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University of Milan
Dip. di Scienze della Terra “Ardito Desio”
Ice mass loss in the polar regions of the Earth
and mantle viscosity from GRACE data
Valentina R. Barletta, Roberto Sabadini and Andrea Bordoni
GRACE Products
• CSR (The University of Texas at Austin: Center for Space Research)
• release 01
• release 02 (not openly available)
• GFZ (GeoForschungsZentrum Potsdam)
• release 03
• JPL (Jet Propulsion Laboratory, California Istitute of Technology)
• release 02
Level-2 data refers to monthly estimates of spherical harmonic
coefficients of the Earth gravity field. Data products from all three
centers are available, as follows:
Monthly Mass Grid from GRACE Tellus Site
Acknowledgements:
GRACE data were processed by D. P. Chambers, supported by the NASA Earth
Science REASoN GRACE Project, and are available at http://grace.jpl.nasa.gov
Destriping Technique:Chambers, D.P.: Evaluation of New GRACE Time-Variable Gravity Data
over the Ocean. Geophys. Res. Lett., in press, 2006.
‘Striping', an error source in the data due to unmodeled fast mass changes
with periods lower than 1 month (tides, ocean, hydrology) that looks like near
N-S stripes in monthly maps.
The CSR 01 needs correction for the pole tide and for long period tides
The CSR 01 data have their (2,0) coefficient from Cheng and Tapley, 2004
Test with GRACE Tellus mass grid
-400
-300
-200
-100
0
100
200
300
400
500
2002 - 12 2003 - 06 2004 - 01 2004 - 07 2005 - 02 2005 - 08 2006 - 03
Time in Month
Mass in
Gt
CSR G500
GFZ G500
JPL G500
-1800
-1300
-800
-300
200
700
1200
1700
2200
2002 - 12 2003 - 06 2004 - 01 2004 - 07 2005 - 02 2005 - 08 2006 - 03
Time in Month
Mass in
Gt
CSR G500
GFZ G500
JPL G500
Diff = 20% Diff = 45%
SaharaAmazonia
-700
-500
-300
-100
100
300
500
700
900
2002 - 12 2003 - 06 2004 - 01 2004 - 07 2005 - 02 2005 - 08 2006 - 03
Time in Month
Mass in
Gt
CSR G500
GFZ G500
JPL G500
-250
-200
-150
-100
-50
0
50
100
150
200
2002 - 12 2003 - 06 2004 - 01 2004 - 07 2005 - 02 2005 - 08 2006 - 03
Time in Month
Mass in
Gt
CSR G500
GFZ G500
JPL G500
Diff = 70% Diff = 65%
GreenlandAntarctica
The suitable series: GFZ R03
The GFZ R03 after the correction
prescribed (GFZ+GAB) are
equivalent to the CSR R02
GFZ 03
CSR 02
GFZ+GAB 03
GAB=Atmospheric and
Oceanic Model
The Post Glacial Rebound
= Mass Variation Seen by GRACEGRACE
!"
PGR!" = Modeled Mass Variation Produced by PGR
= Ice Mass Variation
PGRGRACEICE!!! "#"$"
OthersOHPGRICEGRACE!!!!! "+"+"+"="
2
ICE!"
OH2
!" = Hydrology Cycle
Two Equivalent Processing Methods
( ) )(cos)sin()()cos()(1
12
3),( !""
#"!$
mmm
m
ave
tPmtSmtC
k
alll
l l
l%+%
+
+=% &
!"#$!"! &%&'=( )R
ttdt ),(
!"mm
SandCmll&&l
( ) )(cos)sin()cos(1
12
3),( !""
#"!$
mmm
m
avePmSmC
k
alll
l l
&&l& +
+
+= %
! "=#R
d),( $%&&' &&
1° Method
2° Method
The Averaging Function
Simple Characteristic function of the Region
{ 1
0),( =!"R
Inside the Region
Outside the Region
),( !"R + Gaussian Filter
r/2 = 250 Km
r/2 = 500 Km
r/2 = 750 Km
Inner Region = ),(),( !"#!" RR $
Outer Region = ),(),( !"#!" RR +
-800
-600
-400
-200
0
200
400
600
800
2003 - 01 2003 - 10 2004 - 08 2005 - 06 2006 - 04
Time in Month
Mas
s in
Gt
G500
Linear (G500)
Antarctica: Mass Variation seen by GRACE
GFZ R03
70 Gt/yr
Ma
ss in
Gt
-800
-600
-400
-200
0
200
400
600
800
2003 - 01 2003 - 10 2004 - 08 2005 - 06 2006 - 04
Time in Month
Mas
s in
Gt
Tellus G500
G500
Linear (G500)
Linear (Tellus G500)
Antarctica: Mass Variation seen by GRACE
70 Gt/yr
147 Gt/yr
GFZ R03M
ass in
Gt
Antarctica: Mass Variation seen by GRACE
GFZ R03
-800
-600
-400
-200
0
200
400
600
800
2003 - 01 2003 - 10 2004 - 08 2005 - 06 2006 - 04
Time in Month
Mas
s in
Gt
Int G500
Out G500
Linear (Out G500)
Linear (In G500)
70±8 Gt/yr
Ma
ss in
Gt
-400
-300
-200
-100
0
100
200
300
400
500
2002 - 04 2003 - 01 2003 - 11 2004 - 09 2005 - 07 2006 - 05
Time in Month
Mas
s in
Gt
Tellus G500
G500
Linear (G500)
Linear (Tellus G500)
Antarctica: Mass Variation seen by GRACE
53±7 Gt/yr
113 Gt/yr
CSR R01M
ass in
Gt
Greenland: Mass Variation seen by GRACE
GFZ R03
-300
-200
-100
0
100
200
2003 - 01 2003 - 10 2004 - 08 2005 - 06 2006 - 04
Time in Month
Mas
s in
Gt
G500
Linear (G500)
-67 Gt/yr
Ma
ss in
Gt
-300
-200
-100
0
100
200
2003 - 01 2003 - 10 2004 - 08 2005 - 06 2006 - 04
Time in Month
Mas
s in
Gt
Tellus G500
G500
Linear (G500)
Linear (Tellus G500)
Greenland: Mass Variation seen by GRACE
-45 Gt/yr
-67 Gt/yr
GFZ R03M
ass in
Gt
-400
-300
-200
-100
0
100
200
2003 - 01 2003 - 10 2004 - 08 2005 - 06 2006 - 04
Time in Month
Mas
s in
Gt
Int G500
Out G500
Linear (Out G500)
Linear (In G500)
Greenland: Mass Variation seen by GRACE
Upper Bound: -67±22 Gt/yr
Lower Bound: -88±36 Gt/yr
GFZ R03M
ass in
Gt
-200
-100
0
100
200
300
2002 - 04 2003 - 01 2003 - 11 2004 - 09 2005 - 07 2006 - 05
Time in Month
Mas
s in
Gt
Tellus G500
G500
Linear (G500)
Linear (Tellus G500)
Greenland: Mass Variation seen by GRACE
-66±21 Gt/yr
-42 Gt/yr
Lower Bound : -79±27 Gt/yr
Upper Bound:
CSR R01M
ass in
Gt
The Map of Mass Variation Trend
Water Equivalent in cm/yr
Gaussian Filter Halfwidth = 500Km
The Map of Mass Variation Trend
Water Equivalent in cm/yr
Gaussian Filter Halfwidth = 400Km
Details: Greenland and Antarctica
Water Equivalent in cm/yr
Gaussian Filter Halfwidth = 250Km
Water Equivalent in cm/yr
Antarctica East and West
26!
43!Antarctica West GFZ
Tellus GFZ 123!
24!
Gt/yr
Gt/yr
Gt/yr
Gt/yr
Antarctica East GFZ
Tellus GFZ
The Post Glacial Rebound Effects
Geoid Variation in mm/yr
The Post Glacial Rebound Effects
Water equivalent in cm/yr
The Post Glacial Rebound Effects
Water equivalent in cm/yr
Gaussian Filter Halfwidth = 500Km
Lower Mantle
Upper Mantle
Lithosphere
Core
The Earth Model
2221 Km
3480 Km
80 - 121 - 200 Km Density
1024 Kg/m3
10320 Kg/m3
Rigidity
2.6 1010 Pa
2.9 1011 Pa
Upper Mantle Viscosity 1019-1021 Pa s
Lower Mantle Viscosity 1021-1023 Pa s
Incompressible, Viscoelastic Maxwell Rheology
Tosi et al. 2005:
Most Probable Upper-Lower Mantle Viscosity 1020 - 1022 Pa s
The Deglaciation Process
)(tESLSLISLOceanICE
!+!"#+"#=!
Ice Model: ICE 3G
Sea Level Equation:
! The Convolution
The Ice Model
!
I
The Green Function
The Eustatic Sea Level)(tESL
Geoid Variation:
The subscript stands for the Region of the convolution
SLIGOICEAll
!"#+"#=!
IGICEAll!"=#
IGAntarctica
!"=#
Standard:
NoSL:
Antarctica Only:
8%7%
0%
25%
50%
75%
100%
19-21 19-22 19-23 20-21 20-22 20-23 21-21 21-22 21-23
LOG of Upper-Low er M antle V iscosity (Pa s)
Litho 80 Km
Litho 121 Km
Litho 200 Km
7%
22%
0%
25%
50%
75%
100%
19-21 19-22 19-23 20-21 20-22 20-23 21-21 21-22 21-23
LOG of Upper-Low er M antle V iscosity (Pa s)
Litho 80 Km
Litho 121 Km
Litho 200 Km
Changing The Deglaciation Process
Antarctica
Greenland
4% 7%
0%
20%
40%
60%
80%
19-21 19-22 19-23 20-21 20-22 20-23 21-21 21-22 21-23
LOG of Upper-Lower Mantle Viscosity (Pa s)
ICE 3G
No Sea Level
Antarctica Only
15%
24%
0%
10%
20%
30%
40%
50%
19-21 19-22 19-23 20-21 20-22 20-23 21-21 21-22 21-23
LOG of Upper-Lower Mantle Viscosity (Pa s)
ICE 3G
No Sea Level
Changing The Lithosphere Thickness
Antarctica
Greenland
0
50
100
150
200
250
300
350
21 22 23
LOG of Lower Mantle Viscosity (Pa s)
Ma
ss
Va
ria
tio
n (
Gt/
yr)
10E19 Pa s
10E20 Pa s
10E21 Pa s
-5
5
15
25
35
45
21 22 23
LOG of Lower Mantle Viscosity (Pa s)
Mass V
ari
ati
on
(G
t/yr)
10E19 Pa s
10E20 Pa s
10E21 Pa s
Changing The Mantle Viscosity
280±10
66±6
32±7
4
Gt/yr
Antarctica Greenland
Upper Bound
Lower Bound Gt/yr
Upper Bound
Lower Bound
Gt/yr
Gt/yr
Ice Mass Variation
Antarctica
Greenland
PGR MaxPGR Min
GRACE Tellus GFZ
Our best estimate GFZ
In Gt/yr
In Gt/yr
PGR MaxPGR Min
GRACE Tellus GFZ
Our best estimate GFZ
CSR
GRACE Tellus CSR
-228±17-13±13
-168±10+47±13
Lower bound estimate GFZ
-134±10+81±6
+4±14 -211±18
-77±7
-99±29
-120±43
-49
-71±22
-92±36
Ice Mass Variation
Antarctica
Greenland
PGR MaxPGR Min
GRACE Tellus GFZ
Our best estimate GFZ
In Gt/yr
In Gt/yr
PGR MaxPGR Min
GRACE Tellus GFZ
Our best estimate GFZ
Lower bound estimate GFZ
-172±39
CSR
GRACE Tellus CSR
-228±17-13±13
-168±10+47±13
-134±10+81±6
+4±14 -211±18
-77±7
-99±29
-120±43
-49
-71±22
-92±36
Ice Mass Variation: Antarctica East and West
Antarctica
East
Antarctica
West
GRACE Tellus GFZ
GFZ
PGR MaxPGR Min
414±!490±+
410±+ 794±!
3103±!6!
4! 3101±!
In Gt/yr
GRACE Tellus GFZ
GFZ
PGR MaxPGR Min
In Gt/yr
Ice Mass Variation: Antarctica East and West
Antarctica
East
Antarctica
West
GRACE Tellus GFZ
GFZ
PGR MaxPGR Min
414±!490±+
410±+ 794±!
3103±!6!
4! 3101±!
In Gt/yr
GRACE Tellus GFZ
GFZ
PGR MaxPGR Min
In Gt/yr
-54±57
What Other Works Say
Greenland
-60±20Tosi et al. (2005)SLR
+11±3Zwally et al. (2005)Altimetry
-224±41Rignot & Kanagaratnam (2006)Altimetry
-129±15Ramillien et al. (2006)GRACE
GRACE – LevelB1
GRACE – CSR01
GRACE – CSR01
-101±16Luthcke et al. (2006 )
-239±22Chen et al. (2006)
-238±36Velicogna & Wahr (2006)
-+67±28-107±23Ramillien et al. (2006)GRACE
-240±40--Tosi et al. (2005)SLR
TotalEastWest
+16±11
+0±56
+80±16
-47±4
-148±21
-77±14
-31±12Zwally et al. (2005)Altimetry
GRACE – CSR01
GRACE – CSR01
-152±79Velicogna & Wahr (2005)
-Chen et al. (2006)
Antarctica
-99±29
Our estimate for
Greenland
-172±39
Our estimate for
Antarctica