measuring ice mass loss from melting ice sheets

MEASURING ICE MASS LOSS FROM MELTING ICE SHEETS

Christopher HarigUniversity of Arizona Mar. 07, 2016

NASA

Changes in the climate

New techniques to measure mass better

Mathematical interlude

Antarctica

Greenland

THE STORY

CO2

gas p

pm

250

300

350

400

1850 1875 1900 1925 1950 1975 2000 2025

CO2Global Temperature

Atmospheric CO2 and Global Temperature

0.75

0.5

0.25

0

-0.25

-0.5

-0.75

Temp Anom

aly from 61’-90’ (deg C)

2000 368

CLIMATE CONTEXT

Morice et al., 2012 (UK Met Office)MacFarling Meure et al., 2006, Keeling et al., 2005

2015 398

CO2

gas p

pm

200

350

500

650

800

Year

1850 1900 1950 2000 2050 2100

CO2CO2 Scenario A1BGlobal TemperatureTemperature Projection for A1B

3

2

0

-1

1

Temp Anom

aly from 61’-90’ (deg C)

CLIMATE CONTEXT

IPCC AR4 (2007)

Atmospheric CO2 and Global Temperature

200

350

500

650

800

Year

1850 1900 1950 2000 2050 2100

CO2CO2 Scenario A1BGlobal TemperatureTemperature Projection for A1B

Projected Global Temperature Changes(2090-2099) A1B Scenario

Atmospheric CO2 and Global Temperature3

2

0

-1

1

IPCC AR4 (2007)Figure SPM.6

CLIMATE CONTEXT

Greenland • Average altitude 2,135 meters• Thickness generally more than 2 km and maximum over 3 km• Melt entire sheet for 7.2 meters of sea level

Antarctica • Twice as big as Australia• Avg. thickness 2 km, and max thickness more than 4.7 km• Ice sheet contains 58 meters worth of sea level rise

POLAR ICE SHEETS

NASA

NASA

POLAR ICE SHEETS

How much mass is being lost/gained? Where are these changes occurring? How well do we know this?

NASA

NASA

SATELLITE GEODESYHow do we measure ice sheet mass?


Input Output Method / Surface Mass Balance

Count calories in and calories out




Laser/Radar Altimetry Look in a mirror

5

How Will ICESat Measure Earth’s Ice, Clouds, Oceans,Land, and Vegetation?

The GLAS instrument on ICESat will determine the distance from the satellite to the Earth’s surface andto intervening clouds and aerosols. It will do this by precisely measuring the time it takes for a shortpulse of laser light to travel to the reflecting object and return to the satellite. Although surveyors rou-tinely use laser methods, the challenge for ICESat is to perform the measurement 40 times a secondfrom a platform moving 26,000 km (16,000 mi) per hour. In addition, ICESat will be 600 km above theEarth and the precise locations of the satellite in space and the laser beam on the surface below must bedetermined at the same time.

The GLAS instrument on ICESat will measure precisely how long it takes for photons from a laser topass through the atmosphere, reflect off the surface or clouds, return through the atmosphere, collect inthe GLAS telescope, and trigger photon detectors. After halving the total travel time and applying corrections for the speed of light through the atmosphere, the distance from ICESat to the laser footprinton Earth’s surface will be known. When each pulse is fired, ICESat will collect data for calculating exactly where it is in space using GPS (Global Positioning System) receivers. The angle at which thelaser beam points relative to stars and the center of the Earth will be measured precisely with a star-tracking camera that is integral to GLAS. The data on the distance to the laser footprint on the surface,the position of the satellite in space, and the pointing of the laser are all combined to calculate the elevation and position of each point measurement on the Earth.

GPS

GPS

StarCamera

FOV

70m

170m

Ground Track

SurfacePhotonScatter

Photon Scatterdue to Cloudsand Aerosols

Centerof theEarth

Emitted1064 and532 nmLaserPulses

ReflectedLaserPulses

Orbit

Schematic illustration of the GLAS instrument making measurement from ICESat while orbiting the Earth.Graphic by Deborah McLean.

OPERATIONAL OVERVIEW

SATELLITE GEODESYAltimetry

Laser altimetryRadar altimetry

NASA NASA

Missions starting late 1990s

Missions starting early 1990s



Laser/Radar Altimetry

GRACE Time Variable Gravimetry


Look in a mirror

Step on a scale

SATELLITE GEODESYMeasuring changes in gravity

Seeber (2003)

LAGEOS-1,-2

SATELLITE GEODESYMeasuring gravity

Seeber (2003)

NASA

Wiki Commons

Gravity Recovery and Climate Experiment

Greenland • Launched April 2002. 5 year mission, still running.• Orbit altitude about 400 km. Orbits every 90 minutes.• Follow on mission planned for 2017 launch.

NASA

NASA

GRACE

How GRACE WorksGRACE is different from most Earth Observing satellites. Rather than imaging the Earth, it detects gravity changes by measuring the distance between the satellites themselves. But how does this distance measurement relate to gravity?

The gravity field of a body depends on its mass and shape. For a perfectly spherical and uniform body, the gravity field is simple and symmetric in any direction. The mass distribution of our planet, however, is irregular and ‘lumpy’. Molten rock flows in the Earth’s mantle to drive tectonic plate motion, enormous quantities of water are exchanged between the ocean and land, and atmospheric masses are also in continuous movement.

As the satellites move through this uneven gravity field, the orbits of each satellite are slightly disturbed, which affects the distance between the two spacecraft. GRACE’s uniquely precise microwave ranging system measures changes in the approximately 220 km distance between the satellites with an accuracy of some microns – about one-tenth the width of a human hair!

In addition to measuring the distance between each other, the satellites use the GPS system to determine precisely where and when the measurements were taken. The ultra-precise measurements taken by GRACE, combined with tracking data from the GPS satellites, allows scientists to map the Earth’s gravity field with unprecedented accuracy.

How GRACE WorksGRACE is different from most Earth Observing satellites. Rather than imaging the Earth, it detects gravity changes by measuring the distance between the satellites themselves. But how does this distance measurement relate to gravity?

The gravity field of a body depends on its mass and shape. For a perfectly spherical and uniform body, the gravity field is simple and symmetric in any direction. The mass distribution of our planet, however, is irregular and ‘lumpy’. Molten rock flows in the Earth’s mantle to drive tectonic plate motion, enormous quantities of water are exchanged between the ocean and land, and atmospheric masses are also in continuous movement.

As the satellites move through this uneven gravity field, the orbits of each satellite are slightly disturbed, which affects the distance between the two spacecraft. GRACE’s uniquely precise microwave ranging system measures changes in the approximately 220 km distance between the satellites with an accuracy of some microns – about one-tenth the width of a human hair!

In addition to measuring the distance between each other, the satellites use the GPS system to determine precisely where and when the measurements were taken. The ultra-precise measurements taken by GRACE, combined with tracking data from the GPS satellites, allows scientists to map the Earth’s gravity field with unprecedented accuracy.

GRACEHow it works.

Measure the distance between satellites. This changes as you pass over different land, such

as mountains.

CSR Texas, 2011 edu poster

GRACEGRACE is measuring gravity at an UNPRECEDENTED level of precision and resolution. The dramatically improved map of the mean Earth gravity field helps to refine our knowledge of the composition and structure of the Earth, and it provides the accurate reference surface relative to which deep ocean currents can be determined.

The changes are given in milligal. A milligal is a convenient unit for describing variations in gravity over the surface of the Earth. 1 milligal (or mGal) = 0.00001 m/s2, which can be compared to the total gravity on the Earth’s surface of approximately 9.8 m/s2. Thus, a milligal is about 1 millionth of the standard acceleration on the Earth’s surface. On the front panel the changes after the Sumatra-Andaman earthquake are measured in microgal, which is thousand times smaller than the milligal.

Why is GRACE Special

GRACE is UNIQUE, as it gives a global, consistent and uniform quality measurement of mass flux (movement of material around and within the Earth), observing geophysical processes within every one of the Earth’s sub-systems (land, ocean, atmosphere, terrestrial water storage and ice sheets). See Greenland and Sumatra-Andaman on front

Of particular interest for understanding the Earth’s climate system, GRACE MONITORS the movement of water over the Earth’s surface with a level of detail never seen before. See Amazon on front

GRACE spans ALL of geosciences; the results address questions within the “Climate/Variability”, “Water Cycle” and “Earth Surface & Interior” focus areas of NASA’s Earth science priorities.

The measurements GRACE is providing from Earth orbit would be impossibly expensive if they were done on the ground - THERE IS NO SUBSTITUTE for observing the whole Earth from Space.

GRACE is a joint project of the American space agency NASA, the German Aerospace Center (DLR), the University of Texas Center for Space Research (CSR), GeoForschungsZentrum Potsdam (GFZ) and the Jet Propulsion Laboratory.

Best global gravity map from decadesof satellite data before GRACE Gravity map from four years of GRACE only data

EXPLANATION OF FRONT PANELS

AMAZON: The amount of water stored in the Amazon basin changes with the seasons. When scientists discuss the gravity field and shape of the Earth, they often do so in terms of a surface called the geoid. It is the level surface that approximates sea level in the absence of disturbing forces. An increase in the geoid height indicates an increase in mass; a decrease in the geoid height indicates less mass. The red colors in the images show the increased gravity due to surplus of water storage in the rainy seasons; and the blue colors show the reduced gravity in the dry seasons. Thus the changing colors represent the influence of seasonal weather and climate variations. Measuring total water storage at such continental scales is impossible from ground measurements. The amount of water stored in the Amazon basin changes with the seasons. When scientists discuss the gravity field and shape of the Earth, they often do so in terms of a surface called the geoid. It is the level surface that approximates sea level in the absence of disturbing forces. An increase in the geoid height indicates an increase in mass; a decrease in the geoid height indicates less mass. The red colors in the images show the increased gravity due to surplus of water storage in the rainy seasons; and the blue colors show the reduced gravity in the dry seasons. Thus the changing colors represent the influence of seasonal weather and climate variations. Measuring total water storage at such continental scales is impossible from ground measurements.

GREENLAND: As the ice melts from the edges of the Greenland ice-sheet, the gravitational attraction from the Greenland land-mass decreases, and this is sensed by GRACE. The red color shows area of loss. The measurements in 2008 show a considerably lesser mass in South-East and Western Greenland than was present in 2003. The mass of the Greenland ice sheet acts as a very sensitive barometer of the nature of present day climate variability.

SUMATRA: For mitigation of consequences of an earthquake, it is important to understand the dynamics and changes in the local crustal structure that accompanies an earthquake. In addition to the conventional methods of seismology and surface deformation measurements, gravity changes have proven to be an unexpectedly valuable source of information. GRACE data clearly show the changes to the Earth’s gravity field in the Sumatra-Andaman region due to the SA Earthquake of 2004.

Best global gravity map from decades of satellite data

before GRACE.Gravity map from only 4 years

of GRACE data

Static gravity field

NASA

GRACE DATATime variable gravity field

• Orbits every 90 minutes• Add 1 month worth of orbits• Get a new global gravity field every month in Spherical Harmonics• Can look at signals that change monthly such as seasonal monsoons, ocean currents, and ice sheets.• Also has influence from solid Earth deformation.

THE PROBLEM

THE PROBLEM

Spherical harmonic functions for degree L = 7 and orders m=0,2,4,6.

Spherical harmonics Ylm

are eigenfunctions of Laplace’s equation and form an orthogonal basis for solutions.

Spherical Harmonics

The domain of data availability or region of interest is R ∈ Ω.

R2

R1 ΘΘ

π−Θ

The spherical harmonics Ylm are not orthogonal on R:

Loss of orthogonality leads to signal leakage.So we construct a new basis from the eigenfunctions of D.

These new doubly orthogonal functions are called Slepian functions, g(r).

Z

RYlmYl0m0d⌦ = Dlm,l0m0 .

THE PROBLEM

On the sphere, we solve for the spherical harmonic expansion coefficients of the functions as:

We define the spatiospectral localization kernel, with eigenvalues λ, as

LX

l0=0

l0X

m0=�l0

Z

RYlmYl0m0d⌦

�gl0m0 = �glm

Dlm,l0m0 =Z

RYlmYl0m0d⌦.

The eigenfunctions of D expand to bandlimited Slepian functions, g(r), which form a localized basis orthogonal on R and also on Ω.

THEORY SUMMARY

� =Z

Rg2d⌦

�Z

⌦g2d⌦ = maximum.

These functions satisfy Slepian’s concentration problem to the region R of area A:

THEORY SUMMARY

These functions satisfy Slepian’s concentration problem to the region R of area A:

The Shannon number, or sum of eigenvalues,

is the effective dimension of the space for which the bandlimited g are a basis.

So, we have concentrated a poorly localized basis of (L + 1)2 functions, Ylm, both spatially and spectrally,

to a new basis with only about N functions, g.

� =Z

Rg2d⌦

�Z

⌦g2d⌦ = maximum.

N = (L + 1)2A

4⇡,

THEORY SUMMARY

240˚

260˚

280˚

α=1 λ=1 α=2 λ=0.999 α=3 λ=0.998

60˚

70˚

α=4 λ=0.994

240˚

260˚28

0˚

α=5 λ=0.992 α=6 λ=0.985 α=7 λ=0.979

60˚

70˚

α=8 λ=0.967

240˚

260˚

280˚

300˚ 3

20˚

340˚

α=9 λ=0.94 α=10 λ=0.93

−1.0 −0.5 0.0 0.5 1.0magnitude

α=11 λ=0.898

60˚

70˚

300˚ 3

20˚

340˚

α=12 λ=0.869

Depends on 3 variablesOutline of region (Greenland)Degree of bandwidth (L = 60)Truncation of basis (N = 21)

SATELLITE GEODESYSlepian functions

LX

l0=0

l0X

m0=�l0

Z

RYlmYl0m0d⌦

�gl0m0 = �glm

Localization by optimization

Harig and Simons (2012)

Mathematical benefitsOrthogonalitySparsityIncreased signal to noise

Slepian functionsSATELLITE GEODESY

Harig and Simons (2015b)

Used in the fields of:computer graphicscosmologygeodetic seismologymedical sciencesplanetary magnetismsignal processing

240˚

270˚

α=1 λ=0.999 α=2 λ=0.998 α=3 λ=0.994

−85˚

−85˚

−80˚

−75˚α=4 λ=0.985

240˚

270˚

α=5 λ=0.975 α=6 λ=0.961 α=7 λ=0.926

−85˚

−85˚

−80˚

−75˚α=8 λ=0.908

180˚

210˚

240˚

270˚

α=9 λ=0.877 α=10 λ=0.8

−1.0 −0.5 0.0 0.5 1.0magnitude

α=11 λ=0.766

−85˚

−85˚

−80˚

−75˚−70˚

−65˚

α=12 λ=0.723

ANTARCTICA

NASA

ANTARCTICA

Distinct mass variability in different regions

How do ice sheets lose ice?ANTARCTICA

Credit: NASA

Bot: The calving front of Thwaites Ice Shelf looking at the ice below the water's surface. Credit: NASA / Jim Yungel

Top: The calving front of the Filchner Ice Shelf, Antarctica. Copyright Jonathan Bamber. (NERC)

Sheds ice by flow and calvingANTARCTICA

ANTARCTICA

Radar image of ice speedRignot (2008)

Early estimates

Hanna, et al. (2013)

(Ice, Cloud, and land Elevation Satellite) period: the mass budget estim-ate gave the maximum loss rates at 2260 6 53 Gt yr21 and GRACE theminimum, at 2238 6 29 Gt yr21 (ref. 20). On a basin-by-basin basis,agreement between the mass budget method and other techniques pro-vides validation for the practice of partitioning mass-balance changebetween discharge and SMB components, demonstrating that in thenorthern part of Greenland, the dominant cause of mass change wasatmospheric in origin, while in the southern part it was ice dynamics.

The new, reconciled IMBIE GRACE estimates of whole Antarcticmass balance are now largely in agreement with one another, withspreads of 30–50 Gt yr21 between the largest and smallest 2003–08 rates.Previously published GRACE values show spreads around twice as largefor similar time periods. In the Antarctic Peninsula and WestAntarctica, the IMBIE estimates from laser altimetry and GRACE arein good agreement, in contrast to East Antarctica2. For East Antarctica, amass gain of 1101 Gt yr21 for 2003–08 has been proposed recently onthe basis of laser altimetry19, which is larger than the IMBIE GRACEestimate of 135 Gt yr21 and near the upper end of the laser altimetryestimates2.

Recent advances in ice-sheet modellingKey improvements and future challengesSignificant improvements in ice-sheet modelling have been made sincethe publication of IPCC AR41, motivated by the need to understandcontinuing changes and by the challenge to make more realistic projec-tions for the next few centuries. The primary improvements concernmechanical approximations made to the ice flow equations. The veryfirst generation of ice-sheet models was based on the shallow iceapproximation21. Such models assume that all resistance to flow is pro-vided by shear-stress gradients in the vertical, which is valid for creepingice-sheet flow, but not when other ice-dynamical features such as icestreams and ice sheet/ice shelf coupling come into play in ice-sheet

evolution. More recent ice-sheet models now include horizontal stressgradients, and can be classified into four categories of increasing com-plexity and computational cost. (1) Ice shelf/stream models are based onthe shallow-shelf approximation22. They include horizontal stress gra-dients, but neglect the vertical shear stresses (which is valid for rapid iceflow at low basal traction). (2) Hybrid models use some combination ofsolutions from the shallow-ice approximation (to account for the ver-tical shearing component of flow within grounded ice) and the shallow-shelf approximation (to account for the horizontal stress couplingtaking place in ice shelves or regions of rapid sliding)21,23,24. (3) Moreelaborate higher-order models treat the vertical dimension more rigor-ously, with the only approximation being the hydrostatic assumption(pressure at any point in the ice is due only to the weight of the ice aboveit and not due to ice flow)25,26. (4) Finally, a few models solve the equa-tions of motion without neglecting any terms. These are called ‘FullStokes models’, and have recently demonstrated their ability to performcentury-timescale simulations applied to a whole ice sheet27,28.

Spatial resolution of models is the second aspect that has beenimproved. Hardly any model is now run with a spatial grid size greaterthan 20 km, but this resolution is still not high enough to resolve icestreams, which are often only a few kilometres wide. Moreover, grounding-line migration and calving require subkilometre resolution. Unstructuredgrids (for finite element models27,28) or adaptive mesh refinement29 are twostrategies that have proven efficient at treating this difficulty with accept-able computational cost.

A third improvement has been enabled through satellite and ground-based observations, such as the quantification of surface velocities andvelocity change from satellite interferometry30, surface elevation changethrough satellite and airborne campaigns (IceBridge), and high-resolutionbedrock and ice thickness measurements31. Ice-sheet model behaviour ishighly dependent on initial and boundary conditions and faces the dif-ficulty that drag at the ice–bed interface is poorly known. Inverse methods

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GRACEMass budgetRadar altimetryLaser altimetryIMBIE combinedAntarctica Antarctica

Greenland Greenland

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a b

Figure 1 | Summary of estimates of rates of ice mass change for Antarcticaand Greenland. In the studies published before 2012 (ref. 2, a) and in 2012(b), each estimate of a temporally averaged rate of mass change is representedby a box whose width indicates the time period studied, and whose heightindicates the error estimate. Single-epoch (snapshot) estimates of mass balanceare represented by vertical error bars when error estimates are available, and are

otherwise represented by asterisks. Line colour indicates mass assessmenttechnique (see key); line type indicates data source. 2012 studies in b compriseIMBIE combined estimates2 (solid lines), and estimates by Sasgen andothers16,20 and King and others11 (dashed lines), Zwally and others19 (dot-dashed lines), Harig and Simons89 and Ewert and others90 (dotted lines).

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ANTARCTICA

Radar image of ice speedRignot (2008)

Wilkes Land, and their spatial distribution (Fig. 2A)is strongly suggestive of snowfall-driven growth.Two glaciers in East Antarctica are losing mass(Fig. 2B). From 1992 to 2003, the fast-flowingtrunks of the Totten and Cook glaciers deflated by5.0 ± 0.5 and 2.4 ± 0.2 km3 year−1. Although thesefigures are only in rough coincidence with thosedetermined from interferometry [0 ± 2 and –8 ±5 km3 year−1, respectively, in (9)], the signals areclear and the trends definitely established.

West Antarctica and theAntarctic PeninsulaThe West Antarctic Ice Sheet (WAIS) containsenough ice to raise global sea levels by more than5m and, according to altimetry and interferometry,one key sector is in a state of rapidretreat (23, 34). Glaciers draining intothe Amundsen Sea (Fig. 2A) are los-ing mass because of an ice-dynamicperturbation. During the 1990s, forexample, the Pine Island Glacier re-treated by up to 1.2 km year−1 (34),thinned by up to 1.6 m year−1 (23),and accelerated by around 10%(39); the ice loss has been implicatedin the freshening of the Ross Seasome 1000 km away (40). Through-out the 1990s, independent altimeter(7, 14, 17, 18) and interferometer (9)surveys of the WAIS as a whole werein notable, possibly fortuitous, agree-ment (Table 1), placing its annuallosses in the range 47 to 59Gt year−1.The mass balance of the WAIS hasbeen dominated by the losses fromglaciers of the Amundsen sector, can-celed to a degree by some snowfall-driven coastal growth and growtharising from thewell-established shut-down of the Kamb Ice Stream (41).

There has been a report of an ac-celerated recent sea-level contribution(42) based on satellite and aircraft al-timetry, and the gravimetric surveyshave also estimated a rate ofmass losssince 2002 of between107 and136Gtyear−1 (Table 1). Such an accelera-tion (an increase in sea-level trend of0.2 mm year−1, or about 10%) wouldbe a cause for considerable concern.However, the altimeter data fromwhich accelerated mass losses werederived in (42) span less than 5% oftheWAIS area and use three altimeterswith markedly different measurementerrors. Furthermore, both data setsspan a short time interval in whichforecast models indicate that a 309-Gtaccumulation deficit occurred (38).Taking these factors into account, it isunlikely that the WAIS mass loss hasaltered substantially since the 1990s.

During the past decade, there have beennotable glaciological changes at the AntarcticPeninsula (AP): The Larsen Ice Shelf thinned(43) and sections collapsed (44), accelerating icedischarge into the oceans by some 0.07mmyear−1

ESL rise (45). However, the majority of AP iceforms the continental ice cap of Dyer Plateau.This exhibits snowfall-driven growth (Fig. 2A)that is sufficient to cancel the accelerated flowfrom the Larsen-A and -B catchments. The APcontribution to sea level is negligible.

GreenlandSince the most recent IPCC report, there havebeen seven estimates of Greenland mass im-balance based on satellite altimetry (18), interfer-

ometry (12), and gravimetry (11, 15, 16, 19, 20).There is consensus that during the 1990s the in-terior underwent modest snowfall-driven growth,which appears to be associated with a precipita-tion trend present in the meteorological record(32), offset by losses from lower altitude regions(Fig. 3, A and B). The decadal imbalance is notaccurately determined. The more positive satel-lite altimeter estimate (18) is affected by signal lossin the steeper coastal margins; the aircraft lasermeasurements (8) are relatively sparse, althoughmore sensitive to losses from marginal glaciers;and the mass-budget estimate (12) is underminedby the uncertainty of some 50 Gt year−1 in theaccumulation. Nonetheless, the consensus ofthese measurements suggests a net loss in the1990s of some 50 Gt year−1.

Satellite interferometry (12, 24) has alsoestablished that from 1996 to 2005, mass lossesthrough flow increased by 102 Gt year−1, andmeteorological estimates (32) (Fig. 1B) of thesurface-mass imbalance decreased some 20 Gtyear−1 in the same period because of increasedmelting. Gravimetric surveys too support an in-creased mass loss (11, 15, 16, 19, 20). However,the interferometric and gravimetric records areshort and reflect the considerable variability inthemass flux of tidewater glaciers and the surfacemass balance. For example, the ice fluxes of twoglaciers that by 2005 were responsible for 43 Gtyear−1 of the increased discharge had by late2006 declined to within 10 Gt year−1 of their levelin 2000 (46), whereas in the past 14 years, the3-year variability in surface mass imbalance hasranged from –130 to 120 Gt year−1 (Fig. 1B). Inaddition, not all gravimetric estimates capture theknown spatial distribution of change; one that does(16) (Fig. 3B) is some 120 Gt year−1 more positivethan other estimates, and some understanding ofthe cause of these discrepancies is needed. In-creased mass loss from Greenland has occurred,but the decadal change is probably modest.

Implications for the FutureIt is reasonable to conclude that, today, the EAISis gaining some 25 Gt year−1, the WAIS is losingabout 50 Gt year−1, and the GIS is losing about100 Gt year−1. These trends provide a sea-levelcontribution of about 0.35 mm year−1, a modestcomponent of the present rate of sea-level rise of3.0 mm year−1. Because 50 Gt year−1 is a veryrecent contribution, the ice sheets made little con-tribution to 20th-century sea-level rise. However,what has also emerged is that the losses are dom-inated by ice dynamics.Whereas past assessments(47) considered the balance between accumulationand ablation, the satellite observations reveal thatglacier accelerations of 20 to 100% have occurredover the past decade. The key question today iswhether these accelerations may be sustained, oreven increase, in the future.

The question is difficult because the causes ofthe instabilities have yet to be established. The geo-

Fig. 2. (A) Rate of elevation change of the Antarctic Ice Sheet,1992 to 2003, from ERS satellite radar altimetry [redrawn from(14)]. Also shown (inset) is the bedrock geometry, highlightingfloating (light gray), marine-based (mid-gray) and continental-based (black) sectors. (B) Elevation change of the trunks (flowin excess of 50 m year−1) of the Pine Island [Basin GH in (A)],Thwaites (Basin GH), Totten (Basin C′D), and Cook (Basin DD′)glaciers. All the deflating glaciers coincide with marine-basedsectors of the ice sheet. An ice-dynamic origin of the thinningof the East Antarctic glaciers has yet to be confirmed byinterferometry. However, the correlation of the thinning withflow velocity and the fact that the thinning rate is secular makeice dynamics the likely cause of all Antarctic mass losses.

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(DeConto & Pollard 2003), and then expanding further asthe surrounding ocean cooled (Liu et al. 2009, Pusz et al.2011). Its growth reflects the transition of the Earth froma ‘greenhouse’ to an ‘icehouse’ state at the Eocene-Oligocene (EO) climate transition, which spannedc. 300–400 thousand years and is reflected in deep seabenthic foraminiferal records (Katz et al. 2008, Milleret al. 2008, Pusz et al. 2011). The ice sheet initiated uponthe highland topographies of Antarctica and expanded tocover the entire continent (DeConto & Pollard 2003).Given our previous knowledge of the bed, based largelyon broadly spaced radio-echo sounding surveys, ithas long been assumed that important East Antarctic

inception points were the Gamburtsev SubglacialMountains (GSM), Dronning Maud Land (DML) andthe TransantarcticMountains (TAM; Fig. 1). However, itis possible that other, yet to be discovered, subglacialmountain blocks may have also acted as minor nucleationpoints for East Antarctic ice.

Between 33.7 and 14 Ma, local offshore sedimentcores and the global benthic oxygen isotope recordsuggest that the EAIS margin waxed and waned on ascale similar to Pleistocene Northern Hemisphere icesheet fluctuations (Naish et al. 2001, Miller et al. 2008)before a potentially more stable continental EAIS wasestablished under a colder climate. Along with modelling

Fig. 1. Antarctic BEDMAP2 topography (Fretwell et al. 2013) rebounded after the removal of present ice load. The black lineindicates the modern grounding line (Scambos et al. 2007) and the white line indicates sea level under rebounded topographicconditions. AP = Antarctic Peninsula, CL = Coats Land, DML = Dronning Maud Land, EL = Enderby Land,EW = Ellsworth-Whitmore block, GSM = Gamburtsev Subglacial Mountains, GVL = George V Land, KL = Kemp Land,LG = Lambert Graben, MBL = Marie Byrd Land, MRL = Mac. Robertson Land, PEL = Princess Elizabeth Land,QML = Queen Mary Land, RB = Recovery Basin, TA = Terre Adélie, TAM = Transantarctic Mountains, TT = Thiel Trough,VSH = Vostok Subglacial Highlands, WIIL = Wilhelm II Land, WL = Wilkes Land.

GLACIAL GEOMORPHOLOGY OF THE ANTARCTIC ICE SHEET BED 725

ANTARCTICA

Elevation of Antarctica with ice removal and isostatic compensation

Jamieson et al. (2014)

ANTARCTICA

Surface density change estimate from GRACE

Wilkes Land, and their spatial distribution (Fig. 2A)is strongly suggestive of snowfall-driven growth.Two glaciers in East Antarctica are losing mass(Fig. 2B). From 1992 to 2003, the fast-flowingtrunks of the Totten and Cook glaciers deflated by5.0 ± 0.5 and 2.4 ± 0.2 km3 year−1. Although thesefigures are only in rough coincidence with thosedetermined from interferometry [0 ± 2 and –8 ±5 km3 year−1, respectively, in (9)], the signals areclear and the trends definitely established.

West Antarctica and theAntarctic PeninsulaThe West Antarctic Ice Sheet (WAIS) containsenough ice to raise global sea levels by more than5m and, according to altimetry and interferometry,one key sector is in a state of rapidretreat (23, 34). Glaciers draining intothe Amundsen Sea (Fig. 2A) are los-ing mass because of an ice-dynamicperturbation. During the 1990s, forexample, the Pine Island Glacier re-treated by up to 1.2 km year−1 (34),thinned by up to 1.6 m year−1 (23),and accelerated by around 10%(39); the ice loss has been implicatedin the freshening of the Ross Seasome 1000 km away (40). Through-out the 1990s, independent altimeter(7, 14, 17, 18) and interferometer (9)surveys of the WAIS as a whole werein notable, possibly fortuitous, agree-ment (Table 1), placing its annuallosses in the range 47 to 59Gt year−1.The mass balance of the WAIS hasbeen dominated by the losses fromglaciers of the Amundsen sector, can-celed to a degree by some snowfall-driven coastal growth and growtharising from thewell-established shut-down of the Kamb Ice Stream (41).

There has been a report of an ac-celerated recent sea-level contribution(42) based on satellite and aircraft al-timetry, and the gravimetric surveyshave also estimated a rate ofmass losssince 2002 of between107 and136Gtyear−1 (Table 1). Such an accelera-tion (an increase in sea-level trend of0.2 mm year−1, or about 10%) wouldbe a cause for considerable concern.However, the altimeter data fromwhich accelerated mass losses werederived in (42) span less than 5% oftheWAIS area and use three altimeterswith markedly different measurementerrors. Furthermore, both data setsspan a short time interval in whichforecast models indicate that a 309-Gtaccumulation deficit occurred (38).Taking these factors into account, it isunlikely that the WAIS mass loss hasaltered substantially since the 1990s.

During the past decade, there have beennotable glaciological changes at the AntarcticPeninsula (AP): The Larsen Ice Shelf thinned(43) and sections collapsed (44), accelerating icedischarge into the oceans by some 0.07mmyear−1

ESL rise (45). However, the majority of AP iceforms the continental ice cap of Dyer Plateau.This exhibits snowfall-driven growth (Fig. 2A)that is sufficient to cancel the accelerated flowfrom the Larsen-A and -B catchments. The APcontribution to sea level is negligible.

GreenlandSince the most recent IPCC report, there havebeen seven estimates of Greenland mass im-balance based on satellite altimetry (18), interfer-

ometry (12), and gravimetry (11, 15, 16, 19, 20).There is consensus that during the 1990s the in-terior underwent modest snowfall-driven growth,which appears to be associated with a precipita-tion trend present in the meteorological record(32), offset by losses from lower altitude regions(Fig. 3, A and B). The decadal imbalance is notaccurately determined. The more positive satel-lite altimeter estimate (18) is affected by signal lossin the steeper coastal margins; the aircraft lasermeasurements (8) are relatively sparse, althoughmore sensitive to losses from marginal glaciers;and the mass-budget estimate (12) is underminedby the uncertainty of some 50 Gt year−1 in theaccumulation. Nonetheless, the consensus ofthese measurements suggests a net loss in the1990s of some 50 Gt year−1.

Satellite interferometry (12, 24) has alsoestablished that from 1996 to 2005, mass lossesthrough flow increased by 102 Gt year−1, andmeteorological estimates (32) (Fig. 1B) of thesurface-mass imbalance decreased some 20 Gtyear−1 in the same period because of increasedmelting. Gravimetric surveys too support an in-creased mass loss (11, 15, 16, 19, 20). However,the interferometric and gravimetric records areshort and reflect the considerable variability inthemass flux of tidewater glaciers and the surfacemass balance. For example, the ice fluxes of twoglaciers that by 2005 were responsible for 43 Gtyear−1 of the increased discharge had by late2006 declined to within 10 Gt year−1 of their levelin 2000 (46), whereas in the past 14 years, the3-year variability in surface mass imbalance hasranged from –130 to 120 Gt year−1 (Fig. 1B). Inaddition, not all gravimetric estimates capture theknown spatial distribution of change; one that does(16) (Fig. 3B) is some 120 Gt year−1 more positivethan other estimates, and some understanding ofthe cause of these discrepancies is needed. In-creased mass loss from Greenland has occurred,but the decadal change is probably modest.

Implications for the FutureIt is reasonable to conclude that, today, the EAISis gaining some 25 Gt year−1, the WAIS is losingabout 50 Gt year−1, and the GIS is losing about100 Gt year−1. These trends provide a sea-levelcontribution of about 0.35 mm year−1, a modestcomponent of the present rate of sea-level rise of3.0 mm year−1. Because 50 Gt year−1 is a veryrecent contribution, the ice sheets made little con-tribution to 20th-century sea-level rise. However,what has also emerged is that the losses are dom-inated by ice dynamics.Whereas past assessments(47) considered the balance between accumulationand ablation, the satellite observations reveal thatglacier accelerations of 20 to 100% have occurredover the past decade. The key question today iswhether these accelerations may be sustained, oreven increase, in the future.

The question is difficult because the causes ofthe instabilities have yet to be established. The geo-

Fig. 2. (A) Rate of elevation change of the Antarctic Ice Sheet,1992 to 2003, from ERS satellite radar altimetry [redrawn from(14)]. Also shown (inset) is the bedrock geometry, highlightingfloating (light gray), marine-based (mid-gray) and continental-based (black) sectors. (B) Elevation change of the trunks (flowin excess of 50 m year−1) of the Pine Island [Basin GH in (A)],Thwaites (Basin GH), Totten (Basin C′D), and Cook (Basin DD′)glaciers. All the deflating glaciers coincide with marine-basedsectors of the ice sheet. An ice-dynamic origin of the thinningof the East Antarctic glaciers has yet to be confirmed byinterferometry. However, the correlation of the thinning withflow velocity and the fact that the thinning rate is secular makeice dynamics the likely cause of all Antarctic mass losses.

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Increased losses in other Amundsen Sea coastal areas.

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Coastal-Change and Glaciological Maps of the Antarctic Peninsula

Printed on recycled paper

In#2009,#the#Glacier#Studies#Project#(GSP)#of#the#U.S.#Geological#Survey#(USGS)#and#the#Mapping#and#GeoBgraphic#Information#Centre#(MAGIC)##of#the#British#Antarctic#Survey#(BAS)#completed#a#cooperative#endeavor#to#publish#three#maps#of#the#Antarctic#��'#'+-%��*�!#('��3!+��'��"��maps#are#based#on#a#large#variety#of#cartographic,#aerial#photograph,#satellite#image,#and#ancillary#historical#datasets#�*�"#.��,��"�#'+,#,-,#('��"��&�)+�document#dynamic#changes#on#the#cryoBspheric#coast#of#the#peninsula#during#the#past#50#years.

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Figure 1. Location of the Antarctic Peninsula and principal ice shelves of Antarctica, areas of dynamic coastal change.

1000 KILOMETERS

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Figure 2. Locations and names of three Antarctic Peninsula areas for which the U.S. Geological Survey and the British Antarctic Survey published coastal-change and glaciological maps (I–2600–A, B, and C, scale 1:1,000,000).

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U.S. Department of the InteriorU.S. Geological Survey

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Initial northern mass loss from Larsen A,B areas and western glaciers.

Subtle acceleration of mass loss over past decade, concentrated in the southern half of the Peninsula.

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Most outlet glaciers concentrated in southeast and northwest Greenland. Some lower volume glaciers in the northeast.

Outlet glaciers

Loss from both melt and calving.GREENLAND

Chu (2014)

GREENLANDNATURE GEOSCIENCE DOI: 10.1038/NGEO2167 LETTERS

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Figure 1 | Bed elevation of the Greenland ice sheet colour-coded between �500 and +2,000m, with submarine areas in blue. Details of the large-scalemap for Upernavik Isstrøm and Nunatakassaap Sermia (a), Hayes Gletscher, Allison Gletscher and Illullip Sermia (b), Petermann, Steensby and RyderGletscher (c), Marie Sophie Gletscher, Academy Gletscher and Hagen Bræ (d), F. Graae, Charcot and Daugaard-Jensen (e), and Kangerlussuaq Gletscher(f); glaciers are listed in clockwise order. The white contour line delineates the limit of land ice. The mass conservation method is employed for the glaciers.Kriging is used to map the interior regions.

fundamental geometric constraint on the past, present and futureevolution of the ice-sheet flow.

Ice is channelized to the ocean through a narrow set of flux gatesalong the periphery. Only 8% of the total length of these flux gatescorresponds to ice grounded below sea level, yet this small fractioncontrols 88% of the total ice discharge of Greenland. The subglacialtroughs extend tens to hundreds of kilometres inland, and channelice flow over considerable distances (Supplementary Information).

Particularly revealing, the three main branches of UpernavikIsstrøm (Fig. 1a), in West Greenland, coincide with three troughswith a submarine bed more than 80 km inland of their presenttermini, and for the southern arm more than 140 km. Previousmappings identify no trough (B2001, ref. 7), or reveal a glacier belowsea level for 25 km (B2013, ref. 16), with large deviations (200m) inbed elevation due to interpolation artefacts (Fig. 2). Farther north,near Hayes Gletscher, several unnamed glaciers share a commontrough that is 15 km wide, 2 km deep and grounded below sea levelfor more than 120 km (Fig. 1b). Many glaciers of the northwestcoast are grounded several hundred metres below sea level at their

termini and remain so for 10–50 km inland. This contrasts withexisting bed maps that indicate ice fronts grounded at sea level, notin contact with the ocean (Supplementary Information). Up north,Humboldt Gletscher is submarine 140 km inland of its terminus,and Petermann Gletscher (Fig. 1c) is underlaid by a submarinechannel that connects to the ice-sheet interior, except for a narrowpassage above sea level21.

Few ice-covered, submarine valleys exist in the northernmostsector of Greenland. In the northeast, two large troughs more than100 km long and 10 km wide host Academy Gletscher and HagenBræ (Fig. 1d). In central East Greenland, the bed is generally morethan 1,000m above sea level, so the glacial troughs in that sectorare deeper and narrower than elsewhere in Greenland, but theydo not extend far below sea level and far inland. We attribute thisto the presence of a more resistant bedrock and the presence ofa colder-based ice sheet22. Among them, Daugaard-Jensen Glacier(Fig. 1e) is grounded below sea level for 70 km, before its bed risesquickly above sea level over a broad plateau that would preventany sort of rapid glacier retreat. Ice thickness is shallow on the

NATURE GEOSCIENCE | VOL 7 | JUNE 2014 | www.nature.com/naturegeoscience 419

Bed elevations in most of Greenland are already above sea level, and more would be as the surface rebounds from ice removal.

Morlighem et al., (2014)Chu (2014)

GREENLAND

NASA

Early estimates







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6 J U N E 2 0 1 3 | V O L 4 9 8 | N A T U R E | 5 3








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Hanna, et al. (2013)

GRACE• Great for Total Mass estimates • Harder to make detailed maps

Altimetry• Excellent spatial resolution• Less time resolution than GRACE

Pre 2012

2012 Studies

GREENLANDIntegrated Mass and Spatial Distribution of Changes

Total Mass:

Harig and Simons (2012, 2016)

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http://www.polarice.princeton.eduInt=−417

Harig and Simons (2012)

GREENLAND TRENDS

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ExtendedFit

Harig & Simons (2016)

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Harig & Simons (2016)

We see significant anomalies relative to long term trends.

The GRACE measurement period does not capture the variability we might expect going forward.

WHERE IS THIS WORK GOING

• Increasing timespans GRACE-FO launching in early 2017 will continue long term measurements

• Methodological improvements GRACE-FO should also greatly improve resolution at high latitudes

• Inter-annual variations Research of year-to-year events will shift towards combining more data types and attribution of the cause

240˚

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a) 1/2003 − 2/2015


190˚

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1/2003 − 2/2015b)


CONCLUSIONS

• We measure changes to ice sheets by measuring their changes in gravity over time.• Localization using Slepian functions are ideally suited to these regional problems and GRACE data.• Increases S/N on sparse orthogonal basis, reduces influence from signals in other regions.• Greenland lost 240 billion tons of ice per year over the past decade with 10 Gt/yr2 acceleration.• West Antarctica averaged mass loss of 120 billion tons of each year, doubling its mass loss in the last 6 years.

0˚

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Int=−1125

−85°

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−60°


−400 −300 −200 −100 0 100surface density change (cm water equivalent)

b

a

c

1/2003−10/2013

Thanks!

measuring ice mass loss from melting ice sheets

Science