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Estimation of the Local Response to a Forcing in a High Dimensional System Using the Fluctuation-dissipation Theorem : Volume 20, Issue 2 (26/04/2013)

By Cooper, F. C.

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Book Id: WPLBN0003988662
Format Type: PDF Article :
File Size: Pages 10
Reproduction Date: 2015

Title: Estimation of the Local Response to a Forcing in a High Dimensional System Using the Fluctuation-dissipation Theorem : Volume 20, Issue 2 (26/04/2013)  
Author: Cooper, F. C.
Volume: Vol. 20, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Haynes, P. H., Esler, J. G., & Cooper, F. C. (2013). Estimation of the Local Response to a Forcing in a High Dimensional System Using the Fluctuation-dissipation Theorem : Volume 20, Issue 2 (26/04/2013). Retrieved from

Description: Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, UK. 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%.

Estimation of the local response to a forcing in a high dimensional system using the fluctuation-dissipation theorem

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