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| Titel |
Bayesian source term determination with unknown covariance of measurements |
| VerfasserIn |
Alkomiet Belal, Ondřej Tichý, Václav Šmídl |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250154370
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| Publikation (Nr.) |
 EGU/EGU2017-19454.pdf |
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| Zusammenfassung |
| Determination of a source term of release of a hazardous material into the atmosphere is a
very important task for emergency response. We are concerned with the problem of
estimation of the source term in the conventional linear inverse problem, y = Mx,
where the relationship between the vector of observations y is described using the
source-receptor-sensitivity (SRS) matrix M and the unknown source term x. Since the
system is typically ill-conditioned, the problem is recast as an optimization problem
minR,B(y − Mx)TR−1(y − Mx) + xTB−1x. The first term minimizes the error of the
measurements with covariance matrix R, and the second term is a regularization of the source
term. There are different types of regularization arising for different choices of matrices R
and B, for example, Tikhonov regularization assumes covariance matrix B as the identity
matrix multiplied by scalar parameter.
In this contribution, we adopt a Bayesian approach to make inference on the
unknown source term x as well as unknown R and B. We assume prior on x to
be a Gaussian with zero mean and unknown diagonal covariance matrix B. The
covariance matrix of the likelihood R is also unknown. We consider two potential
choices of the structure of the matrix R. First is the diagonal matrix and the second
is a locally correlated structure using information on topology of the measuring
network.
Since the inference of the model is intractable, iterative variational Bayes algorithm is
used for simultaneous estimation of all model parameters. The practical usefulness of our
contribution is demonstrated on an application of the resulting algorithm to real data from the
European Tracer Experiment (ETEX).
This research is supported by EEA/Norwegian Financial Mechanism under project
MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse
Atmospheric Dispersion Modelling (STRADI). |
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