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Very large inverse problems in atmosphere and ocean modelling
Author(s) -
Johnson C.,
Nichols N. K.,
Hoskins B. J.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.869
Subject(s) - data assimilation , observability , tikhonov regularization , inverse problem , singular value decomposition , nonlinear system , regularization (linguistics) , computer science , mathematics , dynamical systems theory , algorithm , mathematical optimization , meteorology , physics , mathematical analysis , artificial intelligence , quantum mechanics
For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large‐scale systems is generally ill‐posed. In four‐dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal‐to‐noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.