S.S.discussed,commented on and improved the manuscript.S.S.provided the CLM4 hydrology model output. Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Author Information Reprints and permissions information is available at www.nature.com/reprints.The authors declare no competing financial interests Acknowledgements We thank Geruo A for providing the glacial isostatic adjustment Readers are welcome to comment on the online version of this article at model,and G.Cogley,G.Kaser,I.Velicogna,T.Perron and M.Tamisiea for comments. www.nature.com/nature.Correspondence and requests for materials should be This work was partially supported by NASA grants NNXO8AFO2G and NNXIOAR66G, addressed to J.W.(john.wahr@gmail.com). 518 NATURE VOL 48223 FEBRUARY 2012 2012 Macmillan Publishers Limited.All rights reserved
28. Rowlands, D. D. et al. Resolving mass flux at high spatial and temporal resolution using GRACE intersatellite measurements. Geophys. Res. Lett. 32, L04310 (2005). 29. Ivins, E. R. & James, T. S. Bedrock response to Llanquihue Holocene and presentday glaciation in southernmost South America. Geophys. Res. Lett. 31, L24613 (2004). Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Acknowledgements We thank Geruo A for providing the glacial isostatic adjustment model, and G. Cogley, G. Kaser, I. Velicogna, T. Perron and M. Tamisiea for comments. This work was partially supported by NASA grants NNX08AF02G and NNXI0AR66G, and by NASA’s ‘Making Earth Science Data Records for Use in Research Environments (MEaSUREs) Program’. Author Contributions T.J. and J.W. developed the study and wrote the paper.W.T.P. and S.S. discussed, commented on and improved the manuscript. S.S. provided the CLM4 hydrology model output. Author Information Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of this article at www.nature.com/nature. Correspondence and requests for materials should be addressed to J.W. (john.wahr@gmail.com). RESEARCH LETTER 518 | NATURE | VOL 482 | 23 FEBRUARY 2012 ©2012 Macmillan Publishers Limited. All rights reserved
