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| Titel |
Error Dynamics and Instability in Data Assimilation |
| VerfasserIn |
Alexander Moodey, Amos Lawless, Roland Potthast, Peter Jan van Leeuwen |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250092825
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| Publikation (Nr.) |
 EGU/EGU2014-7187.pdf |
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| Zusammenfassung |
| In many applications of data assimilation the observation operator, which maps from
state space to observation space, leads to an ill-posed equation, meaning that the
assimilation problem is unstable to small perturbations in the data. The use of a prior or
background estimate acts to regularize the problem and thus ensure its stability at
each assimilation time. This can be shown to be equivalent to a form of Tikhonov
regularization as used in traditional inverse problems. Several common data assimilation
algorithms, including variational methods and Kalman filters, can be considered in this
framework.
In operational weather forecasting the data assimilation problem is usually cycled,
so that the background state for one assimilation time is provided by a forecast
of the analysis from the previous assimilation time. In this work we examine the
stability of the error in a sequence of analyses as the assimilation process is cycled in
time. Since the data assimilation problem is often solved in very high dimensional
systems (of order 108 and higher), we derive theory using an infinite-dimensional
framework.
We show that for a certain class of linear model dynamics it is possible to guarantee the
stability of the analysis error in time by applying a multiplicative inflation to the background
error variances. In the case of time-varying dynamics the inflation factor can be chosen
adaptively at each assimilation time to ensure stability. However, as the inflation
factor is increased, the assimilation problem at each time is less well-conditioned
and the bound on the analysis error increases [1]. For nonlinear dynamics similar
stability results are obtained under certain Lipschitz continuity and dissapitivity
assumptions on the dynamical operator [1], [2]. The theory is illustrated with numerical
results.
References:
[1] Moodey, A.J.F., Instability and regularization for data assimilation, PhD thesis,
Department of Mathematics and Statistics, University of Reading, 2013.
[2] Moodey, A.J.F., Lawless, A.S., Potthast, R.W.E. and van Leeuwen, P.J., Nonlinear error
dynamics for cycled data assimilation methods, Inverse Problems, vol 29, pp. 025002,
2013. |
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