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 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%.