Talk presented at University of Arizona department seminar, March 2016.

1. MEASURING ICE MASS LOSS
FROM MELTING ICE SHEETS
Christopher Harig
University of Arizona
Mar. 07, 2016
NASA

2. Changes in the climate
New techniques to measure mass better
Mathematical interlude
Antarctica
Greenland
THE STORY

3. CO2gasppm
250
300
350
400
1850 1875 1900 1925 1950 1975 2000 2025
CO2
GlobalTemperature
Atmospheric CO2 and GlobalTemperature
0.75
0.5
0.25
0
-0.25
-0.5
-0.75
TempAnomalyfrom61’-90’(degC)
2000 368
CLIMATE CONTEXT
Morice et al., 2012 (UK Met Office)
MacFarling Meure et al., 2006,
Keeling et al., 2005
2015 398

4. CO2gasppm
200
350
500
650
800
Year
1850 1900 1950 2000 2050 2100
CO2
CO2 Scenario A1B
GlobalTemperature
Temperature Projection for A1B
3
2
0
-1
1
TempAnomalyfrom61’-90’(degC)
CLIMATE CONTEXT
IPCC AR4 (2007)
Atmospheric CO2 and GlobalTemperature

5. 200
350
500
650
800
Year
1850 1900 1950 2000 2050 2100
CO2
CO2 Scenario A1B
GlobalTemperature
Temperature Projection for A1B
Projected GlobalTemperature Changes
(2090-2099) A1B Scenario
Atmospheric CO2 and GlobalTemperature
3
2
0
-1
1
IPCC AR4 (2007)
Figure SPM.6
CLIMATE CONTEXT

6. 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

7. POLAR ICE SHEETS
How much mass is being lost/gained? Where are these
changes occurring? How well do we know this?
NASA
NASA

8. SATELLITE GEODESY
How do we measure ice sheet mass?

9. SATELLITE GEODESY
How do we measure ice sheet mass?
Input Output Method
/ Surface Mass Balance
Count calories in
and calories out

10. SATELLITE GEODESY
How 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

11. 5
Land, and Vegetation?
The GLAS instrument on ICESat will determine the distance from the satellite to the Earth’s surface and
o intervening clouds and aerosols. It will do this by precisely measuring the time it takes for a short
pulse of laser light to travel to the reflecting object and return to the satellite. Although surveyors rou-
inely use laser methods, the challenge for ICESat is to perform the measurement 40 times a second
rom a platform moving 26,000 km (16,000 mi) per hour. In addition, ICESat will be 600 km above the
Earth and the precise locations of the satellite in space and the laser beam on the surface below must be
determined at the same time.
The GLAS instrument on ICESat will measure precisely how long it takes for photons from a laser to
pass through the atmosphere, reflect off the surface or clouds, return through the atmosphere, collect in
he 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 footprint
on 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 the
aser beam points relative to stars and the center of the Earth will be measured precisely with a star-
racking camera that is integral to GLAS. The data on the distance to the laser footprint on the surface,
he 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
Star
Camera
FOV
70m
170m
Ground Track
Surface
Photon
Scatter
Photon Scatter
due to Clouds
and Aerosols
Center
of the
Earth
Emitted
1064 and
532 nm
Laser
Pulses
Reflected
Laser
Pulses
Orbit
Schematic illustration of the GLAS instrument making measurement from ICESat while orbiting the Earth.
Graphic by Deborah McLean.
SATELLITE GEODESY
Altimetry
Laser altimetry
Radar altimetry
NASA
NASA
Missions starting late 1990s
Missions starting early 1990s

12. SATELLITE GEODESY
How do we measure ice sheet mass?
Input Output Method
/ Surface Mass Balance
Laser/Radar Altimetry
GRACETime
Variable Gravimetry
Count calories in
and calories out
Look in a mirror
Step on a scale

13. SATELLITE GEODESY
Measuring changes in gravity
Seeber (2003)

14. LAGEOS-1,-2
SATELLITE GEODESY
Measuring gravity
Seeber (2003)
NASA
Wiki Commons

15. 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

16. How GRACE Works
GRACE 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
bod
any
how
in t
eno
the
in c
As
fiel
wh
GR
me
dis
som
hai
In
oth
pre
tak
GR
sat
fiel
GRACE
How it works.
Measure the distance between
satellites. This changes as you
pass over different land, such
as mountains.
CSRTexas,
2011 edu poster

17. GRACE
GRACE 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
Best global gravity map from decades
of satellite data before GRACE
Gravity map from four years of GRACE only data
Best global gravity map from
decades of satellite data
before GRACE.
Gravity map from only 4 years
of GRACE data
Static gravity field
NASA

18. GRACE DATA
Time 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.

19. THE PROBLEM

20. 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

21. The domain of data availability or region of interest is R ∈ Ω.
R
2
R1 Θ
Θ
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
R
YlmYl0m0 d⌦ = Dlm,l0m0 .
THE PROBLEM

22. 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
l0
X
m0= l0
Z
R
YlmYl0m0 d⌦ gl0m0 = glm
Dlm,l0m0 =
Z
R
YlmYl0m0 d⌦.
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

23. =
Z
R
g2
d⌦
Z
⌦
g2
d⌦ = maximum.
These functions satisfy Slepian’s concentration problem
to the region R of area A:
THEORY SUMMARY

24. 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
R
g2
d⌦
Z
⌦
g2
d⌦ = maximum.
N = (L + 1)2 A
4⇡
,
THEORY SUMMARY

25. 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˚
280˚
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˚
320˚
340˚
α=9 λ=0.94 α=10 λ=0.93
−1.0 −0.5 0.0 0.5 1.0
magnitude
α=11 λ=0.898
60˚
70˚
300˚
320˚
340˚
α=12 λ=0.869
Depends on 3 variables
Outline of region (Greenland)
Degree of bandwidth (L = 60)
Truncation of basis (N = 21)
SATELLITE GEODESY
Slepian functions
LX
l0=0
l0
X
m0= l0
Z
R
YlmYl0m0 d⌦ gl0m0 = glm
Localization by optimization
Harig and Simons (2012)
Mathematical benefits
Orthogonality
Sparsity
Increased signal to noise

26. Slepian functions
SATELLITE GEODESY
Harig and Simons (2015b)
Used in the fields of:
computer graphics
cosmology
geodetic seismology
medical sciences
planetary magnetism
signal processing
240˚
270˚
α=1 λ=0.999 α=2 λ=0.998 α=3 λ=0.994
−
α=4 λ=0.985
240˚
270˚
α=5 λ=0.975 α=6 λ=0.961 α=7 λ=0.926
−
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 1.0
magnitude
α=11 λ=0.766
−
−70˚
−65˚
α=12 λ=0.723

27. ANTARCTICA

28. NASA
ANTARCTICA
Distinct mass variability
in different regions

29. How do ice sheets lose ice?
ANTARCTICA

30. Credit: NASA
Bot:The calving front ofThwaites Ice Shelf looking at
the ice below the water's surface. Credit: NASA /
JimYungel
Top:The calving front of the Filchner Ice Shelf,
Antarctica. Copyright Jonathan Bamber. (NERC)
Sheds ice by flow and calving
ANTARCTICA

31. ANTARCTICA
Radar image of ice speed
Rignot (2008)
Early estimates
Hanna, et al. (2013)
–400
–300
–200
–100
0
100
AISdM/dt(Gtyr−1)
Pre−2012 studies
1990 1995 2000 2005 2010
–400
–300
–200
–100
0
YearGISdM/dt(Gtyr−1)
1990
Antarctica
Greenland
a b
Figure 1 | Summary of estimates of rates of ice mass change for Antarctica
and 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 represented
by a box whose width indicates the time period studied, and whose height
indicates the error estimate. Single-epoch (snapshot) estimates of mass balance
are represented by vertical error bars when error estimates are available, and are
otherwise
technique
IMBIE co
others16,20
dashed lin
(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 the
minimum, 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 change
between discharge and SMB components, demonstrating that in the
northern part of Greenland, the dominant cause of mass change was
atmospheric in origin, while in the southern part it was ice dynamics.
The new, reconciled IMBIE GRACE estimates of whole Antarctic
mass balance are now largely in agreement with one another, with
evolutio
gradient
plexity a
the shall
dients, b
flow at lo
solution
tical shea
shelf ap
taking p
–400
–300
–200
–100
0
100
AISdM/dt(Gtyr−1)
1990 1995 2000 2005 2010
–400
–300
–200
–100
0
Year
GISdM/dt(Gtyr−1)
1990
Antarctica
Greenland
Figure 1 | Summary of estimates of rates of ice mass change for Antarctica
and 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 represented
by a box whose width indicates the time period studied, and whose height
indicates the error estimate. Single-epoch (snapshot) estimates of mass balance
are represented by vertical error bars when error estimates are available, and are
otherwise
techniqu
IMBIE co
others16,2
dashed li
–400
–300
–200
–100
0
100
AISdM/dt(Gtyr−1)
Pre−2012 studies
–100
0
r−1)
–100
0
–400
–300
–200
–100
0
100
2012 studies
GRACE
Mass budget
Radar altimetry
Laser altimetry
IMBIE combinedAntarctica Antarctica
AISdM/dt(Gtyr−1)GIS
a b
REVIEW RESE
–400
–300
–200
–100
0
100
AISdM/dt(Gtyr−1)
Pre−2012 studies
1990 1995 2000 2005 2010
–400
–300
–200
–100
0
Year
GISdM/dt(Gtyr−1)
1990 1995
2
GRACE
Mass bu
Radar al
Laser alt
IMBIE coAntarctica
Greenland
a b
Figure 1 | Summary of estimates of rates of ice mass change for Antarctica otherwise represen

32. ANTARCTICA
Radar image of ice speed
Rignot (2008)
figures are only in rough coincidence with those
determined from interferometry [0 ± 2 and –8 ±
5 km3
year−1
, respectively, in (9)], the signals are
clear and the trends definitely established.
West Antarctica and the
Antarctic Peninsula
The West Antarctic Ice Sheet (WAIS) contains
enough ice to raise global sea levels by more than
5 m and, according to altimetry and interferometry,
one key sector is in a state of rapid
retreat (23, 34). Glaciers draining into
the Amundsen Sea (Fig. 2A) are los-
ing mass because of an ice-dynamic
perturbation. During the 1990s, for
example, 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 implicated
in the freshening of the Ross Sea
some 1000 km away (40). Through-
out the 1990s, independent altimeter
(7, 14, 17, 18) and interferometer (9)
surveys of the WAIS as a whole were
in notable, possibly fortuitous, agree-
ment (Table 1), placing its annual
losses in the range 47 to 59 Gt year−1
.
The mass balance of the WAIS has
been dominated by the losses from
glaciers of the Amundsen sector, can-
celed to a degree by some snowfall-
driven coastal growth and growth
arising from the well-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 surveys
forms the continental ice cap of Dyer Plateau.
This exhibits snowfall-driven growth (Fig. 2A)
that is sufficient to cancel the accelerated flow
from the Larsen-A and -B catchments. The AP
contribution to sea level is negligible.
Greenland
Since the most recent IPCC report, there have
been seven estimates of Greenland mass im-
balance based on satellite altimetry (18), interfer-
(Fig
acc
lite
in t
mea
mo
and
by
acc
thes
199
esta
thro
met
surf
yea
mel
crea
the
sho
the
mas
glac
yea
200
in 2
3-y
rang
add
kno
(16
than
the
crea
but
Imp
It is
1992-2003 Altimetry
Shepherd and Wingham (2007)
Early estimates

33. GLACIAL GEOMORPHOLOGY OF THE ANTARCTIC ICE SHEET BED 725
ANTARCTICA
Elevation of
Antarctica with
ice removal and
isostatic
compensation
Jamieson et al. (2014)

34. ANTARCTICA
Surface density change
estimate from GRACE
5 km3
year−1
, respectively, in (9)], the signals are
clear and the trends definitely established.
West Antarctica and the
Antarctic Peninsula
The West Antarctic Ice Sheet (WAIS) contains
enough ice to raise global sea levels by more than
5 m and, according to altimetry and interferometry,
one key sector is in a state of rapid
retreat (23, 34). Glaciers draining into
the Amundsen Sea (Fig. 2A) are los-
ing mass because of an ice-dynamic
perturbation. During the 1990s, for
example, 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 implicated
in the freshening of the Ross Sea
some 1000 km away (40). Through-
out the 1990s, independent altimeter
(7, 14, 17, 18) and interferometer (9)
surveys of the WAIS as a whole were
in notable, possibly fortuitous, agree-
ment (Table 1), placing its annual
losses in the range 47 to 59 Gt year−1
.
The mass balance of the WAIS has
been dominated by the losses from
glaciers of the Amundsen sector, can-
celed to a degree by some snowfall-
driven coastal growth and growth
arising from the well-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 surveys
have also estimated a rate of mass loss
since2002 ofbetween107 and136 Gt
that is sufficient to cancel the accelerated flow
from the Larsen-A and -B catchments. The AP
contribution to sea level is negligible.
Greenland
Since the most recent IPCC report, there have
been seven estimates of Greenland mass im-
balance based on satellite altimetry (18), interfer-
lite
in t
mea
mo
and
by
acc
thes
199
esta
thro
met
surf
yea
mel
crea
the
sho
the
mas
glac
yea
200
in 2
3-y
rang
add
kno
(16
than
the
crea
but
Imp
It is
is g
abo
0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a c
1/2003−6/2014
Harig and Simons (2015b)
1992-2003 Altimetry
Shepherd and Wingham (2007)

35. −500
0
500
Slope = −17 ± 4 Gt/yr
Acceleration = 1 ± 3 Gt/yr^2
Wilkes Land Regiond)
IJ05_R2
−1000
−500
0
500
1000
2002 2004 2006 2008 2010 2012 2014
Slope = −92 ± 10 Gt/yr
Acceleration = −6 ± 6 Gt/yr^2
All Antarcticae)
IJ05_R2
ANTARCTICA
Total Mass:
Mass(Gt)
0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
Harig and Simons (2015b)

36. −500
0
500
Slope = −17 ± 4 Gt/yr
Acceleration = 1 ± 3 Gt/yr^2
Wilkes Land Regiond)
IJ05_R2
−1000
−500
0
500
1000
2002 2004 2006 2008 2010 2012 2014
Slope = −92 ± 10 Gt/yr
Acceleration = −6 ± 6 Gt/yr^2
All Antarcticae)
IJ05_R2
ANTARCTICA
Mass(Gt)
0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
Harig and Simons (2015b)
92 Gt of ice spread overTucson is
about 167m high, or right around
the height of the Washington
Monument (169m).

37. 0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
ANTARCTICA
West Antarctica
Harig and Simons (2015b)

38. ANTARCTICA
West Antarctica
0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
240˚
270˚
2003 Int=28 2005 Int=−55
−50−40−30−20−10 0 10 20 30 40 50
surface density change (cm/yr water equivalent)
−85˚
−85˚
−80˚
−75˚2007 Int=−114
2009 Int=−156
Min=−50
2011 Int=−181
Min=−46
2013 Int=−177
290˚
300˚
−60˚ Int=−1 Int=−14 −60˚
290˚
300˚
Int=−23
Harig and Simons (2015b)

39. −1000
−500
0
500
Slope = −121 ± 8 Gt/yr
Acceleration = −18 ± 5 Gt/yr^2
West Antarcticaa)
IJ05_R2
Antarctic Peninsulab)
0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a c
1/2003−6/2014
ANTARCTICA
West Antarctica
−500
−500
0
500
Slope = −19 ± 3 Gt/yr
Acceleration = −2 ± 2 Gt/yr^2
Wilkes Land Regiond)
IJ05_R2
−1000
−500
0
500
1000
2002 2004 2006 2008 2010 2012 2014
Slope = −96 ± 7 Gt/yr
Acceleration = −16 ± 5 Gt/yr^2
All Antarcticae)
IJ05_R2
Significant increases in mass losses the
Pine Island andThwaites glacier areas.
Increased losses in other Amundsen Sea
coastal areas.
Mass(Gt)
Harig and Simons (2015b)

40. 0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
ANTARCTICA
Peninsula
Harig and Simons (2015b)

41. ANTARCTICA
Peninsula
0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
2009 Int=−156 2011 Int=−181 2013 Int=−177
290˚
300˚
−70˚
−60˚
2003
Int=−1
2005
Int=−14
−70˚
−60˚
290˚
300˚
2007
Int=−23
−70˚
−60˚
2009
Int=−32
2011
Int=−41
−16 −12 −8 −4 0 4 8 12 16
surface density change (cm/yr water equivalent)
GRACE CSR RL−05 Data, IJ05_R2 GIA
−70˚
−60˚
2013
Int=−45
Harig and Simons (2015b)

42. ANTARCTICA
Peninsula
Printed on recycled paper
completed#a#cooperative#endeavor#to#
publish#three#maps#of#the#Antarctic#
maps#are#based#on#a#large#variety#of#
cartographic,#aerial#photograph,#satellite#
image,#and#ancillary#historical#datasets#
document#dynamic#changes#on#the#cryoB
spheric#coast#of#the#peninsula#during#the#
past#50#years.
coastal#change#and#glaciological#
map#series#(I–2600)#being#published#
by#the#USGS#in#both#paper#and#
digital#format#(see#USGS#Fact#Sheet#
FS#2005–3055#at#http://pubs.usgs.
gov/fs/2005/3055/)N#the#maps#are#of#
#
the#Larsen#Ice#Shelf#area#(I–2600–B),#
and#the#Palmer#Land#area#(I–2600–C).#
between#lats#60°#and#76°#S.#and#longs#
maps#published#in#the#I–2600#series#see#
http://pubs.usgs.gov/imap/2600/.
For#much#of#the#Antarctic#PeninB
sula,#the#BAS#used#a#georeferenced#digiB
Mapper#images#prepared#by#the#InstiB
tut#für#Angewandt#Geodäsie#(now#
the#Bundesamt#für#Kartographie#und#
Geodäsie)#in#Germany#as#an#imageBmap#
Research#Center#of#Ohio#S
versity.#All#digital#cartogr
for#I–2600–A–C#have#bee
Antarctic#Research#Antarc
Database#(ADD)#(see#http
scar.org:8080/add/
tinational#project#to#maint
cartographic#database#of#A
Figure 1. Location of the Antarctic
Peninsula and principal ice shelves of
Antarctica, areas of dynamic coastal change.
1000 KILOMETERS
90 E
0
0 E
180 W
60 S
90 °E90 W90°W
W 0°E
W 180° E
60°S
80 S80°S
Ronne
Ice
Shelf
Cook Ice Shelf
Lazarev
Ice Shelf
Filchner
Ice Shelf
Larsen
Ice Shelf
Voyeykov
Ice Shelf
Voyeykov
Ice Shelf
Shackleton
Ice Shelf
Ross
Ice Shelf
Amery
Ice Shelf
West
Ice Shelf
Sulzberger
Ice Shelf
Getz
Ice Shelf
Abbot
Ice Shelf
George VI
Ice Shelf
EAST
ANTARCTICA
WEST
ANTARCTICA
Weddell%%
%%%%%Sea
Figure2
Brunt
Ice Shelf
Fimbul Ice
Shelf
Rilser-Larsen
Ice Shelf
ANTARCTIC
PENINSULA
Figure 2. Locations and names of three Antarctic Peninsula areas for which
U.S. Geological Survey and the British Antarctic Survey published coastal-ch
glaciological maps (I–2600–A, B, and C, scale 1:1,000,000).
˚
Stang
Ice)Shelf
Bach
Ice)Shelf
A - Trinity Peninsula
S o u t h ) S h e t l a n d ) I s l a n d s
Bransfield
Strait
South)Orkney)
Islands
Weddell%Sea
Ronne
Ice)Shelf
Ronne
Ice)Shelf
Ronne
Ice)Shelf
B - Larsen Ice Shelf
C - Palmer
Land
ANTARCTIC
PENINSULA
Larsen
Ice)Shelf
Wordie
Ice)Shelf
Wordie
Ice)Shelf
Wilkins
Ice)Shelf
George)VI)
Ice)Shelf
A
lexanderIsland
Filchner
Ice)Shelf
Filchner
Ice)Shelf
Berkner
Island
70° W 60° 50°
0 100 200 300
KILOMETERS
Adelaide
Island
Adelaide
Island
PALMER
LAND
GRAHAM
L
A
N
D
U.S. Department of the Interior
U.S. Geological Survey
Fact Sheet FS–0
March 2002. Re
USGS (2011)
2009 Int=−156 2011 Int=−181 2013 Int=−177
290˚
300˚
−70˚
−60˚
2003
Int=−1
2005
Int=−14
−70˚
−60˚
290˚
300˚
2007
Int=−23
−70˚
−60˚
2009
Int=−32
2011
Int=−41
−16 −12 −8 −4 0 4 8 12 16
surface density change (cm/yr water equivalent)
GRACE CSR RL−05 Data, IJ05_R2 GIA
−70˚
−60˚
2013
Int=−45
Harig and Simons (2015b)

43. −1000
−500
0
500
Slope = −121 ± 8 Gt/yr
Acceleration = −18 ± 5 Gt/yr^2
West Antarcticaa)
IJ05_R2
−500
0
500
Slope = −27 ± 2 Gt/yr
Acceleration = −5 ± 1 Gt/yr^2
Antarctic Peninsulab)
IJ05_R2
0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
ANTARCTICA
Peninsula
−500
0
Slope = −19 ± 3 Gt/yr
Acceleration = −2 ± 2 Gt/yr^2
IJ05_R2
−1000
−500
0
500
1000
2002 2004 2006 2008 2010 2012 2014
Slope = −96 ± 7 Gt/yr
Acceleration = −16 ± 5 Gt/yr^2
All Antarcticae)
IJ05_R2
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.
Mass(Gt)

44. 0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
ANTARCTICA
East Antarctica
Harig and Simons (2015b)

45. −1000
Slope = −121 ± 8 Gt/yr
Acceleration = −18 ± 5 Gt/yr^2
−500
0
500
Slope = −27 ± 2 Gt/yr
Acceleration = −5 ± 1 Gt/yr^2
Antarctic Peninsulab)
IJ05_R2
−500
0
500
Slope = 62 ± 4 Gt/yr
Acceleration = 11 ± 3 Gt/yr^2
Dronning Maud Land Regionc)
IJ05_R2
Wilkes Land Regiond)
ANTARCTICA
East Antarctica
−500
0
500
Slope = −19 ± 3 Gt/yr
Acceleration = −2 ± 2 Gt/yr^2
IJ05_R2
−1000
−500
0
500
1000
2002 2004 2006 2008 2010 2012 2014
Slope = −96 ± 7 Gt/yr
Acceleration = −16 ± 5 Gt/yr^2
All Antarcticae)
IJ05_R2
Significant increase in mass
beginning at the end of 2008,
linked to precipitation events.
Mass(Gt)0˚
45˚
135˚
180˚
225˚
315˚
Int=−925
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−500 −250 0 250
surface density change (cm water equivalent)
b
a
c
1/2003−6/2014
Harig and Simons (2015b)

46. GREENLAND

47. GREENLAND
ESA
Most outlet glaciers
concentrated in
southeast and
northwest Greenland.
Some lower volume
glaciers in the
northeast.
Outlet glaciers

48. Loss from both melt and calving.
GREENLAND
Chu (2014)

49. GREENLANDNATURE GEOSCIENCE DOI: 10.1038/NGEO2167
−500 0 500 1,000 2,0001,500
Bed elevation (m)
60° N
65° N
70° N
75° N
80° N
70°W
60°W
50°W
40°W
30°W
300 km
20 km
20 km
50 km
c
b
a
d
e
f
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)

50. GREENLAND
NASA
Early estimates
–400
–300
–200
–100
0
100
AISdM/dt(Gtyr−1) Pre−2012 studies
1990 1995 2000 2005 2010
–400
–300
–200
–100
0
Year
GISdM/dt(Gtyr−1)
1990 1995 2000 2005 2010
–400
–300
–200
–100
0
Year
–400
–300
–200
–100
0
100
2012 studies
GRACE
Mass budget
Radar altimetry
Laser altimetry
IMBIE combinedAntarctica Antarctica
Greenland Greenland
AISdM/dt(Gtyr−1)GISdM/dt(Gtyr−1)
a b
REVIEW
Pre−2012 studies
0
–400
–300
–200
–100
0
100
2012 studies
GRACE
Mass budget
Radar altimetry
Laser altimetry
IMBIE combinedAntarctica Antarctica
AISdM/dt(Gtyr−1)G
b
REVIEW RESEARCH
Hanna, et al. (2013)
GRACE
• Great forTotal Mass estimates
• Harder to make detailed maps
Altimetry
• Excellent spatial resolution
• Less time resolution than GRACE
Pre 2012
2012 Studies

51. GREENLAND
Integrated Mass and Spatial Distribution of Changes
Total Mass:
Harig and Simons (2012, 2016)
240˚
260˚
280˚
300˚
320˚
60˚
70˚
a) 1/2003 − 2/2015
GRACE CSR R
b
−300 −200 −100 0
surface density change (
240˚
260˚
280˚
300˚
320˚
60˚
70˚
a) 1/2003 − 2/2015
GRACE CSR RL−05 Data
190˚200˚
210˚
220˚
1/2003 − 2/2015b)
−300 −200 −100 0 100 200 300
surface density change (cm water equivalent)
−400
−300
−1.0
eus
Acceleration = −8 ± 2 Gt/yr^2
−200
−100
0
100
200
−0.5
0.0
0.5
IceMass(Gt)
Slope = −22 ± 2 Gt/yr
Acceleration = −3 ± 1 Gt/yr^2
eustaticsealevel(mm)
Baffin Regionb)
−2000
−1500
−1000
−500
0
500
1000
1500
2002 2004 2006 2008 2010 2012 2014
−5
−4
−3
−2
−1
0
1
2
3
4
IceMass(Gt)
Time
eustaticsealevel(mm)
Greenland

52. GREENLAND
Surface density
240˚
260˚
280˚
2003 Int=−130 2004 Int=−163 2005 Int=−198
60˚
70˚
2006 Int=−231
240˚
260˚
280˚
2007 Int=−272 2008 Int=−311
−30 −20 −10 0 10 20 30
surface density change (cm/yr water equivalent)
2009 Int=−339
60˚
70˚
300˚
320˚
340˚
2010 Int=−359
240˚
260˚
280˚
300˚
320˚
340˚
2011 Int=−384
300˚
320˚
340˚
2012
GRACE CSR RL−05 Data
http://www.polarice.princeton.eduInt=−417
Harig and Simons (2012)

53. GREENLANDTRENDS−200
−100
−0.5Ice
Slope = −22 ± 2 Gt/yr
Acceleration = −3 ± 1 Gt/yr^2
eustatic
−2000
−1500
−1000
−500
0
500
1000
1500
2002 2004 2006 2008 2010 2012 2014
−5
−4
−3
−2
−1
0
1
2
3
4
IceMass(Gt)
Time
Slope = −243 ± 13 Gt/yr
Acceleration = −10 ± 15 Gt/yr^2
eustaticsealevel(mm)

54. GREENLANDTRENDS
−200
−100
0
−0.5
0.0
IceMas
Slope = −22 ± 2 Gt/yr
Acceleration = −3 ± 1 Gt/yr^2
eustaticseal
−2500
−2000
−1500
−1000
−500
0
500
1000
1500
2002 2004 2006 2008 2010 2012 2014
−6
−5
−4
−3
−2
−1
0
1
2
3
4
IceMass(Gt)
Time
Slope = −244 ± 6 Gt/yr
Acceleration = −28 ± 9 Gt/yr^2
eustaticsealevel(mm)
Greenlandc)
Extended
Fit
Harig & Simons (2016)

55. GREENLAND−100
−100
0
100
200
300
400
0.0
0.5
1.0
eustaticsealevel(mm)
IceMass(Gt)
Baffin Region, seasonalb)
18
−66
24
−22
38
6
33
−18
25
−25
19
−23
13
−34
1
−22
21
−22
29
−17
55
−0
69
13
−500
0
500
1000
1500
2002 2004 2006 2008 2010 2012 2014
−1
0
1
2
3
4
Time
Greenland, seasonalc)
115
−124
57
−42
65
−87
76
−126
6
−92
50
−102
134
−65
139
−12
111
−18
84
−136
324
−103
493
259
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.

56. WHERE ISTHIS 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˚
260˚
280˚
300˚
320˚
60˚
70˚
a) 1/2003 − 2/2015
GRACE CSR RL−05 Data
190˚200˚
210˚
220˚
230˚
50˚
60˚
1/2003 − 2/2015b)
−300 −200 −100 0 100 200 300
surface density change (cm water equivalent)

57. 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˚
45˚
135˚
180˚
225˚
315˚
Int=−1125
−85°
−75°
−60°
GRACE CSR RL−05 Data, IJ05_R2 GIA
−400 −300 −200 −100 0 100
surface density change (cm water equivalent)
b
a
c
1/2003−10/2013

58. Thanks!