Abstract
This paper is devoted to an optimal perturbation (OP) which allows to qualify a capacity of the dynamical system to predict more or less correctly the system behaviour in the future. The different types of OPs, deterministic, stochastic, OP in an invariant subspace, are introduced. The theoretical results on the optimality of the introduced OPs are presented. The different simple and efficient numerical algorithms for computation of the OPs are outlined which constitute a basis for implementation of a stable adaptive filter in a very high dimensional environment.
Highlights
Study in high dimensional systems (HdS) today constitutes one of the most important research subjects thanks to the exponential increase of the power and speed of computers [1]
7.1 Ocean model MICOM To see the impact of optimal Schur vectors (SchVs) in the design of filtering algorithm for HdS, we present the results of the experiment on the Hd ocean model MICOM (Miami Isopycnal Ocean Model)
To illustrate how adaptation can improve the performance of the nonadaptive filter, in figure 3 we show the cost functions resulting from applying the three filters PEF(SCH), PEF(SSP) and AF (i.e. APEF based on PEF(SCH); The same performance is observed for the AF based on PEF(SSP))
Summary
Study in high dimensional systems (HdS) today constitutes one of the most important research subjects thanks to the exponential increase of the power and speed of computers [1]. As will be seen in the sequel, the OPs are the key elements constituting a basis for a subspace of correction, which ensures a stability of the filter for data assimilation in HdS [4]. This allows to obtain an indication of the range of possible future states of the system, with the objective to assess to the information on a correct predicted ensemble spread. 6 for illustrating the different OPs. The experiment on data assimilation in the Hd ocean model MICOM by the filters, constructed on the basis of the Schur ODSs and SSPs, is presented in Sect.
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