1. 1.Reconstruction of the Chukchi Sea water circulation 1990-1991
G. Panteleev, International Arctic Research Center, Fairbanks
Collaborators.
D. Nechaev, University of Southern Mississippi
A Proshutinsky, Woods Hole Oceanographic Institution
R. Woodgate, University of Washington
J. Zhang, University of Washington
M.Yaremchuk, ONR
2. Reduced space 4Dvar approach
AOMIP meeting, WHOI, January 14-16, 2009

2. Motivation and goals
Development of cost efficient 4Dvar data assimilation system for the Arctic Ocean
Reconstruction of the circulation in the Chukchi Sea:
gridded data sets that are physically consistent and optimally constrained by the observations;
operational hindcast/forecast of the circulation;
optimization of sampling strategy in the region.

3. Semi-Implicit Ocean Model (SIOM) was designed specifically for the implementation of 4D-Var methods into regional models controlled by currents at the open boundaries and by surface fluxes. SIOM is a semi-implicit modification of the OPA model [Madec et al., 1999].
Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS) was developed at the Polar Science Center, University of Washington. This is a coupled ice-ocean model capable of assimilating sea ice data through the nudging procedure.

4. Data flow chart for the TWO independent data assimilation procedures
FINAL REANALYSIS
PRODUCTS: sea ice and
Ocean parameters from
PIOMAS

5. Pilot project: reconstruction of the 1990-1991 circulation in the Chukchi Sea.
1. Time series of velocity, temperature and salinity data at 12 moorings in the Chukchi Sea during the period September September 1991
2. T/S data from two hydrological surveys during September-November 1990 (~130 stations)
2.1 T/S climatological background fields
3.1 Realistic (PIOMAS) momentum and heat/freshwater surface fluxes. OR
3.2 Realistic (NCEP/NCAR) momentum and heat/freshwater surface fluxes.

6. Test: PIOMAS vs NCEP/NCAR
Assimilation of the PIOMAS ocean fluxes (instead NCEP/NCAR)
allows to decrease model-data velocity errors!

7. Reconstructed circulation in the Chukchi Sea.

8. “Validation” Evolution of reconstructed (grey) and observed (dashed)
Herald Canyon
Central region
Evolution of
reconstructed (grey)
and observed (dashed)
temperature (a-c)
and salinity (d-f)
at moorings MA3, MC3
and ME2 respectively.
Near Bering Strait

9. Validation Reconstructed Independent Data
Distribution of temperature (a)
and salinity (b) across the
Long Strait in October, 3, 1991.
Thick line in the left panels
shows the bottom topography.
Note salinity maximum near
Siberian coast

10. Volume fluxes

11. Heat fluxes

12. Freshwater fluxes

13. Particle study
Relative portions (in %) of the particles launched in the Bering Strait at the beginning of (a) October, (b) November, (c) December, (d) January, (e) February, (f) March, and residing in the Bering Sea (solid line) Arrows show the typical residence time of the particles in the Chukchi Sea.

14. Momentum balance - 2 SSH slope Cor Bar wind
Vertically averaged amplitude of Coriolis (a), sea surface slope (b), baroclinic (c) and
surface stress (d) terms of the momentum balance (in 1e-6 m/s/s)
averaged over the one year period (October September 1991).

15. Momentum balance - 3 Annual mean
Relative impact of the baroclinic terms
with respect to the Coriolis term.
Summer
Winter

16. SCC
Absence of the Siberian Coastal Current…… [Weingartner et al., 1999]. Four comparable outflows from the Chukchi Sea [Woodgate et al., 2005] ?

17. Circulation in ESS and Chukchi Sea during 1995: model-data synthesis of the American and Japanese field studies
Field studies during 1995:
red dots designate the
trajectories of 39 drifters,
blue dots - T/S measurements,
2 black circles - moorings in
the Bering Strait and in the
Barrow canyon during the
summer-fall 1995.

18. Circulation in ESS and Chukchi Sea during 1995: model-data synthesis of the American and Japanese field studies
ERS-2 along track data in the northeastern
Bering Sea during the September-October 1995.
ERS-2 tracks intersect the Long Strait 15
times every 35 days
Reconstructed SSH 8/25/95-9/30/95
The reconstructed SSH can be used as a “non-stationary “reference SSH.
The proper filtered and de-tided satellite SSH data can be recalculated
into absolute SSH. That will allow to use huge volume of the ERS-2 and
Envisat data since 1992 to present time and to estimate circulation in
the ESS and Chukchi Sea during the summer periods.

19. Conclusions new Reduce Space 4Dvar data assimilation approach
1. Employing two models (SIOM and PIOMAS) for the reconstruction of the
ice-ocean circulation is a relatively cheap way to conduct ice-ocean reanalysis and
hindcast. But, it is still necessary to develop the conventional ice-ocean 4Dvar
data assimilation approach ….
new Reduce Space 4Dvar data assimilation approach
is currently under development
2. 4Dvar approach gives the complex view on the local circulation pattern
2.1 Estimates of the volume transport:
Bering Strait- 0.57Sv, Herald Shoal –Cape Lisburne Sv,
Herald Canyon – 0.27 Sv, Long Strait – 0.01 Sv,
3 major outflow instead 4 derived by Woodgate et al., 2005
2.2 Momentum balance
2.3 Particle studies
3. Siberian Costal Current is strongly variable current even during the summer

20. R4Dvar
Yaremchuk, Nechaev and Pantleev (under review in Monthly Weather Review)
Motivations:
1. Adjoint models (e.g. Marchuk ~1974, Penenko, 1980) are hard to develop andkeep updated in correspondence with continuously developing forward code.
2. Hi-end OGCMs contain a lot of non-differentiable processes (convective
adjustment, upwind advection, etc.) that cannot be rigorously linearized.
3. Community OGCMs with 4Dvar capabilities (MIT, ROMS, OPA) use approximations to
their tangent linear and adjoint codes, employing only partial differentiation of certain
non-linearities and linear interpolation of the reference state.
4. In most of the realistic applications (when unstable jets and eddies are observed)‏
adjoint models are unable to provide sensitivity information due to intrinsic instability
of the code.
5. Automatic adjoint compilers generate less computationally efficient code, which
may require 3-6 times more CPU than the forward code.

21. EOF analysis of model trajectory
C(x,x’) –covariance matrix,
T- time period,
ε, λ - eigenfunctions/values

22. 1. Update suboptimal control:
The method
External loop
External iterations
1. Update suboptimal control:
2. Update control space:
Orthogonalize the basis
with respect to previous
subspace (Gram-Schmidt)
4. Minimize the updated cost
function:
Internal loop

23. QG model: setting and reference solution
L = 480 km Rd = 25 km
x = 15 km T = 45 days
f = 10-4 s-1  = s-1
 = 50 (500) m2/s diss = 52 (5.2) days
curl= 10-7 s-1 sin(4x/L)cos((4x/L)‏

24. Reference solutions and simulated observations Unstable adjoint model

25. QG: Instability of the adjoint model Validity of the TL approximation:
Cost function gradient after 30 iterations
Validity of the TL approximation: [

26. QG model: setting of the twin-data experiments
”True” control field (potential vorticity q at t=0) and
its first-guess approximations generated from the
sparse and dense “data sets” at various noise levels

27. RESULTS: Experiments with n= 50 (unstable adjoint)

28. RESULTS: Experiments with n= 500 (stable adjoint)

29. “True” and reconstructed solutons
R4dVar
Adjoint

30. Conclusions
1. A version of the R4dVar is proposed. The algorithm employs a sequence of low- dimensional subspaces that are iteratively updated in the process of finding a minimum of the cost function
2. Compared to 4dVar, the method provides similar or better reduction of the cost function after several updates of the search subspace.
3. In terms of the computational cost R4dVar performs similarly with 4dVar if the latter is terminated after more than 2N - 4N iterations, where N is the (fixed) dimension of the reduced control subspaces.
4. The method gains substantial advantage over 4dVar when the dynamical constraints have strong non-linear instabilities which cause the breakdown of TLA
Compared to 4dVar, the method gains extra efficiency when observations become more sparse and/or noisy
Algorithm can be applied with any “black box” model

31. Possibility:
1. R4dVar allows to assimilate data into the “black box” model. Thus, it creates a possibility to assimilate data into any of the existing ice-ocean models.
2. The “skill” of the models can be evaluated through the possibility to reconstruct a particular circulation pattern. Note, in that case the problems of initial and boundary conditions is avoided.
3. Models inter-comparison can be quantified through the application of the R4Dvar.

32. Thanks