Is Weather Chaotic? Coexistence of Chaos and Order within a Generalized Lorenz Model

The pioneering study of Lorenz in 1963 and a follow-up presentation in 1972 changed our

view on the predictability of weather by revealing sensitivity of solutions to initial conditions,

which is so-called butterfly effect and also known as chaos. Over 50 years since Lorenz’s 1963

study, the statement of ``weather is chaotic’’ has been well accepted. Such a view turns our

attention from regularity associated with the Laplace’s view of determinism to irregularity

associated with the chaos. Stated alternatively, while Lorenz (1993) documented that “as with

Poincare and Birkhoff, everything centers around periodic solutions,” he himself and chaos

advocates focused the existence of non-periodic solutions and their complexities. Two

interesting questions are: (1) whether two types of regular and irregular solutions appear

exclusively? (2) whether the statement of ``weather is chaotic’’ completely excludes periodic

processes within weather. To answer the two questions, a refined statement on the nature of

weather is proposed based on recent advances in high-dimensional Lorenz models and real world

global models. In this study, we provide a report to: (1) Illustrate two kinds of attractor

coexistence within Lorenz models. Each kind contains two of three attractors including regular

point and periodic, and irregular chaotic attractors corresponding to steady-state, limit cycle,

and chaotic solutions, respectively. (2) Suggest that the entirety of weather possesses the dual

nature of order and chaos associated with regular and irregular processes, respectively. Specific

weather systems may appear chaotic or non-chaotic within their finite lifetime. While chaotic

systems contain a finite practical predictability, non-chaotic systems (e.g., dissipative

processes) could have better predictability (e.g., up to their lifetime). The refined view on the

nature of weather is neither too optimistic nor pessimistic as compared to the Laplacian view

of deterministic unlimited predictability and the Lorenz view of deterministic chaos with finite

predictability. A new focus is on the frequency of stability, instability and chaos.