Analytical probability density function for the statistics of the ENSO phenomenon: Asymmetry and power law tail

Bianucci, Marco

doi:10.1002/2015gl066772

Cited by 15 publications

(67 citation statements)

References 25 publications

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“…The first case refers to laboratory experiments; thus the correlation function and the response function of the perturbing system can be obtained as a fit of the data from targeted experiments. The second case concerns, for example, climatological or geophysical phenomena, as El Niño/La Niña, 32 that are large scale oceanic events induced mainly by the interaction with the fast atmosphere. Here the correlation function can still be obtained from data observation, but the response function of the fast atmosphere (for example) can be only obtained by simplified analytical or numerical models.…”

Section: Applying Proposition 4 To Projection Approachesmentioning

confidence: 99%

“…33,[46][47][48][49] These can be represented as multiplicative perturbations to the ROM. 32,50,51 Considering the dynamics of the atmosphere as the generic "rest of the system" identified by the booster variable ξ and the other "irrelevant" variables π as in Eq. 21, we can writeζ…”

Section: A the Linear Velocity Field Casementioning

confidence: 99%

“…where the interaction vector field (I ζ (T ), I T (T )) depends on the anomalous temperature T as The goal is to describe the statistics of the ENSO, represented by the variables (ζ, T ) perturbed by the atmosphere as in the above equation. Usually, for the sake of simplicity, the perturbation I ζ (ζ, T )ξ of the thermocline depth is not considered, 32,50 but thanks to the results of this paper it is easy to take into account also this contribution. From Eqs.…”

Section: A the Linear Velocity Field Casementioning

confidence: 99%

“…Kurtosis and skewness of the histogram of the frequency of the SST anomalies during El Niño/La Niña phenomena are actually obtained from observations. 32 Moreover, in general, it shall not be possible to get the analytic expression of such stationary DF. However, just from the fact that the diffusion coefficients are second order polynomials of the system of interest variables, we can get closed first order ODE for the moments.…”

Section: A the Linear Velocity Field Casementioning

confidence: 99%

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Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

Bianucci

2018

Journal of Mathematical Physics

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Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

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Section: Applying Proposition 4 To Projection Approachesmentioning

confidence: 99%

Section: A the Linear Velocity Field Casementioning

confidence: 99%

Section: A the Linear Velocity Field Casementioning

confidence: 99%

Section: A the Linear Velocity Field Casementioning

confidence: 99%

See 2 more Smart Citations

Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

Bianucci

2018

Journal of Mathematical Physics

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“…Note that in contrast to the well-known low order model of ENSO, the recharge oscillator [23] and its important stochastic extensions [24], where the influence of the neighbouring regions on the region of interest is modelled as external noise, we consider neighbouring regions as a coupled deterministic dynamical systems. Different parameters yield a rich variety of dynamical patterns in our model, ranging from steady states and homogeneous oscillations to irregular oscillations, without explicit inclusion of noise.…”

Section: Discussionmentioning

confidence: 99%

Coexistence of attractors in a coupled nonlinear delayed system modelling El Niño Southern Oscillations

Meena¹,

Surovyatkina²,

Sinha³

2017

IASCS

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We study the dynamics of the sea surface temperature (SST) anomaly using a model of the temporal patterns of two sub-regions, mimicking behaviour similar to El Niño Southern Oscillations (ENSO). Specifically, we present the existence, stability, and basins of attraction of the solutions arising in the model system in the space of these parameters: self delay, delay and inter-region coupling strengths. The emergence or suppression of oscillations in our models is a dynamical feature of utmost relevance, as it signals the presence or absence of ENSO-like oscillations. In contrast to the well-known low order model of ENSO, where the influence of the neighbouring regions on the region of interest is modelled as external noise, we consider neighbouring regions as a coupled deterministic dynamical systems. Different parameters yield a rich variety of dynamical patterns in our model, ranging from steady states and homogeneous oscillations to irregular oscillations and coexistence of oscillatory attractors, without explicit inclusion of noise. Interestingly, if we take the self-delay coupling strengths of the two sub-regions to be such that the temperature of one region goes to a fixed point regime when uncoupled, while the other system is in the oscillatory regime, then on coupling both systems show oscillations. This implies that oscillations may arise in certain sub-regions through coupling to neighbouring regions. Namely, a sub-region with very low delay, which would naturally go to a steady state when uncoupled, yields oscillations when coupled to another sub-region with high enough delay.We explicitly obtain the basins of attraction for the different steady states and oscillatory states in the model. Our results might be helpful for forecasting of El Niño (or La Niña) progress, as it indicates the combination of initial SST anomalies in the sub-regions that can result in a El Niño/La Niña episodes. In particular, the result suggests using an interval as a criterion to estimate the El-Nino or La-Nino progress instead of the currently used the single value criterion.2

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About the Optimal FPE for Non-linear 1d-SDE with Gaussian Noise: The Pitfall of the Perturbative Approach

Bianucci,

Bologna,

Mannella

2024

J Stat Phys

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This paper deals with the problem of finding the Fokker Planck Equation (FPE) for the single-time probability density function (PDF) that optimally approximates the single-time PDF of a 1-D Stochastic Differential Equation (SDE) with Gaussian correlated noise. In this context, we tackle two main tasks. First, we consider the case of weak noise and in this framework we give a formal ground to the effective correction, introduced elsewhere (Bianucci and Mannella in J Phys Commun 4(10):105019, 2020, https://doi.org/10.1088/2399-6528/abc54e), to the Best Fokker Planck Equation (a standard “Born-Oppenheimer” result), also covering the more general cases of multiplicative SDE. Second, we consider the FPE obtained by using the Local Linearization Approach (LLA), and we show that a generalized cumulant approach allows an understanding of why the LLA FPE performs so well, even for noises with long (but finite) time scales and large intensities.

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Analytical probability density function for the statistics of the ENSO phenomenon: Asymmetry and power law tail

Cited by 15 publications

References 25 publications

Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

Coexistence of attractors in a coupled nonlinear delayed system modelling El Niño Southern Oscillations

About the Optimal FPE for Non-linear 1d-SDE with Gaussian Noise: The Pitfall of the Perturbative Approach

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