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In real-world geophysical applications (such as predicting the climate change), the reduced models of real-world complex multiscale dynamics are used to predict the response of the actual multiscale climate to changes in various global atmospheric and oceanic parameters. However, while a reduced model may be adjusted to match a particular dynamical regime of a multiscale process, it is unclear why it should respond to external perturbations in the same way as the underlying multiscale process itself. In the current work, the authors study the statistical behavior of a reduced model of the linearly coupled multiscale Lorenz 96 system in the vicinity of a chosen dynamical regime by perturbing the reduced model via a set of forcing parameters and observing the response of the reduced model to these external perturbations. Comparisons are made to the response of the underlying multiscale dynamics to the same set of perturbations. Additionally, practical viability of linear response approximation via the Fluctuation-Dissipation theorem is studied for the reduced model.

The response of reduced models of multiscale dynamics to small external perturbations