Normal forms for reduced stochastic climate models
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive highdimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applie...
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ftnerc:oai:nora.nerc.ac.uk:6224 2024-06-09T07:48:17+00:00 Normal forms for reduced stochastic climate models Majda, Andrew J. Franzke, Christian Crommelin, Daan 2009 http://nora.nerc.ac.uk/id/eprint/6224/ http://www.pnas.org/ https://doi.org/10.1073/pnas.0900173106 unknown National Academy of Sciences Majda, Andrew J.; Franzke, Christian; Crommelin, Daan. 2009 Normal forms for reduced stochastic climate models. Proceedings of the National Academy of Sciences, 106 (10). 3649-3653. https://doi.org/10.1073/pnas.0900173106 <https://doi.org/10.1073/pnas.0900173106> Atmospheric Sciences Mathematics Publication - Article PeerReviewed 2009 ftnerc https://doi.org/10.1073/pnas.0900173106 2024-05-15T08:52:26Z The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive highdimensional 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 lowfrequency 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. Article in Journal/Newspaper North Atlantic North Atlantic oscillation Natural Environment Research Council: NERC Open Research Archive Proceedings of the National Academy of Sciences 106 10 3649 3653 |
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Natural Environment Research Council: NERC Open Research Archive |
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Atmospheric Sciences Mathematics |
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Atmospheric Sciences Mathematics Majda, Andrew J. Franzke, Christian Crommelin, Daan Normal forms for reduced stochastic climate models |
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Atmospheric Sciences Mathematics |
description |
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive highdimensional 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 lowfrequency 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 |
Article in Journal/Newspaper |
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://nora.nerc.ac.uk/id/eprint/6224/ http://www.pnas.org/ https://doi.org/10.1073/pnas.0900173106 |
genre |
North Atlantic North Atlantic oscillation |
genre_facet |
North Atlantic North Atlantic oscillation |
op_relation |
Majda, Andrew J.; Franzke, Christian; Crommelin, Daan. 2009 Normal forms for reduced stochastic climate models. Proceedings of the National Academy of Sciences, 106 (10). 3649-3653. https://doi.org/10.1073/pnas.0900173106 <https://doi.org/10.1073/pnas.0900173106> |
op_doi |
https://doi.org/10.1073/pnas.0900173106 |
container_title |
Proceedings of the National Academy of Sciences |
container_volume |
106 |
container_issue |
10 |
container_start_page |
3649 |
op_container_end_page |
3653 |
_version_ |
1801379931640299520 |