Stochastic climate dynamics: Random attractors and time-dependent invariant measures

By Mickaël D. Chekroun, Eric Simonnet, Michael Ghil. 2011

297 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Economics and Econometrics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/7ebd1e5fbd5630bc70b941b5dd953c69a2e16507

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In Computer Networks and Communications

In Economics and Econometrics

In Global and Planetary Change

Citations in the corpus

Mathematical and physical ideas for climate science (2013, background): “eterministic chaos and stochastic perturbations to dynamical systems, respectively. We refer in particular to the 36 idea of constructing time-dependent measures for non autonomous dynamical systems (Chekroun et al., 2011) through the introduction of the so-called pullback attractor, which is the ge”
Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, background): “Recent studies on the pullback or random attractor (Chekroun et al., 2011; Dijkstra, 2013) may open the path to suitable formulations of the estimation problem for non-autonomous systems.”
Data-driven non-Markovian closure models (2014, background): “Condition (H2) and conditions (H3, H4) indicate what the cross-interactions between the x- and y-variables, on the one hand, and the effects of the forcing by the r-variable on the y-equation, on the other, should satisfy for the system (MSM) to be pathwise dissipative in a pullback sense [89].”
Random periodic processes, periodic measures and ergodicity (2014, background): “ic dynamics and modelling real world problems. They include an intriguing observation of random periodic paths in the stochastic Timmerman-Jin model of El Nino phenomenon arising in climate dynamics ([5]); bifurcations of stochastic reaction diusion equations ([31]); periodic random attractors of st”
On Defining Climate and Climate Change (2016, methodology): “Checkroun et al. [2011]; Stone et al.”
Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding (2012, background): “But a more realistic model should include a stochastic effects ([4]).”
Variational Approach for Learning Markov Processes from Time Series Data (2017, background): “As stated in Chekroun et al. (2011), all the trajectories move around the deterministic attractor with small random perturbations and switch between the two lobes.”
The physics of climate variability and climate change (2019, result): “The singular support of the measure is in full agreement with rigorous mathematical results, as well as with the numerical results (Chekroun et al., 2011; Ghil, 2017) on the random attractor of the stochastically perturbed Lorenz (1963) convection model.”
Anticipating Random Periodic Solutions--I. SDEs with Multiplicative Linear Noise (2015, result): “There have been some more recent results including [8] on random attractors of the stochastic TJ model in climate dynamics, [30] on bifurcations of stochastic reaction diffusion equations and [5] on stochastic lattice systems.”