Stiftung Alfred-Wegener-Institut für Polar- und Meeresforschung
2 Gravity field models
Global gravity field solutions are usually represented by spherical harmonic functions. To be used in an ocean model, the series has to be truncated and projected onto the finite ocean model grid.
Due to neglecting small scales, the “omission error” occurs and leaks into large scales.
We show: The omission error should be taken into account!!
latitude (◦S)
Index of singular values
30 10
40 45
50
50 55
60 65
0 -0.05
0.1 0.05 0.15 m2
10−0
10−1
10−2
10−3
Complete covariance matrix ...
... and its singular values
Error covariance matrix of complete geoid model
The omission error has con- siderable influence on the er- ror covariance matrix whose inverse is used as the weight- ing matrix during the opti- mization.
No MDT
Omission error neglected
Omission error partly considered
Full omission
error
0 20 40 60 80 Sv
Formal errors for transport across section
Mass transport across section: 174 ± 48 Sv
(with geoid model and full omission error) RESULTS:
• The omission error is not negligible for the overall error esti- mate.
• Considering the omission error reveals that GRACE data are not accurate enough for improving transport estimations by ocean models significantly.
• Assimilating mean dynamic topography (MDT) into the ocean model leads to high mass and heat transport estimations.
YES, but
• improvements are not as large as expected
• other methods lead to similar results
• further refinement of geoid models is required for ocean modeling
1 Stationary inverse ocean models ...
... compute oceanic flow fields from input vari- ables such as temperature, salinity and current velocities v.
It is very expensive to measure mean velocities of ocean currents!
But surface velocity v can be determined by the geostrophic relation balance
v = g f
∂η
∂x
from the mean dynamic topography η
- the departure of the sea surface from the geoid.
130
oO
140oO 150oO 160oO
170o
O
70oS 60oS 50oS 40oS 30
oS
SAF COUN
PF
EAC
Section model FEMSECT Tasmania - Antarctica.
satellite orbit sea surface
η
geoid reference ellipsoid
Mean dynamic topography (MDT)
latitude (°S)
depth (m)
45 50 55 60 65
−4500
−4000
−3500
−3000
−2500
−2000
−1500
−1000
−500 0
−0.4
−0.3
−0.2
−0.1 0
0.1 0.2 0.3 0.4
Velocity field from ocean model without MDT Mass transport across section: 159 ± 64 Sv
Formal errors are calculated from inverting the Hessian of the cost function.
Can we use current geoid models
for improving ocean state estimation
Grit Freiwald1, Martin Losch1, Wolf-Dieter Schuh2 and Silvia Becker2
1Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany
2University Bonn, Institute of Theoretical Geodesy, Germany Email: grit.freiwald@awi.de
3 Ocean surface currents from ice drift
The presence of sea ice at high latitudes impedes altimetric measurements. But satellite imagery allows for detection of mean sea ice motion, whose features are mainly attributable to atmospheric forcing.
Surface ocean currents beneath the ice cover can be derived by subtracting the wind effect from the ice motion via
c¯u c¯v
=
U¯ V¯
− F ·
cos θ − sin θ sin θ cos θ
u¯ v¯
with turning angle θ = arctan
P u′V ′ − P v′U′
P u′U′ + P v′V ′
and F = cos θ P u′U ′ + sin θ P v′U′ − sin θ P u′V ′ + cos θ P v′V ′
P u′2 + P v′2 , called the speed reduction factor. u′ = u − u¯ etc.
(N. Kimura: Sea Ice Motion in Response to Surface Wind and Ocean Current in the Southern Ocean, JMSJ 2004.)
Mass transport across section: 173 ± 46 Sv (with ice drift model)
RESULTS:
• Transports are higher than expected and
• Error reduction is of same scale as with geoid model.
130
oE 140oE 150oE 160oE
170o
E
70
oS 60
oS 50
oS 40
oS 30
oS
5~cm/s 130
oE 140oE 150oE 160oE
170o
E
70
oS 60
oS 50
oS 40
oS 30
oS
5~m/s
130
oE 140oE 150oE 160oE
170o E
70
oS 60
oS 50
oS 40
oS 30
oS
5~cm/s
Mean ocean surface current
Mean NCEP wind field
Mean ice drift data
