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Modeling Surface Currents in the Eastern Levantine Mediterranean
Leila Issa, Julien Brajard, Milad Fakhri, Laurent Mortier, Pierre-Marie Poulain
To cite this version:
Leila Issa, Julien Brajard, Milad Fakhri, Laurent Mortier, Pierre-Marie Poulain. Modeling Surface Currents in the Eastern Levantine Mediterranean. EGU General Assembly Conference, Apr 2015, Vienna, Austria. 17, pp.8888. �hal-01191755�
Modeling surface currents in the Eastern Levan5ne
Mediterranean
Leila Issa (LAU), Julien Brajard (UPMC, LOCEAN), Milad Fakhri (Lebanese CNRS), Laurent Mor5er (UPMC, LOCEAN), and Pierre-‐Marie Poulain (OGS, Trieste)
Abstract
We consider the problem of reconstruc5ng the meso-‐scale features of the currents in the Eastern Levan5ne Mediterranean from combining in-‐situ and satellite al5metry data. Mathema5cally, this is an inverse problem where the objec5ve is to invert Lagrangian trajectories, which are posi5ons of driQers launched at sea, in order to improve the coarse Eulerian velocity, provided by the al5metry satellite measurements. We shall use a varia5onal assimila5on approach, whereby the Eulerian velocity correc5on is obtained by minimizing the distance between the simulated posi5on from a velocity background and actual observa5ons. One important property of our approach is that it is model-‐free, hence inexpensive and can be easily cast into real-‐5me oceanic opera5onal products.
Acknowledgement
The atlimeter products were produced by Ssalto/Duacs and distributed by Aviso, with support from Cnes (hVp://
www.aviso.al5metry.fr/duacs)/
Conclusion
• A fast and robust algorithm was proposed to correct velocity using observa5on of driQer posi5ons.
• The algorithm was validated on twin experiments.
• The performance of the algorithm will be tested on real data.
• The possibility of correc5ng model output will also be inves5gated or model may be used for valida5on of correc5on?
Atlimetric data :
Merged Mediterranean Sea Gridded Asolute Geostrophic Veloci5ed SSALTO/Duacs L4 product
Lagrangian data :
DriQer trajectory deployed by Lebanese marine research center, corrected from iner5al oscilla5on.
Figure 1. Velocity field from al5metric data and 3 driQer trajectories (real and simulated) for one week star5ng on 2013 August, 28.
x
Ini5al posi5on of the driQersReal driQer posi5on (every 6 hour)
Simulated posi5on using al5metric velocity
1 . Data
Causes of discrepancy : 1) Only geoststrophic
2) Errors of al5metry near the coast 3) Low resolu5on of al5metry data
4. Sensi5vity studies
Frequency of observa5ons Number of driQers Assimila5on window
Figure 3 Backround error
One observa5on every 1h One observa5on every 2h One observa5on every 6h
Figure 4 Backround error
4 driQers 2 driQers 1 driQer
Figure 5 Backround error
28h 42h 56h
3. Twin experiment
To test the validity of the approach, we conduct some twin experiments (see Figure 2.) :
• The driQer posi5ons is simulated using velocity field from al5metry star5ng on August 31, 2013 for a period of 7 days (with a 5me step of 1h), considered as the “truth“.
• The background state to adjust is the velocity field from al5metry star5ng on August 28, 2013.
• Filter length (matrix B) is 20 km.
x
True velocity field Background
Corrected Ini5al posi5on
Domain used to calculate error (Fig 3-‐5)
Configura5on :
Frequency : 1 observa5on every 6h Number of driQers : 4
Assimila5on window : 42h
2. Assimila5on method
U
0M
U G
r
advection
?
observed can be observed
“simple” model
: velocity vector to adjust
: background velocity vector given by al5metry : interpola5on
: advec5on
: observed posi5on of the driQer With
And ; is the autocorrela5on period of driQers (1-‐3 days) The Objec5ve is to minimize :
To take into account small linearity in a numerically efficient way, the incremental formula5on is minimized, assuming:
and The func5on to minimize is :
about the variance-‐covariance B matrix :
-‐ Dual purpose : regulariza5on and informa5on spreading (smoothing)
-‐ Implementa5on : diffusion filter [Weaver and Cour5er 2001]
U~0 U~b M G
~r o
i = 1, · · · Ndrif t m = 1, · · · TL/ t
J ( ~U0) = 1 2
8<
: X
i,m
kGM( ~U0) ~rio(m t)k2 + k ~U0 U~bk2B
9=
;
U~0 = ~Ub + ~U
~r = ~rb + ~r
J ( U~ ) = 1 2
(X
i
X
m
k~rib + ~ri( U~ ) ~rio(m t)k2 + k ~Uk2B
) TL
