Relationships between the limit of predictability and initial error in the uncoupled and coupled lorenz models

Ding, Ruiqiang; Li, Minglu

doi:10.1007/s00376-012-1207-8

Cited by 14 publications

(8 citation statements)

References 27 publications

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“…NLLE theory is required to describe the error growth and obtain the predictability limit. Therefore, the NLLE approach is more suitable for describing infinitesimal error evolution with the long-time interval (Chen et al, 2006;Ding and Li, 2012).…”

Section: The Nlle Approachmentioning

confidence: 99%

The Predictability Limit of Ocean Mesoscale Eddy Tracks in the Kuroshio Extension Region

et al. 2021

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In this study, the nonlinear local Lyapunov exponent and nonlinear error growth dynamics are employed to estimate the predictability limit of oceanic mesoscale eddy (OME) tracks quantitatively using three datasets. The results show that the mean predictability limit of OME tracks is about 53 days for cyclonic eddy (CE) and 52 days for anticyclonic eddy (AE) in the Kuroshio Extension (KE). The predictability limit varies spatially. The predictability limit of OME tracks is higher for the eastern region (about 62.5 days) than that for the western part (about 46 days). The CEs (AEs) predictability limit is relatively high in the southern (northern) region. Additionally, the lifetime, amplitude, and radius of OME are closely related to the predictability limit. The long-lived, large-amplitude, and large-sized OMEs tend to be more predictable. The eastern region often generates long-lived and large-size OMEs, thereby obtaining a higher predictability limit of OME tracks. Furthermore, the relationship between the predictability limit and the smoothness of the OME tracks was investigated using a metric to describe the track’s complexation. Usually, OMEs with high predictability limit values often show extender and smoother trajectories. The effects of the surface ocean circulations and the surface winds are also investigated. The strong and energetic currents lead to a short limitation in the west region.

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Section: The Nlle Approachmentioning

confidence: 99%

The Predictability Limit of Ocean Mesoscale Eddy Tracks in the Kuroshio Extension Region

et al. 2021

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“…An ensemble of 800 errors, which M n (Φ 0 + φ 0 ) − M n (Φ 0 ) − M l (φ 0 ) , at each time step was obtained by integrating solutions of the Lorenz model. The ensemble average of the magnitude of the errors was defined as the average error E. The ensemble average was taken as the geometric mean [Ding and Li (2012)]. Fig.…”

Section: Relationship Between Initial Perturbation and The Predictionmentioning

confidence: 99%

“…The chaotic system is characterized by a "sensitive dependence on initial condition" [Lorenz (1963)], such that the predictability of the future state is often severely limited by the chaotic dynamics of the system. The Lorenz model is one of the most popular models in dynamic systems, and has been studied by Wu et al [Wu, Xie, Fang et al (2007); Richter (2001); Yang, Chen and Yau (2002); Aniszewska and Rybaczuk (2005); Foias and Jolly (2005); Ding and Li (2012)]. In Shepelev et al [Shepelev, Strelkova and Anishchenko (2018)], the transition from the regime of spatio-stationary structures and solitary states to complete incoherence in the network of nonlocally coupled Lorenz systems is numerically studied and a typical property of nonhyperbolic chaotic systems is obtained.…”

Section: Introductionmentioning

confidence: 99%

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

Zhao¹,

Zhang²,

Li³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

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The validity of the tangent linear model (TLM) is studied numerically using the example of the Lorenz equations in this paper. The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method. A new error function between the nonlinear and the linear evolution of the perturbations is proposed. Furthermore, numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM, such as the initial perturbation, the prediction time, the time step size and so on, by the method of mathematical statistics.

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“…Actually, the Lorenz model has been used as an idealized model in forecast research, not only for its simplicity and strong nonlinearity, but also for its comprehensive analysis of the property and stability of the solution. Some results from predictability studies based on the Lorenz model have been applied to help predict practical situations (Ding and Li 2012;Zheng et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Study on the dependence of the two-dimensional Ikeda model on the parameter

Zhou

2016

Atmospheric and Oceanic Science Letters

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Based on the property of solutions of the nonlinear differential equation, this paper focuses on the behavior of solutions to the two-dimensional Ikeda model, especially the dependence of the solutions on the parameter. The dependency relationship of the two-dimensional Ikeda model on the parameter is revealed by a large sample of proper numerical simulations. With the parameter varying from 0 to 1, the numerical solutions change from a point attractor to periodic solutions, then to chaos, and end up with a limit cycle. Furthermore, the route from bifurcation to chaos is shown to be continuous period-doubling bifurcations. The nonlinear structures presented by the solution of the two-dimensional Ikeda model indicate that, by setting different model parameters, one can test a new method that will be adopted to study atmospheric or oceanic predictability and/or stability. The corresponding test results provide some useful information on the ability of the new approach overcoming the impacts of strong nonlinearity. 摘要中文题名：探究二维Ikeda模式解对参数的依赖研究目的：探索二维Ikeda模式数值解的性态及解对模式参数的依赖创新要点：首次对二维Ikeda模式解的性态进行全面细致的探究；结合非线性方程相关理论和数值试验结果给出解的分析；探究了各个分岔点大致的分岔值。研究方法：数值试验与理论分析相结合重要结论：二维Ikeda模式对于控制参数具有高度依赖性；参数值从0到1的变化过程中，模式经历了从单点吸引子、多点吸引子、产生混沌直至出现极限环的变化；模式通过倍周期分岔的方式从分岔到混沌，且分岔过程是连续的。

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Relationships between the limit of predictability and initial error in the uncoupled and coupled lorenz models

Cited by 14 publications

References 27 publications

The Predictability Limit of Ocean Mesoscale Eddy Tracks in the Kuroshio Extension Region

The Predictability Limit of Ocean Mesoscale Eddy Tracks in the Kuroshio Extension Region

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

Study on the dependence of the two-dimensional Ikeda model on the parameter

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