Open AccessA numerical framework to understand transitions in high-dimensional stochastic dynamical systems
Author(s) -
Henk A. Dijkstra,
Alexis Tantet,
Jan Viebahn,
Erik J. Mulder,
Mariët Hebbink,
Daniele Castellana,
Henri van den Pol,
Jason Frank,
Sven Baars,
Fred W. Wubs,
Mickaël D. Chekroun,
Christian Kuehn
Publication year - 2016
Publication title -
dynamics and statistics of the climate system
Language(s) - English
Resource type - Journals
ISSN - 2059-6987
DOI - 10.1093/climsys/dzw003
Subject(s) - dynamical systems theory , sketch , computer science , stochastic differential equation , mathematics , partial differential equation , statistical physics , stochastic modelling , mathematical optimization , numerical analysis , dynamical system (definition) , algorithm , physics , mathematical analysis , statistics , quantum mechanics
Dynamical systems methodology is a mature complementary approach to forward simulation which can be used to investigate many aspects of climate dynamics. With this paper, a review is given on the methods to analyse deterministic and stochastic climate models and show that these are not restricted to low-dimensional toy models, but that they can be applied to models formulated by stochastic partial differential equations. We sketch the numerical implementation of these methods and illustrate these by showing results for two canonical problems in climate dynamics.
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