Lorenz models, butterfly effect, and predictability

Department of Hydrology and Atmospheric Sciences

4 pm on Thursday, March 18, 2021
Contact the department for zoom details or to subscribe to the seminar email list

Bo-Wen Shen
Department of Mathematics and Statistics, San Diego State University


In this talk, recent studies that have applied classical and generalized Lorenz models for providing insights on the butterfly effect and predictability are summarized.

Classical and Generalized Lorenz Models: Two studies of Prof. Lorenz (Lorenz 1963, 1972) laid the foundations for chaos theory, yielding a paradigm shift from Laplace’s view of determinism to Lorenz’s view of deterministic chaos. The physical relevance of findings within Lorenz models for real world problems has recently been reiterated by providing mathematical universality between the Lorenz and Pedlosky models, as well as amongst the non-dissipative Lorenz model, the Duffing, the Nonlinear Schrodinger, and the Korteweg–de Vries equations (Shen 2020). In contrast to monostability within the classical Lorenz model, the multistability of coexisting chaotic and regular solutions within a generalized Lorenz model (GLM, Shen 2019a) has been emphasized, suggesting a revised view for weather that possesses a dual nature of chaos and order with distinct predictability (Shen et al. 2021a, b).

Butterfly Effects of the First and Second Kinds (BE1 and BE2) were introduced in order to indicate the sensitive dependence of solutions on initial conditions and the hypothesized enabling role of initial tiny perturbations in producing an organized large-scale system (e.g., a tornado), respectively. BE1 is known as chaos and BE2 is a metaphorical analogy. The revised view suggests that BE1 does not always appear.

Intrinsic and Practical Predictability were suggested by Lorenz (1963b) to indicate the dependence on flow, and imperfect numerical tools and observations, respectively. The multistability of coexisting attractors indicates distinct intrinsic (and practical) predictability. Two mechanisms that contribute to the coexistence of attractors include: (1) the aggregated negative feedback of small-scale convective processes and (2) the modulation of large-scale, time varying forcing.

The refined view may unify our theoretical understanding of different predictability and recent global model simulations that display promising results over two-week time scales (e.g., Shen 2019b; Judt 2020). At the end of the talk, I will discuss new opportunities and challenges in predictability research with the aim of improving predictions at extended-range time scales, including sub-seasonal to seasonal time scales.


Dr. Bo-Wen Shen is an Associate Professor in the Department of Mathematics and Statistics at San Diego State University (SDSU). He received his Ph.D. from North Carolina State University in 1998. He has more than 25 years of experience in mesoscale/global modeling, high-end computing, model applications to numerical weather prediction, and nonlinear dynamics. Following graduation, he joined the modeling group of Dr. S.-J. Lin at the NASA Goddard Space Flight Center (GSFC) and worked to develop a unified weather and climate model in 1999. Since late 2002, he and his colleagues have applied a high-resolution global model (that was improved to become a global mesoscale model) for real-time hurricane prediction, producing promising results and articles highlighted by the American Geophysical Union, Science, and other media. In 2006, he began working on computational coupling of the multiscale modeling framework. He was the principle investigator of NASA CAMVis (Coupled Advanced global Modeling and concurrent Visualization systems) projects between 2009 and 2015. During that time, he led efforts to: (i) implement a 2D domain decomposition with load balancing into the Goddard Multiscale Modeling Framework (MMF), obtaining a nearly 80-fold speedup using 3,335 cores; and (ii) implement three-level parallelism into the ensemble Empirical Mode Decomposition (EMD), achieving a scaled performance of 5,000 cores. In 2011, Dr. Shen began working on nonlinear dynamics and chaos theory with the aim of understanding the predictability of high-resolution global model simulations. He joined SDSU in 2014 and since that time has published major articles that have developed a generalized Lorenz model and has proposed a revised view on the dual nature of weather that challenges the validity of the statement “weather is chaotic” (potentially unifying our theoretical understanding of different predictability and recent global model simulations that display promising results for extending forecasts beyond two weeks).