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Zoom on HF corrections

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•Ocean tide (water column deformation due to lunar/solar attraction) •Earth tide (Earth layer deformation due to lunar/solar attraction) •Polar tide (water column deformation due to the movement of the pole of rotation) + Load effect They are deduced from numerical models (GOT4.10, FES2014)

Ex: 1 year of the Jason 1 mission (2004 : cycles 73 to 109).

GOT00.2 correction mean GOT00.2 correction variance

-5cm 5 cm 0.26 m²

Tide Corrections

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Sampling of a temporal signal of period T

With a sampling period of T0, we cannot reconstruct a periodic signal of period lower than 2T0 (Nyquist period)

If T0 > T/2 → Ta is the aliased period

T

T 0

T a

Time

Amplitude

Aliasing phenomena

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T/P-Jason altimeter : 10 days sampling (9,9156 days exactly)

Nyquist period = 20 days for TP/Jason

Signal theory aliasing of all signals T < 20 days

High frequency spectrum (T < 20 days) is aliased in the low frequency band (T > 20 days)

Tidal aliasing in altimeter measurement

T/P; Jason GFO ENVISAT; ERS-

2

9,9156 17,0505 35Nom de

Darwin

Période (jours) Aliasing (jours) Aliasing (jours) Aliasing (jours)

On

de

s

lon

gu

es

pé

rio

de

s Ssa 182,62109 182,621095 182,621095 182,621095Mm 27,554551 27,5545507 44,727399 129,530031Mf 13,660791 36,1676995 68,7148383 79,9227517

On

de

s d

iru

ne

s Q1 1,1195149 69,364499 74,0495979 132,806118O1 1,0758059 45,7141825 112,953531 75,0669737P1 1,0027454 88,8908701 4466,66574 365,24219K1

L0,9972696 173,192245 175,447852 365,24219

K1S

0,9972696 173,192245 175,447852 365,24219

On

de

s se

mi

diu

rne

s

N2 0,5274312 49,5281768 52,0720468 97,3929566M2 0,5175251 62,1074853 317,108085 94,4864493S2 0,5 58,7417062 168,816832 #DIV/0!K2

S0,4986348 86,5961223 87,7239259 182,621095

pollution of climatic/mesoscale

signals estimations

need to remove tides from

altimeter measurements = need

accurate global tide models !

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T/P-Jason altimeter : 10 days sampling (9,9156 days exactly)

Nyquist period = 20 days for TP/Jason

Signal theory aliasing of all signals T < 20 days

High frequency spectrum (T < 20 days) is aliased in the low frequency band (T > 20 days)

Tidal aliasing in altimeter measurement

► pollution of climatic/mesoscale signals estimations ► remove tides from altimeter measurements ► need accurate tide models

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2 types of Global models Empirical models

exclusively based on observations

Estimation of altimeter residuals preliminary corrected with FES model

Examples= GOT (R. Ray), EOT (Bosch et al.), DTU (Andersen et al.) …

Hydrodynamic models with/without data assimilation

Hydrodynamic equations = shallow water equations

2D models at present time

3D models just start to be developed mostly for SWOT issues (small scales, internal tides …)

Examples= FES , TPXO

Tidal models

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Regular grid /finite difference discretization: GOT, DTU, TPXO

Finite elements discretization : FES, TUGO models

Resolution of Tidal models

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Centimetric in deep ocean

Thanks to the use of altimeter measurements

Thanks to the modeling of the barotropic tide dissipation via internal tides generation (FES)

Stronger errors in coastal regions

> 10 cm rms

Complex bathymetry (modelisation errors)

Strong non linear interaction areas = many non linear tides arise

These non linear waves are not/a few modeled (omission and modeling error)

Accuracy of Tidal models

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9

Performances vs tide gauge databases

– Coastal = BODC + WOCE + R. Ray database (shallow_fes09) + SONEL

– Shelf = GLOUP (shelf) + ROSAME

– Deep = ACCLAIM + DART + GLOUP (open ocean)

Coastal Shelf Deep

Complex

differences

(cm)

K1 M2

Accuracy of tidal models

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To get more accurate tidal solutions locally, one can develop regional tidal models

Improved bathymetry from regional databases (hydrographic services …)

Improved coastlines

Higher resolution mesh more adapted to shallow water/coastal scales

OBC from global ocean models

Regional tidal models

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Example on NEA region

Grid cells from 1 km to 20 km

Pairaud et al. 2008

Regional tidal models

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Example of Amazone estuary

(Le Bars et al. 2010)

Regional tidal models

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The ocean static response to atmospheric pressure forcing (inverse barometer 1 mbar ↔1 cm) [ Low frequency (> 20 days) signal only]

Pressure anomalies P’ are calculated using pressure estimates from the ECMWF model P’=Pressure-<P> where <P> is the spatial average (over the ocean) of the instantaneous pressure map (every 6 hours).

Motivation: known, static response + necessity to remove this signal before mapping

Barotropic response to pressure and wind from the MOG2D model [High frequency (<20 days) signal only]

Motivation : avoid high frequency oceanic signal to be aliased in the final products.

Dynamic Atmospheric Correction (DAC)

DAC = IB_LF + MOG2D_HF

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Limits: The high frequency baroclinic signals are not removed. The 20 days cut-off length corresponds to the JASON/TOPEX aliasing period. For ERS/ENVISAT, the cut-off length should be 70 days.

Ex: 1 year of the Jason 1 mission (2004 : cycles 73 to 109).

MOG2D-HR correction mean MOG2D-HRcorrection variance

-0.12 m 0.15 m 0.012 m²

DAC = IB_LF + MOG2D_HF

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MOG2D model

• Barotropic model, « time-stepping », non linear (Lynch and Gray,

1979; Greenberg and Lyard; Carrère and Lyard 2003)

• Shallow water equations

Movement:

Continuity:

temporal

derivation

Coriolis

Advectio

n Bottom

friction

horizontal

viscosity Forcing Pressur

e effect

Dissipatio

n

DhEhFhuhghuhfuuhtuh

.

21

0

uh

t

h

The MOG2D model

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Finite elements discretization • Allows increasing resolution in all regions of interest: shallow waters, ocean ridges, slope of continental shelves, small straits …

• at a reasonable computation cost

Finite elements grid used for operational correction: • ~240 000 nodes

• cell size from 150 km to 10 km

MOG2D model The MOG2D model

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MOG2D model

• Meteorological forcing

• ECMWF operational analysis

• Spatial resolution from 1° until 1/8° today

• Atmospheric pressure and 10 m wind speed

• 6-hours temporal resolution → aliasing problem for S2 atmospheric tide …

• At present time S1 and S2 atmospheric signals are removed with a

climatology and then the corrected atmospheric fields are injected in the

model

→ DAC and tide corrections are consistent at S1S2 freq.

The MOG2D model

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Impact of the Dynamic Atmospheric correction • Comparison with tidal gauges database (GLOSS):

• DAC correction is better than IB on most regions. •Weak improvement in the equatorial regions (ocean response is mostly barolinic) • DAC in shallow water regions -> strong reduction of the TG residual variance • not so good in some regions, mostly around Indonesia.

Discussion Which dynamics would/do you want to validate with altimetry or assimilate in your models?

Equivalent modeled SLA: how to compute it to be consistent with altimetry in regional/coastal seas?

For assimilation, is it possible to manage the low-frequency altimetry time sampling of the HF phenomena?

Locally replace the global DAC by a regional DAC, extracted from your 3D system ?