1. An oceanographic assessment of the GOCE geoid models accuracy S. Mulet 1, M-H. Rio 1, P. Knudsen 2, F. Siegesmund 3, R. Bingham 4, O. Andersen 2, D. Stammer 3, J. Benveniste 5 and the GUT consortium 3 1 2 3 4 5

2. Overwiew Assessment of satellite only geoid model: GOCE R5 by computation of MDT, mean current and comparison with unfiltered and filtered drifters Assessment of satellite only geoid model though assimilation in numerical model Toward higher resolution – Combined geoid model (with altimetry) – Combined MDT (with oceanic in-situ data) 3

3. Computation of geodetic MDT from GOCE Mean Sea Surface MSS CNES-CLS11 Spatial scale ~ 10km Geoid height DIR5 Spatial scale ~ 100km Mean Dynamic Topography (MDT) - = (m) (cm) Omission and commission errors - Difficulty in subduction areas and at the boundary (land/sea)  need to be filtered

4. Mean Dynamic Topography (MDT)

5. Filtering MDT at different scales 80 km MDT from GOCE (DIR5) filtered with a Gaussian filter

6. 80 km 100 km MDT from GOCE (DIR5) filtered with a Gaussian filter Filtering MDT at different scales

7. 80 km 100 km 125 km MDT from GOCE (DIR5) filtered with a Gaussian filter Filtering MDT at different scales

8. 80 km 100 km 125 km 200 km MDT from GOCE (DIR5) filtered with a Gaussian filter Filtering MDT at different scales

9. Compute associated mean geostrophic currents 80 km Mean currents from GOCE (DIR5)

10. 80 km 100 km Mean currents from GOCE (DIR5) Compute associated mean geostrophic currents

11. 80 km 100 km 125 km Mean currents from GOCE (DIR5) Compute associated mean geostrophic currents

12. 80 km 100 km 125 km 200 km Mean currents from GOCE (DIR5) Compute associated mean geostrophic currents

13. Comparison with independant estimate: unfiltered drifters 80 km 100 km 125 km 200 km Velocity estimate from surface drifters processed to match the physical content of the mean geostrophic currents Standard deviation of the difference with drifters (cm/s) Optimal resolution between 100 and 125 km zonal meridional 80100125150200 (km)

14. Improvement of geoid models: from GRACE to GOCE R5 80100125150200(km) zonal Standard deviation of the difference with drifters (cm/s) meridional R5

15. Improvement of geoid models: from GRACE to GOCE R5 80100125150200(km) Standard deviation of the difference with drifters (cm/s) zonal meridional GRACE R5

16. Improvement of geoid models: from GRACE to GOCE R5 80100125150200(km) zonal Standard deviation of the difference with drifters (cm/s) meridional GRACE R2 R5

17. Improvement of geoid models: from GRACE to GOCE R5 80100125150200(km) zonal Standard deviation of the difference with drifters (cm/s) meridional GRACE R2 R3 R5

18. Improvement of geoid models: from GRACE to GOCE R5 80100125150200(km) zonal Standard deviation of the difference with drifters (cm/s) meridional GRACE R2 R3 R4 R5

19.  Comparison to unfiltering drifters  Huge improvement of GOCE over GRACE  Improvement of the differente releases (GOCE models go closer and closer to the 100 km resolution !)  Optimal resolution of mean velocities computed from GOCE = 100-125 km and  At 100 km (GOCE targeted resolution) StD ~ 7.5 cm/s (include omission and commission error) This include: - ~3 cm/s on drifter velocity estimate - an ~1 cm on MSS Note also that - velocities (gradient of the height) are much more sensible that height - we use gaussian filter that is not an ideal filter Improvement of geoid models: from GRACE to GOCE R5 ! 80100125150200(km) Zonal (Tx) Standard deviation of the difference with drifters (cm/s) Meridional (Ty) GRACE R2 R3 R4 R5

20.  Comparison to filtering drifters  estimation of commision error only !!  TIM and DIR5: similar results  At 100km StD ~ 5cm/s  Error impacted by geoid but also MSS, filtering, drifter !  Error > error only due to GOCE !! Comparison with independant estimate: filtered drifters DIR4 DIR5 TIM5 zonal Standard deviation of the difference with filtered drifters (cm/s) meridional 80100125150200(km)

21. Regional Comparison Regional comparison with independant estimate: filtered drifters 125 km

22. Regional comparison with independant estimate: filtered drifters 125 km

23. Assessment though assimilation in numerical model

24. GECCO Setup MITgcm-Model (PE-eqn. C-grid) Resolution:1 o horizontal, 23 layers Region: global, 80 o S-80 o N Includes sea ice model Closed boundaries towards the Arctic KPP mixed layer model Gent & McWilliams eddy param. Adjoint assimilation method Assimilated data: - SLA from altimetry - surface S and T - S,T profiles - MDT Control parameters Salinity and temperature initial state Atmospheric state near ocean surface:  Wind vector  Temperature  Specific humidity  Precipitation  Downward longwave radiation MDT (DTU10 – GOCO01s) = assimilated MDT Siegismund et al. (2014)  Iteration 0 : no assimilation  GECCOref : reference synthesis without MDT assimilation (45 iterations)  GECCOmdt : synthesis with MDT assimilation (GOCO01s; 89 iterations) Stop criterion: cost function reduction per iteration step < 0.5% [m] Assessment though assimilation in numerical model

25.  In comparison to a reference synthesis without MDT assimilation but otherwise same configuration, the cost function for all major components significantly reduces when the MDT is added as constraint.  Especially, model-data residuals for SST and MDT fields strongly reduce Major contributions to the cost function (normalized) [K] SST model-data residuals [K] GECCOref GECCOmdt Assessment though assimilation in numerical model

26. Toward higher resolution

27.  GOCE better than combined geoid model between 100-200 km !!  GOCE improved combined geoid model !  Scales < 100 km have to be estimated with other data: Combined geoid model (altimetry) Combined MDT (oceanic in-situ data) Comparison filtered drifters What about combined geoid model ??

28. Combined geoid models Combination models including altimetric marine gravity combine geoid and mean sea surface at observation equation level: Augment the series of spherical harmonic functions, hereby reducing the unmodelled parts of the geoid, Reduce errors due to inhomogeniety and anisotropy Eigen-6c minus Eigen-6s

29. Comparing two combination models EGM 2008 and Eigen-6c: GRACE Mean Sea Surface GRACE ------- GOCE ------------- MSS MSS – Geoid model: ---------------- MDT ----------------------------- ----- 0 ------ >> easier filtering Combined geoid models Andersen and Knudsen, 2014

30. An example using DTU13MSS with Dir-r5 (upper/read) and with Eigen-6C3 (lower/blue): MSS-geoid (left) Power spectrum (below) 2D power spectrum (right) Most signal >0.6 cy/deg (≈ d/o 220) have been removed. Combined geoid models

31. New model - DTU13MDT: Similar to DTU12MDT updated with DTU13MSS Eigen-6C3 Improved mainly in the Arctic and in the equatorial region.. 20 year reference period Consistent with the new AVISO altimetry reference period.

32. Geostrophic Currents (DTU13MDT):

33. Geodetic MDT MDT=MSS CNES-CLS11 – Geoid (DIR4) filtering Large scale MDT=First guess Synthetic Method The short scales of the MDT (and corresponding geostrophic currents) are estimated by combining altimetric anomalies and in-situ data Multivariate Objective Analysis High resolution MDT Other way to compute HR MDT, combination with oceanic in-situ data  CNES-CLS13 MDT Rio et al., 2014

34. The CNES-CLS13 MDT

36. Have a look at the poster:

37. CONCLUSION Optimal resolution of GOCE MDT = 100-125 km (due to geoid model but also to MSS and filtering method) GOCE geoid model helps to improved combined geoid model between 100 and 200 km Positive impact for assimilation in numerical model 3

38. Conclusion !