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Environmental Research Letters
TOPICAL REVIEW • OPEN ACCESS
The land ice contribution to sea level during the
satellite era
To cite this article: Jonathan L Bamber et al 2018 Environ. Res. Lett. 13 063008
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Environ. Res. Lett. 13 (2018) 063008 https://doi.org/10.1088/1748-9326/aac2f0
TOPI CAL REVIEW
The land ice contribution to sea level during the satellite
era
Jonathan L Bamber1,4, Richard M Westaway1, Ben Marzeion2and Bert Wouters3
1School of Geographical Sciences, University of Bristol, Bristol, United Kingdom
2Institute fur Geographie, University of Bremen, Bremen, Germany
3Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands
4Author to whom any correspondence should be addressed.
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E-mail: j.bamber@bristol.ac.uk
Keywords: land ice, sea level rise, satellite remote sensing, sea level budget
Supplementary material for this article is available online
Abstract
Since 1992, there has been a revolution in our ability to quantify the land ice contribution to sea level
rise using a variety of satellite missions and technologies. Each mission has provided unique, but
sometimes conflicting, insights into the mass trends of land ice. Over the last decade, over fifty
estimates of land ice trends have been published, providing a confusing and often inconsistent
picture. The IPCC Fifth Assessment Report (AR5) attempted to synthesise estimates published up to
early 2013. Since then, considerable advances have been made in understanding the origin of the
inconsistencies, reducing uncertainties in estimates and extending time series. We assess and
synthesise results published, primarily, since the AR5, to produce a consistent estimate of land ice
mass trends during the satellite era (1992–2016). We combine observations from multiple missions
and approaches including sea level budget analyses. Our resulting synthesis is both consistent and
rigorous, drawing on (i) the published literature, (ii) expert assessment of that literature, and (iii) a
new analysis of Arctic glacier and ice cap trends combined with statistical modelling.
We present annual and pentad (five-year mean) time series for the East, West Antarctic and
Greenland Ice Sheets and glaciers separately and combined. When averaged over pentads, covering
the entire period considered, we obtain a monotonic trend in mass contribution to the oceans,
increasing from 0.31 ±0.35 mm of sea level equivalent for 1992–1996 to 1.85 ±0.13 for 2012–2016.
Our integrated land ice trend is lower than many estimates of GRACE-derived ocean mass change for
the same periods. This is due, in part, to a smaller estimate for glacier and ice cap mass trends
compared to previous assessments. We discuss this, and other likely reasons, for the difference
between GRACE ocean mass and land ice trends.
1. Introdution
Permanent ice covers 12.5% of the land surface of
the Earth and contains about 70% of the world’s
freshwater. It comprises the two great ice sheets
that cover Antarctica (the AIS) and Greenland (the
GrIS) and glaciers and ice caps (GIC). The distinc-
tion between these two categories is one of size.
Figure 1shows the geographic distribution of land
ice, alongside the area and percentage of glaciers that
are marine versus land terminating. Almost all land
ice (99.5%) is locked in the ice sheets, with a volume
in sea level equivalent (SLE) terms of 7.4 m for Green-
land, and 58.3 m for Antarctica, while glaciers is
estimated at around 41 cm (Vaughan et al 2013).
Thus, the ice sheets are the largest potential source
of future sea level rise (SLR) and represent the largest
uncertainty in projections of future sea level.
Despite their diminutive size in comparison to
the ice sheets, GIC have dominated the land ice con-
tribution to SLR during the 20th century (Vaughan
et al 2013). This has only changed over the last decade
due, primarily, to the accelerating contribution of
the GrIS since about 1995 (Rignot et al 2011). GIC
© 2018 The Author(s). Published by IOP Publishing Ltd
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 1. Distribution of land ice over the surface of the Earth. The 19 numbered, yellow shaded areas represent the GIC regions
or sectors that are typically chosen for regional mass balance studies of GIC. The blue shading illustrates the ice sheets covering
Antarctica and Greenland. The size of the coloured circles indicates the glacierized area for each sector and the green colour is used
for the proportion of land-terminating glaciers with blue shading for marine-terminating (Vaughan et al 2013). Section S4.2 of the
supplement available at stacks.iop.org/ERL/13/063008/mmedia provides the names of the regions.
were the dominant source partly because, on short
time scales, they are more sensitive to external forcing
compared to the ice sheets. While GIC contain a much
smaller reservoir of ice, they are of considerable impor-
tance for water resources (Immerzeel et al 2010)and
local economies (Huss et al 2017). Changes in down-
stream discharge rates, glacier extent and exposure
of previously pristine permafrost will have important
socio-economic consequences.
1.1. The importance of understanding present-day
and future land ice trends
Sea level rise is considered to be one of the most serious
consequences of future climate change. It is estimated
that up to 187 million people could be displaced by a
global mean sea level rise of 1 m (Nicholls et al 2011)
and the cost of infrastructure damage and land
degradation will be immense (Nicholls and Cazenave
2010). The AR5 produced projections for SLR to
2100 for different future climate scenarios. The dom-
inant uncertainty, for high end emission scenarios,
in these projections is the potential contribution of
land ice (Church et al 2013). Indeed, for the ice
sheets, the dynamic contribution (the part due to
changes in ice flow rate rather than surface pro-
cesses) was independent of climate scenario because
‘the current state of knowledge does not permit a quan-
titative assessment’, except for the GrIS and the most
extreme warming scenario. More recent studies sug-
gest that the potential contribution from Antarctica,
in particular, could be larger than forecast in the AR5
(DeConto and Pollard 2016). That study, and many
other ice sheet modelling studies, used past behaviour
to either calibrate the model or as a target for it (Price
et al 2017). Thus, robust and reliable estimates of
land ice trends and their relationship to external forc-
ing and internal variability in the climate system, are
essential for improved projections of future behaviour.
They are also important, as we will explain in sec-
tion 1.4, for constraining and closing the sea level
budget (SLB).
Another important reason for constraining the
recent contribution from land ice is in the use of
so called Semi-Empirical Models used for SLR pro-
jections. These models use the relationship between
past changes in SLR and surface air temperature to
predict future changes based on climate warming sce-
narios (Jevrejeva et al 2010,Rahmstorf2007). There
is a lag between a change in temperature and SLR,
and there will be multiple lags depending on what part
of the climate system is responding: the oceans (via
thermal expansion), land hydrology, GIC or the ice
sheets. Improved estimates of the land ice response to
external forcing and internal variability will, in turn,
improve the predictive skill of semi-empirical models.
Thus, for a range of reasons, knowledge of past and
future mass trends of both GIC and the ice sheets
is important. It is worth noting that this has not
always been the consensus view. Prior to the advent
of high fidelity satellite observations in the 1990s, it
was generally believed that the ice sheets responded
slowly (over millennia) to external forcing and required
a large amplitude perturbation to demonstrate a
significant response (Vaughan 2008).
2
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
M
e
a
n
s
e
a
l
e
v
e
l
I
ce be
low
sea level
Grou
n
d
i
ng
li
ne
Be
dr
ock
Figure 2. Schematic representation of the marine-terminating portion of an ice sheet or glacier with bedrock below sea level.
1.2. Mass balance of GIC and ice sheets
The mass balance of a glacier or an ice sheet repre-
sents the trade-off between gains, primarily through
snowfall, and losses, through melting at the upper
surface (also called surface ablation), iceberg calving
(in the case of marine-terminating land ice), bot-
tom melting underneath floating ice shelves and basal
melting at the ice/bedrock interface, which is gener-
ally a small term. Snowfall and surface ablation are
the key terms that make up the surface mass balance
(SMB). Calving and bottom melting (beneath float-
ing ice shelves) can be aggregated into a single term,
which is the ice discharge (D) across the grounding
line (figure 2). If the SMB equals D, then the ice mass
is in balance: the net accumulation of ice at the sur-
face is balanced by discharge across the grounding line,
assuming that basal melt beneath the grounded ice is
negligible. This does not, however, necessarily mean
that the ice mass is in equilibrium as we shall discuss
in section 1.6.
For land terminating glaciers, such as those in Asia
and the European Alps, only surface melting is impor-
tant as D is zero (there is no grounding line flux). In
the case of marine-terminating glaciers, such as those
in most of the Arctic (see figure 1), discharge is an
important, and sometimes dominant, component of
mass loss. For Antarctica, surface melting is negligible
because air temperatures, even in summer, are generally
below freezing and it is a reasonable approximation to
assume that all mass is lost through discharge across the
grounding line (see box 1). For Greenland, about 60%
of the present-day mass removal is from ice discharge,
and 40% from surface ablation but their influence
on recent imbalance is the other way around (van
den Broeke et al 2009,vandenBroekeet al 2016).
In other words, the change in surface processes has
been responsible for 60% of the imbalance and change
in D for 40%.
Both Greenland and Antarctica contain GIC
around the margins of the main ice sheets (regions
5and19infigure1), often referred to as peripheral
GIC (PGIC). Some studies consider the mass balance
of the ice sheets and the PGIC separately but there
has been, in general, no consistency in the treatment
of PGIC and many studies do not specify if they are
included or excluded from the total. For Greenland,
the PGIC are a significant proportion of the total mass
imbalance (circa 15%–20%) (Bolch et al 2013). The
GRACE satellites have an approximate spatial resolu-
tion of 300 km and the large number of studies that
use GRACE, by default, include all land ice within the
domain of interest. For this reason, in the following
sections, when discussing AIS or GrIS mass trends,
the values include PGIC. To avoid double counting
PGIC in estimates of GIC, such as modelling stud-
ies, that include these regions, we have subtracted
the best estimates for PGIC contribution from the
total GIC value. However, it is not always possible to
determine what the GIC estimate refers to (Yi et al
2015), most likely because the authors are not aware
of the difference. In general, where a study has used
GRACE to determine the GIC trend, we assume that
this does not include PGIC as this will be part of the ice
sheet estimates.
The AIS is usually partitioned into the West
(WAIS) and East (EAIS) separated by the natural geo-
graphic barrier of the Transantarctic Mountains. Other
factors, however, also differentiate the two. The WAIS
is a predominantly marine ice sheet—one that is rest-
ing on bedrock below sea level—on a retrograde bed
3
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Box 1. Jargon box/primer.
Altimetry: Satellite radar (ERS-1, ENVISat, CryoSat 2) and laser (ICESat) altimetry can be used to measure, with high accuracy, the
changing surface elevation (and hence volume) of an ice sheet or ice cap and, in the case of ICESat, larger glaciers. To go from a volume
change (ΔV) to a mass change (ΔM) requires knowledge of the density of the medium that has changed. Over polar ice masses, this
may be that of the surface layer (called firn), which can have a density of 350 kg m−3 or that of ice, with a density of 918 kg m−3.
Clearly, the difference between these two results in a concomitant difference in the inferred mass trend. Knowing what density to use
requires knowledge about the process driving the volume change: is it due to surface processes such as changes in snowfall and runoff,
or is it due to a change in ice motion (usually termed ice dynamics). In general, it is some combination of the two resulting in the
effective density of the volume change having an intermediate value. In addition, the rate of densification from firn to ice depends on
temperature and accumulation rate. A change in either of these can affect, what is called, the firn compaction rate, and hence surface
elevation without having any change in mass. Over sub-polar glaciers these issues are of less significance because the surface firn layer is
thinner and closer in density to that of ice.
GRACE: The Gravity Recovery and Climate Experiment was launched in 2002 and comprised two satellites flying in tandem at about
200 km separation (Tapley et al 2004). They measure changes in the gravity field at the Earth’s surface and below it within the mantle.
From these gravity anomalies, it is possible to infer a mass change. The effective resolution of GRACE is about 300 km so it cannot
measure changes of individual glaciers or ice caps but integrates the changes over larger areas. To determine ice mass trends from
GRACE, it is necessary to remove any signals from other sources of mass movement. These are primarily due to land hydrology and a
process called glacial isostatic adjustment (GIA).
Glacial isostatic adjustment (GIA): GIA is the solid Earth response to past loading of the lithosphere by ice sheets during the last
glacial period which ended about12,000 years BP. Removal of the ice results in uplift of the land and redistribution of the mantle at
depth. It makes an important contribution to contemporary sea level changes at a regional scale but also directly affects the gravity
anomaly measured by GRACE. Models of the response of the Earth tothis loading can be used to predict present-day GIA (Peltier
2004), or it can be reconstructed using a data inversion approach (Wu et al 2010).
Grounding line: when a glacier or ice mass is in direct contact with the ocean, there will be a triple junction formed of sea water, bedrock
and ice (figure 2). This junction is called the grounding line and is important for several reasons. First, it forms the point at which ice is
no longer on land but has become part of the ocean system. At some distance (typically a few kilometres downstream) the ice is freely
floating on the ocean (it is in hydrostatic equilibrium) and has almost no influence on sea level anymore. Second, the grounding line is
the first point at which the ocean can influence ice mass. Warm ocean water in the vicinity of the grounding line can cause high melt
rates (Rignot 1996) and changes in water temperature can directly influence the inland ice speed and discharge into the ocean (Holland
et al 2008). Third, under certain circumstances the position ofthe grounding line can be inherently unstable and small changes in, for
example, ocean temperatures, can result in a rapid retreat of the grounding line and, as a consequence, ice mass loss (Schoof 2007).
slope (where the bed deepens inland). This config-
uration is believed to be inherently unstable and is
associated with the marine ice sheet instability hypoth-
esis first posited in the 1970s (Hughes 1973,Mercer
1978) and now, potentially, already underway (Joughin
et al 2014). The Antarctic Peninsula, often considered
part of the WAIS, but geographically and climato-
logically distinct from it, also has regions that satisfy
the marine instability criteria (Bamber et al 2009).
It is a region that, until recently, has experienced a
marked warming and dramatic changes to a num-
ber of fringing ice shelves, with associated changes to
grounded ice motion (Rignot et al 2004,Rottet al
1998,Scamboset al 2014,vandenBroeke2005,
Vaughan and Doake 1996). More recently accelerated
mass loss has also been identified for the southern
Peninsula (Wouters et al 2015). In contrast, the EAIS
is predominantly resting on bedrock above sea level
although some sectors are marine with limited areas
of retrograde bed slopes (Bamber et al 2009)andhave
shown recent signs of dynamic change (Greenbaum
et al 2015). It is, therefore, believed to be, largely,
more stable than its western neighbour and recent
observationstend to support this view (Mart´
ın-Espanol
et al 2016a), although paleo-proxy data suggests vari-
ability in ice extent for part of East Antarctica during
previous warm epochs (Gulick et al 2017).
1.3. How mass balance is determined
There are three main methods for estimating or mea-
suring the mass balance of an ice mass, each of which
relies on different types of satellite instrument, based
on observations (but, typically, including model output
to address one or more unobserved processes).
The first method involves measuring changes in
elevation of the ice surface over time either from
imagery or from altimetry (see box 1). Radar and laser
altimeters have been flown on both satellite and air-
borne platforms and all have been used to make repeat
measurements of elevation change over both GIC and
the ice sheets (Arendt et al 2008,Helmet al 2014,
Krabill et al 2000). ERS-1 was launched in 1991 and
was the first satellite to carry a radar altimeter that
covered a substantial proportion of both the GrIS and
AIS. It had a latitudinal limit of 81.5◦which meant it
covered almost allof the GrIS and four-fifths of the AIS
(Bamber and Kwok 2003). It was succeeded by ERS-2
in 1995, ENVISat in 2000 and CryoSat-2 in 2010, which
extended the latitudinal limit to 88◦. Autonomous
satellite laser altimeter observations over the same area
were provided from 2003–2009 by ICESat.
This first method involves interpolating a heteroge-
neous distribution of elevation differences (dh/dt) into
a volume change and from volume to mass (dm/dt),
requiring knowledge of the density of the volume
4
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 3. Mean elevation rates for 2010–2017 for the Antarctic and Greenland Ice Sheets, derived from CryoSat-2 radar altimetry
(updated from Hurkmans et al (2014)andMart
´
ın-Espanol et al (2016a)). Both ice sheets are shown at the same scale. Regions of mass
loss, concentrated around the southeast and western margins of the GrIS and the Amundsen sea Embayment (ASE) of the WAIS, are
shown in red. The solid black polygons show where CryoSat- 2 switches between different modes, which introduces some artefacts in
dh/dt near the boundary between them.
change (Sørensen et al 2011). For GIC, it is usually
assumed that this is the density of ice but for the ice
sheets this is not the case as the upper layer is com-
pacted snow known as firn, which can have a density
around 2.5 times smaller than ice (see box 1). Changes
in firn compaction rate can alter the ice sheet vol-
ume without any change to its mass (Sørensen et al
2011). Although, GIC, and in particular Arctic ice
caps, can have an extensive firn layer, it is roughly an
order of magnitude less deep compared to the inte-
rior of the ice sheets and, as a consequence, generally
has less impact on volume changes. Figure 3illus-
trates the mean elevation trends for 2010–2017 for the
GrIS and AIS, obtained from CryoSat-2 radar altime-
ter data. It shows the sectors of both ice sheets that
have been the primary contributors to SLR during the
satellite era, as these same regions have dominated
mass loss over most of the period from 1992–2016.
In the interior of both ice sheets, the elevation rates
are small and close to the signal threshold for detect-
ing a mass change from volume change estimates.
This is discussed in more detail in section 2.1 on the
EAIS.
For glaciers, mass balance can also be measured via
direct, field-based, observations although these only
exist for a small proportion (<200) of the >200 000
glaciers that have been identified (Zemp et al 2009).
Attempts have been made to extrapolate these in-situ
data to cover all glacier sectors shown in figure 1(Cog-
ley 2009, Dyurgerov and Meier 1997), but because
of the non-uniform sampling in altitude, aspect, cli-
matic setting and size of the field-based data, scaling
up to entire mountain ranges/sectors introduces large
uncertainties (Gardner et al 2013). In general, the
agreement between scaling up of these direct obser-
vations and other estimates, both regional and global,
has been mixed (Gardner et al 2013). Length and vol-
ume change records extend back over a century for
some glaciers and these can be used to calibrate glacier
mass balance models that are driven by global clima-
tologies such as surface air temperature data (Marzeion
et al 2015) and re-analysis products (Radic and Hock
2010,Radi
´
cet al 2014). This approach differs from
using a regional climate model (RCM) to estimate,
directly, the surface mass balance of an ice mass, as
it is based on a statistical scaling relationship. We
term this method statistical modelling (e.g. Marzeion
et al 2015,Radi
´
cet al 2014). While RCMs work
well for larger ice masses, such as the ice sheets and
Arctic ice caps, the complex topography, and cor-
responding micro-climatological effects this creates,
makes them less suitable for GIC on a smaller scale
and/or in mountainous terrain.
More recently, airborne and satellite-based stereo
photogrammetry has been used to estimate volume
changes of some of the glaciated regions sh own in figure
1. With the aid of historical photo archives, this has
provided observational reconstructions extending as
far back as the 1930s for some sectors (Bjørk et al 2012,
Nuth et al 2010).
The second method for estimating mass balance is
known as the mass budget or Input-Output Method
(IOM) and, as the name suggests, involves estimat-
ing the difference between the surface mass balance
5
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 4. Comparison of cumulative mass balance tren ds for the Greenland Ice Sheet and peripheral glaciers and ice caps fo r 1992–2016,
based on satellite altimetry, the input/output method (IOM) and GRACE.
(SMB) and ice discharge (D). The former is com-
prised of primarily snowfall minus runoff (surface
ablation) and, for large ice masses, is often estimated
from regional climate models (RCMs) that are forced
at their boundaries by re-analyses (Fettweis 2007,
Lenaerts et al 2012). The RCMs are coupled to snow
diagenesis models so that they can realistically repro-
duce both atmospheric conditions and processes at
and within the snowpack. Discharge comprises ice
velocity multiplied by ice thickness across a gate, usu-
ally taken to be the grounding line or a short distance
inland from it (Rignot et al 2008a,Rignotet al 2008b).
As mentioned previously, for land-terminating ice
masses D is zero and it is only SMB that determines
the state of the ice mass. As will be shown later,
when discussing Arctic ice caps, RCMs are of sufficient
resolution and sophistication that they can reliably
reproduce mass trends without the use of in-situ data.
The third and final approach, and the most recently
developed, only became viable with the launch of the
Gravity Recovery and Climate Experiment (GRACE)
satellites in 2002 (see box 1). They have provided grav-
ity anomaly measurements continuously from 2002
until September 2017 when one of the satellites failed.
The gravity anomalies provide information about
redistribution of mass at, and below, the surface
of the Earth at relatively coarse resolution of about
300 km (see box 1).
The most appropriate approach depends on the
location and size of the ice mass. For example, satel-
lite radar altimetry is compromised in areas of high
relief such as mountain ranges, while GRACE integrat es
changes in the gravity field over a characteristic length
scale of about 300 km. As a consequence, GRACE can-
not provide trends for single glaciers but rather over
larger areas such as the whole Svalbard archipelago or
basins of the ice sheets (e.g. Jacob et al 2012). Another
limitation of using GRACE data to determine mass
balance for land-locked GIC is if the redistribution of
mass from a glacier to an aquifer is local (within the
resolution of GRACE), then the satellites will not see a
significant change in gravity even though the glacier
imbalance may be large and, in principle, measur-
able by GRACE. Another constraint is local tectonics,
which can affect the solid-earth gravity anomalies in
areas of seismic activity (Jacob et al 2012). For exam-
ple, for High Mountain Asia (HMA; regions 13–15
in figure 1), the uncertainties due to land hydrology
and solid-Earth processes are larger than the signal,
which is also the case for several other smaller mountain
ranges (Jacob et al 2012).
Ice sheet wide agreement between the three
approaches has been previously demonstrated for
Greenland by Sasgen et al (2012) for the period 2003–
2011, although there was less consistency at a basin
scale. In figure 4we present a similar, but longer,
time series based on methods published elsewhere
(Hurkmans et al 2014,vandenBroekeet al 2009,
van den Broeke et al 2016,Wouterset al 2013). The
results extend the analysis of Sasgen et al (2012), using
6
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
CryoSat-2 altimetry data, updated RCM simulations
downscaled to 1 km (No¨
el et al 2016)andaGRACE
inversion approach (Wouters et al 2008). Excellent
agreement is seen between the methods, including for
the exceptional melt event in 2012, which has the poten-
tial to bias altimeter-derived mass changes estimates
(Nilsson et al 2015). It is also apparent the trends from
satellite altimetry (in this instance ERS-2, ENVISat,
ICESat I and CryoSat-2) are smooth in time and do
not capture sub-annual behaviour before 2003. This
is because, to achieve adequate sampling in space, it
was necessary to average a large number of individ-
ual dh/dt estimates and to interpolate to unobserved
sectors, especially, prior to CryoSat-2 (Hurkmans et al
2014).
Prior to 2003, we are reliant on satellite radar
altimetry (Hurkmans et al 2014)andIOM(vanden
Broeke et al 2016) alone and it is apparent that there
is greater divergence between these two approaches for
this epoch (for example from 1995–1998). Observed
discharge estimates were used from 2000 onward
and are assumed to decrease linearly to 1996 and to
be stationary before that (van den Broeke et al 2016).
Radar altimetry does not fully sample coastal thinning
and requires interpolation to capture the high rates near
the margins (e.g. Hurkmans et al 2014). An approach
called kriging with external drift was used, which was
effective in determining the rates but with a poten-
tial delayed signal (by 1–2 years) due to the time it
takes for thinning at the margin to propagate suffi-
ciently far inland to be observed by radar altimetry
(Hurkmans et al 2014). Thus, our understanding of ice
mass changes prior to 2003 is more uncertain.
A promising approach that attempts to address
these limitations is to combine GRACE with other
gravity data derived from satellite laser ranging (Talpe
et al 2017). The advantage of this approach is that
it is a more direct measurement of mass movement
at the surface with data extending as far back as
1976. The disadvantage is its low spatial resolution
and the subsequent challenges in separating mass-
movement signals from different sources and processes
and the comparatively large errors (Talpe et al 2017).
Using this approach, the total error estimate for the
GrIS is between 150 and 200 Gt yr−1 and for the AIS
around 100–120 Gt yr−1 (Talpe et al 2017).
1.4. The sea level budget and role of land ice
The SLB is relevant with respect to land ice for two
interlinked reasons. The first is the central role land
ice contributes towards it and the second is that esti-
mates of the SLB can be compared with independent
assessments of the land ice contribution. For exam-
ple, GRACE can measure the global change in mass
of the oceans, which should equal the total contri-
bution from land ice along with some other smaller
contributions.
Changesinglobalmeansealevel(ΔGMSLTot al )
is influenced by a number of geophysical processes
defined in equation (1), which is commonly termed
the SLB:
ΔGMSLTot al =GMSL
ster ic +GMSL
mass
+GMSLVLM.(1)
Where ΔGMSLster ic is the term related to changes
in density caused by temperature (thermosteric) and
salinity (halosteric) variations, ΔGMSLmass is the term
due to mass exchange between the land and ocean and
ΔGMSLVLM is the term related to changes in ocean
basin volume due to vertical land motion (VLM). The
mass term (ΔGMSLmass ) can be further broken down
to include the different land ice components (the focus
of this paper):
ΔGMSLmass =ΔM
GIC +ΔM
GrIS +ΔM
AIS+
ΔMLWS +ΔM
other .(2)
Where ΔMGIC,ΔMGr IS and ΔMAIS are the change
in mass due to glaciers and ice caps, Greenland and
Antarctica, respectively. ΔMLWS is land water stor-
age including both natural and anthropogenic factors
such as secular trends in precipitation minus evapo-
ration, water impoundment and extraction. ΔMother
captures several other smaller contributions including
secular trends in atmospheric water vapour loading and
seasonal snow cover.
Since 1992 we have had a reliable record of
ΔGMSLTot al for the oceans up to a latitude of ±60◦
from satellite radar altimetry. In principle, ΔGMSLTota l
as measured by altimetry should equal the sum of the
three terms on the right-hand side of equation (1),
which is termed closing the SLB. Various attempts
to close the SLB have been made with considerable
progress being made after the launch of the GRACE
satellites in March 2002. GRACE allowed, for the
first time, a direct measurement of changes in ocean
mass and exchange with land. This roughly coincided
with a step change in observations of ΔGMSLste ric
from the network of Argo buoys that was near-
complete by 2005 (Freeland and Cummins 2005,Riser
et al 2016). These buoys measure temperature and
salinity variations down to a depth of 2000 m and pro-
vide the most complete observational record of steric
changes in the upper ocean. Vertical land motion is
a relatively small term in the range 0.2–0.4 mm yr−1
(Spada 2017, Tamisiea 2011) due, predominantly, to
glacial isostatic adjustment (GIA) (see box 1)with
an uncertainty of about 0.2 mm yr−1. Thus for 2003
to the present, each term in equation (1)isrel-
atively well constrained. There are, however, other
terms related to vertical land motion, as a result of
present-day mass exchange that have, in general, been
ignored in SLB studies (Frederikse et al 2017,Lickley
et al 2018).
For the prior epoch (1993–2003), the steric and
mass terms are less well constrained by observations
and drift in the altimeter instrument electronics (specif-
ically Topex A from 1993–1998) has also impacted the
7
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
reliability of the ΔGMSLTot al observations (Watson
et al 2015). Despite these limitations, Dieng et al
(2017) investigated the SLB for the satellite era (1993–
2015) by comparing multiple estimates of each term
in equation (1), including the integrated ocean mass
trend from GRACE versus the sum of each contribu-
tion to this term, namely GIC, Greenland, Antarctica,
land water storage, snow storage and atmospheric
water vapour changes. The residual difference between
the left-hand and right-hand side of equation (1)was
found to be 0.0 ±0.22 mm yr−1 (Dieng et al 2017).
This provides, in principle, some confidence in the
individual component estimates. However, other stud-
ies have obtained both higher and lower estimates
of the various components that make up the mass
term in equation (1) (section 3.1). Indeed, the uncer-
tainty in the solid Earth influence due to GIA on the
GRACE estimate of ocean mass is ±0.5 mm yr−1 alone
(Tamisiea 2011). Thus, choices made in the estimates
used, and corrections applied, can result in an appar-
ent closure of the budget. We will return to the SLB
later in this review, when assessing the veracity of mass
trend estimates for the ice sheets and GIC. What the
SLB does provide are bounding limits for ΔGMSLma ss
given estimates of the other terms from recent
observations.
1.5. The difference between mass balance and sea
level contribution
Understanding of the global land ice contribution to
sea level rise is complicated by the fact that ice mass
balance and sea level contribution are not the same
quantity. In the case of an ice mass with a marine-
terminating margin and bedrock elevation below mean
sea level, some proportion of the volume of ice lost
is below mean sea level. Figure 2illustrates the typi-
cal geometry of most of the WAIS, parts of the EAIS,
GrIS and many marine-terminating glaciers in the Arc-
tic. Seaward of the grounding line, the floating ice
shelf is in hydrostatic equilibrium with the ocean. If
it melts, it has a negligible impact on sea level (there
is a small halosteric effect due to dilution of the ocean
by freshwater). A change in mass on the landward side,
however,doeshaveadirectimpact.Thegroundingline
represents, therefore, a natural and logical boundary
for defining the mass balance of a marine-terminating
glacier/ice mass.
There is a further complication to this apparently
simple situation. Imagine a scenario (as is the case for
parts of the WAIS) where the grounding line is migrat-
ing inland. The change in mass of the grounded ice
sheet is the integral of the total ice thickness along
the grounding line multiplied by the distance it has
moved inland. Consider a 20 km wide glacier (similar
to Pine Island Glacier, WAIS) and ice thickness at the
grounding line of 1 km. For a grounding line migra-
tion rate of 1 km yr−1, the mass loss is 20 km3yr−1 .
This is, however, not the same as the SLE contribu-
tion, as that comes only from the proportion of ice
above buoyancy (tens to over a hundred metres above
the black dashed line in figure 2). Typically, grounding
lines of fast moving outlet glaciers are close to flota-
tion and this means that the SLE contribution is an
order of magnitude smaller than the total mass imbal-
ance. This only matters where the grounding line is
moving, which is relevant primarily for parts of the
WAIS. However, previous studies of the WAIS have
not been clear on whether it is the SLE or the mass
imbalance they are estimating when using altimetry
and/or IOM (e.g. Rignot et al 2011,Shepherdet al
2012, Sutterley et al 2014). GRACE measurements
only detect the SLE contribution and do not measure
mass imbalance. Volume change and IOM estimates
may do either depending on whether they account
for grounding line migration in their calculations. If
they do not, then they may be measuring a volume
change over floating ice. If they do, then they must
estimate the proportion of ice above floatation and dis-
count the remainder if it is the SLE contribution that
is being estimated. Later, we investigate the impact of
this effect on SLE and mass balance estimate for the
WAIS and show that the error is significant if ignored.
For GIC, there may also be a difference between ice
mass balance and sea level contribution due to the fact
that the meltwater from land-locked GIC may never
reach the ocean (Brun et al 2017). For example, in
HMA (regions 13–15 in figure 1), it is likely that some
proportion of the glacial meltwater is taken up by
aquifer recharge, irrigation or other forms of impound-
ment, particularly for endorheic (or closed) drainage
basins (Brun et al 2017).
1.6. The 20th century sea level contribution from
land ice
As land ice has a relatively slow response time to exter-
nal forcing, it is useful to consider its longer-term
behaviour, prior to the satellite era. There are, how-
ever, limited observational data on the 20th century
behaviour of land ice, especially for the ice sheets.
ThelastIPCCreport(theAR5)consideredwhether,
modellingandobservationaldatacouldbeusedto
close the SLB for 1900–1990 (Church et al 2013).
Ice sheets were excluded from this assessment, due to
lack of reliable estimates. Observations from a small
number of in-situ mass balance measurements of indi-
vidual glaciers (outside of the ice sheets) and upscaling
to the 19 regions shown in figure 1gavearateof
0.54 ±0.7 mm yr−1, while statistical modelling pro-
duced a slightly higher rate of 0.63 ±0.28 mm yr−1.
Taking into account the other terms in equation (1)
(thermal expansion and land hydrology) they obtained
a residual (i.e. difference from sea level rise observed
by tide gauges) of 0.5 mm yr−1, with an uncertainty
range of 0.1 to 1.0 mm yr−1. This could be accounted
for by contributions from the GrIS and AIS, but in
what proportion was largely unknown.
Since then, two notable advances have been made
that help resolve the ice sheet contribution during the
8
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
20th century. First, reassessment of the long-term tide
gauge record, used to reconstruct SLR, suggests that
the 20th century rate has likely been overestimated by
0.3–0.4 mm yr−1 (Dangendorf et al 2017,Hayet al
2015). Second, a reconstruction of the Little Ice Age
volume of the GrIS from aerial stereo photogramme-
try has provided the first robust estimate of the 20th
century contribution from this source (Kjeldsen et al
2015). While the estimate lacks temporal fidelity, it
does provide a mean rate of mass loss equivalent to
0.21 ±0.08 mm yr−1 for the period 1900–1983, with a
similar rate for 1983–2003 (Kjeldsen et al 2015).
Combining these two advances with the remaining
terms in the SLB provides a constraint on the AIS con-
tribution. Using the value for SLR of 1.2 ±0.2 mm yr−1
for 1901–1990 (Hay et al 2015), the new GrIS estimate
reduces the residual in the AR5 SLB to 0.1 mm yr−1
(−0.4 to 0.5). Although the combined uncertainties are
large, this suggests that the AIS was likely close to bal-
ance up to 1990. To date, there are, unfortunately, few
other approaches available to constrain the behaviour
of the AIS prior to the satellite era. The ice sheet has an
area of about 13 million km2, larger than the contermi-
nous USA and the only reliable way to make direct,
continent-wide observations is, as a consequence,
using Earth observation (EO) techniques.
It is also worth noting that, although the SLB
approach suggests a near balance for the AIS, it pro-
vides no information about regional variations and, by
inference, if the ice sheet is in equilibrium. For exam-
ple, estimates for about the last decade indicate that
mass loss from the WAIS has been partly compen-
sated for by gains from the EAIS (Mart´
ın-Espanol et al
2016a). Furthermore, velocities derived from satellite
imagery suggest that mass loss for part of the Amund-
sen Sea Embayment of West Antarctica began as early
as the 1970s (Rignot 2008). It is possible, therefore,
that recent regional trends (i.e. gains over the EAIS
and losses in the WAIS) may have existed for decades
prior to our ability to detect them. In terms of the ice
sheet contribution to SLR, this may not appear rele-
vant, but it is critical for understanding the evolution
of the trends, their origin and drivers, and therefore
for predicting their future behaviour. The origins of
the losses/gains are also likely different: one due to
changes in the ocean and the other, potentially, due to
changes in the atmosphere. Likewise in the case of the
GrIS, it has been assumed that the ice sheet was close
to balance from about 1960 to 1990 (van den Broeke
et al 2009). This may be a reasonable assumption, but
examination of the longer term (20th century) recon-
struction of the SMB over the ice sheet indicates that
this was a period of slight cooling with lower abla-
tion and higher snowfall resulting in a more positive
SMB (Fettweis et al 2017) that likely compensated the
long-term negative dynamic response of the ice sheet
to the end of the Little Ice Age (Kjeldsen et al 2015).
These two examples highlight the importance of con-
straining not just the overall balance but the origin of
the losses and gains and how they relate to external
forcing.
GIC are considerably smaller than the ice sheets.
Their individual mass balance can often, therefore, be
derived from in-situ observations, but due to the large
number of glaciers (about 200 000 are included in
the Randolph glacier inventory (Pfeffer et al 2014),
the sampling of directly observed glaciers is necessarily
sparse. The EO techniques applicable to the ice sheets
can, in principle, be applied to GIC, but the small size
of individual GIC and their location in often complex
terrain reduces the ability of these approaches to pro-
vide reliable data with a useful signal to noise ratio. In
the first half of the 20th century, glacier length records
(Leclercq et al 2014) provide the only direct observa-
tions of GIC change that allow for a global assessment
of their contribution to sea-level change. These length-
change records indicate that glacier retreat, and thus
presumable glacier mass loss, started on the global
scale around 1850, at the end of the Little Ice Age
(Leclercq et al 2011). Glacier statistical modelling,
using climate observations as forcing, corroborates
the finding that mass loss rates from GIC increased
slightly until the 1930s or 1940s, peaking around
1 mm SLE/yr (but with large associated uncertainties),
before decreasing until the 1960s or 1970s to around
0.5 mm SLE/yr. The subsequent increase of mass loss
rates until present day is apparent in estimates based
on glacier length retreat, direct and geodetic observa-
tions, and GIC statistical modelling alike (Marzeion
et al 2015).
2. Synthesis of mass balance assessments
During the satellite era, and particularly since 2002,
there has been an unprecedented increase in the num-
ber of studies investigating land ice mass trends. The
IPCC AR5 provided a thorough and careful synthesis
of those studies published up to early 2013. In prepa-
ration for the AR5, two studies were undertaken to
attempt to provide so called reconciled estimates of
mass trends for the ice sheets (Shepherd et al 2012)
and GIC (Gardner et al 2013). In both studies, esti-
mates from the various approaches available (dh/dt,
IOM, GRACE and extrapolation of terrestrial data)
were compared, and for GIC, combined. Consistency
between methods was improved by, for example, focus-
ing on a common time period and common drainage
basin definitions and/or areal extent of glaciated land
yet inconsistencies remained between published results
for specific regions (Gardner et al 2013) or ice sheet
sectors and methods. To describe these studies as rec-
onciled is, therefore, not entirely accurate but more a
shorthand for a reduction in the inconsistency between
results. Since then, new estimates for both GIC regions
and the ice sheets have been published, which further
explore or challenge the consistency (or lack thereof)
between methods and approaches.
9
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Here, we focus primarily on studies published
since the AR5 to: (i) present and update ice sheet
trends for GrIS and AIS to 2016 based on previously
published results; (ii) present a new synthesis of GIC
trends by combining the latest satellite observations
and statistical modelling; and (iii) assess the consis-
tency between land ice mass loss and the global SLB.
The outcome is a comprehensive, consistent and rig-
orous assessment of the land ice contribution to SLR
from 1992–2016.
A complete list of previously published results con-
sidered in this review are provided in tables S1 (AIS),
S3 (GrIS) and S5 (GIC) in the supplementary data.
In our assessment of consistency between the various
results, we have used a new approach for presenting
time-averaged trends. Typically, results have been com-
pared by plotting mass balance values as boxes where
the width is the time span and the height is the uncer-
tainty (e.g. Hanna et al 2013). As an increasing number
of results are plotted, this becomes harder to inter-
pret, and is also misleading because, in general, each
box does not reflect a stationary value in time but
plotting it this way tends to make it appear so.
This final point is important as many studies
have published a mean rate over a given time period
based on the data available, which varies substantially
between methods. For both ice sheets and GIC, inter-
annual variability in the mass balance is relatively large
(Marzeion et al 2017,vandenBroekeet al 2011,
Wouters et al 2013). We have estimated the 1-sigma
(68% confidence level) range due to inter-annual vari-
ability usingan updated GRACE time series for the GrIS
covering the period 2003–2016 (Wouters et al 2013)
and an updated annual time series from a Bayesian
Hierarchical Model (BHM) combination of data sets
for the period 2003–2015 for the AIS (Mart´
ın-Espa nol
et al 2016a). For GrIS and WAIS we identified and
removed a linear trend and estimated the variability as
the residual. For EAIS, we assumed there was no overa ll
trend in mass balance as the variations seen during the
GRACE epoch, at least, are dominated by inter-annual
variability in SMB (Groh et al 2014,Mart
´
ın-Espa nol
et al 2016a). This gives estimates of inter-annual vari-
ability of ±228, ±220 and ±114 Gt yr−1 for the GrIS,
EAIS and WAIS, respectively. For short timescale stud-
ies (≤5 years) differences in the epoch chosen can
have, therefore, a significant impact on the overall
trend. For the GrIS, for example, a 5 year mean
value can vary by ±102 Gt (i.e. 228 / √5) due solely
to inter-annual variability. This also highlights cau-
tion required in inferring a trend and/or acceleration
from a short record (Wouters et al 2013a).
We take the inter-annual variability into account
by ‘collapsing’the time-averaged rate onto the cen-
tral year of the reported estimate and including both
the measurement error (the height of the box) and
inter-annual variability (the height of the ‘whisker’)
to illustrate the overall uncertainty (e.g. figure 5). We
assume that the year-to-year differences are uncorre-
lated so that both components are reduced by √n,
where n is the number of years the trend is esti-
mated over. All errors are quoted as 1-sigma (68%
confidence interval) unless otherwise stated. When
combining time series from different studies we assume
the errors between studies are uncorrelated. This is a
reasonable assumption for the different approaches dis-
cussed in section 1.3 but is less valid when combining,
for example, GRACE time series from different stud-
ies. Systematic biases may exist between these due, for
example, to uncertainties in GIA, the atmospheric and
hydrology correction applied to the data and signal
leakage between land and ocean. Nonetheless, differ-
ent studies tend toemploy different corrections, which
will reduce these biases.
We consider the WAIS and EAIS separately for
reasons explained earlier: they are behaving differ-
ently, because they are experiencing different external
forcing and respond differently to the same forcing
(Pritchard et al 2012). There is a general consensus that
the EAIS has been close to balance or slightly gaining
mass over at least the last decade (e.g. Helm et al 2014,
Mart´
ın-Espanol et al 2017,Shepherdet al 2012), while
the WAIS has been doing the opposite but at a greater
rate (e.g. Mart´
ın-Espanol et al 2016b,Shepherdet al
2012,Talpeet al 2017,Gardneret al 2018).
We include two further elements on each plot. First,
a dashed black line which is a weighted mean (weighted
by the formal error) of published solutions that pro-
vide annual mass balance data. The datasets used to
derive the weighted mean are listed in tables S2 and
S4, and further details about the method are provided
in the supplementary data. It should be noted that the
weighted mean annual values for GIC are for a bal-
ance year (end of summer to end of summer), while
the annual values for GrIS and AIS are for calendar
years (January–December). The balance year is typi-
cally September–August in the Northern Hemisphere,
and April–March in the Southern Hemisphere.
Second, ‘boxes’and ‘whiskers’have been added to
illustrate the IPCC AR5 synthesis estimates. For the
ice sheets, these were presented as four ‘pentad’(i.e.
5 year average) values spanning the period 1992 to
2011. The IPCC AR5 pentad estimates for Antarc-
tica were not divided into separate values for EAIS
and WAIS, so we have partitioned them based on
the ratio of mass balance described in previously pub-
lished papers for equivalent time periods: Rignot et al
(2008b) for 1992–1996 and 1997–2001; Shepherd et al
(2012) for 2002–2006; update from Mart´
ın-Espa nol
et al (2016b) for 2007–2011. The AR5 did not tabu-
late equivalent pentad values for GIC. Instead, it gave
detailsofaverageratesofglobalmasschangefrom
all glaciers globally as estimated in published stud-
ies. Two of these estimates (Cogley 2009/Marzeion
et al 2012 and Gardner et al 2013) provide three
estimates wholly within the satellite era (1993–2009,
2003–2009 and 2005–2009), and it is these that are
included as the IPCC AR5 synthesis values.
10
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 5. Post AR5 estimates of EAIS mass balance and the IPCC AR5 synthesis values. Horizontal whiskers indicate the time span of
the estimate. The boxes are colour-coded to reflect measurement technique used (altimetry, GRACE or Bayesian hierarchical model,
BHM, which is a statistical combination of methods). Vertical whiskers are the sum of quoted measurement uncertainty and the
1-sigma range due to inter-annual variability (see text for more details). Black dashed line is th e weighted mean of the st udies listed in
table S2. Solid black boxes and whiskers represent the values stated in the AR5.
2.1. EAIS
Figure 5shows the results of the analysis described
abovefortheEAIS.IntableS6wedetailtheannual
rates, which possess high variability, while the pentad
values are given in table 2, based on a weighted mean
of the estimates from the studies in table S2. Overall
there is no clear trend in ice mass balance, although
there is reasonable consistency between estimates. One
set of altimetry-derived results (the two positive green
boxes in figure 5) appear to be an outlier (Zwally et al
2015) and merit further discussion.
In this study, Zwally et al combined a satellite
radar and laser record of elevation changes for two
epochs, 1992–2003 and 2003–2008, to infer a volume
and, subsequently, mass change for both the WAIS
and EAIS. Of any ice mass considered here, the EAIS
presents the greatest challenges. It is the least well sam-
pled by in-situ data that could be used to validate or
improve satellite data and is the largest by an order of
magnitude. A 1 cm yr−1 change in elevation over the
whole ice sheet (about the magnitude of the signal)
is equivalent to a about 35 Gt yr−1 change in snow-
fall or 90 Gt change in ice volume or no change at
all in mass but a change in density of the upper sur-
face due to variations in firn compaction (see box 1).
Clearly, a drift in the altimeter data, when integrated
over the ice sheet, results in a large error in estimated
mass change. Issues with the approach used for cal-
ibration of the altimetry by Zwally et al have been
identified (Scambos and Shuman 2016) and an attempt
to replicate the trends using similar assumptions for
the physical mechanism could not reproduce the
large positive balance they found (Mart´
ın-Espanol
et al 2017). For these reasons, we believe that the
estimates from this study are likely erroneous.
2.2. WAIS
Figure 6shows the results of the analysis described
above for the WAIS. In table S6 we detail the annual
rates, while the pentad values are given in table 2,based
on a weighted mean of the estimates from the stud-
ies in table S2. There is generally good agreement on
the trend of mass balance and increase due to changes
in discharge (Rignot 2008), and mass loss is concen-
trated in the Amundsen Sea Embayment (ASE) and
Bellinghausen Sea sectors of the WAIS (figure 2).
The altimetry-based estimate covering 2010–2013
(McMillan et al 2014) appears markedly less negative
than the weighted mean annual time series (dashed
line). A study that compared four approaches for
deriving mass trends for the ASE of West Antarc-
tica obtained a mean value of −144 Gt yr−1 (Sutterley
et al 2014) compared with the altimetry estimate of
−120 Gt yr−1, suggesting that the altimetry may be
underestimating mass loss in this region. There was
an SMB trend (Mart´
ın-Espanol et al 2016a)overthe
ASE for the relevant period, and if this is not cor-
rected for, could explain the smaller mass loss inferred
from the volume change obtained using radar altime-
try (McMillan et al 2014). This is because part of the
dynamic signal is compensated by a positive elevation
rate due to snowfall (see box 1). Nonetheless, it is also
11
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 6. Post AR5 estimates of WAIS mass balance and the IPCC AR5 synthesis values. Horizontal whiskers indicate the time span
of the estimate. The boxes are colour-coded to reflect measurement technique used (altimetry, GRACE or BHM, which is a statistical
combination of methods). Vertical whiskers are the sum of quoted measurement uncertaintyand the 1-sigma range due to inter-annual
variability (see text for more details). Black dashed line is the weighted mean of the studies listed in table S2. Solid black boxes and
whiskers represent the values stated in the AR5.
apparent from the weighted mean time series that the
annual mass balance for WAIS, following a period of
relatively constant loss between 2009 and 2013, has
become less negative (160 Gt or less) in recent years,
most likely due to an increase in snowfall rather than a
slowdown of the outlet glaciers (Seroussi et al 2017).
Our WAIS estimates are SLE values (see section
1.5) as opposed to mass imbalance. It is less clear what
the AR5 values and other studies plotted in figure 5
refer to. Based on the approaches used, we infer that
they are SLE values but, for altimetry, are based on
a static grounding line and, therefore, include volume
changes taking place over floating ice at some point dur-
ing the measurement period. This error is significantly
smaller than the difference between SLE contribution
and mass imbalance. For the WAIS, we estimate that,
since 1992, the mean volume loss due to ground-
ing line retreat (the mass imbalance) is 137 km3yr−1
(Christie et al 2016,Parket al 2013,Rignotet al 2014,
Scheuchl et al 2016) but that only 15% (21 km3yr−1)
of this volume is above flotation, which is the SLE
value. As mentioned in section 1.5, GRACE-derived
mass trends only observe the SLE change. Defining
what is observed by other methods will depend on
whether grounding line migration is included in the
estimation process.
2.3. Greenland
Figure 7shows the results of the analysis described
abovefortheGrIS.IntableS6wedetailtheannual
rates, while the pentad values are given in table 2,based
on a weighted mean of the estimates from the studies in
table S4. A number of features are evident. First, there is
generally excellent agreement between estimates. This is
not surprising since some of the factors that introduce
uncertainty in AIS mass trends are less critical here.
The GIA correction for GRACE is smaller (around
20 Gt yr−1) and less uncertain (Barletta et al 2008).
Accumulation rates and SMB are around an order of
magnitude larger than for the EAIS, which improves
the signal to noise ratio for estimates using a volume
change approach. Finally, there are a greater number
and density of in-situ data to calibrate and evaluate
regional climate models compared to Antarctica.
Second, several studies have identified an accelera-
tion in mass loss over the ice sheet for various epochs
ending by, or before, 2012 (Rignot et al 2011, Velicogna
2009). In 2012, the ice sheet experienced exceptional
surface melting reaching as far as summit (Nghiem
et al 2012) and a record mass loss since at least 1958
exceeding 400 Gt (van den Broeke et al 2016). The fol-
lowing years, however, show a reduced loss (e.g. less
than 100 Gt in 2013). Including these years in an esti-
mation of an acceleration term reduces its rate and
statistical significance. A simple extrapolation of the
trends over the last 20 years forward in time is, clearly,
unwise and unjustified (Wouters et al 2013).
2.4. GIC
Marzeion et al (2017) provides a comparison of
assessments of GIC trends from 1900–2015 based
on all available approaches. This demonstrates that,
for a common period 2003–2009, there is agree-
ment between observational, statistical modelling and
12
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 7. Post AR5 estimates of Greenland (GrIS) mass balance and the IPCC AR5 synthesis values. Horizontal whiskers indicate the
time span of the estimate. The boxes are colour-coded to reflect measurement technique used (altimetry, GRACE, IOM or geodetic).
Vertical whiskers are the sum of quoted measurement uncertainty and the 1-sigma range due to inter-annual variability (see text for
more details). Black dashed line is the weighted mean of the studies listed in table S2. Solid black boxes and whiskers represent the
values stated in the AR5.
Table 1. Comparison of observational (ICESat, GRACE and CryoSat2) and modelled (RCM and Marzeion et al 2017) estimates of mean
trends for two periods for Arctic GIC and the southern Andes. Years are balance years from September to August.
Region Mass balance estimates 2003–2009 Mass balance estimates 2010–2014
ICESat GRACE RCM M15 CryoSat2 GRACE RCM M15
3(ArcticCanadaNorth) −37 −34 −34 −47 −38 −38 −39 −29
4(ArcticCanadaSouth) −27 −26 −27 +8−29 −32 −29 −6
7(Svalbard) −5−5−6−42 −17 −18 −13 −52
5 (Greenland PGIC) −39 −39 −34 −34 −32 −27
9 (Russian Arctic) −9−11 −23 −14 −16 −32
17 (S Andes) −29 −9
upscaled direct estimates (from in-situ or terrestrial
mass balance data) within the respective uncertain-
ties, and at the global scale. Significant disagreement,
however, between the different methods was found to
persist at regional scales. Itis important tonote that the
values discussed in Marzeion et al (2017)includeGrIS
PGIC, whereas here we include this sector (region 5,
figure 1) in the GrIS totals.
2.4.1. A new synthesis of GIC trends
Here we update the Marzeion et al (2015) time series
(as extended in Marzeion et al 2017, and hereafter
labelled M15) using new estimates of mass trends
for Arctic GIC, HMA and Patagonia; areas that rep-
resent 84% of the total GIC contribution to SLR
estimated by Marzeion et al 2017.Figure8and table
1compare M15 results for regional sectors of the
Canadian Arctic Archipelago, Svalbard and Iceland
with observational (altimetry and GRACE ) and/or time
series derived from regional climate modelling. We
find poor agreement with M15 for regions 3, 4, 7,
9 and 17 which are all Arctic sectors with signifi-
cant marine (and lacustrine in the case of Patagonia)
margins and, therefore, a significant discharge term.
This is expected as for some regions, in particular
those with a significant proportion of marine-
terminating margins (figure 1), statistical modelling
is less reliable than observational-based approaches as
it does not include variations in frontal ablation (ice-
berg calving and sub-aerial melt). Consequently, for
these sectors we substitute the original M15 data with
observational and/or time series from regional climate
modelling (Noel et al 2018).
For HMA, we utilise a recently published obser-
vational estimate of volume change from stereo
photogrammetry covering the period 2000–2016 (Brun
et al 2017). We only include those basins that are
exorheic but even for these, it is likely that not all
the glacial melt contributes directly to SLR (Brun et al
2017). For these basins the mean trend is −14.6 Gt yr−1
compared to a total for the whole of the High Moun-
tains Asia of 16 Gt yr−1. This is consistent with an
estimate derived from ICESat elevation changes for a
shorter epoch (2003-08) (K¨
a¨
ab et al 2012). To extend
13
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
2016201420122010200820062004
-1500 -1000 -500 0
Date
Mass Anomaly [Gt]
GRACE
Cryosat-2
ICESat
IOM
Figure 8. Comparison of cumulative mass balance trends for Arctic glaciers and ice caps for 1992–2016, based on satellite altimetry,
the IOM and GRACE illustrating the agreement between the three approaches. The regions covered are 3, 4, 5, 7 and 9 in figure 1(see
also table 1).
Table 2. Pentad mass balance rates for all land ice areas for the period 1992–2016 as plotted in figure 11. Further details about how these
values were derived are provided in the supplementary data.
Pentad EAIS WAIS GrIS GIC TOTAL
1992–1996 Δmass Gt yr−1 28 ±76 −55 ±30 31 ±83 −117 ±44 −113 ±125
(SLE mm yr−1)(−0.08 ±0.21) (0.15 ±0.08) (−0.09 ±0.23) (0.32 ±0.12) (0.31 ±0.35)
1997–2001 Δmass Gt yr−1 −50 ±76 −53 ±30 −47 ±81 −149 ±44 −299 ±123
(SLE mm yr−1) (0.14 ±0.21) (0.15 ±0.08) (0.13 ±0.22) (0.42 ±0.12) (0.83 ±0.34)
2002–2006 Δmass Gt yr−1 52 ±37 −77 ±17 −206 ±28 −173 ±33 -405 ±60
(SLE mm yr−1)(−0.14 ±0.10) (0.21 ±0.05) (0.57 ±0.08) (0.48 ±0.09) (1.13 ±0.17)
2007–2011 Δmass Gt yr−1 80 ±17 −197 ±11 −320 ±10 −197 ±30 -634 ±38
(SLE mm yr−1)(−0.22 ±0.05) (0.55 ±0.03) (0.89 ±0.03) (0.55 ±0.08) (1.76 ±0.11)
2012–2016 Δmass Gt yr−1 −19 ±20 −172 ±27 −247 ±15 −227 ±31 -665 ±48
(SLE mm yr−1) (0.05 ±0.06) (0.48 ±0.08) (0.69 ±0.04) (0.63 ±0.08) (1.85 ±0.13)
the GIC time series back to 1992, we estimate a
scaling factor from the climate-forced M15 modelled
data.
In summary, where reliable observations or val-
idated RCM simulations exist we use these and
where they do not we use the original M15 global
statistical modelling time series, resulting in about
86% of the mass trends being updated. Using this
approach, we obtain agreement between GRACE-
derived trends for 2003–2010 (Jacob et al 2012)and
the statistical model simulations to within 10 Gt yr−1.
Accounting for a 12 Gt yr−1 difference for HMA, we
also obtain agreement with the synthesis results in
Gardner et al (2013)towithin25Gtyr
−1.Wepar-
tition the errors for GIC in proportion to the data
source: i.e. 84% from the errors in the GRACE,
RCM and stereo photogrammetry data used and 16%
from the uncertainties in the statistical modelling
(Marzeion et al 2017).
Figure 9shows the results of this updated synthesis
of GIC (black dashed line; excluding PGIC) compared
with other published estimates. In table S6 we detail
the annual rates, while the pentad values are given
in table 2. There is, in general, less consistency between
published studies compared to the ice sheets, with stud-
ies that use GRACE typically giving a less negative
mass balance than those obtained from other meth-
ods. Marzeion et al (2017) estimated an average annual
mass loss of −184 Gt from several GRACE studies
for the period 2003–2009 (not including PGIC). The
equivalent mass loss value from studies using other
methods (WGMS 2017, Marzeion et al 2015, update
from Cogley 2009); update from Leclercq et al 2011)
was 230 Gt or more.
There are no studies on global GIC trends with a
central year more recent than 2007, making it difficult
to compare our new synthesis of GIC trends with other
work over the past decade. The most recent World
14
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 9. Post AR5 estimates of GIC mass balance and the IPCC AR5 synthesis values. Horizontal whiskers indicate the time span
of the estimate. The boxes are colour-coded to reflect measurement technique used (GRACE, empirical, geodetic or direct). Vertical
whiskers are the sum of quoted measurement uncertainty and the 1-sigma range due to inter-annual variability (see text for more
details). Dashed line is the synthesis of observations and modelled mass balance discussed in the main text.
Glacier Monitoring Service Global Glacier Change
Bulletin (WGMS 2017) suggests an average mass
loss from global glaciers of ∼179 Gt yr−1 and
∼237 Gt yr−1 for the period 2007–2015, using direct
and volume change methods, respectively (both values
adjusted for PGIC by subtracting the Greenland esti-
mate in Gardner et al 2013). These compare favourably
to our estimate of 181 Gt yr−1 for the same period.
3. Synthesis
Figures 10 and 11 and table 2summarise our synthe-
sis of land ice mass trends discussed in section 2(with
further details provided in the supplementary data).
The error bars, in this case, do not incorporate inter-
annual variability and are comprised of the combined
errors of the data sets used. In keeping with previ-
ous assessments, we also provide pentad means but
have also plotted and tabulated the annual land ice
mass balance values (figure 11 and table S6). These are
useful, for example, for comparing with inter-annual
estimates of ocean mass from GRACE and/or other
approaches (e.g. Dieng et al 2017).
Our total land ice mass contribution is smaller than
some estimates from, for example, an assessment of
the sum of the individual terms or GRACE-derived
ocean mass (Cheng et al 2017,Dienget al 2017)
or from a global GRACE-derived land ice estimate
(Jacob et al 2012). It is, however, consistent with other
assessments of the total change in ocean mass (minus
land hydrology) (Chen et al 2013).Inthecaseof
the GRACE-derived land ice mass trends (Jacob et al
2012), the difference, for the same period (2003–2010),
is due predominantly to the difference in estimates
for the AIS. Jacob et al (2012)usestheICE-5GGIA
model to correct GRACE data which over Antarc-
tica results in a correction that is about 60 Gt yr−1
larger than more recent studies, including our syn-
thesis, based on newer GIA solutions (Mart´
ın-Espanol
et al 2016b). Accounting for this, results in reason-
able agreement with our synthesis: −476 ±93 and
−516 ±39 Gt yr−1, respectively. If we also substitute
the most recent HMA estimate of −14 Gt yr−1 ,for
the −4±20 Gt yr−1 used in Jacob et al this brings the
numbers even closer (−486 versus −516 Gt yr−1 ).
Prior to the availability of GRACE data from 2003,
our synthesis incorporates data from other approaches
discussed previously and it is evident from figure
11 that this is reflected by larger uncertainties for
the total SLE contribution. It is also interesting to
note that the year-to-year differences in the total
SLE can exceed 400 Gt (1.1 mm SLE). Thus, even
the pentad estimates shown in figure 10 incorpo-
rate substantial inter-annual variability. This further
emphasises the challenges in extrapolating a rela-
tively short time series such as this (Wouters et al
2013b). For example, 1992 appears to be an excep-
tionally positive mass balance year in terms of the total
land ice contribution. This coincides with maximum
global cooling (of about 0.6 ◦C) after the eruption of
Mount Pinatubo in 1991, which may be a contributory
factor (Soden et al 2002).
3.1. Comparison with SLB studies
A number of studies have attempted to solve the
global SLB (i.e. equation 1) by directly estimating (or
15
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Figure 10. Pentad estimates of mass balance for the EAIS, GrIS, WAIS and GIC for the period 1992–2016 as listed in table 2.Vertical
whiskers indicate the one-sigma uncertainty derived from the errors in the data used to generate the estimates. Further details about
how these values were derived are provided in the supplementary data.
Figure 11. Our synthesis annual time series of mass trends for the ice sheets and GIC and the total SLE contribution of land ice (black
line).
synthesising published values for) all mass terms in
equation (2). Others have estimated change in total
ocean mass using either GRACE observations or by
subtracting ΔGMSLste ric (i.e. changes in sea level
due to thermal expansion and salinity, and there-
fore not due to mass) measured by Argo buoys from
ΔGMSLTot al obtained via satellite altimetry. Table 3
shows a comparison of a selection of these studies
with our synthesised land ice contributions for identical
epochs.
Attempting to close the SLB in this way requires
consideration of the contribution of land water
storage (LWS; also called terrestrial water storage,
TWS). Estimates of ΔMLWS are both highly uncer-
tain, particularly prior to the launch of GRACE, and
sensitive to the epoch chosen because of the large inter-
annual variability in the water cycle (Llovel et al 2011).
For example, both Reager et al (2016)andRietbroek
et al (2016) estimate that LWS provides a negative
contribution to the SLB (−0.33 and −0.29 mm yr−1
16
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Table 3. Published SLB estimates of ocean mass and land ice contributionsderived from the sum of land ice contributions, GRACE or
altimetry minus Argo (ΔGMSLtotal −ΔGMSLsteric ). In the case of the latter two, the inferred mass includes the land hydrology term
(see equation (2)). The values in brackets indicate the difference between each estimate and our synthesis land ice contributions for identical
epochs.
Study Time period Δocean mass from
sum of land ice mass
contributions
(mm yr−1)
Δocean mass
from GRACE
(mm yr−1)
Δocean mass from
altimetry/Argo
(mm yr−1)
Land ice sum
from this study
(mm yr−1)
Dieng et al 2017 January 2004–December 2015 1.93 (+0.71) 2.24 (+1.02) 2.35 (+1.13) 1.22
Chambers et al 2017 January 1992–December 2010 1.35 (+0.6) 1.99 (+1.04) 0.95
Chambers et al 2017 January 2005–December 2015 2.11 (+0.54) 2.20 (+0.63) 1.67
Leuliette and Nerem
2016
January 2005–December 2015 2.3 (+0.73) 1.67
Chen et al 2013 January 2005–December 2011 1.80 (+0.24) 1.79 (+0.23) 1.56
Purkey et al 2014 January 2003–December 2013 1.53 (0.0) 1.53
Purkey et al 2014 August 1995–March 2006 1.47 (0.60) 0.87
Dieng et al 2015a January 2003–December 2013 1.68 (+0.15) 1.85 (+0.32) 2.03 (+0.5) 1.53
Reager et al 2016 April 2002–November 2014 1.58 (+0.05) 1.53
Rietbroek et al 2016 January 2002–December 2014 1.37 (−0.16) 1.08 (−0.45) 1.53
Dieng et al 2015b January 2005–December 2013 2.04 (+0.44) 1.60
for the period 2002–2014, respectively), while both
Chambers et al (2017)andDienget al (2017) attribute
positive contributions (0.45 mm yr−1 for 1992–2013
and 0.25 mm yr−1 for 2004–2015, respectively). LWS
adds, therefore, considerable uncertainty in attempt-
ing to close the SLB. An additional uncertainty is the
influence of GIA on vertical land motion of ocean
basins and the resultant change in their volume. Obser-
vations of vertical land motion in mid ocean basins
are absent and rates depend on GIA models that
present a substantial spread in term of the impact on
absolute sea level, as measured by satellite altimetry
(Tamisiea 2011).
Our estimates of SLE contributions from land ice
are consistently smaller than the ocean mass estimates
in the SLB studies listed in table 3apart from one
study (Rietbroek et al 2016). For example, for the
epoch 1993–2015, our land ice sum produces a SLE
contribution of 28 mm compared to 38 mm in Dieng
et al (2017). Using our land ice estimate would not
permit closure of the SLB in that study and requires
a positive value for ΔMLW S and/or ΔMother .How-
ever, it is clear from table 3that global ocean mass
estimates, particularly those derived from GRACE,
are currently inconsistent and present challenges for
closing the SLB. An outstanding issue for these esti-
mates is the GIA model used to correct for solid Earth
effects, which have a spread equivalent to 1.4 mm yr−1
SLE but which alsodirectly impacts the GMSL measure-
ment made by altimetry (Tamisiea 2011). In addition,
the earlier part of the satellite altimeter record of GMSL
(relevant to column five in table 3), obtained from
Topex/Poseidon is subject to a drift term that has
been accounted for in some studies but not others
(Watson et al 2015). There are also small, but non-
random, effects from other factors including ocean
floor deformation (Frederikse et al 2017)andwater
vapour (e.g. Dieng et al 2017).
4. Summary and outlook
In this review, we have concentrated, primarily, on
post-AR5 estimates of the land ice contribution to SLR
from 1992–2016, and compiled a single time series of
global ice mass trends for this period (figure 11).
Since 2003, in particular, with the addition of
GRACE data, uncertainties in both ice sheet and
GIC contributions have been reduced and agreement
between GIC estimates has improved significantly
(Marzeion et al 2017). Despite some issues of sig-
nal to noise limitations for smaller GIC sectors, and
acknowledging the uncertainties associated with High
Mountains Asia, we have demonstrated that GRACE
can provide unbiased land ice trends. Incorporating
other techniques such as satellite-based stereo pho-
togrammetry (e.g. Brun et al 2017) and altimetry for
regions with poor signal to noise (Scandinavia, Cen-
tral Europe, Caucasus, low latitudes and New Zealand)
has reduced the trend uncertainties and provides an
optimised global approach.
Taking this approach, our combined land ice con-
tribution for the satellite era is in broad agreement,
for example, with the AR5 synthesis for the ice sheets
up to 2012, (figures 5,6and 7) and at the lower end
for GIC up to 2010 (figure 9). For the most recent
5 year period (2012–2016 in table 2), we found an aver-
age global contribution of 665 Gt yr−1 (1.85 mm yr−1
SLE), with Greenland contributing 37% (247 Gt yr−1
or 0.69 mm yr−1 SLE) and GIC contributing 34%
(227 Gt yr−1 or 0.63 mm yr−1 SLE). Antarctica as a
whole contributed the remainder, though the vast
majority was from WAIS (172 Gt yr−1 or 0.48 mm yr−1
SLE) with EAIS close to balance.
Our land ice contribution time series results,
in general, in a smaller contribution to SLR than
other assessments of both individual components of
ΔGMSLmass and SLB estimates based on the total
17
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
change in mass of the ocean (e.g. Chambers et al
2017,Dienget al 2017). There are several possible
reasons for this. First, the largest difference is in our
GIC estimates where we use an updated statistical
modelling time series (Marzeion et al 2017)thathas
lower mass loss rates compared to the previous version.
In addition, for several regions, we have substituted
modelled values for 2003–2016 with observation-based
estimates (from GRACE and, for HMA, from satel-
lite stereo-photogrammetry), all of which have lower
mass loss values. This means we obtain a mean mass
contribution of 189 Gt yr−1 (0.53 mm yr−1 SLE) for
2003–09 compared with, for example, 215 Gt yr−1 in
the consensus study of Gardner et al (2013). Most
of the difference between these values is explained by
our lower estimate for the HMA (14.5 vs 26 Gt yr−1).
Second, for the GrIS, we use a new 1 km downscaled
version of the regional climate model that results in a
marginally smaller mass loss for the period 1992–2002
compared with previous IOM trends (e.g. Van den
Broeke et al 2016)ofabout0.1mmyr
−1 SLE. Third,
the most recent GIA solutions for Antarctica are con-
verging on a smaller mass correction for GRACE data
compared with earlier solutions (Mart´
ın-Espanol et al
2016b).Thedifferenceisasmuchas60Gtyr
−1 or the
equivalent to 0.2 mm yr−1 SLE when using GRACE
data to determine AIS trends. Finally, we have taken
care to ensure that PGIC are not double counted in
our time series. This has occurred in some, but not all,
previous studies and, in particular, in SLB assessments
where the authors may be unaware that the ice sheet
mass trends implicitly include PGIC, but where they
are also included in the GIC trends used (e.g. Dieng
et al 2017). In Greenland, the PGIC contribution is
on the order of 0.1 mm yr−1 (table 1). These three fac-
tors, combined, could be responsible for as much as
a0.4mmyr
−1 difference for the land ice contribution
to SLR. Combined, our updates and improvements
to previous land ice time series have resulted in a
reduction of 6±1.1 mm SLE compared to a recent
SLB estimate of the land ice contribution for 2003–
2015 (Dieng et al 2017), equivalent to a difference
of 0.46 mm yr−1. Our smaller land ice contribution
makes closing the SLB, potentially, more challenging.
It implies a positive contribution from land hydrol-
ogy and/or other factors such as a GIA trend on ocean
basin volume closer to the lower end of estimates of
−0.15 mm yr−1 (Tamisiea 2011).
Whilst it has been instructive to compare our land
ice time series with SLB estimates of ocean mass (table
3), either from GRACE or from altimetry minus Argo
(ΔGMSLtotal −ΔGMSLster ic), uncertainties in global
GIA (e.g. Tamisiea 2011, Spada 2017), low degree and
order corrections to GRACE, steric estimates for high
latitudes and the deep ocean and the land hydrology
component of the SLB limit the value of a quantita-
tive comparison with our land ice time series. We note,
in addition, that there is a large spread in GRACE-
derived ocean mass trends in table 3,varyingby
more than a factor of 2, which cannot be explained
by the slightly different epochs used. Nonetheless, with
a longer time series of observations, improvements
in the corrections mentioned above and the addition
of GRACE follow on data, SLB assessments will be a
helpful tool for constraining land ice mass trends.
The GRACE mission ended in September 2017 with
the failure of one of the satellites and the quality of the
data during the last year of the mission was degraded
due to aging electronics. A GRACE follow on mis-
sion was launched in May 2018 and, with a successful
deployment, will provide continuity of gravity-derived
mass trends over land ice. CryoSat-2 is still in orbit and
has enough fuel to last until at least 2020, continuing
the elevation change measurements over the ice sheets
and larger ice caps that began in 2010. In addition, the
next generation laser altimeter mission, ICESat-2, also
has a planned launch date of 2018. With three pairs
of beams, this system will provide improved coverage
of GIC, in particular, offering an additional measure-
ment tool for land ice trends (Markus et al 2017).
Together these satellite missions will provide unprece-
dented accuracy and resolution over land ice globally
and help further refine and improve our understand-
ing of land ice contributions to contemporary sea level
rise. They will also provide robust and reliable calibra-
tion and validation for statistical scaling and numerical
modelling approaches that can, and have been, used
to extend the mass trend record back in time (e.g.
Leclercq et al 2011, Marzeion et al 2015)andfor
projecting future changes, driven by climate forcing
scenarios. We have developed, and presented, a well
constrained and robust record of the land ice contri-
bution to SLR for the last 25 years. With successful
deployment of slated satellite missions, we have the
potential for both improved accuracy and resolution for
monitoring land ice trends in the future.
Acknowledgments
JLB and RMW were supported by the European
Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme
under grant agreement No 694188 (GlobalMass). JLB
was also supported by a Leverhulme Trust Fellowship
RF-2016-718. The authors would like to thank the fol-
lowing colleagues for providing datasets used in this
study: Valentina Barletta; Stephen Chuter; Ellyn Ender-
lin; Andreas Groh; Martin Horwath; Bryant Loomis;
Scott Luthcke; Ingo Sasgen; Ernst Schrama; Michiel
van den Broeke; and David Wiese.
ORCID iDs
Jonathan L Bamber https://orcid.org/0000-0002-
2280-2819
Richard M Westaway https://orcid.org/0000-0001-
6102-1540
18
Environ. Res. Lett. 13 (2018) 063008 JBamberet al
Ben Marzeion https://orcid.org/0000-0002-6185-
3539
Bert Wouters https://orcid.org/0000-0002-1086-
2435
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