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Some Continuum Aspects of Data AssimilationA long-sought goal in data assimilation is to build more fully the time dimension into the data assimilation process. Truly four-dimensional data assimilation requires evolving second-moment information, namely the estimation error covariance, along with the state estimate itself. The continuum evolution equations for the estimation error covariance constitute a system of partial differential equations in six space dimensions, forced by a model error covariance and by the observations themselves. The high dimensionality of this system poses a difficult computational problem. Numerous methods have been proposed for approximate, discrete solution of this system of equations. Four-dimensional variational schemes solve these equations indirectly, while schemes based on Kalman filtering solve the equations more directly, usually on a small subspace of the full six-dimensional space. In both cases, most proposed solution methods are not derived from the continuum covariance evolution equations themselves. Instead, most methods simply inherit the discretization used for evolving the state estimate, either in the form of a discrete tangent linear model or, in the case of ensemble schemes, in the form of a fully nonlinear discrete model. In this lecture we show that solutions of the continuum covariance evolution equations possess simple properties that are not readily satisfied upon discretization of the equations. we give numerical examples illustrating that "inherited" discretizations sometimes fail to produce meaningfully accurate solutions. Finally, we suggest alternative discretization methods that may yield more faithful approximate solutions of the continuum problem.
Document ID
19990077337
Acquisition Source
Goddard Space Flight Center
Document Type
Reprint (Version printed in journal)
Authors
Cohn, Stephen E.
(NASA Goddard Space Flight Center Greenbelt, MD United States)
Menard, Richard
(NASA Goddard Space Flight Center Greenbelt, MD United States)
Date Acquired
August 19, 2013
Publication Date
January 1, 1999
Subject Category
Documentation And Information Science
Meeting Information
Meeting: Assimilation of Observations in Meteorology and Oceanography
Location: Quebec
Country: Canada
Start Date: June 7, 1999
End Date: June 11, 1999
Sponsors: World Meteorological Organization
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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