Nonlinear Dynamics and Chaos: Applications in Atmospheric Sciences

TL;DR

This paper reviews how nonlinear dynamics and chaos theory can improve understanding and modeling of atmospheric flows, which exhibit fractal fluctuations, long-range correlations, and sensitive dependence on initial conditions.

Contribution

It synthesizes existing knowledge on nonlinear dynamics in meteorology and highlights the need to incorporate chaos theory into classical weather and climate models.

Findings

Atmospheric flows exhibit fractal, inverse power law spectra.

Long-range correlations indicate self-organized criticality.

Chaos theory is essential for realistic weather prediction.

Abstract

Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm -sec to climate scales of thousands of kilometers - years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long - range correlations identified as self - organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the selfsimilar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and incorporate basic physical concepts of nonlinear dynamics and chaos into classical meteorological theory for more realistic simulation and prediction of weather and climate. A review of nonlinear dynamics and chaos in meteorology and atmospheric physics is summarized in this paper.