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| Titel |
Multiproxy Paleoclimate Reconstruction Using Gaussian Graphical Models |
| VerfasserIn |
D. Guillot, B. Rajaratnam, J. Emile-Geay |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250060546
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| Zusammenfassung |
| Understanding centennial-scale climate variability hinges on the availability of datasets that
are accurate, long, continuous, and of broad spatial coverage. Since instrumental
measurements are generally only available after 1850, temperature fields must be
reconstructed by using information embedded in proxy records spanning all or part of the
Common Era. Various climate field reconstructions (CFR) methods have heretofore been
proposed to infer past climate from multiproxy networks. A popular one is the regularized
EM algorithm (RegEM) with several regularization schemes like truncated total least squares
(TTLS) and individual ridge regression (iRIDGE). Like RegEM, most CFR methods are
based on multivariate regression. The cornerstone of such methods is to obtain
an accurate estimate of the covariance matrix Σ of the data. In the paleoclimate
context, this is a challenging problem because the number of variables (number of
temperature grid points, p) vastly exceeds the number of observations (number of years of
instrumental data, n). The matrix Σ is often estimated by the sample covariance matrix of
the dataset, but this estimator is known to be very poor when p > n. Significant
improvements can be made by estimating Σ using a Gaussian graphical model
(GGM). A GGM (a.k.a. Markov random field) is a multivariate normal model where
variables display certain conditional independence relations encoded by a graph. Such
relations are inherent to climate fields and can be exploited to yield better temperature
reconstructions.
In this work, we propose a new CFR method based on GGMs. By modeling the
conditional independence structure of climate fields, the number of parameters to estimate
can be greatly reduced. Precise and well-conditioned estimates of Σ can then be computed,
even when the sample size is much smaller than the number of variables. Those estimates can
then be used in various reconstruction procedures like the EM algorithm. I will discuss
efficient algorithms to discover the conditional independence structure of climate data and
show how GraphEM (GGM + EM algorithm) can be used to reconstruct past climate
variability. I will then compare the performance of GraphEM to RegEM TTLS using
pseudoproxy experiments and real datasets. Our results show that, in many cases, GraphEM
outperforms RegEM TTLS. This increase in performance is directly tied to the sparsity of the
covariance model, confirming the usefulness of -1 model selection prior to -2 regularization. |
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