ice mass loss in the polar regions of the earth and mantle...

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)


70 Gt/yr

147 Gt/yr

GFZ R03M

ass in

Gt


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)



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)



-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)


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)



-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



Details: Greenland and Antarctica




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


Water equivalent in cm/yr

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


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


In Gt/yr

In Gt/yr

PGR MaxPGR Min

GRACE Tellus 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

ice mass loss in the polar regions of the earth and mantle...

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