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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ftunivutrecht:oai:dspace.library.uu.nl:1874/44423 2023-07-23T04:20:43+02:00 Normal forms for reduced stochastic climate models Majda, A.J. Franzke, C. Crommelin, D.T. 2009-03 image/pdf https://dspace.library.uu.nl/handle/1874/44423 en eng 0027-8424 https://dspace.library.uu.nl/handle/1874/44423 info:eu-repo/semantics/ClosedAccess Natuur- en Sterrenkunde low-frequency teleconnection patterns nonlinearity correlated noise Article 2009 ftunivutrecht 2023-07-01T23:43:35Z 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 Utrecht University Repository |
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Open Polar |
collection |
Utrecht University Repository |
op_collection_id |
ftunivutrecht |
language |
English |
topic |
Natuur- en Sterrenkunde low-frequency teleconnection patterns nonlinearity correlated noise |
spellingShingle |
Natuur- en Sterrenkunde low-frequency teleconnection patterns nonlinearity correlated noise Majda, A.J. Franzke, C. Crommelin, D.T. Normal forms for reduced stochastic climate models |
topic_facet |
Natuur- en Sterrenkunde low-frequency teleconnection patterns nonlinearity correlated noise |
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, A.J. Franzke, C. Crommelin, D.T. |
author_facet |
Majda, A.J. Franzke, C. Crommelin, D.T. |
author_sort |
Majda, A.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 |
publishDate |
2009 |
url |
https://dspace.library.uu.nl/handle/1874/44423 |
genre |
North Atlantic North Atlantic oscillation |
genre_facet |
North Atlantic North Atlantic oscillation |
op_relation |
0027-8424 https://dspace.library.uu.nl/handle/1874/44423 |
op_rights |
info:eu-repo/semantics/ClosedAccess |
_version_ |
1772185382235930624 |