Multiplicative Noise and Non-Gaussianity: A Paradigm for Atmospheric Regimes?

Sura, Philip; Newman, Matthew; Penland, Cécile; Sardeshmukh, Prashant D.

doi:10.1175/jas3408.1

Cited by 121 publications

(129 citation statements)

References 72 publications

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“…These results provide further support for the Legras and Ghil (1985) conjecture that (i) certain atmospheric flow regimes are associated with unstable fixed points in the flows' phase space; and, hence, (ii) exit from such regimes and subsequent transitions to other regimes originate along preferred directions of unstable growth of perturbations. Our results do not appear to be consistent with other theories for the origin and maintenance of weather regimes, as reviewed by Ghil and Robertson (2002), Molteni (2002), andSura et al (2005). A natural development of the present work would be to study in greater detail the physical nature of the instabilities associated with the preferential directions of regime breaks.…”

Section: Discussioncontrasting

confidence: 79%

“…An alternative theory for the non-Gaussianity of atmospheric PDFs relies on the hypothesis that the stochastic forcing due to high-frequency transients depends, in fact, on the large-scale flow (Sura et al 2005). This state dependence may also be connected to the often discussed eddy feedback on the large-scale flow (Robinson 2000;Kravtsov et al 2005).…”

Section: Introductionmentioning

confidence: 99%

“…In the multiplicative-noise paradigm, there are no multiple equilibria, only an enhancement of the noise near the unique equilibrium; consequently, no preferential directions of evolution exist. Sura et al (2005) provide a very clear discussion of the predictability properties associated with the two paradigms.…”

Section: Introductionmentioning

confidence: 99%

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Weather Regime Prediction Using Statistical Learning

Deloncle

Berk

D’Andrea

et al. 2007

Journal of the Atmospheric Sciences

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Two novel statistical methods are applied to the prediction of transitions between weather regimes. The methods are tested using a long, 6000-day simulation of a three-layer, quasigeostrophic (QG3) model on the sphere at T21 resolution.The two methods are the k nearest neighbor classifier and the random forest method. Both methods are widely used in statistical classification and machine learning; they are applied here to forecast the break of a regime and subsequent onset of another one. The QG3 model has been previously shown to possess realistic weather regimes in its northern hemisphere and preferred transitions between these have been determined. The two methods are applied to the three more robust transitions; they both demonstrate a skill of 35%-40% better than random and are thus encouraging for use on real data. Moreover, the random forest method allows one, while keeping the overall skill unchanged, to efficiently adjust the ratio of correctly predicted transitions to false alarms.A long-standing conjecture has associated regime breaks and preferred transitions with distinct directions in the reduced model phase space spanned by a few leading empirical orthogonal functions of its variability. Sensitivity studies for several predictors confirm the crucial influence of the exit angle on a preferred transition path. The present results thus support the paradigm of multiple weather regimes and their association with unstable fixed points of atmospheric dynamics.

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Section: Discussioncontrasting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

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Weather Regime Prediction Using Statistical Learning

Deloncle

Berk

D’Andrea

et al. 2007

Journal of the Atmospheric Sciences

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“…12 predicts a probability density function (PDF) whose tails decay according to a power law. This is certainly at odds with studies that examined a subspace spanned by the first few leading Empirical Orthogonal Functions (EOFs) from data generated by long integrations of general circulation models (8,14) and reanalysis data (13,15). These studies find only small, though significant, deviations from Gaussianity.…”

mentioning

confidence: 95%

“…The proposed reduced model form from ref. 12 has several implications for scalar stochastic models of climate variables that are at odds with systematic procedures for the derivation of reduced stochastic models of climate variables (3,(6)(7)(8) and climate data (8,13,14). The linear CAM noise model of ref.…”

mentioning

confidence: 99%

Normal forms for reduced stochastic climate models

Majda

Franzke

Crommelin

2009

Proc. Natl. Acad. Sci. U.S.A.

112

137

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The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive highdimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. The use of a few Empirical Orthogonal Functions (EOFs) (also known as Principal Component Analysis, Karhunen-Loéve and Proper Orthogonal Decomposition) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low-and high-frequency subspaces of the dynamics. It is shown below that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large scales by the small scales and simultaneously strong cubic damping. These normal forms should prove useful for developing systematic strategies for the estimation of stochastic models from climate data. As an illustrative example the one-dimensional normal form is applied below to lowfrequency patterns such as the North Atlantic Oscillation (NAO) in a climate model. The results here also illustrate the short comings of a recent linear scalar CAM noise model proposed elsewhere for low-frequency variability.low-frequency teleconnection patterns | nonlinearity | correlated noise T here is recent interest in deriving reduced stochastic models for climate and extended-range weather prediction. An attractive property of atmospheric low-frequency variability is that it can be efficiently described by just a few large-scale teleconnection patterns. These patterns exert a huge impact on surface climate and seasonal predictability. Thus, such reduced stochastic models are an attractive alternative for extended range prediction and climate sensitivity studies because they are computationally much more efficient than state-of-the-art climate models and have been shown to have comparable prediction skill (1). Because such reduced models capture the essence of low-frequency processes they allow for a better understanding of the climate system. Thus, systematic strategies are essential in successfully developing reduced models. The recently developed stochastic mode reduction strategy provides a systematic procedure for the derivation of reduced stochastic models (2-6). In these studies the functional form of reduced models is systematically derived for geophysical flow models. In refs. 7 and 8 the procedure is refined to allow a seamless way of deriving stochastic low-order models from data of complex geophysical flow...

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Low‐frequency nonlinearity and regime behavior in the Northern Hemisphere extratropical atmosphere

Hannachi

Straus

Franzke³

et al. 2017

Reviews of Geophysics

140

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The extratropical atmosphere is characterized by robust circulations which have time scales longer than that associated with developing baroclinic systems but shorter than a season. Such low-frequency variability is governed to a large extent by nonlinear dynamics and, hence, is chaotic. A useful aspect of this low-frequency circulation is that it can often be described by just a few quasi-stationary regime states, broadly defined as recurrent or persistent large-scale structures, that exert a significant impact on the probability of experiencing extreme surface weather conditions. We review a variety of techniques for identifying circulation regimes from reanalysis and numerical model output. While various techniques often yield similar regime circulation patterns, they offer different perspectives on the regimes. The regimes themselves are manifest in planetary scale patterns. They affect the structure of synoptic scale patterns. Extratropical flow regimes have been identified in simplified atmospheric models and comprehensive coupled climate models and in reanalysis data sets. It is an ongoing challenge to accurately model these regime states, and high horizontal resolutions are often needed to accurately reproduce them. The regime paradigm helps to understand the response to external forcing on a variety of time scales, has been helpful in categorizing a large number of weather types and their effect on local conditions, and is useful in downscaling. Despite their usefulness, there is a debate on the "nonequivocal" and systematic existence of these nonlinear circulation regimes. We review our current understanding of the nonlinear and regime paradigms and suggest future research

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Multiplicative Noise and Non-Gaussianity: A Paradigm for Atmospheric Regimes?

Cited by 121 publications

References 72 publications

Weather Regime Prediction Using Statistical Learning

Weather Regime Prediction Using Statistical Learning

Normal forms for reduced stochastic climate models

Low‐frequency nonlinearity and regime behavior in the Northern Hemisphere extratropical atmosphere

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