Global mass balances reconstructed from GRACE
level 2 temporal gravity data
Ernst Schrama
Delft University of Technology
[email protected]
13-16 November 2012 | ESA-ESRIN | Frascati (Rome), Italy
This talk
• GRACE data processing
– Source data
– Degree 1 and 2 corrections
– Mascon inversion method
• Mass balances
– Consequences of degree 1 and 2
– Accelerations and episodic events
– Sea level budget
• Outlook
Equivalent water thickness
• We approximate it via a spectral relation:
H ( , ;t)   H lm (t)Ylm ( ,  )
l m
aee (2l 1)
H lm (t) 
' Wl ( )Clm (t)
3 w (1 kl )
• H: water thickness, Y: spherical harmonics, kl’ are
load Love numbers, ae: equatorial radius, ρe:
density earth, ρw: density water, Wl(τ) block
 average smoother
How do we get △Clma
•
•
•
•
•
GRACE level 2 data is used: CSR RL4 and RL5
An average is determined between 2002.7 and 2012.2
Replace C20 by satellite laser ranging values
Added geo-center: C10 C11 S11 coefficients
Corrected for Glacial Isostatic Adjustment effect:
–
–
–
–
–
•
Paulson/Geruo A based on ICE5G (global)
Ivins James 05 R2 (Antarctica only)
Whitehouse 2012 (Antarctica only)
Simpson 2009 (Greenland only)
ANU models (Greenland only)
Equivalent water height are computed for 3 degree
block averages truncated at Lmax=60
Geo-center discussion
• Geo-center physics:
–
–
–
Water thickness from GRACE is modeled in the CM frame
where we don’t see the effect
In the CF frame geophysical loading isn’t evenly
distributed over the globe, land is overrepresented.
As a result, in the CF frame the CM is slightly moving
around
• Solutions: “Borrow” or “Assess your own” geo-center
• Replace the ocean-signal by something we model
ourselves
• Comparison to Swenson’s degree 1 terms
Geo-center discussion (2)
• The center of mass variations follow from the
surface load
1
xi 
m(x ) xi d

Me 
• The relation to degree 1 coefficients is:

' 
C10
C10 
 '  1 k1  
C11  a C11  
e
' 


S
S11 

 11 
' 
C10
X 
 ' 
 
Y  3 a C11 
'


Z 

S11 

Sea level equation
The model ocean is a surface that we get by solving the sea level equation
RSL = Geoid - Uplift : S  N  U
  

i 
w
S  Gs i I   Gs i I d Gs o S   Gs i S d SE
 
  



Eustatic world
SLE world
Rotational feedback
w
x
• Whenever we put mass into the ocean we
modify the Earth’s moment of inertia tensor
• This tensor should be used in excitation
functions that follow from the Euler Liouville
equations
• In the end we insert the rotational terms in
the centrifugal potential.
• For the SAL term in the sea level equation it
means:
C20 
0.00086  C20 
 


C21    0.35  C21 

S21 
SAL 
 0.35  S21 
EWH
Amplitude
Phase
Slope
dx
0.96
104
-0.04
dy
1.27
284
-0.006
dz
1.20
90
-0.138
mm, DOY and mm/yr
Greenland equivalent water rates
Antarctic equivalent water rates
Mass time series reconstruction
Observing system with infinite resolving power:
N
y i (x) =  ij b j (x)   i (x)  x  
j=1
Real world GRACE system comes with finite resolving power
because of spherical harmonic limit (60) and Gaussian filtering:

N
G(y i (x)) =   ij G(b j (x))  G( i (x))  x  
j=1
or
N
zi (x) =   ij  j (x)   i (x)  x  
j=1
Lmax truncated Gaussian smoothed dish response function
L max
, ,Lmax ,cap   G(,l)  l (cap)Pl cos 
l 0
cap
1
 l (cap)   Pl (cos  )sin  d
2  0
cap


M ascon method implementation
zi  1 L N i  i  Ai  i
with N = 10242. The scaling parameters are :
ˆ i  ( A A W ) A  zi

1
T
1 1
T
1
with
E(ii )  I and W = I
t
where  is small relative to 
Mass time series, Greenland, Antarctica, West Antarctica, Dronning Maud Land
Accelerations
Source: Michiel van den Broeke
Mass balances between 2002.7 to 2012.2
Domain
Rate
Acceleration
AIS
WAIS
-177 +/- 11
-140 +/- 4
-15 +/- 9
-29 +/- 3
EAIS
AP
GRIS
0 +/- 8
-38 +/- 2
-265 +/- 5
18 +/- 7
-4 +/- 2
-25 +/- 4
LIC
Ocean
-174 +/- 7
557 +/- 39
0 +/- 6
59 +/- 31
This assessment EXCLUDES the possibility of GIA model errors,
Paulson’s GIA model was used as a reference
Sensitivity to degree 1 terms and C20
Antarctica
Greenland
Augment degree 1
+13
+3
Replace degree 2
+32
-8
Provided rate corrections are in Gt/yr between 2002.7 and 2012.2.
Sensitivity to GIA models
Ice Sheet
ICE5g ANU
Simpson
Rate IJ05R2
Rate W12a
Rate ICE5G
37
6
3
1
Antarctic
-90 +/- 30
-88 +/- 24
-177 +/- 11
-15 +/- 8
West Antarctic
-116 +/- 9
-132 +/- 6
-140 +/- 4
-29 +/- 3
East Antarctic
56 +/- 19
78 +/- 15
1 +/- 8
18 +/- 6
Peninsula
-30 +/- 3
-34 +/- 5
-38 +/- 2
-4 +/- 2
Amundsen
-100 +/- 2
-106 +/- 2
-100 +/- 2
17 +/- 1
-265 +/- 5
-24 +/- 4
Greenland
-271 +/- 21
Acc
Conclusions: Mass balances over Antarctica are cut in half by the new GIA
models, the difference is due to an updated ice history. No evidence that the
Greenland mass balance is significantly affected by other GIA models. The time
window runs between 2002.71 and 2012.21
Outlook and Conclusions (1)
• The GRACE system is near to its end of lifetime, is has
demonstrated to be able to observe the global mass
balances to within approximately 10% if we ignore the GIA
problem
• C20 and degree 1 terms are respectively poorly or not
observed by GRACE. Together they affect the Antarctic MB
by +60 Gt/yr
• For all studied GIA models, the GRIS is hardly affected by
GIA (-271 +/- 21) Gt/yr. For Antarctica it is -90 +/- 30 Gt/yr
with the new GIA models, which if 87 Gt/yr less compared
to GIA models based upon ICE-5G.
Conclusions (2)
• Ice sheet dynamics is a 2nd elephant in the room
– 10 years is still a short data dataset, we need GFO
– All solutions show an uplift signal in Dronning Maud land
which are related to accumulation events
• Accelerations:
– The Amundsen sector and the Antarctic Peninsula show a
large steady acceleration of mass loss
– Mass loss wandered within the GRIS from SE to NW
– How long can accelerations be maintained? That would
motivate any new mass balance monitoring system.
• Sea level: 1.30 +/-
0.05 mm/yr 0.17 +/- 0.09 mm/yr2
which is 26 +/- 11 cm in 2050 and 95 +/- 42 cm in 2100