Estimation of the local response to a forcing in a high dimensional system using the fluctuation-dissipation theorem
The fluctuation-dissipation theorem (FDT) has been proposed as a method of calculating the response of the earth's atmosphere to a forcing. For this problem the high dimensionality of the relevant data sets makes truncation necessary. Here we propose a method of truncation based upon the assump...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2013-04-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/20/239/2013/npg-20-239-2013.pdf |
| Summary: | The fluctuation-dissipation theorem (FDT) has been proposed as a method of calculating the response of the earth's atmosphere to a forcing. For this problem the high dimensionality of the relevant data sets makes truncation necessary. Here we propose a method of truncation based upon the assumption that the response to a localised forcing is spatially localised, as an alternative to the standard method of choosing a number of the leading empirical orthogonal functions. For systems where this assumption holds, the response to any sufficiently small non-localised forcing may be estimated using a set of truncations that are chosen algorithmically. We test our algorithm using 36 and 72 variable versions of a stochastic Lorenz 95 system of ordinary differential equations. We find that, for long integrations, the bias in the response estimated by the FDT is reduced from ~75% of the true response to ~30%. |
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| ISSN: | 1023-5809 1607-7946 |