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

TL;DR

This paper investigates how reduced models of multiscale geophysical systems respond to small external perturbations, comparing their responses to the full system and assessing the effectiveness of linear response theory.

Contribution

It provides a detailed analysis of the response behavior of reduced multiscale models and evaluates the applicability of the Fluctuation-Dissipation theorem for these models.

Findings

Reduced models can approximate the response of full multiscale systems under certain conditions.

Linear response theory via Fluctuation-Dissipation theorem is practically viable for some reduced models.

Differences in response highlight limitations of reduced models in capturing full system dynamics.

Abstract

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.