Prof. Shen presented a seminar titled “Butterfly Effects and Chaos:
New Insights Revealed by a Generalized Lorenz Model”.
Resumen
Is weather chaotic? A view that weather is chaotic was proposed and is recognized based on the pioneering work of Prof. Lorenz who first introduced the concept of deterministic chaos. Chaos is defined as the sensitive dependence of solutions on initial conditions, also known as the butterfly effect. The appearance of deterministic chaos suggests finite predictability, in contrast to the Laplacian view of deterministic predictability. After a follow-up study in 1972, the butterfly effect has come to be known as a metaphor for indicating that a tiny perturbation such as a butterfly’s flap may ultimately cause a large impact, such as the creation of a tornado. The two studies discussed above, as well as Lorenz’s 1969 study, laid the foundation for chaos theory that is viewed as one of the three scientific achievements of the 20th century, inspiring numerous studies in multiple fields. Our daily experiences with weather predictions largely support Lorenz’s view of a finite predictability.
On the other hand, under some conditions, better predictability, as compared to the predictability limit documented within the scientific literature, has also been observed. For example, while some studies have suggested that a theoretical limit of predictability is two weeks, recent advances in supercomputing and high-resolution modeling technology (Atlas et al., 2005; Shen et al., 2006; 2013) have yielded promising 30-day simulations for high impact weather systems (Shen et al., 2010). In a brief report highlighting remarkable simulations in 2011, Dr. Richard Anthes, former President of the University Corporation for Atmospheric Research (UCAR), proposed a visioning question: is the atmosphere more predictable than we assume (Anthes, 2011)? Since that time, the view of weather being chaotic has been revisited using newly developed Lorenz models (Shen, 2014, 2015, 2016, 2017, 2018, 2019; Faghih-Naini and Shen, 2018).
Recently, by conducting a comprehensive literature review (Shen et al., 2018a, b) and developing a new generalized Lorenz model (GLM, Shen, 2019), we (1) illustrate two kinds of butterfly effects in Lorenz’s studies; (2) discuss two kinds of attractor coexistence as well as various types of solutions (e.g., chaotic, linearly unstable, and nonlinear limit cycle solutions) in Lorenz models; and (3) propose that the entirety of weather is a superset that consists of both chaotic and non-chaotic processes. Depending on the time-varying collective impact of heating, dissipation, and nonlinearity, specific weather systems may appear on a chaotic or non-chaotic orbit with different predictability. A ten-year analysis of real world data using the newly developed parallel ensemble mode decomposition method (e.g., Wu and Shen, 2016; Shen et al., 2017) indicated the role of large-scale processes in providing a determinism for the small-scale processes. The revised view on the nature of weather suggests a potential for obtaining longer predictability. To achieve this goal, methods with recurrence analysis and kernel principal component analysis have been implemented to detect and identify non-chaotic (as well as chaotic) processes within the GLM (Reyes and Shen, 2019; Cui and Shen, 2019). New opportunities and challenges for improving predictability will be discussed at the end.
A recording of the presentation is available on the anonymous ftp site: ftp://ftp.aoml.noaa.gov/hrd/pub/blog/seminars/2019/Shen_AOML_Seminar_20190225.mp4
