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标题：Convergence of data assimilation by periodic updating in simple Hamiltonian and dissipative systems
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作者：A. Hannachi ; K. Haines
期刊名称：Tellus A: Dynamic Meteorology and Oceanography
电子版ISSN：1600-0870
出版年度：1998
卷号：50
期号：1
页码：58-75
DOI：10.3402/tellusa.v50i1.14512
摘要：In this paper, we study the influence of the interval between data insertion events on theconvergence of sequential data assimilation problems. An example of a conservativeHamiltonian system is presented (that of Hénon and Heiles (1964)) where sequential assimilationwith periodic data insertion every Dt achieves a more rapid convergence if data is not insertedat the smallest possible update interval,∆t. It is shown analytically that this is true for allHamiltonian systems when the updated variables produce convergence of the assimilation,because the resolvent matrix then varies as O(D∆2) to highest order. The theory successfullypredicts the turnover point for the He´non and Heiles system when a larger ∆t leads to slowerconvergence and also the assimilation interval at which convergence may cease altogether. Theapplication to a simplified low order shallow water model describing coupled Rossby andgravity waves and with a forced-dissipative perturbation extends the previous result to systemswhich are a more realistic model for the atmosphere and the ocean. Formally, the same behaviourstill holds when a realistic dissipation scheme is applied with increasing amplitudes or whenstrongly dissipative systems, which are not forced-dissipative perturbations of Hamiltonians,are used.