Joint OS & SWH meeting in support of Wide-Swath Altimetry Measurements Washington D.C. – October 30th, 2006

Baptiste MOURREICM – Barcelona (Spain)

Pierre DE MEYMatthieu LE HENAFFYves MENARDChristian LE PROVOSTFlorent LYARDLEGOS – Toulouse (France)

Pierre-Yves LE TRAONIFREMER – Brest (France)

Performance of a Wide Swath Altimeter to control a model of

North Sea dynamics

Outline

Model and data assimilation approach

Spatio-temporal scales of model error

Wide Swath Altimeter performance

• First case: with uncorrelated observation error

• Impact of the along track correlated roll error

1

2

3

Perform Observing-Systems Simulation Experiments (OSSEs) to estimate the contribution of a Wide Swath Altimeter to monitor North Sea dynamics.

Objective

Particular case of Coastal ocean/continental shelf region.

Integrated approach: optimal combination of the observations with a numerical ocean model thanks to data assimilation techniques.

• Simulated processes: ocean response to meteorological forcing (wind and pressure). No tides included.

high-frequency gravity waves (Kelvin-type, characteristic scales: 1d / 100 km / 50 cm)

(2D Gravity Wave Model)

Barotropic

Finite-element

Nonlinear

7 31 Dec 1998

• Modelling area: the European shelf

focus on the North Sea

Model and study area

MOG2D model

Mo

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Assimilation of observations: the ensemble Kalman filter

(Evensen 2003)

N analysis

Observations

time t2

Pf(t2)

N analysis

Observations

time t1

Pf(t1)

N modelintegrations ...

N model

integrations

Proper representation of model error covariances: tricky issue when approaching coastal areas !

Mo

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In our case, bathymetry perturbations

Use of ensemble methods: model error statistics are empirically computed from an ensemble of “possible states” of the ocean. Ensemble variances approximate model error variances.

30

Sap

tio

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ral s

cale

s o

f m

od

el e

rro

r

Mean variances over the study period (cm2).

Sea level ensemble variances

100 km

10 15 20 25 30Days (December 1998)

12

0

10 15 20 25 30Days (December 1998)

0

10

2 days

2 days

1 day

200-km swath

15-km resolution

Jason 10-day orbit

Contribution of a Wide Swath AltimeterW

ide

Sw

ath

Alt

imet

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Observation error:White noise, from 3,9 to 5,3 cm rms, depending on the distance to nadir.

(Uncorrelated observation error first)

Sea level ensemble variances before analysis (cm2)

12/31/1998 0am

0 5

One example : track on 31 December 1998, 0am.

Jason

0 5

Jason+T/P

0 5

Instantaneous reduction of sea level ensemble variances

WS Alt.

0 5

Sea level ensemble variances after analysis (cm2)

Wid

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per

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ANALYSIS

50

TideGauges

- 29.7 %

Sea level ensemble variances (cm2)

Days (December 1998)

Jason

Wide Swath Atlimeter

- 52.6 %

Reduction by the assimilation

Local reduction of sea level ensemble variancesW

ide

Sw

ath

Alt

imet

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Local reduction of sea level ensemble variances

- 39.7 %

Sea level ensemble variances (cm2)Jason

Wide Swath Atlimeter

- 24.3 %

Wid

e S

wat

h A

ltim

eter

per

form

ance

Days (December 1998)

36,3

27,7

21,2

0 5 10 15 20 25 30 35 40 45

Wide Swath (10 days)

Jason + T/P

Jason

Global space-time reduction of ensemble variancesW

ide

Sw

ath

Alt

imet

er p

erfo

rman

ce

Jason + T/P

Jason

Wide Swath (10-day orbit)

Sea level ensemble variance reduction (%)

36,3

27,7

21,2

15,4

10,2

6,6

0 5 10 15 20 25 30 35 40 45

Wide Swath (10 days)

Jason + T/P

Jason

Global space-time reduction of ensemble variances

Sea level ensemble variance reduction (%)

Zonal velocity ensemble variance reduction (%)

Wid

e S

wat

h A

ltim

eter

per

form

ance

Jason + T/P

Jason

Wide Swath (10-day orbit)

32,7

19,6

33,1

21,4

36,3

27,7

21,2

13,4

5,5

13,0

5,5

15,4

10,2

6,6

0 5 10 15 20 25 30 35 40 45

Wide Swath (17 days)

Nadir (17 days)

Wide Swath (3 days)

Nadir (3 days)

Wide Swath (10 days)

Jason + T/P

Jason

Global space-time reduction of ensemble variancesW

ide

Sw

ath

Alt

imet

er p

erfo

rman

ce

Jason + T/P

Jason

Wide Swath (10-day orbit)

Nadir (3-day o.)

Wide Swath (3d)

Nadir (17-day o.)

Wide Swath (17d)

Sea level ensemble variance reduction (%)

Zonal velocity ensemble variance reduction (%)

45,2

36,4

36,3

27,7

21,2

14,0

9,6

15,4

10,2

6,6

0 5 10 15 20 25 30 35 40 45

3 Jason (time offset)

2 Jason (time offset)

Wide Swath (10 days)

Jason + T/P

Jason

Global space-time reduction of ensemble variancesW

ide

Sw

ath

Alt

imet

er p

erfo

rman

ce

Jason + T/P

Jason

Wide Swath (10-day orbit)

2 Jason

3 Jason

Temporally interleaved

Sea level ensemble variance reduction (%)

Zonal velocity ensemble variance reduction (%)

Significant contribution compared to conventional altimeters. Performance score: + 70 % for sea level correction

+ 130 % for velocity correction

1 Wide Swath Altimeter ~ 2 nadir alt. for sea level control ~ 3 nadir alt. for velocity control

Here (particular context of high-frequency oceanic processes), temporal resolution is still lacking to control the main part of model error.

Interesting complementarity with tide gauges.

Summary of Wide Swath performance (with uncorrelated obs. error)

Wid

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Impact of the along-track correlated roll errorW

ide

Sw

ath

Alt

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New study with simplified measurement model:

White noise 3,9 cm rms

White noise 4 cm rms

xh /

x

h

Direction of the satellite

nadir

h

+ along-track correlated roll error f 0.02 Hz ≃ L 350 km≃

amplitude = 11.6 cm(Enjolras, 2006)

1 nadir + 1 slope measurement

Observation error

0 5 10 15 20

Wide Swath (= Nadir+ Slope)

Nadir

Wid

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wat

h A

ltim

eter

per

form

ance

Global space-time reduction of ensemble variances

Sea level ensemble variances reduction (%)

Zonal velocity ensemble variances reduction (%)

Nadir alone (no roll error)

Nadir + slope (no roll error)

0 5 10 15 20

With correlated roll error (in bothobs. & analysis)

Wide Swath (= Nadir+ Slope)

Nadir

Wid

e S

wat

h A

ltim

eter

per

form

ance

Global space-time reduction of ensemble variances

Sea level ensemble variances reduction (%)

Zonal velocity ensemble variances reduction (%)

Nadir alone (no roll error)

Nadir + slope (no roll error)

Nadir + slope

(roll error - in obs. & analysis)

0 5 10 15 20

With correlated roll error (in obs.only)

With correlated roll error (in bothobs. & analysis)

Wide Swath (= Nadir+ Slope)

Nadir

Wid

e S

wat

h A

ltim

eter

per

form

ance

Global space-time reduction of ensemble variances

Sea level ensemble variances reduction (%)

Zonal velocity ensemble variances reduction (%)

Nadir alone (no roll error)

Nadir + slope (no roll error)

Nadir + slope

(roll error - in obs. & analysis)

Nadir + slope

(roll error - correlations ignored in the analysis)

Conclusions

Without roll error:1 Wide Swath Altimeter ~ 2 nadir alt. for sea level control

~ 3 nadir alt. for velocity control With roll error:

- Slight degradation of the performance, but contribution still valuable (if correlations represented in the analysis !). - True even if the roll frequency is not precisely known (not shown here).

Results linked to the particular North Sea dynamics.

Generalization 1) to other model error sources (e.g. wind & pressure): reasonable (same spatio-temporal scales)

2) to other shelf/coastal areas: with maximum caution ! (spatio-temporal scales have to be considered,

generalization a priori only possible in areas with energetic

wind-driven barotropic dynamics…)

!

The contribution of the Wide Swath should improve when considering longer time scales and shorter spatial scales...

Results in:Mourre et al., Ocean Dynamics, 2006Le Hénaff et al., in preparation, 2006