1. OSTST 2007 - March, 12-15 - Hobart, Tasmania Ocean Mean Dynamic Topography from altimetry and GRACE: Toward a realistic estimation of the error field Marie-Helene Rio(1), Philippe Schaeffer(1), Jean-Michel Lemoine(2), Gilles Larnicol(1) (1) CLS, 8-10 rue Hermes, 31256 Ramonville saint agne, France (2) GRGS, 14 avenue Edouard Belin, 31400 toulouse, France

2. Context MSSGeoid - = MDT - Oceanographic analysis - Assimilation into operationnal ocean forecasting systems Combination of MSS and geoid for MDT computation Computation of high resolution MDT (Rio et al, 2004, 2005) A number of key issues + SLA = ADT Computation of a realistic error field Error on the geoid, error on the MSS, error on the MDT computation method ? MDT Large scale (400 km) High resolution (<50 km) ?

3. Combination of MSS and geoid for MDT computation MSS CLS01 – EIGEN-GL04S Rc=133 kmRc=200 kmRc=300 kmRc=400 km Gaussian filter A

4. Limits of the gaussian filtering No error estimate on the resulting MDT Creation of spurious strong gradients in specific areas (around islands, along coasts, in strong subduction areas…) r c =133km r c =200kmr c =300kmr c =400km cm

5. Optimal combination method MDTH obs =MSS-Geoid Eigen-4S Eigen-3S Eigen-3C GGM02S GGM02C EGM96 19 cm RMS A: Covariance matrix of the observations: = F c (r) + MSS CLS01 error field cm The CMDT RIO05 (Rio et al, 2005) field is low-pass filtered to 400 km and its variance is computed in 600 km radius domains. cm =A-priori variance ε 2 obs = ε 2 MSS + ε 2 Geoid R c =133kmR c =400km Different correlation functions have been tested

6. Results MDT Estimated error field cm r c =133km r c =200km r c =300km r c =400km

7. Validation Is the estimated error field realistic? A- Method: Comparison to independent synthetic MDT estimates -In-situ temperature and salinity from XBT and CTD are used to compute dynamic heights relative to 1000m for the period 1993-2005. h insitu geoid z=-1000m h 1000 -the dynamic topography at 1000m as estimated by (Willis et al, 2007) is added to the dynamic heights. h z=0 -Altimetric Sea Level Anomalies from AVISO are then subtracted to compute synthetic estimates of the Mean Dynamic Topography. h’ alti Synthetic MDT estimates MDT synth

8. B- Results RMS differences between synthetic heights and: 1- Gaussian filtered MDTs Dashed line: comparison to unfiltered synthetic heights: 133 km filter Solid line: comparison to filtered synthetic heights: 400 km filter 2- Optimal MDTRMS difference to unfiltered synthetic heights = 8.5 cm ~ 8.5² 222 om synth MDT  2 RMS  6.0² 2² 6.0²+ +

9. Conclusions We investigated the efficiency of optimal method to compute realistic large scale MDT from altimetry and geoid and associated error field. We showed consistency between the obtained error field and how the large scale MDT compares to independent synthetic estimates of the MDT. Improvements need to be made for the better estimation of the altimetric data error (on MSS and SLA - error on the different corrections used during altimeter data processing) Impact of using the covariance error information in the optimal MDT computation needs to be investigated (available in the case of future GOCE data) Method based on the knowledge of the observation errors and a-priori statistics of the error field Further improvements are possible: Future work MDT=MSS-Geoid Improved estimates of high resolution « combined » MDT EIGEN05S, EGM07,… GOCE! New MSS estimations and realistic error field

10. First Guess:EIGEN-GRACE03S 400 km In-situ data: drifters and dynamic heights 1993-2002 Global: 1/2° resolution grid The Combined Mean Dynamic Topography RIO05 Rio et al, 2005 cm