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| Titel |
Balancing aggregation and smoothing errors in inverse models |
| VerfasserIn |
A. J. Turner, D. J. Jacob |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1680-7316
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| Digitales Dokument |
URL |
| Erschienen |
In: Atmospheric Chemistry and Physics ; 15, no. 12 ; Nr. 15, no. 12 (2015-06-30), S.7039-7048 |
| Datensatznummer |
250119858
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| Publikation (Nr.) |
 copernicus.org/acp-15-7039-2015.pdf |
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| Zusammenfassung |
| Inverse models use observations of a system (observation vector) to
quantify the variables driving that system (state vector) by
statistical optimization. When the observation vector is large,
such as with satellite data, selecting a suitable dimension for the
state vector is a challenge. A state vector that is too large
cannot be effectively constrained by the observations, leading to
smoothing error. However, reducing the dimension of the state
vector leads to aggregation error as prior relationships between
state vector elements are imposed rather than optimized. Here we
present a method for quantifying aggregation and smoothing errors as
a function of state vector dimension, so that a suitable dimension
can be selected by minimizing the combined error. Reducing the
state vector within the aggregation error constraints can have the
added advantage of enabling analytical solution to the inverse
problem with full error characterization. We compare three methods
for reducing the dimension of the state vector from its native
resolution: (1) merging adjacent elements (grid coarsening),
(2) clustering with principal component analysis (PCA), and (3) applying
a Gaussian mixture model (GMM) with Gaussian pdfs as state vector
elements on which the native-resolution state vector elements are
projected using radial basis functions (RBFs). The GMM method leads
to somewhat lower aggregation error than the other methods, but more
importantly it retains resolution of major local features in the
state vector while smoothing weak and broad features. |
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