Coexisting Chaotic and Non-chaotic Attractors, Multistability, Multiscale Instability, and Predictability within Lorenz ModelsProf. Bo-Wen Shen (Department of Mathematics and Statistics San Diego State University)

Following Lorenz’s studies (Lorenz 1963, 1969, 1972), deterministic, chaotic solutions, and closurebased, linearly unstable solutions have been an explicit and/or implicit focus for understanding predictability in weather and climate. For this talk, I will first provide the physical relevance of findings within Lorenz models for real world problems by showing mathematical universality between the Lorenz and Pedlosky models (Shen 2021), as well as amongst the non-dissipative Lorenz model and the Duffing, the Nonlinear Schrodinger, and the Korteweg–de Vries equations (Shen 2020). Using the classical Lorenz 1963 (L63), 1969 (L69), and generalized Lorenz models (GLM) (e.g., Lorenz 1963, 1969; Shen 2014-2019), I will then discuss monostability (for single type solutions), multistability (for two kinds of attractor coexistence), multiscale instability, and predictability in support of the revised view that “weather possesses chaos and order; it includes emerging organized systems (such as tornadoes) and recurrent seasons” (Shen et al. 2021a, b, 2022). Additional details for monostability and multistability will be provided by applying skiing and kayaking as an analogy. Based on the perspective of dynamical systems, I will also provide comments on the conceptual model of a chain process.

The above findings are applied in order to revisit a conceptual model for illustrating the predictability dependence of medium-scale processes on the modulation of large-scale processes and aggregated feedback by small-scale processes. Examples from earlier studies, published by myself and collaborators, have examined the relationship between: (1) Tropical Cyclone (TC) Nargis (2008) and an equatorial Rossby wave (Shen et al. 2010a); (2) Twin TCs (2002) and a mixed Rossby gravity wave (Shen et al. 2012) during an active phase of a Madden–Julian oscillation (MJO); (3) Hurricane Helene (2006) and an intensifying African Easterly Wave (Shen et al. 2010b; Wu and Shen 2016; Shen 2019b); and (4) Hurricane Sandy (2012) and upper-level tropical waves associated with a MJO (Shen et al. 2013a; Shen et al. 2016). The 3rd case will be discussed in this talk. At the end of the talk, I will discuss new opportunities and challenges in predictability research, including computational chaos and saturation dependence on various types of solutions for improving our understanding of the butterfly effect and predictions at extended-range time scales, including subseasonal to seasonal time scales. Selected References:

1. Shen, B.-W., R. A. Pielke Sr., X. Zeng, 2022: Special Issue "50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Multistability, Multiscale Predictability, and Sensitivity in Numerical Models". https://www.mdpi.com/journal/atmosphere/special_issues/predictability_numerical_models

2. Shen, B.-W., R. A. Pielke Sr., X. Zeng, J.-J. Baik, S. Faghih-Naini, J. Cui, and R. Atlas, 2021a: Is Weather Chaotic? Coexistence of Chaos and Order within a Generalized Lorenz Model. Bulletin of American Meteorological Society. 102(1), E148-E158. https://doi.org/10.1175/BAMS-D-19-0165.1

3. Shen, B.-W., 2019a: Aggregated Negative Feedback in a Generalized Lorenz Model. International Journal of Bifurcation and Chaos, Vol. 29, No. 3 (2019) 1950037 (20 pages). https://doi.org/10.1142/S0218127419500378