Numerical Generation of Stochastic Differential Equations in Climate Models

Ewald, Brian D.; Penland, Cécile

doi:10.1016/s1570-8659(08)00206-8

Cited by 9 publications

(11 citation statements)

References 19 publications

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“…The (N1) SDE can be simulated using numerical methods for Stratonovich SDEs (e.g., Ewald and Penland 2009), but the derivatives associated with these methods may be costly to compute in high-dimensional models (as at each step the diffusion s would need to be computed not just at the present climate state but at neighboring states). These models form a hierarchy from the least accurate (A) model to the (in principle) most accurate (N1) model, which best accounts for the climate-weather interactions.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Stochastic Parameterization Schemes for Use in Realistic Climate Models

Culina

Kravtsov

Monahan

2011

Journal of the Atmospheric Sciences

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Stochastic parameterizations of fast-evolving, subgrid-scale processes are increasingly being used in a range of models from conceptual models to general circulation models. However, stochastic terms are generally included in an ad hoc fashion. In this study, a systematic method-''Hasselmann's method''-of stochastic parameterization is developed through the direct application of rigorously justified limit theorems that predict the effective slow dynamics in systems with coupled slow and fast variables. The multiple Hasselmann models form a hierarchy of models ordered by the time scales over which they are expected to provide good approximations to the slowly evolving variables. Adaptable, efficient algorithms for integrating these reduced models are developed that require minimal changes to the unreduced model.Hasselmann's method is tested on an O(10 000)-dimensional (planetary and synoptic scale) quasigeostrophic model of atmospheric low-frequency variability. Low-dimensional deterministic and stochastic models in the planetary-scale modes alone are derived, which accurately generate the statistics of the corresponding modes of the unreduced model, including the statistical signatures of jet regime behavior. It is shown that deterministic nonlinearity through slow forcing averaged with respect to the fast modes distribution dominates over multiplicative noise in generating the regime behavior.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Stochastic Parameterization Schemes for Use in Realistic Climate Models

Culina

Kravtsov

Monahan

2011

Journal of the Atmospheric Sciences

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“…Unfortunately, the transformation from one description to the other can be prohibitively difficult in physical applications. For longer discussions on the difference between Itô and Stratonovich systems, we refer the reader to Arnold (1974), Horsthemke & Lefever (1984), Kloeden & Platen (1992) and Ewald & Penland (2008). The important message here is for when one wishes to approximate a continuous real system with short but finite correlation time in a general circulation model (GCM) with a Gaussian stochastic variable.…”

Section: (C ) the Central Limit Theoremmentioning

confidence: 99%

“…Kloeden & Platen 1992), enormous tomes on the theory and practice of numerically integrating SDEs. A review of some of these techniques, including longer discussions of the schemes we present here, may be found in Ewald & Penland (2008). In this subsection, we confine ourselves to discussing the procedure and results of using an explicit stochastic Euler scheme (Rümelin 1982), an explicit stochastic Heun scheme (Rümelin 1982) and an implicit stochastic integration scheme developed by Ewald & Temam (2005; see also Ewald et al 2004) especially for spectral versions of GCMs.…”

Section: (D ) Notes On Numerical Techniques Involving Sdesmentioning

confidence: 99%

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On modelling physical systems with stochastic models: diffusion versus Lévy processes

Penland

Ewald

2008

Phil. Trans. R. Soc. A.

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Stochastic descriptions of multiscale interactions are more and more frequently found in numerical models of weather and climate. These descriptions are often made in terms of differential equations with random forcing components. In this article, we review the basic properties of stochastic differential equations driven by classical Gaussian white noise and compare with systems described by stable Lévy processes. We also discuss aspects of numerically generating these processes.

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“…Each LIM (equations and ) is then integrated forward 200,000 years using the Heun stochastic integration method (Ewald & Penland, ; Rümelin, ) with a time step of 3 hr; then monthly output is sampled. Deviations from Gaussianity in observed and modeled time series, represented by a centered variable x , are determined by the sample skewness

S = \frac{⟨ x^{3} ⟩}{{⟨ x^{2} ⟩}^{3 false/ 2}}

and sample kurtosis

K = \frac{⟨ x^{4} ⟩}{{⟨ x^{2} ⟩}^{2}}

(Joanes & Gill, ).…”

Section: Lim Driven By Cam Noise (Cam‐lim)mentioning

confidence: 99%

Observed El Niño‐La Niña Asymmetry in a Linear Model

Martinez‐Villalobos

Newman

Vimont

et al. 2019

Geophysical Research Letters

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Previous studies indicate an asymmetry in the amplitude and persistence of El Niño (EN) and La Niña (LN) events. We show that this observed EN‐LN asymmetry can be captured with a linear model driven by correlated additive and multiplicative (CAM) noise, without resorting to a deterministic nonlinear model. The model is derived from 1‐month lag statistics taken from monthly sea surface temperature (SST) data sets spanning the twentieth century, in an extension of an empirical‐dynamical technique called Linear Inverse Modeling. Our results suggest that noise amplitudes tend to be stronger for EN compared to LN events, which is sufficient to generate asymmetry in amplitude and also produces more persistent LN events on average. These results establish a null hypothesis for EN‐LN asymmetry and suggest that strong EN events may not be more predictable that what can be accounted for by a multivariate linear system driven by CAM noise.

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Numerical Generation of Stochastic Differential Equations in Climate Models

Cited by 9 publications

References 19 publications

Stochastic Parameterization Schemes for Use in Realistic Climate Models

Stochastic Parameterization Schemes for Use in Realistic Climate Models

On modelling physical systems with stochastic models: diffusion versus Lévy processes

Observed El Niño‐La Niña Asymmetry in a Linear Model

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