The Dual Nature of Chaos and Order in the Atmosphere

Abstract

In the past, the Lorenz 1963 and 1969 models have been applied for revealing the chaotic nature of weather and climate and for estimating the atmospheric predictability limit. Recently, an in-depth analysis of classical Lorenz 1963 models and newly developed, generalized Lorenz models suggested a revised view that “the entirety of weather possesses a dual nature of chaos and order with distinct predictability”, in contrast to the conventional view of “weather is chaotic”. The distinct predictability associated with attractor coexistence suggests limited predictability for chaotic solutions and unlimited predictability (or up to their lifetime) for non-chaotic solutions. Such a view is also supported by a recent analysis of the Lorenz 1969 model that is capable of producing both unstable and stable solutions. While the alternative appearance of two kinds of attractor coexistence was previously illustrated, in this study, multistability (for attractor coexistence) and monostability (for single type solutions) are further discussed using kayaking and skiing as an analogy. Using a slowly varying, periodic heating parameter, we additionally emphasize the predictable nature of recurrence for slowly varying solutions and a less predictable (or unpredictable) nature for the onset for emerging solutions (defined as the exact timing for the transition from a chaotic solution to a non-chaotic limit cycle type solution). As a result, we refined the revised view outlined above to: “The atmosphere possesses chaos and order; it includes, as examples, emerging organized systems (such as tornadoes) and time varying forcing from recurrent seasons”. In addition to diurnal and annual cycles, examples of non-chaotic weather systems, as previously documented, are provided to support the revised view.

Keywords

• dual nature
• chaos
• generalized Lorenz model
• predictability
• multistability