Systematic physics constrained parameter estimation of stochastic differential equations

Peavoy, Daniel; Franzke, Christian; Roberts, Gareth O.

doi:10.1016/j.csda.2014.10.011

Cited by 19 publications

(17 citation statements)

References 28 publications

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“…This will enable us to fit more complex models with the currently available amount of data. Majda and Harlim (2013), Peavoy et al (2015) and Kondrashov et al (2015) put forward such physics constrained approaches which are based on energy conservation and global stability. Such reduced order models are used in many practical applications like long-range climate forecasts (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Chib et al (2004); Golightly and Wilkinson (2008)) in Bayesian inference and MCMC methods for diffusion processes, by imposing physical constraints such as global stability. This methodology can handle nonlinear drifts and non-constant diffusions, and is demonstrated on examples with dimensions of the state vector with d = 1 and d = 2 in Peavoy et al (2015), but can be extended to higher dimensional problems.…”

Section: Inference For General Diffusion Processesmentioning

confidence: 99%

“…Finally, we mention here the recent work presented in Peavoy et al (2015), where a Bayesian framework is developed for parameter estimation using Markov Chain Monte Carlo (MCMC) methods, which is, in principle, applicable to high-dimensional systems. In this work, the structural form of the diffusion process is motivated by the stochastic mode reduction (MTV) methods for climate models discussed in the previous section.…”

Section: Inference For General Diffusion Processesmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Climate Theory

Gottwald¹,

Crommelin²,

Franzke³

2016

Nonlinear and Stochastic Climate Dynamics

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In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of stochastic noise. Within this framework we express standard model reduction methods such as averaging and homogenization which eliminate the memory term. We further discuss ways to deal with the memory term and how the type of noise depends on the underlying deterministic chaotic system. Secondly, we review current approaches in stochastic data-driven models. We discuss how the drift and diffusion coefficients of models in the form of stochastic differential equations can be estimated from observational data. We pay attention to situations where the data stems from multi scale systems, a relevant topic in the context of data from the climate system. Furthermore, we discuss the use of discrete stochastic processes (Markov chains) for e.g. stochastic subgrid-scale modeling and other topics in climate science.

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Section: Discussionmentioning

confidence: 99%

Section: Inference For General Diffusion Processesmentioning

confidence: 99%

Section: Inference For General Diffusion Processesmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Climate Theory

Gottwald¹,

Crommelin²,

Franzke³

2016

Nonlinear and Stochastic Climate Dynamics

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“…In future research we will attempt to also derive nonlinear models with explicit multiplicative noise for the NAO and compare their predictive skill with the additive model developed here. Multiplicative noise processes are harder to estimate and require long time series (Peavoy et al 2015). Rennert and Wallace (2009) show that the nonGaussian properties of the NAO might be the results of cross-frequency coupling.…”

Section: Discussionmentioning

confidence: 99%

Predictability and Non-Gaussian Characteristics of the North Atlantic Oscillation

Önskog

Franzke²,

Hannachi

2018

J. Climate

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The North Atlantic Oscillation (NAO) is the dominant mode of climate variability over the North Atlantic basin and has a significant impact on seasonal climate and surface weather conditions. It is the result of complex and nonlinear interactions between many spatiotemporal scales. Here, the authors study the statistical properties of two time series of the daily NAO index. Previous NAO modeling attempts only considered Gaussian noise, which can be inconsistent with the system complexity. Here, it is found that an autoregressive model with non-Gaussian noise provides a better fit to the time series. This result holds also when considering time series for the four seasons separately. The usefulness of the proposed model is evaluated by means of an investigation of its forecast skill.

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“…The general potential of Bayesian parameter inference such as MLE has recently been discussed for stochasticdynamic climate models from incomplete data (Peavoy et al, 2015). A Bayesian framework to compare different types of models has also recently been used for the specific case of the NGRIP δ 18 O record, including a double-well potential model, a relaxation oscillator, and two versions of a mixture of locally linear stochastic models.…”

Section: G(t S; X(s))ds + η(T)mentioning

confidence: 99%

Inverse stochastic–dynamic models for high-resolution Greenland ice core records

et al. 2017

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Abstract. Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ 18 O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP), and we focus on the time interval 59-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ 18 O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the δ 18 O and dust time series, and (iv) non-Markovian contributions that represent short-term memory effects.

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Systematic physics constrained parameter estimation of stochastic differential equations

Cited by 19 publications

References 28 publications

Stochastic Climate Theory

Stochastic Climate Theory

Predictability and Non-Gaussian Characteristics of the North Atlantic Oscillation

Inverse stochastic–dynamic models for high-resolution Greenland ice core records

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