INRIA --- Moscow State University.

Nancy, France.

- Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche,
- Institut National de Recherche en Informatique et en Automatique (INRIA),
- Conseil régional de Lorraine,
- Communauté Urbaine du Grand Nancy,
- Université Henri Poincaré Nancy 1,
- Institut Elie Cartan Nancy.

1. New method was suggested for the solution of inverse problem in the space of expansion coefficients with respect to empirical orthogonal functions with the filtration of high-frequency harmonics in the fields, optimal summing of the Fourier series and the estimation of reliability parameter. 2. It was shown that 73% of variations of anomaly field of H in European region can be restored with functionals obtained as a result of averaging the anomalies over "squares" 43*25 degrees.

The structure of the attractor of the barotropic ocean model is studied in this paper. This structure is partially explained by the sequence of bifurcation the system is subjected by variations of the leading parameters. The principal feature of the studied system is the existence of two "almost invariant" basins of chaotic attractor with very rare transitions between them. This fact related to the rise of the couple of non-symmetric stable stationary solutions in the model with symmetric forcing. The "memory" of chaos appears also in the presence of maxima in the spectrum of energy. These maxima correspond either to the principal frequency of the limit cycle arose in the Hopf bifurcation, or to the frequencies of the Feigenbaum phenomenon.

In this paper we discuss how the notion of attractor and its dimension and of the predictibility, in dynamical systems, can be exploited to construct an operational data assimilation scheme for large systems such as those encountered in Geophysics. Two versions of a reduced rank Kalman filter for this purpose are described. Some numerical computations in a simple example of ocean model, are given.

A numerical primitive equation World ocean model in sigma-coordinates
with 5*4*10 resolution is presented. The computational algorithms are based
on the decomposition of the space operator and implicit splitting schemes.
The model is applied to calculate a climatic equilibrium thermohaline
circulation under momentum flux and prescribed temperature and salinity
at the sea surface.
The global ocean circulation is computed for a number of different initial and
boundary conditions.
The timescale to reach an equilibrium is around 2 000 years.
The simulated velocity field
satisfactory reproduces the principal properties of the observed ocean
circulation. The global distribution of temperature and salinity are
consistent with observations.
Equilibrium regime contains oscillations with different
timescales from a few to hundreds years.
Most pronounced in these experiments
are variations with a period of 10, 75, 150, 500 and 1 000 years.
There are different thermohaline regimes under the same
atmospheric forcing when using Dirichlet boundary conditions for temperature
and salinity.