 
Summary: Q. J. R. Meteorol. Soc. (2003), 129, pp. 239275 doi: 10.1256/qj.01.174
Inferring instantaneous, multivariate and nonlinear sensitivities for the analysis
of feedback processes in a dynamical system: Lorenz model casestudy
By FILIPE AIRES1;2¤
and WILLIAM B. ROSSOW3
1Columbia University, NASA Goddard Institute for Space Studies, USA
2
Laboratoire de M´et´eorologie Dynamique du CNRS, France
3NASA Goddard Institute for Space Studies, USA
(Received 17 October 2001; revised 17 May 2002)
SUMMARY
As an alternative to classical linear feedback analysis, we present a nonlinear approach for the determination
of the sensitivities of a dynamical system from observations of its variations. The new methodology consists of
statistical estimates of all the pairwise relationships among the system state variables based on a neuralnetwork
modelling of the system dynamics (its time evolution). The model can then be used to estimate the instantaneous,
multivariate, nonlinear sensitivities. Classical feedback analysis is reexamined in terms of these sensitivities,
which are shown to be more fundamental in the analysis of feedback processes than estimates of feedback factors
and to provide a more appropriate representation of the system's behaviour. The method is described and tested
on synthetic observations of the time variations of the Lorenz loworder atmospheric model where the correct
sensitivities can be evaluated analytically.
