A Multivariate Reduced-order Optimal Interpolation Method and its Application to the Mediterranean Basin-scale Circulati
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.
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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 N. Pinardi et al. (eds.), Ocean Forecasting © Springer-Verlag Berlin Heidelberg 2002
282 Pierre De Mey and Mounir Benkiran and De Mey, 1997) and consistent with the large-scale conservation of properties (Cooper and Haines, 1996). One of the advantages of the method presented here over previous statistical methods based on regression in the ocean (e.g. Mellor and Ezer, 1991; Oschlies and Willebrand, 1996) lies in the fact that it directly derives from the Reduced-Order Extended Kalman Filter (ROEKF) equations. Therefore the assumptions and limitations
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