OSTST 2007 - March, 12-15 - Hobart, Tasmania

Ocean Mean Dynamic Topography from altimetry and GRACE:

Toward a realistic estimation of the error field

Marie-Helene Rio(1), Philippe Schaeffer(1), Jean-Michel Lemoine(2), Gilles Larnicol(1)

(1) CLS, 8-10 rue Hermes, 31256 Ramonville saint agne, France (2) GRGS, 14 avenue Edouard Belin, 31400 toulouse, France

ContextMSS Geoid- = MDT

- Oceanographic analysis- Assimilation into operationnal ocean forecasting systems

Combination of MSS and geoid for MDT computation

Computation of high resolution MDT (Rio et al, 2004, 2005)

A number of key issues

+SLA=ADT

Computation of a realistic error field

Error on the geoid, error on the MSS, error on the MDT computation method

?

MDT

Large scale (400 km)

High resolution (<50 km)

?

Combination of MSS and geoid for MDT computation

MSS CLS01 – EIGEN-GL04S

Rc=133 km

Rc=200 km

Rc=300 kmRc=400 km

Gaussian filter

A

Limits of the gaussian filtering

No error estimate on the resulting MDT

Creation of spurious strong gradients in specific areas (around islands, along coasts, in strong subduction areas…)

rc=133km

rc=200km rc=300km rc=400km

cm

Optimal combination method

)r(Hα)r(H iobs

N

1ii

~

N

1jrj

1iji CA

N

1iriirr

2 CC)r(~

MDT Hobs=MSS-Geoid

Eigen-4SEigen-3S

Eigen-3C

GGM02S

GGM02C

EGM96

19 cm RMS

A: Covariance matrix of the observations:<Hobs,Hobs> = <H2>Fc(r) + <ε2

obs>

MSS CLS01 error field

cm

The CMDT RIO05 (Rio et al, 2005) field is low-pass filtered to 400 km and its variance is computed in 600 km radius domains.

cm

<H2>=A-priori variance

ε2obs= ε2

MSS+ ε2

Geoidcrar

e*)3cr

3r3a61

2cr

2r2a61

crr

a(1(r)cF

Rc=133km

Rc=400km

Different correlation functions have been tested

ResultsMDT Estimated error field

cm

cmcm

rc=133km

rc=200km

rc=300km

rc=400km

Validation

Is the estimated error field realistic?

A- Method: Comparison to independent synthetic MDT estimates

-In-situ temperature and salinity from XBT and CTD are used to compute dynamic heights relative to 1000m for the period 1993-2005.

hinsitu

geoid

z=-1000mh1000

-the dynamic topography at 1000m as estimated by (Willis et al, 2007) is added to the dynamic heights.

h

z=0

22insitu 3ε

22willis 4ε

22sla 3ε

22sla

2willis

2insitu

2synth 6εεεε

-Altimetric Sea Level Anomalies from AVISO are then subtracted to compute synthetic estimates of the Mean Dynamic Topography.

h’alti

Synthetic MDT estimates

MDTsynth

B- Results RMS differences between synthetic heights and:

22221 omsynthMDTRMS

1- Gaussian filtered MDTs

Dashed line: comparison to unfiltered synthetic heights:

133 km filter

2222 fsynthMDTRMS

Solid line: comparison to filtered synthetic heights:

400 km filter

22222

21

2 658 RMSRMSom

2- Optimal MDT RMS difference to unfiltered synthetic heights = 8.5 cm

~ 8.5²

222omsynthMDT 2

RMS

6.0²2² 6.0²+ +

Conclusions

We investigated the efficiency of optimal method to compute realistic large scale MDT from altimetry and geoid and associated error field.We showed consistency between the obtained error field and how the large scale MDT compares to independent synthetic estimates of the MDT.

Improvements need to be made for the better estimation of the altimetric data error (on MSS and SLA - error on the different corrections used during altimeter data processing)

Impact of using the covariance error information in the optimal MDT computation needs to be investigated (available in the case of future GOCE data)

Method based on the knowledge of the observation errors and a-priori statistics of the error field Further improvements are possible:

Future workMDT=MSS-Geoid

Improved estimates of high resolution « combined » MDT

EIGEN05S, EGM07,… GOCE!New MSS estimations and realistic error field

First Guess:EIGEN-GRACE03S 400 kmIn-situ data: drifters and dynamic heights 1993-2002Global: 1/2° resolution grid

The Combined Mean Dynamic Topography RIO05

Rio et al, 2005

cm