Can a Butterfly in Brazil Really Cause a Tornado in Texas?

Contrary to common belief, a new paper argues that the answer is "No"

The butterfly did it!

It has been a little while since we heard from Roger Pielke Sr. here at THB. (see his previous THB posts on carbon dioxide, ocean heat content, and land use effects on climate). He is a difficult guy to schedule — Right now he and my Mom are somewhere in Texas searching for clear skies to view today’s solar eclipse. Today, I am happy to share my father’s latest paper on the “Butterfly Effect,” forthcoming in Weatherwise and co-authored with Bo-Wen Shen of San Diego State University and Xubin Zeng of the University of Arizona. My father and colleagues have published many papers on chaos theory and predictability, and this paper brings some of that work to a broader audience. Below, I excerpt their forthcoming paper in a Q&A format and at the bottom of the post provide a link to the uncorrected page proofs (courtesy Dr. Shen). In the comments, please feel free to ask questions about the paper and I’ll be sure to corral my dad to join in and discuss! — RP2

Pielke Sr. et al. 2024.

What is the “Butterfly Effect”?

Almost everyone has heard the claim that a butterfly can flap its wings in one part of the world and cause a chain reaction of events that ultimately results in a major event on the other side of the world. For example, a butterfly wing flap in Brazil could cause a tornado in Texas. Indeed, this concept has permeated popular society. . .

In academia, the concept of the butterfly effect apparently first appeared in an article in the Bulletin of the American Meteorological Society by J. Smagorinsky in 1969, but the specific question “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” was introduced by Ed Lorenz at the 1972 Meeting of AAAS Section on Environmental Sciences. . .

Chaos theory explained in Jurassic Park (1993).

Can the “Butterfly Effect” be captured by weather forecasting models?

. . . existing numerical models cannot accommodate a disturbance as small as the flap of a butterfly’s wing, meaning we cannot accurately predict the resulting weather phenomena using numerical models.

But despite the lack of scientific evidence supporting the idea that a butterfly wing flap could create a tornado in Brazil, the prevailing opinion, even among many in the atmospheric science community, continues to be that it is, indeed, possible.

It looks like a butterfly, right? Source: Pielke et al. 2024.

So, is the flap of a butterfly’s wings capable of causing a tornado in Texas?

To answer this question, the following additional question needs to be answered: “Can a kinetic energy disturbance as small as a butterfly wing flap convert available potential energy into kinetic energy and an organized, large atmospheric circulation, or will dissipation of motion into heat by viscous forcing make such energy transfer impossible?” In other words, is the behavior of the atmosphere unstable with respect to disturbances of all sizes, regardless of size?

In order for a kinetic energy disturbance to grow in size and/or travel large distances, production of kinetic energy needs to exist at a rate larger than the loss of this energy into heat (called dissipation). The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters, although it occurs on all spatial scales. At and below this scale, nonlinear turbulent motions essentially do not exist.

The flap of the butterfly's wings involves a spatial scale close to 10 millimeters, meaning that it is so small that the energy it produces would dissipate nearly immediately and not be capable of causing a tornado.

OK, how about a sea gull’s wings? Or the wings of a 787?

So if a butterfly cannot cause a tornado many miles away, the question to be asked, then, is what could? How big would a disturbance have to be in order to cause a chain reaction of events leading to such a powerful atmospheric phenomenon? Clearly, the spatial scale of the disturbance would have to be much larger than 10 millimeters. Current weather models use much larger spatial scale in their own predictions.

Although we cannot answer this question definitively, we can infer some information from weather prediction models that show that large atmospheric events like hurricanes can, in fact, cause an INCREASE in kinetic energy over distances as these extract energy from the larger scales, rather than a loss of energy.

Thus, while a butterfly in Brazil cannot cause a tornado in Texas, since dissipation dominates at the size of a butterfly, a thunderstorm in Brazil CAN result in significant weather effects at large distances because it can cause an increase in kinetic energy over distances.

Additional research will be needed to answer the question of how large an atmospheric disturbance needs to be in order to not be dominated by dissipation processes . . .

The bottom line?

[W]e can finally answer the primary question at hand and correct a widespread scientific misconception: A butterfly flapping its wings in Brazil cannot cause a tornado in Texas.

You can read the full paper (uncorrected pre-publication page proofs) here in PDF courtesy of Dr. Shen.

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An innocent bystander

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