Inferring instantaneous, multivariate and nonlinear sensitivities for the analysis of feedback processes in a dynamical system: Lorenz model case‐study
Filipe Aires, William B. Rossow · Quarterly Journal of the Royal Meteorological Society · 2003
Abstract 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 pair‐wise relationships among the system state variables based on a neural‐network 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 re‐examined 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 low‐order atmospheric model where the correct sensitivities can be evaluated analytically. Copyright © 2003 Royal Meteorological Society