A sequential data assimilation method based on the properties of a diffusion-type process

• Published in: Applied mathematical modelling Vol. 33; no. 5; pp. 2165 - 2174
• Main Authors: Tanajura, Clemente A.S., Belyaev, Konstantin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2009
• Subjects: Data assimilation methods; Diffusion stochastic process; Optimal filtering; Sequence of Markov chains; Sequence of Markov chains; Data assimilation methods; Optimal filtering; Diffusion stochastic process
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2008.05.021

Data assimilation method, as commonly used in numerical ocean and atmospheric circulation models, produces an estimation of state variables in terms of stochastic processes. This estimation is based on limit properties of a diffusion-type process which follows from the convergence of a sequence of Markov chains with jumps. The conditions for this convergence are investigated. The optimisation problem and the optimal filtering problem associated with the search of the best possible approximation of the true state variable are posed and solved. The results of a simple numerical experiment are discussed. It is shown that the proposed data assimilation method works properly and can be used in practical applications, particularly in meteorology and oceanography.