Numerical solution of systems of stochastic differential equations

Аверина, Т. А.; Artemiev, S. S.

doi:10.1515/rnam.1988.3.4.267

Cited by 15 publications

(15 citation statements)

References 2 publications

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“…To automatically restrict the value of I wc between 21.0 and 1.0, we consider a multiplicative noise coefficient (see Fig. 1a) based on the stochastic theory (Averina and Artemiev 1988;Chen and Majda 2020). As shown by Table 2, the variable I wc switches the solution toward the EP (CP) El Niño regime without (with) the background Walker circulation when its value is close to 0 (1.0).…”

Section: A Governing Equationsmentioning

confidence: 99%

ENSO Diversity in a Tropical Stochastic Skeleton Model for the MJO, El Niño, and Dynamic Walker Circulation

2021

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The El Niño-Southern Oscillation (ENSO) diversity has a significant impact on global climate and seasonal prediction. However, it is still a challenging problem for present-day global climate models to simulate different types of ENSO events with realistic features simultaneously. In this paper, a tropical stochastic skeleton model for the interactions among wind bursts and the Madden-Julian Oscillation (MJO), the El Niño, and the Walker circulation is developed to reproduce both dynamical and statistical features of the ENSO diversity. In this model, the intraseasonal component with state-dependent noise captures general features of wind bursts and the MJO, both of which play important roles in triggering the El Niño. The thermocline feedback is the dominant mechanism for generating the eastern Pacific (EP) El Niño, while a nonlinear zonal advection is incorporated into the model that contributes to the central Pacific (CP) El Niño. Besides, a simple but effective stochastic process describing the multidecadal variation of the background Walker circulation modulates the spatial patterns and occurrence frequency of the EP and CP El Niño. This model succeeds in simulating the quasi-regular moderate EP El Niño, the super El Niño, and the CP El Niño as well as the La Niña simultaneously. It also captures the observed non-Gaussian characteristics of sea surface temperature anomalies in different Niño regions. Individual case studies highlight the outstanding skill of the model in reproducing the observed El Niño episodes and their underlying mechanisms.

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Section: A Governing Equationsmentioning

confidence: 99%

ENSO Diversity in a Tropical Stochastic Skeleton Model for the MJO, El Niño, and Dynamic Walker Circulation

2021

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“…To characterize such a non-Gaussian feature, a linear model with a state-dependent noise coefficient σ k (û k ) in ( 13) is utilized as an approximate model [5],…”

Section: Efficient and Statistically Accurate Linear Stochastic Model...mentioning

confidence: 99%

An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models

Chen,

Fu,

Manucharyan

2021

Preprint

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Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that significantly accelerates the computational efficiency of Lagrangian data assimilation. The algorithm starts with a Fourier transform of the high-dimensional flow field, which is followed by an effective model reduction that retains only a small subset of the Fourier coefficients corresponding to the energetic modes. Then a linear stochastic model is developed to approximate the nonlinear dynamics of each Fourier coefficient. Effective additive and multiplicative noise processes are incorporated to characterize the modes that exhibit Gaussian and non-Gaussian statistics, respectively. All the parameters in the reduced order system, including the multiplicative noise coefficients, are determined systematically via closed analytic formulae. These linear stochastic models succeed in forecasting the uncertainty and facilitate an extremely rapid data assimilation scheme. The new Lagrangian data assimilation is then applied to observations of sea ice floe trajectories that are driven by atmospheric winds and turbulent ocean currents. It is shown that observing only about 30 non-interacting floes in a 200km×200km domain is sufficient to recover the key multi-scale features of the ocean currents. The additional observations of the floe angular displacements are found to be suitable supplements to the center-of-mass positions for improving the data assimilation skill. In addition, the observed large and small floes are more useful in recovering the large-and small-scale features of the ocean, respectively. The Fourier domain data assimilation also succeeds in recovering the ocean features in the areas where cloud cover obscures the observations. Finally, the multiplicative noise is shown to be crucial in recovering extreme events.

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“…We refer e.g., to [1,11,17,24] for results equivalent to Theorem 1 as well as additonal material on the topic of SODEs.…”

Section: Example 1 (Sodes)mentioning

confidence: 99%

One-step approximations for stochastic functional differential equations

Buckwar

2006

Applied Numerical Mathematics

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Numerical solution of systems of stochastic differential equations

Cited by 15 publications

References 2 publications

ENSO Diversity in a Tropical Stochastic Skeleton Model for the MJO, El Niño, and Dynamic Walker Circulation

ENSO Diversity in a Tropical Stochastic Skeleton Model for the MJO, El Niño, and Dynamic Walker Circulation

An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models

One-step approximations for stochastic functional differential equations

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