Metingen van getijden dissipatie uit satelliet observaties

1. Metingen van getijden dissipatie uit satelliet observaties E. Schrama, TU Delft / DEOS The Netherlands schrama@geo.tudelft.nl

2. This talk • Altimetry to observe ocean tides • Global energy dissipation • Local energy dissipation • Extraction of internal tide signals • Comparison to dissipation

3. Satellite altimetry and tides • Altimetry: • Topex/Poseidon (and Jason), provide estimates of ocean tides at one second intervals in the satellite flight (along track) direction. • Quality Models: • The quality of these models can be verified by means of an independent comparison to in-situ tide gauge data, • RMS difference for M2: 1.5 cm, S2: 0.94, O1: 0.99, K1: 1.02, • Other consituents are well under the 0.65 cm level, • Assimilation: • There are various schemes that assimilate altimeter information in barotropic ocean tide models. (empirical, representer method, nudging)

4. Satellite altimetry Source: JPL

5. Mesoscale variability

6. M2 ocean tide

7. Global tidal energy dissipation • Integrated contribution over the oceanic domain • Integrated contribution over tidal cycles • Weak quality estimator for global ocean tides. • Independent astronomic and geodetic estimates. • Secular trend in Earth Moon distance • Earth rotation slow down • Consequences on the planet: • Phase lags ocean, body or atmospheric tides

8. 3.82 cm/yr M2 : 2.50 +/- 0.05 TW Tidal energy dissipation (Munk,1997)

9. Global energy dissipation

10. Global Dissipations Estimates Units: TeraWatts

11. Results Global Dissipation • High coherence between models, SW80 is an exception because it is pre-Topex/Poseidon. For this reason global dissipation estimates are not a good quality indicator. • M2: oceanic 2.42, astronomic 2.51 TW, the difference is dissipated in the solid Earth tide (Ray, Eanes and Chao, 1996). Independent body tide dissipation measurements by gravimeters are not convincing at the moment (only a 0.1 of a degree lag is expected) • S2: oceanic 0.40, geodetic 0.20 TW, the difference is mostly dissipated in the atmosphere (Platzman,1984)

12. Local Dissipation (1) W: Work P: Divergence Energy Flux D: Dissipation

13. Local dissipation (2) Notice: 1) Forcing terms are related to tide generating potential, self-attraction and loading, 2) the equations assume volume transport rather then velocity

14. Local dissipation (3) • In order to compute local dissipations you must specify the forcing terms and the velocities • Altimetry only observes tidal elevations, it does not provide us global tidal velocies (perhaps acoustic sounding can independent values) • The computation of barotropic velocities requires a numerical inversion scheme. • The forcing terms involve self-attraction and tidal loading and the tide generating potential.

15. How to get barotropic velocities • Bennett/Egbert method: the representer technique is applied to a linear spectral barotropic tide model. • Ray method: Least squares inversion constraining the elevation field • Schrama method (see poster): Similar inversion scheme with different treatment of the elevation field. • Local inversion: ongoing activities but no realistic results have been obtained so far. (Church, Anderson, Coleman approach).

16. Dissipation from TPXO51

18. Solution t4v6

19. Solution t6v6

20. Internal tides (1) • High frequency oscillation is imposed on the along track tide signal, wavelength typically 160 km for M2, (Mitchum and Ray, 1997). • The feature stands above the background noise level. • The phenomenon is visible for M2 and S2 (hardly for K1). • There is some contamination in the T/P along track tides in regions with increased mesoscale variability. • “Clean” Along track tide features are visible around Hawaii, French Polynesia and East of Mozambique. • AT tides seem to appear near oceanic ridge systems.

21. Track 223 Hawaii H dG D

22. Internal tides (2) 160 km 5 cm 1 h1 20 m 2 h2

23. Internal tides (3) (Apel, 1987)

24. Area’s of interest

32. Tidal bores and SAR Courtesy: ESA + uni Hamburg

33. Conclusions (1) • Global dissipation: • There are consistent values for most models, • The M2 dissipation converges at 2.42 TW to within 2% • Independent methods to determine the rate of energy dissipation (LLR, satellite geodesy). LLR arrives at 2.5 TW for M2 • Comparison to astronomic/geodetic values: • 0.2 TW at S2 for dissipation in the atmosphere • 0.1 TW at M2 for dissipation in the solid earth • gravimetric confirmation of the 0.1 TW is very challenging • History of Earth rotation relies of dissipation estimates from paleooceanographic ocean tide models.

34. Conclusions (2) • Local dissipation: • it is the same tidal energetics equation, the integration domain is however local and you need tidal transport estimates at the boundary of the local integration domain • realistic estimates are more difficult to obtain and require an inversion of tidal elevations into currents • Along track tide signal: • so far only results for standing waves • appears as high frequency tidal variations in along track altimetry, • appear to be related to internal wave features, • coherence to local dissipations, • visibility: Hawaii, Polynesia, Mozambique, Sulu Celebes region

35. Discussion • Why relate internal tides to dissipation? • Mixing in the deep ocean is according to (Egbert and Ray, 2000) partially caused by internal tides. • Their main conclusion is that the deep oceanic estimate for M2 is about 0.7 TW. • According to Munk 2 TW is required for maintaining the deep oceanic stratification. • 1 TW could come from wind • The remainder could be caused by internal tides.