A Recurrence Analysis of Multiple African Easterly Waves during Summer 2006

Reyes, Tiffany; Shen, Bo-Wen

doi:10.5772/intechopen.86859

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Therefore, when considering the temporal and spatial variations of forcing and dissipation processes, which are often neglected in autonomous systems, it becomes essential to consider "recurrence" instead of "periodicity". As defined in Thompson and Stewart (2002) [92] and studied using highdimensional Lorenz models by Shen (2019, 2020) [93,94], recurrence refers to a trajectory returning to the vicinity of its previous location. Recurrence can be seen as a more inclusive concept that encompasses quasi-periodicity with multiple frequencies and chaos.…”

Section: Analogues and Recurrencementioning

confidence: 99%

The 50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Multistability, Multiscale Predictability, and Sensitivity in Numerical Models

2023

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Lorenz rediscovered the butterfly effect, which is defined as the sensitive dependence on initial conditions (SDIC), in 1963. In 1972, he used the term “butterfly” as a metaphor to illustrate how a small perturbation can lead to a tornado with a complex structure. The metaphorical butterfly effect, which celebrated its 50th anniversary in 2022, is not precisely the same as the original butterfly effect with SDIC. To commemorate the 50th anniversary, a Special Issue was launched and invited the submission of research and review articles that can help to enhance our understanding of both the original and metaphorical butterfly effects. The Special Issue also sought recent developments in idealized Lorenz models and real-world models that address multistability, multiscale predictability, and sensitivity. The call for papers was opened 15 months prior to the completion of the Special Issue and features nine selected papers. This editorial provides a brief review of Lorenz models, introduces the published papers, and summarizes each one of them.

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Section: Analogues and Recurrencementioning

confidence: 99%

The 50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Multistability, Multiscale Predictability, and Sensitivity in Numerical Models

2023

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“…From a perspective of steering flows, two types of TC track errors, as shown in Fig. 6, include: (i) an Ivan ( 2004)-type with a persistent track bias associated with an underestimated sub-tropical ridge (Stewart 2004;Shen et al 2006) and (ii) a Sandy (2012) type with rapid diverged tracks associated with a steering flow that contains a saddle point (Blake et al 2013;Shen et al 2013). Very slight differences determine whether a TC (e.g., Sandy) recurves to the northeast, or wraps back west.…”

Section: Chaotic and Non-chaotic Solutions As Steering Flowsmentioning

confidence: 99%

Is Weather Chaotic? Coexisting Attractors, Multistability, and Predictability

Shen

Pielke

Zeng

et al. 2021

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Since Lorenz’s 1963 study and 1972 presentation, the statement “weather is chaotic’’ has been well accepted. Such a view turns our attention from regularity associated with Laplace’s view of determinism to irregularity associated with chaos. In contrast to single type chaotic solutions, recent studies using a generalized Lorenz model (Shen 2019a, b; Shen et al. 2019) have focused on the coexistence of chaotic and regular solutions that appear within the same model, using the same modeling configurations but different initial conditions. The results suggest that the entirety of weather possesses a dual nature of chaos and order with distinct predictability. Furthermore, Shen et al. (2021a, b) illustrated the following two mechanisms that may enable or modulate attractor coexistence: (1) the aggregated negative feedback of small-scale convective processes that enable the appearance of stable, steady-state solutions and their coexistence with chaotic or nonlinear limit cycle solutions; and (2) the modulation of large-scale time varying forcing (heating). Recently, the physical relevance of findings within Lorenz models for real world problems has been reiterated by providing mathematical universality between the Lorenz simple weather and Pedlosky simple ocean models, as well as amongst the non-dissipative Lorenz model, and the Duffing, the Nonlinear Schrodinger, and the Korteweg–de Vries equations (Shen 2020, 2021). We additionally compared the Lorenz 1963 and 1969 models. The former is a limited-scale, nonlinear, chaotic model; while the latter is a closure-based, physically multiscale, mathematically linear model with ill-conditioning. To support and illustrate the revised view, this short article elaborates on additional details of monostability and multistability by applying skiing and kayaking as an analogy, and provides a list of non-chaotic weather systems. We additionally address the influence of the revised view on real-world model predictions and analyses using hurricane track predictions as an illustration, and provide a brief summary on the recent deployment of methods for multiscale analyses and classifications of chaotic and non-chaotic solutions.

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