15 A Multivariate Reduced-order Optimal
Interpolation Method and its Application to
the Mediterranean Basin-scale Circulation
PIERRE DE MEY AND MOUNIR BENKIRAN
LEGOS, 18 avenue Edouard Belin, 31401 Toulouse Cedex, France
15.1 Introduction
For more than a decade, the Ocean Circulation and Prediction Team at LEGOS,
Toulouse, has been developing data assimilation methods and conducting data
assimilation experiments in various basins of the World Ocean, and in particular in
the Mediterranean. Our aims are to study the feasibility of multivariate control of a
model trajectory, and to characterize the predictability of the general circulation,
seasonal and interannual variability mesoscale eddies, meanders, sub-basin-scale
gyres, and response to wind. This chapter deals with the design and modus operandi of a practic al algorithm for data assimilation and application to the Mediterranean.
Data assimilation (or "state estimation") consists in calculating the "best" estimate ofthe state of a physical system (usually the atmosphere or the ocean) and its
evolution in time, given observations and a prognostic numeric al model. An
increasing number of ocean modelling projects now involve data assimilation.
Simultaneously, numerical models become more sophisticated and more expensive, and the choice of an assimilation approach becomes critic al. Specific reanalysis efforts left aside, the cost of rigorous, physically consistent state estimation
algorithms such as the Kalman Filter, Kalman Smoother and adjoint variational
methods is usually still too high, even if reduced-order variants of these methods
have been proposed for meteorologic al applications (e.g. Courtier et al., 1994).
Suboptimal algorithms such as nudging and optimal interpolation (OI) have been
used in the ocean (e.g. Carton and Hackert, 1989; Derber and Rosati, 1989) and are
much more economical for large-scale problems, but they do not usually ensure
that the solution is consistent with physics and with our understanding of how the
ocean works.
The method discussed and applied here is based on four-dimensional Optimal
Interpolation on a base ofpre-calculated EOFs (Empirical Orthogonal Functions).
Since this is an OI-based algorithm, time-dependent dynamical constraints are not
explicitly enforced. However, the dominant coherent physical and statistical relationships between variables can be introduced via the EOFs. Reduced-order estimation has been reviewed e.g. by De Mey (1997) in the ocean and by Bemstein
and Hyland (1985) presenting the algorithmic details. For instance, the use of
EOFs in isopycnal coordinates for the basis functions seems promising (e.g. Gavart
Interpolation Method and its Application to
the Mediterranean Basin-scale Circulation
PIERRE DE MEY AND MOUNIR BENKIRAN
LEGOS, 18 avenue Edouard Belin, 31401 Toulouse Cedex, France
15.1 Introduction
For more than a decade, the Ocean Circulation and Prediction Team at LEGOS,
Toulouse, has been developing data assimilation methods and conducting data
assimilation experiments in various basins of the World Ocean, and in particular in
the Mediterranean. Our aims are to study the feasibility of multivariate control of a
model trajectory, and to characterize the predictability of the general circulation,
seasonal and interannual variability mesoscale eddies, meanders, sub-basin-scale
gyres, and response to wind. This chapter deals with the design and modus operandi of a practic al algorithm for data assimilation and application to the Mediterranean.
Data assimilation (or "state estimation") consists in calculating the "best" estimate ofthe state of a physical system (usually the atmosphere or the ocean) and its
evolution in time, given observations and a prognostic numeric al model. An
increasing number of ocean modelling projects now involve data assimilation.
Simultaneously, numerical models become more sophisticated and more expensive, and the choice of an assimilation approach becomes critic al. Specific reanalysis efforts left aside, the cost of rigorous, physically consistent state estimation
algorithms such as the Kalman Filter, Kalman Smoother and adjoint variational
methods is usually still too high, even if reduced-order variants of these methods
have been proposed for meteorologic al applications (e.g. Courtier et al., 1994).
Suboptimal algorithms such as nudging and optimal interpolation (OI) have been
used in the ocean (e.g. Carton and Hackert, 1989; Derber and Rosati, 1989) and are
much more economical for large-scale problems, but they do not usually ensure
that the solution is consistent with physics and with our understanding of how the
ocean works.
The method discussed and applied here is based on four-dimensional Optimal
Interpolation on a base ofpre-calculated EOFs (Empirical Orthogonal Functions).
Since this is an OI-based algorithm, time-dependent dynamical constraints are not
explicitly enforced. However, the dominant coherent physical and statistical relationships between variables can be introduced via the EOFs. Reduced-order estimation has been reviewed e.g. by De Mey (1997) in the ocean and by Bemstein
and Hyland (1985) presenting the algorithmic details. For instance, the use of
EOFs in isopycnal coordinates for the basis functions seems promising (e.g. Gavart