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| Titel |
Estimating the full posterior pdf with particle filters |
| VerfasserIn |
Melanie Ades, Peter Jan van Leeuwen |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250083600
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| Zusammenfassung |
| The majority of data assimilation schemes rely on linearity assumptions. However as the
resolution and complexity of both the numerical models and observations increases, these
linearity assumptions become less appropriate. A need is arising for fully non-linear data
assimilation schemes, such as particle filters. Recently, new particle filter schemes have been
generated that explore the freedom in proposal densities and that are quite effective in
estimating the mean of the posterior probability density function (pdf), even in very high
dimensional systems. However, in non-linear data assimilation the solution to the
data assimilation problem is the full posterior pdf. At the same time we can only
afford a limited number of particles. Here we concentrate on the equivalent weights
particle filter in conjunction with a 65,000 dimensional Barotropic Vorticity model.
Specifically we test the ability of the scheme to represent the posterior in three important
areas.
In many actual geophysical applications, observations will be sparse and may well be
unevenly distributed. We discuss the effect of changing the frequency, number and
distribution of the observed variables on the ensemble representation of the posterior pdf.
Specifically we show that the filter has remarkably good convergence in marginal and joint
pdfs with ensemble size, and the rank histograms are quite flat, even with low observation
numbers and low observation frequencies. Only when the observation frequency is much
larger than the typical decorrelation time scale of the system do we see underdispersive
ensembles when using 32 particles.
The second area attempts to replicate the realistic situation of using a geophysical model
designed without a full understanding of the error statistics of the truth. This is done by using
deliberately erroneous error statistics in the ensemble equations compared to those used to
generate the truth. Specifically we consider changes in the correlation length-scales and
variances in the model error statistics. Again the filter is remarkably successful in generating
correct posterior pdfs, although rank histograms tend to point to under- or overdispersive
ensembles. One of the interesting results is that when we overestimate the model
error amplitude the ensemble is underdispersive. We present an explanation for this
counter-intuitive phenomenon.
Finally we show that the computational effort involved in the equivalent-weights particle
filter is comparable to running a simple resampling particle filter with the same number of
particles. |
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