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

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.

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.

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

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 1990- 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.

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

Reconstructed circulation in the Chukchi Sea.

“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

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

Volume fluxes

Heat fluxes

Freshwater fluxes

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.

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 1990- September 1991).

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

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

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.

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.

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 -0.32 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

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.

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

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

QG model: setting and reference solution L = 480 km Rd = 25 km x = 15 km T = 45 days f = 10-4 s-1  = 2 10-13 s-1  = 50 (500) m2/s diss = 52 (5.2) days curl= 10-7 s-1 sin(4x/L)cos((4x/L)‏

Reference solutions and simulated observations Unstable adjoint model

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

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

RESULTS: Experiments with n= 50 (unstable adjoint)

RESULTS: Experiments with n= 500 (stable adjoint)

“True” and reconstructed solutons R4dVar Adjoint

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

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.

Thanks