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| Titel |
Normal Forms for Reduced Stochastic Climate Models |
| VerfasserIn |
C. Franzke, A. Majda, D. Crommelin |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250020575
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| Zusammenfassung |
| The systematic development of reduced low-dimensional stochastic climate models from
observations or comprehensive high-dimensional climate models is an important topic for
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 (EOF) 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 will be shown
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. This normal form should prove useful for developing
systematic regression fitting strategies for stochastic models of climate data. The
validity of the one and two dimensional normal forms will be presented. Also the
analytical PDF form for one-dimensional reduced models will be derived. This PDF
can exhibit power-law decay only over a limited range and its ultimate decay is
determined by the cubic damping. This cubic damping produces a Gaussian tail. |
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