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| Titel |
Universal Covariance Inflation Factors in the Synchronization Approach to Data Assimilation |
| VerfasserIn |
G. Duane, J. Tribbia |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250031008
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| Zusammenfassung |
| A theoretical paradigm that seems appropriate for data assimilation is that of the
synchronization of loosely coupled chaotic systems. Two or more chaotic systems, loosely
coupled through only a few of many degrees of freedom, fall into synchronized
motion along their strange attractors under a surprisingly wide variety of conditons,
despite sensitivity to differences in initial conditions. The phenomenon has been
used to establish a new framework for data assimilation as the synchronization of
two systems, corresponding to “truth” and “model”, respectively. One seeks to
introduce coupling between the two systems in a way that minimizes synchronization
error.
In previous work, the introduction of observational noise in the coupling channel led to a
system of stochastic differential equations that could be analyzed for the optimal value of a
coupling coefficient in simple cases. That optimization procedure reproduced the Kalman
filter algorithm under certain linearity conditions. In the presence of nonlinearities, if one
generalizes the Kalman filter in a way that corresponds to inflating background error, one can
derive optimal values for the covariance inflation factor that happen to agree roughly with
those used in operational practice. Further, the optimization is robust against the introduction
of model error.
Here we generalize these previous results in several ways: First, we show that sampling
error can be introduced as multiplicative noise. Optimal inflation factors can then
be calculated to take account of this additional source of error. Second, we show
that the previous optimization of an idealized one-dimensional system captures
the essential effects of nonlinearities in higher dimensions. Lastly, in the optimal
synchronization context, we compare covariance inflation to other ways of treating
nonlinearities, such as adding noise to elements of the analysis error covariance matrix. The
near-universality of the traditional inflation approach is explained, and its limits are explored. |
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