Stiftung Alfred-Wegener-Institut für Polar- und Meeresforschung
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The picture shows the geodetic Rifu- gio MDT from section 1 before mod- ification by the any ocean model.
The Rifugio MDT is now combined with the ocean model IFEOM.
The inverse error covariance matri- ces are used for weighting the data.
1 Mean dynamic topography modeling
Mean dynamic topography (MDT) η is the departure of the sea surface from the geoid. The geostrophic relation balance
v = g f
∂η
∂x
is used for deriving ocean surface velocities v. These can be assimilated into inverse ocean models.
satellite orbit sea surface
η
geoid reference ellipsoid
Mean dynamic topography (MDT)
Common problems of MDT models are the different scales, accuracies and basis functions of altimetry data and geoid data.
These issues are avoided by combining the normal equations directly. The MDT is calculated on the ocean model grid and no additional smoothing of the MDT is required.
A stochastic model accounts for the omission error in the respective frequency domains.
GRACEAltimetrySmoothness
=
=
=
Combination
=
Elimination of xcs
Normal equation for MDT
Integration
into ocean model
xcs1 xcs2 xcs3 xFE
Frequency domains of observations and parametrization
Combining
mean dynamic topography (MDT) and steady-state ocean models
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
2 Inverse 2D ocean model: FEMSECT
FEMSECT describes a 2D section from Tasmania to Antarctica.
The full combined Rifugio approach is not applicable to a 2D section model. However, the effects of different omission error models are studied.
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SAF COUN
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EAC
Section location. latitude [°S]
depth [m]
Across−section velocities, positive eastward [m/s]
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Velocity profile across the section.
The velocity profile across the section is already well repre- sented without additional MDT information. When MDT is included, the transport error estimates change.
FEMSECT transport errors:
0 Ref.
5 10 15 [Sv]
0 0.1 0.2 0.3
[PW]
−−−−−−−−−−−−−−−−−→
increasing consideration of omission error
Final transports across section:
Mass: 159 ± 17 Sv Heat: 1.91 ± 0.26 PW
4 Results
FEMSECT:
• Additional MDT information reduces the transport error.
• Neglecting the omission error underestimates the true error.
IFEOM:
• Model-data deviations are consistent with error estimates.
• Estimation of posterior errors is not straightforward and a sub- ject for further research.
• The geodetic MDT is improved by the ocean model.
BLABLA BLABLA BLABLA BLABLA
• The ocean model is improved by the new MDT:
– more detailed current structure
– steeper temperature gradients
– more realistic MOC
– increased heat transports
3 Inverse 3D ocean model: IFEOM
IFEOM is a 3D Finite Element model for the North Atlantic ocean.
Without Rifugio MDT: With Rifugio MDT:
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Resulting IFEOM MDT.
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IFEOM barotropic stream function.
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IFEOM meridional overturning circulation (MOC).
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IFEOM heat transports.
A full MDT error covariance matrix is also estimated.
