N = 6371439.61  0.2 m

1. High resolution sea surface topography for the northern Atlanticusing the Iterative Combination Method Roger Hipkin & Addisu Hunegnaw School of GeoSciences University of Edinburgh

2. Geoid has been the weak link (mean) sea surface z = 0.66  0.2m geoid (zero height) h = 6371440.270.02m N = 6371439.610.2m

3. Why is the Geoid so poorly determined?

4. Rawmarine gravity data have • incomplete coverage and are • inaccurate

5. Rawmarine gravity data have • incomplete coverage and are • inaccurate

6. The problem of gravity data coverage To compute a geoid you need complete coverage of detailed gravity overlocalregion plus lower resolution global coverage

7. The geoid is a weighted surface integral of gravity

8. Marine gravity data gaps must be filled interpolated gravity measured gravity Dgint(x,y)

9. ~ 2 m free interpolation is very noisy

10. Patching with altimetric gravity anomalies

11. MDT from geoid EDINP & KMS04 Manual patching with altimetric anomalies is better but still noisy

12. There is a fundamental inconsistency with using altimetric gravity anomalies for patching Need a more rigorous way to combine altimetry, an MDT model and along-track gravity

13. By analogy with a real gravity anomaly and the geoid,define analtimetric gravity anomalyas a vertical derivative of the sea surface height ‘real’ gravity anomaly gravity effect of sea surface topography

14. KMS altimetric-gravity anomalies  250 mGal Ole Anderssen & Per Knudsen,1998

15. Gravity effect of composite model of dynamic sea surface topography  2 mGal

16. Although the bias of altimetric gravity anomaliesis small, for geodetic oceanography the 2 mGalis the signal and the250 mGalisnoise

17. Using analtimetric gravity anomalyas a proxy forreal gravitymakes MDTzero(or alternatively represents it by an a priori long-wavelength model) ‘real’ gravity anomaly gravity effect of sea surface topography

19. The Iterative Combination Method • generates a model of sea surface topography and interpolates gravity from ship tracks to a grid in a way that is rigorous and mutually consistent

20. Constraint on gravity interpolation The area integral of gravityinterpolated into between-track gapsmust generate ageoidthat fits thealtimetric sea surfaceminus theMDT model sea surface heightderived from altimetry geoid derived from infilled gravity MDT model

21. Constraint on the MDT model The modelfor mean dynamic sea surface topography must generate a gravity effect that fits altimetric gravity minus real gravityalong ship tracks observed along-track gravity ± fixed gravityderived from altimetry fixed gravity effect of MDT model iteratively modified

22. Constraint on the MDT model The modelfor mean dynamic sea surface topography must generate a gravity effect that fits altimetric gravity minus real gravityalong ship tracks No interpolation of gravity needed observed along-track gravity ± fixed gravityderived from altimetry fixed gravity effect of MDT model iteratively modified

23. The Iterative Combination Method • generates a model of sea surface topography and interpolates gravity from ship tracks to a grid in a way that is rigorous and mutually consistent

24. FFT (combined geoid) n (combined gravity) n adjust datum (combined gravity) n+1 weighted combination start initial gravity FFT weighted combination initial pseudo-geoid (gravity-based geoid)n+1 adjust datum next iteration

25. Pseudo - geoid GOCINA Composite Mean Dynamic Topography (extended) GRACE geoid GGM01c (n  90) Altimetric Mean Sea Surface – –  Residual Pseudo - geoid

26. Pseudo - geoid GOCINA Composite Mean Dynamic Topography (extended) GRACE geoid GGM01c (n  90) Altimetric Mean Sea Surface removed & restored just to make quantities small

27. Pseudo - geoid GOCINA Composite Mean Dynamic Topography (extended) GRACE geoid GGM01c (n  90) Altimetric Mean Sea Surface Initial MDT model gets iteratively modified

28. Pseudo - geoid GOCINA Composite Mean Dynamic Topography (extended) GRACE geoid GGM01c (n  90) Altimetric Mean Sea Surface fixed

29. altimetric mean sea surface

30. extended composite MDT

31. residual pseudo-geoid

32. Pseudo - geoid weight Weight of pseudo-geoid determined from expected uncertainty in composite MDT model

33. FFT (combined geoid) n (combined gravity) n adjust datum (combined gravity) n+1 weighted combination start initial gravity FFT weighted combination initial pseudo-geoid (gravity-based geoid)n+1 adjust datum next iteration

34. Gravity Composite of ship, airborne and land free-air anomalies, manually patched with adjusted altimetric free-air anomalies, GRACE freeair anomalies GGM01c (n  90) –  Residual Gravity

35. Residual gravity

36. Gravity weight ± zero weight where no data

37. Convergence of iterative weighting algorithm

38. Iterative combination Method MDT purely terrestrial data - no GRACE input

39. Long wavelength components of the finally interpolated free-air gravity must match GRACE free-air anomalies Long wavelength components of altimetric sea surface minus MDT model must match GRACE geoid Impact of GRACE data

40. Residual between surface gravity and GRACE GGM01s free-air anomalies, smoothed with a 450km low-pass filter Make surface gravity consistent with GRACE by adding this residual

41. Residual between composite MDT and MDT consistent with GRACE GGM01s smoothed with a 450km low-pass filter Make composite MDT consistent with GRACE by adding this residual

42. ICM MDT on a 2 km gridsmoothed to 450 km With this smoothing,the MDT model is constrained by GRACE and satellite altimetry

43. Shorter wavelengths, not controlled by GRACE, may be due to geoid errors or MDT errors However, their rms residual is only 2.3 cm

44. Some residuals correspond to an intensification on shelf-edge gradients

45. Other residuals have the characteristic ‘bulls eye’ pattern of a gravity field error

46. ICM MDT on a 2 km gridsmoothed to 450 km This corresponds to all residuals being gravity errors

47. Unsmoothed ICM MDT on a 2 km grid This corresponds to all residuals being corrections to the MDT model

48. ICM MDT on a 2 km grid smoothed to l > 75 km Some gravity field errors suppressed by smoothing Smoothed MDT l > 75 km

49. Geostrophic current velocities deduced from ICM MDT models GRACE-corrected GOCINA composite MDT ICM MDT with 75 km smoothing

50. Mean surface flow from Lagrangian drifters (Jakobsen et al, 2003) ICM model with 75 km smoothing Drifters assimilated into circulation model (Nøst & Isachsen, 2003)