Becker, S.

Freiwald, Grit

Losch, Martin

Schuh, W. D.

English

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Stiftung Alfred-Wegener-Institutfür Polar- und Meeresforschung  75oW   50oW   25oW    0o    15oN   30oN   45oN   60oN   75oN   [m]−1 −0.5 0The picture shows the geodetic Rifu-gio MDT from section 1 before mod-ification by the any ocean model.The Rifugio MDT is now combinedwith the ocean model IFEOM.The inverse error covariance matri-ces are used for weighting the data.1 Mean dynamic topography modelingMean dynamic topography (MDT) η is the departure of the seasurface from the geoid. The geostrophic relation balancev =gf∂η∂xis used for deriving ocean surface velocities v. These can beassimilated into inverse ocean models.satellite orbitsea surfaceηgeoidreference ellipsoidMean 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 equationsdirectly. The MDT is calculated on the ocean model grid andno additional smoothing of the MDT is required.A stochastic model accounts for the omission error in therespective frequency domains.GRACEAltimetrySmoothness===Combination=Eliminationof xcsNormal equationfor MDTIntegrationinto ocean modelxcs1xcs2xcs3xFEFrequency domains of observations and parametrizationCombiningmean dynamic topography (MDT)and steady-state ocean modelsGrit Freiwald1, Martin Losch1, Wolf-Dieter Schuh2 and Silvia Becker21Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany2University Bonn, Institute of Theoretical Geodesy, GermanyEmail: grit.freiwald@awi.de2 Inverse 2D ocean model: FEMSECTFEMSECT describes a 2D section from Tasmania to Antarctica.The full combined Rifugio approach is not applicable to a 2Dsection model. However, the effects of different omission errormodels are studied.130o O140oO 150oO 160oO170 oO  70oS   60oS   50oS   40oS   30oS SAFCOUNPFEACSection location. latitude [°S]depth [m]Across−section velocities, positive eastward [m/s]  45 50 55 60 65−4500−4000−3500−3000−2500−2000−1500−1000−5000−0.4−0.3−0.2−0.100.10.20.30.4Velocity profile across the section.The velocity profile across the section is already well repre-sented without additional MDT information. When MDT isincluded, the transport error estimates change.FEMSECT transport errors:Ref.051015[Sv]00.10.20.3[PW]−−−−−−−−−−−−−−−−−→increasing consideration of omission errorFinal transportsacross section:Mass: 159 ± 17 SvHeat: 1.91 ± 0.26 PW4 ResultsFEMSECT:•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.BLABLABLABLABLABLABLABLA•The ocean model is improvedby the new MDT:– more detailed currentstructure– steeper temperaturegradients– more realistic MOC– increased heat transports3 Inverse 3D ocean model: IFEOMIFEOM is a 3D Finite Element model for the North Atlantic ocean.Without Rifugio MDT: With Rifugio MDT:  75oW   50oW   25oW    0o    15oN   30oN   45oN   60oN   75oN   [m]−0.5 0 0.5  75oW   50oW   25oW    0o    15oN   30oN   45oN   60oN   75oN   [m]−0.5 0 0.5Resulting IFEOM MDT.  75oW   50oW   25oW    0o    15oN   30oN   45oN   60oN   75oN   [Sv]−50 0 50  75oW   50oW   25oW    0o    15oN   30oN   45oN   60oN   75oN   [Sv]−50 0 50IFEOM barotropic stream function.[m]   20oN  40oN  60oN  80oN    −5000−4000−3000−2000−10000[Sv]0 5 10 15 20[m]   20oN  40oN  60oN  80oN    −5000−4000−3000−2000−10000[Sv]0 5 10 15 20IFEOM meridional overturning circulation (MOC).00.511.52[PW] 10oN  20oN  30oN  40oN  50oN  60oN  70oN  First guessRif05IFEOM heat transports.A full MDT error covariancematrix is also estimated.

Combining mean dynamic topography (MDT) and steady-state ocean models

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