New linear response formulas for unperturbed chaotic (stochastic) complex dynamical
systems with time periodic coefficients are developed here. Such time periodic systems arise
naturally in climate change studies due to the seasonal cycle. These response formulas are developed
through the mathematical interplay between statistical solutions for the time-periodic dynamical
systems and the related skew-product system. This interplay is utilized to develop new systematic
quasi-Gaussian and adjoint algorithms for calculating the climate response in such time-periodic systems.
These new formulas are found in section 4. New linear response formulas are also developed
here for general time-dependent statistical ensembles arising in ensemble prediction including the effects
of deterministic model errors, initial ensembles, and model noise perturbations simultaneously.
An information theoretic perspective is developed in calculating those model perturbations which
yield the largest information deficit for the unperturbed system both for climate response and finite
ensemble predictions.
Publié le : 2010-03-15
Classification:
Linear response theory,
fluctuation-dissipation theory,
time periodic coefficients,
quasi-Gaussian and Gaussian approximation,
climate response,
information content,
relative entropy,
37N10,
82C31,
86A99,
60H10,
34C28,
94A15
@article{1266935017,
author = {Majda, Andrew and Wang, Xiaoming},
title = {Linear response theory for statistical ensembles in complex systems with time-periodic forcing},
journal = {Commun. Math. Sci.},
volume = {8},
number = {1},
year = {2010},
pages = { 145-172},
language = {en},
url = {http://dml.mathdoc.fr/item/1266935017}
}
Majda, Andrew; Wang, Xiaoming. Linear response theory for statistical ensembles in complex systems with time-periodic forcing. Commun. Math. Sci., Tome 8 (2010) no. 1, pp. 145-172. http://gdmltest.u-ga.fr/item/1266935017/