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
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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 !
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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.
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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
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er p
erfo
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ce
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
e S
wat
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ltim
eter
per
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ance
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
er p
erfo
rman
ce
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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wat
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ltim
eter
per
form
ance
Impact of the along-track correlated roll errorW
ide
Sw
ath
Alt
imet
er p
erfo
rman
ce
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
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)
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