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| Titel |
Statistical modelling in data assimilation |
| VerfasserIn |
N. D. Smith, C. N. Mitchell, C. J. Budd |
| 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 |
250023428
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| Zusammenfassung |
| A data assimilation technique typically optimises a forward model to best replicate a
sequence of observations. In geophysical applications, the forward model and underlying
physical process yielding the observations are often driven. For example, Earth’s ionosphere
is influenced by solar radiation and Earth’s magnetosphere. Both the forward model and
underlying process may be linear or nonlinear. In optimising the forward model, an objective
function is required. From a certain perspective, often the objective function makes
implicit statistical assumptions, for example conditional independences between
observations and the existence of Gaussian distributions. Even when these assumptions are
incorrect, techniques based on them often prove remarkably robust. However with the
anticipated future increase in availability of data, for example from satellites, it
may be possible to begin to model more accurately the statistical dependencies and
variation.
This presentation discusses some ideas from statistical modelling and pattern
classification in the context of data assimilation for driven systems, where all variables are
discretised. As known, data assimilation schemes may often be cast into a Maximum
A-Posteriori (MAP) estimation framework. In this framework, the true statistical model
associated with the underlying physical process minimises the ‘overall risk’ under a
‘classification’ or ‘0/1’ loss function. Unfortunately the true statistical model is rarely known.
Instead, in this framework, the objective function and forward model together imply a
statistical model which is only an estimate, and often a poor one, of the true statistical model.
Within the context of model selection from the field of statistical modelling, quantities such
as overall risk may be used to evaluate and compare alternative statistical models implied by
different objective functions and/or forward models. Mutual information may also be used.
However these evaluation techniques require some knowledge of the truth (e.g. the true
values of driver variables) and are in the context of classification. Also of interest is
the effect on overall risk of a failure to adequately model variables or conditional
dependencies.
However improving the statistical modelling is a challenging task. In geophysical
applications, the underlying physical process is often nonstationary and it is expected that the
statistical distributions will generally be difficult to estimate, particularly for infrequent
extreme conditions. However an awareness of the above concepts may help us better
understand the limitations of present data assimilation schemes. |
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