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Metingen van getijden dissipatie uit satelliet observaties

E. Schrama, TU Delft / DEOS

The Netherlands

schrama@geo.tudelft.nl

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This talk

• Altimetry to observe ocean tides

• Global energy dissipation

• Local energy dissipation

• Extraction of internal tide signals

• Comparison to dissipation

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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)

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Satellite altimetry

Source: JPL

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Mesoscale variability

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M2 ocean tide

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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

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Tidal energy dissipation

3.82 cm/yr

M2 : 2.50 +/- 0.05 TW

(Munk,1997)

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Global energy dissipation

nmnmmnm

nmnmmnm

m

mmm

bcD

daD

DAhkRD

21

2

21

2

2

22222

2

sin

cos

sin

cos14

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Global Dissipations Estimates

Q1 O1 P1 K1 N2 M2 S2 K2

SW80 0.007 0.176 0.033 0.297 0.094 1.896 0.308 0.024

FES99 0.008 0.185 0.033 0.299 0.109 2.438 0.367 0.028

GOT992 0.008 0.181 0.032 0.286 0.110 2.414 0.428 0.029

TPXO51 0.008 0.186 0.032 0.293 0.110 2.409 0.376 0.030

NAO99b 0.007 0.185 0.032 0.294 0.109 2.435 0.414 0.035

Mean 0.008 0.184 0.032 0.294 0.110 2.424 0.396 0.030

Units: TeraWatts

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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)

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Local Dissipation (1)

FuHD

uHgP

uHW

DPW

Hu

Fgufu

t

t

.

.

.

).(

W: Work

P: Divergence Energy Flux

D: Dissipation

Ttt

tt

dtFuT

D0

0

).(1

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Local dissipation (2)

),(12

)(31

.1

.

''1

1

nmanmaew

nmannsal

an

nnne

sale

Yn

hkg

Uhkg

UgUgUgD

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

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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.

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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).

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Dissipation from TPXO51

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Solution t4v6

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Solution t6v6

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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.

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Track 223 Hawaii

1900 2000 2100 2200 2300 2400 2500 26000

10

20

30

40

1900 2000 2100 2200 2300 2400 2500 2600-4

-2

0

2

4

1900 2000 2100 2200 2300 2400 2500 2600-8000

-6000

-4000

-2000

0

H

dG

D

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Internal tides (2)

20 m

5 cm

160 km

1

2

h1

h2

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Internal tides (3)

)( 21

212

2

1

hh

hhgc

m 5000

m 300

m kg 1025

003.0

2

1

3-

h

h

kmL

msc

140 3*3600*42.12

3 1

(Apel, 1987)

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Area’s of interest

-3 0 -2 0 -10 0 1 0 2 0 3 0 m W / m2

R R a y, G S F C

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27

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Tidal bores and SAR

Courtesy: ESA + uni Hamburg

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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.

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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

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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.