What is the Butterfly Effect?

There is a popular notion that the “butterfly effect” describes a climate system that is exceptionally sensitive to very small perturbations. As just one example, a google search turned up the following description of it,

“In the arcane field of chaos theory, there is what scientists call “the butterfly effect,” the popular notion that when a butterfly flaps its wings in Asia the action may eventually alter the course of a tornado in Kansas.” (http://ww2.roanoke.com//politics/32390.html).

Even the scientific community presents this perspective, e.g., see http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html, from which the following text is extracted,

“The ‘Butterfly Effect’, or more technically the “sensitive dependence on initial conditions”, is the essence of chaos……..The “Butterfly Effect” is often ascribed to Lorenz. In a paper in 1963 given to the New York Academy of Sciences he remarks: ‘One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings would be enough to alter the course of the weather forever.’ By the time of his talk at the December 1972 meeting of the American Association for the Advancement of Science in Washington, D.C. the sea gull had evolved into the more poetic butterfly – the title of his talk was ‘Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?’ In the applet we also see a second incarnation of the Butterfly – the amazing geometric structure discovered by Lorenz in his numerical simulations of three very simple equations that now bear his name.”

The solution of the Lorenz equations from this informative website illustrates the “butterfly” looking field that results. Figure 6 from Tsonis and Elsner (1989) has a particularly clear illustration of the butterfly solution.

This second definition of the butterfly effect is the correct use of the term “butterfly effect.” However, the first usage of the “butterfly effect” in that “when a butterfly flaps its wings in Asia the action may eventually alter the course of a tornado in Kansas” is incorrect. The information from the butterfly is quickly lost on scales close to the size of the butterfly, as the atmosphere is a dissipative system such that only particularly significant powerful forcings, or small climate forcings near a climate transition (but certainly not as small as a butterfly’s flapping winds) can upscale (i.e., teleconnect) to the global scale. Indeed, if we accepted the first definition of the “butterfly effect”, everything that an individual human does on any scale (e.g., brushing your teeth) would be a climate forcing that would influence weather thousands of kilometers away. Of course, that is preposterous.

To communicate accurately in climate science, we need to make sure we properly present the significance of Lorenz’s seminal research. There certainly are thresholds (i.e., “tipping points”) that can result in sudden and large changes in climate regimes. This is a characteristic of chaotic nonlinear systems which we discuss for example, in

Pielke, R.A., 1998: Climate prediction as an initial value problem. Bull. Amer. Meteor. Soc., 79, 2743-2746.644.

Zeng, X., R.A. Pielke, and R. Eykholt, 1993: Chaos theory and its applications to the atmosphere. Bull. Amer. Meteor. Soc., 74, 631-644.

Pielke, R.A. and X. Zeng, 1994: Long-term variability of climate. J. Atmos. Sci., 51, 155-159.

Zeng., X. and R.A. Pielke, 1993: What does a low-dimensional weather attractor mean? Phys. Lett. A., 175, 299-304.

The consequences of this chaotic nonlinearity is the ocureence of the concept of critical thresholds which we discuss in Rial, J., R.A. Pielke Sr., M. Beniston, M. Claussen, J. Canadell, P. Cox, H. Held, N. de Noblet-Ducoudre, R. Prinn, J. Reynolds, and J.D. Salas, 2004: Nonlinearities, feedbacks and critical thresholds within the Earth’s climate system. Climatic Change, 65, 11-38.

The flap of a butterfly’s wings, however, while it seeks to capture the concept of the “sensitivity of the climate system to small perturbations of the initial conditions” overstates the true characteristic of the Earth’s climate system.