French-Russian A.M.Liapunov Institute in Computer Science and Applied Mathematics.
INRIA --- Moscow State University.

Proceedings of the third bilateral conference

Predictability of atmospheric and oceanic circulations.

Project No 4

9-11 of April 1997,
Nancy, France.



The conference was supported by:



Procedings.

Published by French-Russian A.M.Liapunov Institute on Applied Mathematics and Computer Science.


Some results on the uniqueness of the solution of the quasi-geostrophic two-layer ocean model with prescribed upper-layer.

Ch. Bernier-Kazantsev, fn I. D. Chueshov

Abstract.

In this paper, we consider a two-layer quasi-geostrophic model of the ocean dynamics and we prove that under some conditions the dynamics of the bottom layer is completely determined by parameters connected with the upper layer only. It means that the information about the bottom layer is not essential for a description of the long-time behaviour of the system under consideration.

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Adaptive mesh refinement for finite difference ocean models.

Eric Blayo, Laurent Debreu and François-Xavier Le Dimet, jpg

Abstract.

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Statement of Inverse Problems for the Restoration of Regional Geophysical Fields

A.I.Chavro.jpg

Abstract.

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.

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On the genetic "memory" of chaotic attractor of the barotropic ocean model.

V. Dymnikov,jpg E. Kazantsev. jpg

Abstract.

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.

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Globally stable difference schemes for nonlinear dissipative systems and approximation of attractors.

A.N. Filatov

Abstract.

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Global semi-Lagrangian atmospheric model based on compact finite-differences and its implementation on a parallel computer

Mikhail Tolstykh jpg

Abstract.

The semi-Lagrangian atmospheric model on the sphere based on compact finite differences is presented. In the two-dimensional case, the potential vorticity is used as one of the prognostic variables. Fourth-order compact finite differences are used to discretize first- and second-order derivatives. The results including real data tests presented for 2D shallow water version with orography demonstrate its accuracy with the time steps several times greater than in Eulerian model. The 3D version of the model uses the absolute vorticity equation. Some results including a real data forecast are presented. The parallel implementation of the 3D model on a distributed memory parallel computer is described.

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Dimension, Predictibility and Reduced Rank Kalman Filtering in Data Assimilation

Dinh Tuan Pham jpg

Abstract.

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.

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Analyse of winter circulation predictability using INM model output for SMIP experiment.

E.M. Volodin. jpg

Abstract.

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Mathematical modelling of the World Ocean thermohaline circulation variability.

V. B. Zalesny jpg

Abstract.

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.

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Program of the conference.

Kazantsev Eugene Wed Jan 7 09:10:10 MET 1998