Communications in Mathematical Sciences

Volume 14 (2016)

Number 3

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

Pages: 831 – 855



Rafail V. Abramov (Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Il., U.S.A.)

Marc Kjerland (Disaster Prevention Research Institute, Kyoto University, Gokasho, Kyoto, Japan)


In real-world geophysical applications (such as predicting 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.


multiscale dynamics, reduced models, response to external forcing

2010 Mathematics Subject Classification

37Mxx, 37Nxx

Published 26 February 2016