Normal forms for reduced stochastic climate models
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from appli...
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ftpubmed:oai:pubmedcentral.nih.gov:2645348 2023-05-15T17:34:21+02:00 Normal forms for reduced stochastic climate models Majda, Andrew J. Franzke, Christian Crommelin, Daan 2009-03-10 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2645348 http://www.ncbi.nlm.nih.gov/pubmed/19228943 https://doi.org/10.1073/pnas.0900173106 en eng National Academy of Sciences http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2645348 http://www.ncbi.nlm.nih.gov/pubmed/19228943 http://dx.doi.org/10.1073/pnas.0900173106 © 2009 by The National Academy of Sciences of the USA Freely available online through the PNAS open access option. Physical Sciences Text 2009 ftpubmed https://doi.org/10.1073/pnas.0900173106 2013-09-02T10:56:52Z The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. The use of a few Empirical Orthogonal Functions (EOFs) (also known as Principal Component Analysis, Karhunen–Loéve and Proper Orthogonal Decomposition) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low- and high-frequency subspaces of the dynamics. It is shown below that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large scales by the small scales and simultaneously strong cubic damping. These normal forms should prove useful for developing systematic strategies for the estimation of stochastic models from climate data. As an illustrative example the one-dimensional normal form is applied below to low-frequency patterns such as the North Atlantic Oscillation (NAO) in a climate model. The results here also illustrate the short comings of a recent linear scalar CAM noise model proposed elsewhere for low-frequency variability. Text North Atlantic North Atlantic oscillation PubMed Central (PMC) Proceedings of the National Academy of Sciences 106 10 3649 3653 |
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Physical Sciences Majda, Andrew J. Franzke, Christian Crommelin, Daan Normal forms for reduced stochastic climate models |
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Physical Sciences |
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The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. The use of a few Empirical Orthogonal Functions (EOFs) (also known as Principal Component Analysis, Karhunen–Loéve and Proper Orthogonal Decomposition) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low- and high-frequency subspaces of the dynamics. It is shown below that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large scales by the small scales and simultaneously strong cubic damping. These normal forms should prove useful for developing systematic strategies for the estimation of stochastic models from climate data. As an illustrative example the one-dimensional normal form is applied below to low-frequency patterns such as the North Atlantic Oscillation (NAO) in a climate model. The results here also illustrate the short comings of a recent linear scalar CAM noise model proposed elsewhere for low-frequency variability. |
format |
Text |
author |
Majda, Andrew J. Franzke, Christian Crommelin, Daan |
author_facet |
Majda, Andrew J. Franzke, Christian Crommelin, Daan |
author_sort |
Majda, Andrew J. |
title |
Normal forms for reduced stochastic climate models |
title_short |
Normal forms for reduced stochastic climate models |
title_full |
Normal forms for reduced stochastic climate models |
title_fullStr |
Normal forms for reduced stochastic climate models |
title_full_unstemmed |
Normal forms for reduced stochastic climate models |
title_sort |
normal forms for reduced stochastic climate models |
publisher |
National Academy of Sciences |
publishDate |
2009 |
url |
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2645348 http://www.ncbi.nlm.nih.gov/pubmed/19228943 https://doi.org/10.1073/pnas.0900173106 |
genre |
North Atlantic North Atlantic oscillation |
genre_facet |
North Atlantic North Atlantic oscillation |
op_relation |
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2645348 http://www.ncbi.nlm.nih.gov/pubmed/19228943 http://dx.doi.org/10.1073/pnas.0900173106 |
op_rights |
© 2009 by The National Academy of Sciences of the USA Freely available online through the PNAS open access option. |
op_doi |
https://doi.org/10.1073/pnas.0900173106 |
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Proceedings of the National Academy of Sciences |
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106 |
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10 |
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3649 |
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3653 |
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1766133145600524288 |