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Recent Contributions of Glaciers and Ice Caps to Sea Level Rise

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Abstract

Glaciers and ice caps (GICs) are important contributors to present-day global mean sea level rise. Most previous global mass balance estimates for GICs rely on extrapolation of sparse mass balance measurements 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 ± 30 Gt yr(-1) from January 2003 to December 2010, contributing 0.41 ± 0.08 mm yr(-1) 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 km(2). The GIC rate for 2003-2010 is about 30 per cent smaller than the previous mass balance estimate that most closely matches our study period. The high mountains of Asia, in particular, show a mass loss of only 4 ± 20 Gt yr(-1) for 2003-2010, compared with 47-55 Gt yr(-1) in previously published estimates. For completeness, we also estimate that the Greenland and Antarctic ice sheets, including their peripheral GICs, contributed 1.06 ± 0.19 mm yr(-1) 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 ± 0.26 mm (-1), which agrees well with independent estimates of sea level rise originating from land ice loss and other terrestrial sources.
LETTER doi:10.1038/nature10847
Recent contributions of glaciers and ice caps to sea
level rise
Thomas Jacob
1
{, John Wahr
1
, W. Tad Pfeffer
2,3
& Sean Swenson
4
Glaciers and ice caps (GICs) are important contributors to present-
day global mean sea level rise
1–4
. Most previous global mass balance
estimates for GICs rely on extrapolation of sparse mass balance
measurements
1,2,4
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 148 630 Gt yr
21
from
January 2003 to December 2010, contributing 0.41 60.08 mm yr
21
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 km
2
. The GIC rate for 2003–2010 is about
30 per cent smaller than the previous mass balance estimate that
most closely matches our study period
2
. The high mountains of
Asia, in particular, show a mass loss of only 4 620 Gt yr
21
for
2003–2010, compared with 47–55 Gt yr
21
in previously published
estimates
2,5
. For completeness, we also estimate that the Greenland
and Antarctic ice sheets, including their peripheral GICs, con-
tributed 1.06 60.19 mm yr
21
to sea level rise over the same time
period. The total contribution to sea level rise from all ice-covered
regions is thus 1.4860.26 mm yr
21
, which agrees well with inde-
pendent estimates of sea level rise originating from landiceloss and
other terrestrial sources
6
.
Interpolation of sparse mass balance measurements on selected
glaciers is usually used to estimate global GIC mass balance
1,2,4
.
Models are also used
3,7
, 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 yr
21
to
sea level rise (SLR) during 1961–2004
3,7,8
,0.77mmyr
21
during
2001–2004
8
,1.12mmyr
21
during 2001–2005
1
and 0.95 mm yr
21
during
2002–2006
2
.
The Gravity Recovery and Climate Experiment (GRACE) satellite
mission
9
has provided monthly, global gravity field solutions since
2002, allowing users to calculate mass variations at the Earth’s sur-
face
10
. GRACE has been used to monitor the mass balance of selected
GIC regions
11–14
that show large ice mass loss, as well as of Antarctica
and Greenland
15
.
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 Supplemen-
tary 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 World
17
and the Circum-Arctic Map
of Permafrost and Ground-Ice Conditions
18
. 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 iso-
lated regions with glacierized areas less than 100 km
2
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 ingeneral agreement with previous GRACE
studies for the large mass loss regions of the Canadian Arctic
12
and
Patagonia
11
, 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
34
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.
00 MONTH 2012 | VOL 000 | NATURE | 1
their PGICs
19
. 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 dataspans
(Supplementary Information). The global GIC mass balance, exclud-
ing Greenland and Antarctic PGICs, is 2148 630 Gt yr
21
, con-
tributing 0.41 60.08 mm yr
21
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 subsetsof 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 229 682 Gt yr
21
(0.63 60.23 mm yr
21
SLR), and that the combined ice sheets without
their PGICs lost mass at 303 6100 Gt yr
21
(0.84 60.28 mm yr
21
SLR). Although no other study encompasses the same time span,
published non-GRACE estimates for GICs plus PGICs are larger:
0.98 60.19 mm yr
21
over 2001–2004
8
,1.4160.20 mm yr
21
over
2001–2005
1
and 0.765 mm yr
21
(no uncertainty given) over 2006–
2010
20
. 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 2005
20
.
Our results for HMA disagree significantly with previous studies.
A recent GRACE-based study
5
over 2002–2009 yields significantly
Table 1
|
Inverted 2003–2010 mass balance rates
Region Rate (Gt yr
21
)
1. Iceland 211 62
2. Svalbard 2362
3. Franz Josef Land 0 62
4. Novaya Zemlya 2462
5. Severnaya Zemlya 2162
6. Siberia and Kamchatka 2 610
7. Altai 3 66
8. High Mountain Asia 24620
8a. Tianshan 2566
8b. Pamirs and Kunlun Shan 2165
8c. Himalaya and Karakoram 2566
8d. Tibet and Qilian Shan 7 67
9. Caucasus 1 63
10. Alps 2263
11. Scandinavia 3 65
12. Alaska 246 67
13. Northwest America excl. Alaska 5 68
14. Baffin Island 233 65
15. Ellesmere, Axel Heiberg and Devon Islands 234 66
16. South America excl. Patagonia 26612
17. Patagonia 223 69
18. New Zealand 2 63
19. Greenland ice sheet 1PGICs 2222 69
20. Antarctica ice sheet 1PGICs 2165 672
Total 2536 693
GICs excl. Greenland and Antarctica PGICs 2148 630
Antarctica 1Greenland ice sheet and PGICs 2384 671
Total contribut ion to SLR 1.48 60.26 mm yr
21
SLR due to GICs excl. Greenland and Antarctica PGICs 0.41 60.08 mm yr
21
SLR due to Antarctica 1Greenland ice shee t and PGICs 1.06 60.19 mm yr
21
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. Bafn 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.
RESEARCH LETTER
2 | NATURE | VOL 000 | 00 MONTH 2012
larger mass loss for HMA than does ours; we explain why the resultof
ref. 5 may be flawed in Supplementary Information. Conventional
mass balance methods have been used to estimate a 2002–2006 rate
of 255 Gt yr
21
for this entire region
2
, with 229 Gt yr
21
over the
eastern Himalayas alone, by contrast with our HMA estimate, of
24620 Gt yr
21
(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 loss
16,21
. 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 yr
21
. 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 glaciersignal in HMA. To see whatthis positive ratewould 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 ,3cmyr
21
equivalent
water thickness, equivalent to ,1cmyr
21
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 yr
21
in
some places
22,23
. 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 gravity
24
and, consequently,
no significant contribution to the GRACE results. The effects of com-
pensation 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
32.4 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
32.4 1.8 1.2 0.6 0 0.6 1.2 1.8 2.4 3
Elevation (m)
ab
GRACE trend (cm w.e. yr
1
)
GRACE trend – s
y
nthetic trend (cm w.e.
y
r
1
)
Longitude east
Longitude east
Latitude northLatitude north
S
y
nthetic trend (cm w.e.
y
r
1
)
cd
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 GRACErates that would be caused by a total massloss of 55 Gt yr
21
over HMA mascons, with 29 Gt yr
21
over the eastern Himalayas, after ref. 2.
d, The difference between band c.
LETTER RESEARCH
00 MONTH 2012 | VOL 000 | NATURE | 3
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 field
25
. The topography leaves no apparent sig-
nature 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 GRACE
15
. But for com-
parison withnon-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 1.48 60.26 mm yr
21
during 2003–2010. Within the uncertainties, this value compares
favourably with the estimate of 1.8 60.5 mm yr
21
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 measurements
6
. The most recent new-water SLR
estimate, comparing the two methods, is 1.3 60.6 mm yr
21
for
2005–2010
6
, which agrees with our total ice-covered SLR value to
within the uncertainties. The difference, 0.2 60.6 mm yr
21
, could rep-
resent 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 distribution
9,10
. We use
monthly values of C
20
(the zonal, degree-2 spherical harmonic coefficient of the
geopotential) from satellite laser ranging
26
, and include degree-one terms
27
.
To determine mass variability for each mascon, we find the set of Stokes coeffi-
cients produced by a unit mass distributed uniformly across that mascon. We fit
these sets of Stokescoefficients, simultaneously, to theGRACE Stokes coefficients,
to obtain monthly mass values for each mascon. This method is similar to prev-
iously published mascon methods
28
, 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 severalpossible configurations, and choose the
configuration that optimizes that kernel andminimizes the GRACE trendresiduals
(Supplementary Fig. 1c).
The average of two land surface models is used to correct forhydrology,and the
model differences are usedto estimate uncertainties (Supplementary Information).
LIA loading corrections have been previously derived for Alaska
13
and
Patagonia
29
, and equal 7 and 9 Gt yr
21
, respectively. These numbersare 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 yr
21
. There, the model suggests we remove 5Gt yr
21
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 differ-
ence (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.
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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 EarthScience Data Records for Use in Research Environments
(MEaSUREs) Program’.
Author ContributionsT.J. and J.W. developedthe study and wrotethe paper. W.T.P. and
S.S. discussed,commented on and improved themanuscript. 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).
LETTER RESEARCH
00 MONTH 2012 | VOL 000 | NATURE | 5
... If each mascon was covered by a uniformly distributed unit EWT (m j ), which can be decomposed into SH coefficients ∆c j lm and ∆s j lm (j = 1, 2, · · · , M) with Equations (3) and (4) by Xiang et al. [9] (except that Ω now represents the mascon region considered), according to Jacob et al. [34], the mass change (by EWT) can be computed for each mascon at any time with the spectral domain inverse (SEDI) [34,35] and the space domain inverse (SADI) [35]. ...
... If each mascon was covered by a uniformly distributed unit EWT (m j ), which can be decomposed into SH coefficients ∆c j lm and ∆s j lm (j = 1, 2, · · · , M) with Equations (3) and (4) by Xiang et al. [9] (except that Ω now represents the mascon region considered), according to Jacob et al. [34], the mass change (by EWT) can be computed for each mascon at any time with the spectral domain inverse (SEDI) [34,35] and the space domain inverse (SADI) [35]. ...
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... Variations in the TWS in endorheic basins are not entirely dependent on sparse precipitation, with glacial melting and alpine precipitation being the major sources of water recharge Li et al., 2018;Yao et al., 2018;Zhu et al., 2021). Even though glaciers are melting at an accelerated rate due to climate change (Aizen et al., 2007;Khan and Holko, 2009;Jacob et al., 2012;Unger-Shayesteh et al., 2013;Brun et al., 2017), the current rate of glacial melting is not sufficiently high to offset the land surface water depletion caused by excessive dissipation which raises concerns about the future availability of water resources (Rodell et al., 2018). ...
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