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Adjoint model of the GYRE configuration of NEMO by using the YAO software
M. Berrada , C. Talandier, M. Crépon, F. Badran, S. ThiriaWork supported by the SHOM (Hydrographic and Oceanographic Department of the French Navy)
under SINOBAD project
LOCEAN-UPMC
NEMO user meeting Paris, 2-3, July 2009
Idealized configuration of the physical part of NEMO
The domain is a limited area in the North of the Atlantic ocean (Gulf stream region)
The horizontal dimension 32x22 and 31 vertical levels
GYRE area localisation
GYRE configuration
The forecasting of the ocean state depends on the initial environment Accurate initial ocean environment
V=(u,v,w) velocity ssh the sea surface height T Temperature S salinity
Data assimilation by the variational approach Control parameters
)S,T,ssh,(V 0000
Initial ocean environment
)S,T,ssh,(Vx 0000
YAO
Semi- automatic generator of the adjoint code Based on a modular graph structure The modular graph is a data flow diagram which
describes the underlying physical model It consists of a set of modules, where the input of
each one is provided by the output of its predecessors
YAO: Modular Graph
M1
x11y12
y11
x31
x32
x33y32
y31
x21
x22y21
Forward model
dd
d
d
dd
d
d
d
d
d
1i
1j1 x
yF
)(xfy 111
)(xfy qqq
)(xfy 333
)(xfy 222
3i
3j3 x
yF
2i
2j2 x
yF
M3
M2
Backward model qTqq dydx F
M’2
1. Define the modular graph structure of the model
2. Coding of the local functions fq
3. Coding of the Jacobean
Modular graph in a point of the grid
Modular graph in a point of the grid
Modular raph of the space
M1
M2
M3 M1
M2
M3
M1
M2
M3
M1
M2
M3
M1
M2
M3
Time evolution of the modular graph of the space
M1
M2
M3
M1
M2
M3
M1
M2
M3
M1
M2
M3
M1
M2
M3
M1
M2
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M1
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M1
M2
M3
M1
M2
M3
M1
M2
M3
M1
M2
M3
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M2
M3
t2t1 t3
x x
xx
t0
Accomplished work
M1
x11
1i
1j1 x
yF
)(xfy 111 y11
y12
Defined the modular graph structure of the GYRE model under YAO
Coded the forward model
It remains the implementation of the Jacobean of each module which is needed for the backpropagation (This will be done at the end of September)
d
d
d
I shall be ready to cooperate with people wishing to solve assimilation problems
Accomplished work
Comparison: GYRE-YAO vs GYRE-Fortran (accuracy )
Comparison of the intensity of the horizontal velocity in the sea surface at
t=100
Comparison of the ssh at t=100
1110
Comparison of the temperature in the sea surface at t=100
Comparison of the salinity in the sea surface at t=100
Accomplished work
Conclusion
Flexibility: Modifying the model and its adjoint is straightforward due to modular graph structure
One can consider a more complex function as a module for the YAO graph and uses Tapenade (or other) to get the local adjoint
Very useful for sensitivity experiments