1. The OC in GOCE: A review The Gravity field and Steady-state Ocean Circulation Experiment Marie-Hélène RIO

2.  From Gravity to ocean circulation: Basic concepts  The GOCE breakthrough  Main Research Topics during the mission’s life  Conclusions OUTLINE

3. From Gravity to ocean circulation: Basic concepts h = Sea level above geoid Altimetry AND GOCE

4. GOCE AND Altimetry h G SSH h SSH=h+G Some very simple equations SSH-MSSH=h-MDT=SLA Altimeter Sea Level Anomalies h’ P SLA MDT=MSSH-G h=SLA+MDT Surface currents Surface mean currents h=SSH-G MDT=MSSH-G MSSH=MDT+G

5. cm/s The GOCE breakthrough Mean geostrophic currents speed From in-situ measurements

6. The GOCE breakthrough Mean geostrophic currents speed GRACE, 2010 : Resolution 100 km

7. The GOCE breakthrough Mean geostrophic currents speed GOCE R1, 2010 : Resolution 100 km

8. The GOCE breakthrough Mean geostrophic currents speed GOCE R5, 2014 : Resolution 100 km

9. Mulet et al, Journal of Geodesy, 2012 Sanchez-Reales et al, Marine Geodesy, 2012 Feng et al, Journal of Geodynamics, 2013 Siegesmund et al, JGR, 2013 Jin et al, JAOT, 2014 Bingham et al, JGR, 2014 Bruinsma et al, GRL, 2013, 2014 7 cm/s error on mean circulation at 80km Impact of orbit lowering is significant at 80 km resolution: RMS differences to observation reduced by 4 % for both components The GOCE breakthrough Validation using external drifting buoy velocities Accuracy of R5 release for mean currents 4 cm/s error on mean circulation at 100km Courtesy, S. Mulet meridional zonal RMS differences with in-situ mean velocities R2 R5 R2 R5 GRACE R3 R4 R3 R4 80 100 150 200 km

10. How to best extract the MDT information from Altimetry and GOCE (MDT=MSS-G)? Which filter? Which accuracy? Main research focus during the mission’s life

11. MDT=MSS CNES-CLS11 – EGM-DIR-R5RAW DIFFERENCE 80 km 150 km MDT=MSS-Geoid The filtering issue 100 km

12. Two main approaches the so-called ‘Heuristic’ approach: Bingham et al, 2011,2014 ; Siegesmund et al, 2013… Optimal filter length obtained by minimising the root mean squared (RMS) difference between the currents derived from the filtered Geodetic MDT and an independent reference (surface drifter velocities, independent MDT) Rigorous propagation of GOCE and MSS error is done (Becker et al, 2012) to obtain the full MDT error covariance matrix, that is further used to obtain the optimally filtered MDT (Freiwald et al, 2013; Becker et al, 2014) An optimaly filtered MDT is obtained together with its error covariance, a mandatory information for assimilation into ocean general circulation models. Optimal filter length for GRACE (left) and GOCO03S (right) from Siegesmund et al, 2013, JGR See Rory Bingham’s talk later this morning MDT=MSS-Geoid The filtering issue

13. How to best extract the MDT information from Altimetry and GOCE (MDT=MSS-G)? Which filter? Which accuracy? Feasability of the « direct » approach h=SSH-GOCE? Main research focus during the mission’s life

14. G Crossing a new frontier in altimeter data exploitation: The « direct » method Over the Arctic ice is melting much faster than expected: more and more ice-free areas for which no mean profile is available. The MSSH needed for MDT calculation through MDT=MSSH-GOCE is unaccurate/undefined. For 20 years, the estimation of the sea level h (and derived currents) from altimetry and gravimetry has required the use of intermediate ‘reference’ surfaces: h=(SSH-MSSH)+MDT h SSH Mulet et al, 2014 Pack Ice limit on Sept18th, 2012 Median 1979-2000 Mapping (objective analysis) at 100 km of resolution SLA along track (SSH-MSS DTU13 Andersen et al, 2013) SLA map + MDT DUT13 (Andersen et al, 2013) h map 12 September 2012 classical method 1 2

15. G For 20 years, the estimation of the sea level h (and derived currents) from altimetry and gravimetry has required the use of intermediate ‘reference’ surfaces: h=(SSH-MSSH)+MDT h SSH Mulet et al, 2014 Pack Ice limit on Sept18th, 2012 Median 1979-2000 Mapping (objective analysis) at 100 km of resolution h along track (SSH-DIR5 Bruinsma et al, 2014) h map 12 September 2012 Direct method Crossing a new frontier in altimeter data exploitation: The « direct » method At 100km, the the ‘direct’ method : h=SSH-GOCE provides more accurate information

16. G For 20 years, the estimation of the sea level h (and derived currents) from altimetry and gravimetry has required the use of intermediate ‘reference’ surfaces: h=(SSH-MSSH)+MDT h SSH Mulet et al, 2014 Pack Ice limit on Sept18th, 2012 Median 1979-2000 RMSMean Differences between the classical and the direct approach for the period 15/08/2012-31/10/2012 Crossing a new frontier in altimeter data exploitation: The « direct » method

17. Janczic et al, 2012, Ocean Science Increased agreement of model outputs to Argo floats temperature at 800m depth (not assimilated) compared to free run Assimilation into Finite Element Ocean Model (FEOM) Dynamic Ocean Topography from TOPEX, Jason-1, GFO and ENVISAT obtained from data within 10 day interval around 25 April 2004 and geoid from GOCO01S model. The profile approach filtering was applied using Jekeli- Wahr filter of 121km resolution Free run Assimilated run Crossing a new frontier in altimeter data exploitation: The « direct » method

18. How to best extract the MDT information from Altimetry and GOCE (MDT=MSS-G)? Which filter? Which accuracy? Feasability of the « direct » approach h=SSH-GOCE? Beyond GOCE resolution: synergy with in-situ data Main research focus during the mission’s life

19. SAR Drifters GOCE Beyond GOCE resolution: Synergy with space-borne and in-situ data

20. The CNES-CLS13 MDT Rio et al, 2014, GRL Direct Method MDT=MSS-GOCE R4 Optimal filtering (Rio et al, 2011) GOCE 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 (Argo floats, drifting buoys) Multivariate Objective Analysis High resolution (1/4°) MDT and associated mean geostrophic currents Beyond GOCE resolution:Synergy with in-situ data

21. The CNES-CLS13 MDT Rio et al, 2014, GRL Beyond GOCE resolution:Synergy with in-situ data

22. The GOCE only MDT (First Guess) cm/s

23. The CNES-CLS13 mean geostrophic currents cm/s CNES-CLS13 velocity = Drifter mean velocity+ GOCE MDT velocity

24. CONCLUSIONS The GOCE mission has allowed major advance for depicting the Ocean Circulation through the calculation of the ocean Mean Dynamic Topography The mission objective has been achieved (1-2 cm accuracy at 100 km resolution) This translates into error on mean circulation of less than 4 cm/s at 100 km and less than 7cm/s at 80km Important impact of end of mission satellite orbit lowering to achieve this accuracy/resolution. During the mission life, research has focused on optimizing GOCE information for MDT calculation (optimal filtering approach, error calculation, validation through drifter comparison) New ways of combining GOCE and altimetry have also started to be investigated, in order to avoid the use of intermediate reference surfaces (MSSH, MDT) for sea level and ocean currents calculation.

25. New research is now exploring high resolution modelling (global model assimilating altimeter data are 1/12°), high resolution altimetry data (SWOT coming in 2020), estimation of high resolution surface currents (not only geostrophic: ESA project GLOBCURRENT). In that context,  Strong synergy with other space-borne and in-situ data is needed to go toward high resolution estimates of ocean surface currents, globally or regionally.  New future dedicated gravity missions are needed to further enhance the spatial and temporal resolution of gravity field modeling. CONCLUSIONS