A mathematical framework for stochastic climate models

By Andrew J. Majda, Ilya Timofeyev, Eric Vanden Eijnden. 2001

432 citations recorded by the source corpus.

Subfields: Atmospheric Science, Global and Planetary Change, Oceanography

View Paper: https://www.semanticscholar.org/paper/1fb37b78754ebd4d9df836b06fe6affa88998f26

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Citations in the corpus

Physics constrained nonlinear regression models for time series (2012, background): “The objective here is to develop theory which blends natural physical analytic constraints with the attractive memory effects of multi-level quadratic regression in a seamless fashion and then to illustrate this new approach on a suite of models.”
Mathematical and physical ideas for climate science (2013, methodology): “Another rather successful attempt in this direction is given in Majda et al. (2001).”
Normal forms for reduced stochastic climate models (2009, background): “In the special case where the orthonormal basis of variables ei are eigenfunctions of the Laplacian in spherical or periodic geometry, the eigenfunctions are exact solutions of the nonlinear operator and satisfy B(ei, ei) = 0; thus, the summands in 3 are non trivial only for i = j = k and are called”
Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability (2005, methodology): “Majda et al. (1999, 2001, 2002, 2003) have developed a strategy for systematic mode reduction in deterministic models that govern geophysical flows.”
Stochastic climate theory and modeling (2015, neutral): “The stochastic mode reduction approach 37,38,89,90 then predicts the functional form of reduced climate models for the slow variable ~x alone: Structurally new terms are a deterministic cubic term which acts predominantly as nonlinear damping and both additive and multiplicative (state-dependent)…”
NUMERICAL TECHNIQUES FOR MULTI-SCALE DYNAMICAL SYSTEMS WITH STOCHASTIC EFFECTS ⁄ (2003, neutral): “One way to proceed then is to make some suitable approximations on (1.1) to simplify the dynamics of Y εt so as to make possible the calculation of B(x), b(x), and σ(x) (see, e.g., [6] for application of this philosophy to problems arising in atmosphere-ocean science).”
Diffusion approximation for fully coupled stochastic differential equations (2020, neutral): “[30, 36]), geophysical fluid flows (see e.”
Analysis of multiscale methods for stochastic differential equations (2005, background): “side [12, 17, 24] (see also [3, 4, 20]), the following is known about (1.”
Heterogeneous Multiscale Methods: A Review (2007, neutral): “1) [74,98,115,128].”
FUNDAMENTAL LIMITATIONS OF AD HOC LINEAR AND QUADRATIC MULTI-LEVEL REGRESSION MODELS FOR PHYSICAL SYSTEMS (2012, neutral): “The approaches to address these issues range from analytic stochastic mode reduction strategies [1, 2, 3, 4] to purely data driven strategies [5, 6, 7, 23] to methods which use physical analytic properties to constrain data driven methods [8, 9, 10, 21].”