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| Titel |
Robust ensemble filtering in handling uncertainties in data assimilation |
| VerfasserIn |
Xiaodong Luo, Ibrahim Hoteit |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250049118
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| Zusammenfassung |
| Sequential data assimilation methods, including the ensemble Kalman filter (EnKF) and the
particle filter (PF), traditionally apply the Bayes’ rule to update the background statistics. In
order to achieve the prescribed optimality under the Bayes’s rule, the complete
knowledge of the statistical properties (for example, the pdfs) of both the mathematical
model and the corresponding observations is needed, and one also has to assume the
assimilation algorithm is able to attain the exact optimal estimates even in the presence of
nonlinearity. In reality, however, often neither of the above two assumptions is satisfied.
Instead, uncertainties arise from several sources, including errors in specifying
initial conditions, the model error, the observation error, and so on. As a result,
it is not unusual that a Bayesian filter fails to achieve a reasonable performance.
For instance, if implemented straightforwardly, the EnKF may suffer from filter
divergence, and it is customary to introduce covariance inflation to overcome this
problem.
In this contribution, we propose a robust ensemble filtering scheme based on the H- filtering
theory. The optimal H- filter uses the minimax rule to update the background estimates. By
design, it is more robust than the Kalman filter in the sense that the estimation error of its
analysis has a finite growth rate with respect to the uncertainties in assimilation, except for a
special case that corresponds to the Kalman filter (KF). The original form of the H-
filter contains global constraints in time, which may be inconvenient for sequential
data assimilation problems. Therefore, we introduce a variant that solves some
time-local constraints instead, and hence we call it the time-local H- filter (TLHF). By
analogy to the EnKF, we also propose the concept of ensemble time-local H-
filter (EnTLHF). We outline the general form of the EnTLHF, and discuss some
of its special cases. In particular, we show that an EnKF method with a certain
covariance inflation technique is essentially an EnTLHF. In this sense, the EnTLHF
provides a general framework for conducting covariance inflation in the EnKF-based
methods. We use two numerical examples to assess the relative robustness of the
TLHF/EnTLHF in comparison with the corresponding KF/EnKF method without covariance
inflation. |
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