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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 present-                                   hydrology and for glacial isostatic adjustment (GIA) computed using
day global mean sea level rise1–4. 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
measurements1,2,4 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 6 30 Gt yr21 from                                         effects on the GRACE solutions are discussed in Supplementary
January 2003 to December 2010, contributing 0.41 6 0.08 mm yr21                                       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 World17 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 period2. The high mountains of                                         lated regions with glacierized areas less than 100 km2 in area are
Asia, in particular, show a mass loss of only 4 6 20 Gt yr21 for                                      excluded. Because GRACE detects total mass change, its results for
2003–2010, compared with 47–55 Gt yr21 in previously published                                        an ice-covered region are independent of the glacierized surface area
estimates2,5. 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 6 0.19 mm yr21 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 6 0.26 mm yr21, 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 ice loss and                                inversion with GRACE fields from the GFZ German Research Centre
other terrestrial sources6.                                                                           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 balance1,2,4.                                       The results in Table 1 are in general agreement with previous GRACE
Models are also used3,7, but these depend on the quality of input                                     studies for the large mass loss regions of the Canadian Arctic12 and
climate data and include simplified glacial processes. Excluding                                      Patagonia11, 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 mm yr21 to
                                                                                                                              15
sea level rise (SLR) during 1961–20043,7,8, 0.77 mm yr21 during                                                                           19
2001–20048, 1.12 mm yr21 during 2001–20051 and 0.95 mm yr21 during                                                                                      2
                                                                                                                                                                  3            5
                                                                                                                                                                      4
2002–20062.                                                                                                                   14                             11
   The Gravity Recovery and Climate Experiment (GRACE) satellite                                                                                 1
                                                                                                                                                                                   7
mission9 has provided monthly, global gravity field solutions since                                           12
                                                                                                                         13                                 10                                    6
2002, allowing users to calculate mass variations at the Earth’s sur-                                                                                             9
                                                                                                                                                                           8
face10. 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                                                               16
balance results for every region of Earth with large ice-covered areas.
The main focus of this paper is on GICs, excluding Antarctic and                                                              17                                                                 18
Greenland PGICs. For completeness, however, we also include results
                                                                                                                                                            20
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.
1
 Department of Physics and Cooperative Institute for Environmental Studies, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 2Institute of Arctic and Alpine Research, University of
Colorado at Boulder, Boulder, Colorado 80309, USA. 3Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 4National Center
                                                                                                      ´
for Atmospheric Research, Boulder, Colorado 80305, USA. {Present address: Bureau de Recherches Geologiques et Minie      `res, Orleans 45060, France.
                                                                                                                                  ´


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                                                              ©2012 Macmillan Publishers Limited. All rights reserved
LETTER RESEARCH

Table 1 | Inverted 2003–2010 mass balance rates
Region                                                                   Rate (Gt yr21)

1. Iceland                                                          211 6 2                                     7. Altai
2. Svalbard                                                          23 6 2
3. Franz Josef Land                                                   062
4. Novaya Zemlya                                                     24 6 2                                    11. Scandinavia
5. Severnaya Zemlya                                                  21 6 2
6. Siberia and Kamchatka                                              2 6 10                                   18. New Zealand
7. Altai                                                              366
8. High Mountain Asia                                                24 6 20
8a. Tianshan                                                         25 6 6                                    9. Caucasus
8b. Pamirs and Kunlun Shan                                           21 6 5
8c. Himalaya and Karakoram                                           25 6 6
8d. Tibet and Qilian Shan                                             767                                      3. Franz Joseph Land
9. Caucasus                                                           163
10. Alps                                                             22 6 3                                    6. Siberia and Kamchatka
11. Scandinavia                                                       365
12. Alaska                                                          246 6 7
13. Northwest America excl. Alaska                                    568
14. Baffin Island                                                   233 6 5
15. Ellesmere, Axel Heiberg and Devon Islands                       234 6 6
                                                                                                               13. North America excl. Alaska
16. South America excl. Patagonia                                    26 6 12
17. Patagonia                                                       223 6 9
18. New Zealand                                                       263
19. Greenland ice sheet 1 PGICs                                    2222 6 9
20. Antarctica ice sheet 1 PGICs                                   2165 6 72                                   10. Alps
Total                                                              2536 6 93
GICs excl. Greenland and Antarctica PGICs                          2148 6 30                                   5. Severnaya Zemlya
Antarctica 1 Greenland ice sheet and PGICs                         2384 6 71
                                                                                                               4. Novaya Zemlya
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
                                                                                                               2. Svalbard
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.
                                                                                                  Mass (Gt)




                                                                                                               8. High Mountain Asia
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, exclud-                                              16. South America excl. Patagonia
ing Greenland and Antarctic PGICs, is 2148 6 30 Gt yr21, con-
tributing 0.41 6 0.08 mm yr21 to SLR.
   Mass balance time series for all GIC regions are shown in Fig. 2. The
                                                                                                  100 Gt




seasonal and interannual variabilities evident in these time series have
contributions from ice and snow variability on the glaciers, as well as                                        1. Iceland
from imperfectly modelled hydrological signals in adjacent regions
and from random GRACE observational errors. Interannual variability                                            17. Patagonia
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                                                  15. Ellesmere, Axel Heiberg and Devon Islands
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                                         14. Baffin Island
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                                               12. Alaska
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                                            2003    2004   2005   2006   2007    2008   2009   2010   2011
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. 1 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 study5 over 2002–2009 yields significantly                             contributions from GIA, LIA and hydrology have been removed.

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                                                            ©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 255 Gt yr21 for this entire region2, with 229 Gt yr21 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
24 6 20 Gt yr21 (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 yr21 equivalent
used to generate the figure. The plains signal has previously been                                            water thickness, equivalent to ,1 cm yr21 of uncompensated crustal
identified as groundwater loss16,21. 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 yr21 in
of 35 Gt yr21. Our plains results are consistent with the results of refs                                     some places22,23. 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 gravity24 and, 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

                    a                                                                                          b
                                                                                                                                                    0.6




                                                                                                                                                                                                         0.6
                                                                                                                                                              8a−0.6
                                                                                                                                6
                                                                    8a
                                                                                                                                0.

                                            40˚                                                                         40˚

                                                                                                                                                          8b                                8d
                     Latitude north




                                                             8b                     8d

                                       30˚                                                                          30˚                             −2
                                                                                                                                                      .4
                                                                                               8c                                                                                                         8c
                                                                                                                                                     −3
                                                                                                                                                        . 0




                                                                                                                                                                                                            −0.6
                                                                                                                                                                      −1.2




                                                                                                                                                                                                           .2
                                                                                                                                 0.6                      −1.8                              .2



                                                                                                                                                                                                        −1
                                                                                                                                                                                       −1
                                                                                                                                           −0.




                                                                                                                          0.6
                         20˚                                                                                  20˚
                                                                                                                                              6




                                                                                                                                                                                                 −0.6


                                                                                                                                                                                                            .2
                                                                                                                                                                                                          −1
                                                                                                                                                                                           0.6
                                      60˚                                                            100˚       60˚                                                                                                100˚
                                                       70˚         80˚              90˚               Longitude east                 70˚                        80˚                    90˚



                    −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)                                                     GRACE trend (cm w.e. yr −1)
                    c                                                                                         d
                                                                                                                                                          0.6




                                                                                                                                                                                                          0.6
                                                                                                                                       0.6




                                                                  8a                                                                                            8a
                                        40˚                                                                           40˚
                     Latitude north




                                                                                                                                                            0.
                                                             8b                     8d                                                                    8b 6                              8d
                                                                                     −0
                                                                                                                                                                                                 1.2




                                                                                          .6
                                      30˚                                  −1.2                                   30˚
                                                                             −1
                                                                          −2.4 .8
                                                                                                                          0.6




                                                                                               8c                                                                                                         8c
                                                                          −3.0                                                       0.6
                                                                                                                                                                                2.4




                                                                                                                                               −2
                                                                                                                                           −1.2
                                                                                                                                            −1.




                                                                                                                                                    .4                  1.8
                                                                                                                                                8




                    20˚                                                    −0.6                               20˚
                                                                                                                                                                                                                −0.




                                                                                                                                                                           .6
                                                                                                                                                                      −0                                        −1
                                                                                                                                                                                                                   6




                                                                                                                                                                                        6                         .2
                                                                                                                                                                                      0.
                                60˚                                                                 100˚        60˚                                                                                                100˚
                                                      70˚         80˚             90˚                                                70˚                        80˚                    90˚
                                                                                                      Longitude east



                     −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
                                                      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 caused by a total mass loss of 55 Gt yr21
lines delimit the four HMA subregions (labelled as in Table 1). b, GRACE mass                                 over HMA mascons, with 29 Gt yr21 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.

5 1 6 | N AT U R E | VO L 4 8 2 | 2 3 F E B R U A RY 2 0 1 2
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LETTER 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 field25. The topography leaves no apparent sig-                        LIA loading corrections have been previously derived for Alaska13 and
                                                                                        Patagonia29, and equal 7 and 9 Gt yr21, respectively. These numbers are subtracted
nature on the static gravity field at these scales, indicating near-perfect
                                                                                        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. Of all the additional GIC regions, only HMA has a predicted LIA correction
scales would require characteristic timescales of the same order or less                that reaches 1 Gt yr21. There, the model suggests we remove 5 Gt yr21 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
                                                                                        HMA uncertainty.
investigated this effect, as well as possible contributions from erosion,
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               2.    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
                                                                                              around Antarctica make a large sea-level rise contribution. Geophys. Res. Lett. 36,
would be this complete. Much of HMA, for example, is permafrost, so                           L07501 (2009).
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the frozen ground would inhibit local recharge and there would be                       6.    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                       progress and challenges for the decade to come. Oceanography (Wash. DC) 23,
                                                                                              26–35 (2010).
have to travel before finding recharge pathways, we do not know. It is                  7.    Hirabayashi, Y., Doll, P. & Kanae, S. Global-scale modeling of glacier mass balances
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                         J. Hydrol. (Amst.) 390, 245–256 (2010).
                                                                                        8.    Kaser, G., Cogley, J. G., Dyurgerov, M. B., Meier, M. F. & Ohmura, A. Mass balance of
feed the Aral Sea but have been diverted for irrigation. Any fraction 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
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affect the HMA mascon solutions significantly.                                          10.   Wahr, J., Swenson, S., Zlotnicki, V. & Velicogna, I. Time-variable gravity from GRACE:
    Our emphasis here is on GICs; the Greenland and Antarctic ice                             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
sheets have previously been well studied with GRACE15. But for com-                           icefield melting observed by gravity recovery and climate experiment (GRACE).
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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
                                                                                              Canadian Arctic Archipelago. Nature 473, 357–360 (2011).
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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 6 0.5 mm yr21 for 2006 from                               J. Glaciol. 54, 767–777 (2008).
                                                                                        14.   Riva, R. E. M., Bamber, J. L., Lavallee, D. A. & Wouters, B. Sea-level fingerprint of
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results, which need further study and reconciliation.                                         L19605 (2010).
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                                                                                              sheets revealed by GRACE. Geophys. Res. Lett. 36, L19503 (2009).
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to determine month-to-month variations in Earth’s mass distribution9,10. We use
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rather than to raw satellite measurements and we do not impose smoothness                     Model 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
                                                                                              years. J. Geophys. Res. 109, B09402 (2004).
we construct a sensitivity kernel for several possible configurations, and choose the   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).

                                                                                                               2 3 F E B R U A RY 2 0 1 2 | VO L 4 8 2 | N AT U R E | 5 1 7
                                                    ©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. and J.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 NNX08AF02G and NNXI0AR66G,              addressed to J.W. (john.wahr@gmail.com).




5 1 8 | N AT U R E | VO L 4 8 2 | 2 3 F E B R U A RY 2 0 1 2
                                                      ©2012 Macmillan Publishers Limited. All rights reserved

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Recent contributions of_glaciers_and_ice_caps_to_sea_level_rise

  • 1. 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 present- hydrology and for glacial isostatic adjustment (GIA) computed using day global mean sea level rise1–4. 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 measurements1,2,4 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 6 30 Gt yr21 from effects on the GRACE solutions are discussed in Supplementary January 2003 to December 2010, contributing 0.41 6 0.08 mm yr21 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 World17 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 period2. The high mountains of lated regions with glacierized areas less than 100 km2 in area are Asia, in particular, show a mass loss of only 4 6 20 Gt yr21 for excluded. Because GRACE detects total mass change, its results for 2003–2010, compared with 47–55 Gt yr21 in previously published an ice-covered region are independent of the glacierized surface area estimates2,5. 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 6 0.19 mm yr21 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 6 0.26 mm yr21, 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 ice loss and inversion with GRACE fields from the GFZ German Research Centre other terrestrial sources6. 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 balance1,2,4. The results in Table 1 are in general agreement with previous GRACE Models are also used3,7, but these depend on the quality of input studies for the large mass loss regions of the Canadian Arctic12 and climate data and include simplified glacial processes. Excluding Patagonia11, 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 mm yr21 to 15 sea level rise (SLR) during 1961–20043,7,8, 0.77 mm yr21 during 19 2001–20048, 1.12 mm yr21 during 2001–20051 and 0.95 mm yr21 during 2 3 5 4 2002–20062. 14 11 The Gravity Recovery and Climate Experiment (GRACE) satellite 1 7 mission9 has provided monthly, global gravity field solutions since 12 13 10 6 2002, allowing users to calculate mass variations at the Earth’s sur- 9 8 face10. 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 16 balance results for every region of Earth with large ice-covered areas. The main focus of this paper is on GICs, excluding Antarctic and 17 18 Greenland PGICs. For completeness, however, we also include results 20 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. 1 Department of Physics and Cooperative Institute for Environmental Studies, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 2Institute of Arctic and Alpine Research, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 3Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA. 4National Center ´ for Atmospheric Research, Boulder, Colorado 80305, USA. {Present address: Bureau de Recherches Geologiques et Minie `res, Orleans 45060, France. ´ 5 1 4 | N AT U R E | VO L 4 8 2 | 2 3 F E B R U A RY 2 0 1 2 ©2012 Macmillan Publishers Limited. All rights reserved
  • 2. LETTER RESEARCH Table 1 | Inverted 2003–2010 mass balance rates Region Rate (Gt yr21) 1. Iceland 211 6 2 7. Altai 2. Svalbard 23 6 2 3. Franz Josef Land 062 4. Novaya Zemlya 24 6 2 11. Scandinavia 5. Severnaya Zemlya 21 6 2 6. Siberia and Kamchatka 2 6 10 18. New Zealand 7. Altai 366 8. High Mountain Asia 24 6 20 8a. Tianshan 25 6 6 9. Caucasus 8b. Pamirs and Kunlun Shan 21 6 5 8c. Himalaya and Karakoram 25 6 6 8d. Tibet and Qilian Shan 767 3. Franz Joseph Land 9. Caucasus 163 10. Alps 22 6 3 6. Siberia and Kamchatka 11. Scandinavia 365 12. Alaska 246 6 7 13. Northwest America excl. Alaska 568 14. Baffin Island 233 6 5 15. Ellesmere, Axel Heiberg and Devon Islands 234 6 6 13. North America excl. Alaska 16. South America excl. Patagonia 26 6 12 17. Patagonia 223 6 9 18. New Zealand 263 19. Greenland ice sheet 1 PGICs 2222 6 9 20. Antarctica ice sheet 1 PGICs 2165 6 72 10. Alps Total 2536 6 93 GICs excl. Greenland and Antarctica PGICs 2148 6 30 5. Severnaya Zemlya Antarctica 1 Greenland ice sheet and PGICs 2384 6 71 4. Novaya Zemlya 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 2. Svalbard 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. Mass (Gt) 8. High Mountain Asia 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, exclud- 16. South America excl. Patagonia ing Greenland and Antarctic PGICs, is 2148 6 30 Gt yr21, con- tributing 0.41 6 0.08 mm yr21 to SLR. Mass balance time series for all GIC regions are shown in Fig. 2. The 100 Gt seasonal and interannual variabilities evident in these time series have contributions from ice and snow variability on the glaciers, as well as 1. Iceland from imperfectly modelled hydrological signals in adjacent regions and from random GRACE observational errors. Interannual variability 17. Patagonia 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 15. Ellesmere, Axel Heiberg and Devon Islands 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 14. Baffin Island 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 12. Alaska 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 2003 2004 2005 2006 2007 2008 2009 2010 2011 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. 1 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 study5 over 2002–2009 yields significantly contributions from GIA, LIA and hydrology have been removed. 2 3 F E B R U A RY 2 0 1 2 | VO L 4 8 2 | N AT U R E | 5 1 5 ©2012 Macmillan Publishers Limited. All rights reserved
  • 3. 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 255 Gt yr21 for this entire region2, with 229 Gt yr21 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 24 6 20 Gt yr21 (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 yr21 equivalent used to generate the figure. The plains signal has previously been water thickness, equivalent to ,1 cm yr21 of uncompensated crustal identified as groundwater loss16,21. 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 yr21 in of 35 Gt yr21. Our plains results are consistent with the results of refs some places22,23. 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 gravity24 and, 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 a b 0.6 0.6 8a−0.6 6 8a 0. 40˚ 40˚ 8b 8d Latitude north 8b 8d 30˚ 30˚ −2 .4 8c 8c −3 . 0 −0.6 −1.2 .2 0.6 −1.8 .2 −1 −1 −0. 0.6 20˚ 20˚ 6 −0.6 .2 −1 0.6 60˚ 100˚ 60˚ 100˚ 70˚ 80˚ 90˚ Longitude east 70˚ 80˚ 90˚ −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) GRACE trend (cm w.e. yr −1) c d 0.6 0.6 0.6 8a 8a 40˚ 40˚ Latitude north 0. 8b 8d 8b 6 8d −0 1.2 .6 30˚ −1.2 30˚ −1 −2.4 .8 0.6 8c 8c −3.0 0.6 2.4 −2 −1.2 −1. .4 1.8 8 20˚ −0.6 20˚ −0. .6 −0 −1 6 6 .2 0. 60˚ 100˚ 60˚ 100˚ 70˚ 80˚ 90˚ 70˚ 80˚ 90˚ Longitude east −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 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 caused by a total mass loss of 55 Gt yr21 lines delimit the four HMA subregions (labelled as in Table 1). b, GRACE mass over HMA mascons, with 29 Gt yr21 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. 5 1 6 | N AT U R E | VO L 4 8 2 | 2 3 F E B R U A RY 2 0 1 2 ©2012 Macmillan Publishers Limited. All rights reserved
  • 4. LETTER 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 field25. The topography leaves no apparent sig- LIA loading corrections have been previously derived for Alaska13 and Patagonia29, and equal 7 and 9 Gt yr21, respectively. These numbers are subtracted nature on the static gravity field at these scales, indicating near-perfect 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. Of all the additional GIC regions, only HMA has a predicted LIA correction scales would require characteristic timescales of the same order or less that reaches 1 Gt yr21. There, the model suggests we remove 5 Gt yr21 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 HMA uncertainty. investigated this effect, as well as possible contributions from erosion, 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 2. 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 around Antarctica make a large sea-level rise contribution. Geophys. Res. Lett. 36, would be this complete. Much of HMA, for example, is permafrost, so L07501 (2009). local storage capacity is small (see the Circum-Arctic Map of 4. Meier, M. F. et al. Glaciers dominate eustatic sea-level rise in the 21st century. Permafrost and Ground-Ice Conditions; http://nsidc.org/fgdc/maps/ Science 317, 1064–1067 (2007). 5. 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 6. 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 progress and challenges for the decade to come. Oceanography (Wash. DC) 23, 26–35 (2010). have to travel before finding recharge pathways, we do not know. It is 7. Hirabayashi, Y., Doll, P. & Kanae, S. Global-scale modeling of glacier mass balances 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 J. Hydrol. (Amst.) 390, 245–256 (2010). 8. Kaser, G., Cogley, J. G., Dyurgerov, M. B., Meier, M. F. & Ohmura, A. Mass balance of feed the Aral Sea but have been diverted for irrigation. Any fraction 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 climate experiment: mission overview and early results. Geophys. Res. Lett. 31, HMA mascons, and so even if there is notable recharge it is unlikely to L09607 (2004). affect the HMA mascon solutions significantly. 10. Wahr, J., Swenson, S., Zlotnicki, V. & Velicogna, I. Time-variable gravity from GRACE: Our emphasis here is on GICs; the Greenland and Antarctic ice 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 sheets have previously been well studied with GRACE15. But for com- 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 Canadian Arctic Archipelago. Nature 473, 357–360 (2011). contribution from all ice-covered regions of 1.48 6 0.26 mm yr21 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 6 0.5 mm yr21 for 2006 from J. Glaciol. 54, 767–777 (2008). 14. Riva, R. E. M., Bamber, J. L., Lavallee, D. A. & Wouters, B. Sea-level fingerprint of ref 4. However, there are regional differences between these and prior 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, I., van den Broeke, M. R., Monaghan, A. & Lenaerts, J. Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea GRACE alone as well as by subtracting Argo steric heights from level rise. Geophys. Res. Lett. 38, L05503 (2011). altimetric SLR measurements6. 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 6 0.6 mm yr21 for 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 2005–20106, which agrees with our total ice-covered SLR value to requests for the ASTER satellite instrument for monitoring a globally distributed within the uncertainties. The difference, 0.2 6 0.6 mm yr21, could rep- target: 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 Permafrost and Ground-Ice Conditions. National Snow and Ice Data Center/World but we note that it is not significantly different from zero. 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). 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 K.) 189–214 (Elsevier, 2012). 21. Rodell, M., Velicogna, I. & Famiglietti, J. S. Satellite-based estimates of groundwater to determine month-to-month variations in Earth’s mass distribution9,10. We use depletion in India. Nature 460, 999–1002 (2009). monthly values of C20 (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 ranging26, and include degree-one terms27. 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. Lett. 27, 3009–3012 (2000). iously published mascon methods28, 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 Model 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 years. J. Geophys. Res. 109, B09402 (2004). we construct a sensitivity kernel for several possible configurations, and choose the 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). 2 3 F E B R U A RY 2 0 1 2 | VO L 4 8 2 | N AT U R E | 5 1 7 ©2012 Macmillan Publishers Limited. All rights reserved
  • 5. 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. and J.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 NNX08AF02G and NNXI0AR66G, addressed to J.W. (john.wahr@gmail.com). 5 1 8 | N AT U R E | VO L 4 8 2 | 2 3 F E B R U A RY 2 0 1 2 ©2012 Macmillan Publishers Limited. All rights reserved