The Butterfly Effect Makes Precise Weather Prediction Impossible

Why Small Differences in Measurement Make Massive Differences in the Outcome of Weather Prediction Mathematical Models

Feb 07, 2024

Excerpt from my book The Truth About Energy, Global Warming, and Climate Change: Exposing Climate Lies in an Age of Disinformation

If a single flap of a butterfly’s wing can be instrumental in generating a tornado, so also can all the previous and subsequent flaps of its wings, as can the flaps of the wings of millions of other butterflies, not to mention the activities of innumerable more powerful creatures, including our own species. If the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.

Edward N. Lorenz, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas,” 1972¹

Edward Norton Lorenz was a mathematician and meteorologist who followed in John von Neumann’s footsteps. As a professor in the Department of Meteorology at MIT in the 1960s, Lorenz used an early digital computer, a Royal McBee LGP-30, to run a computer model he constructed to predict the weather. The computer model used twelve independent variables to measure various aspects of the weather, including temperature and wind speed. One day, in February 1961, Lorenz repeated a simulation he had run earlier. This time, he rounded off one variable from .056127 to .506, and then he went to get a cup of coffee. When he returned to his office, he was shocked to find “this tiny alteration drastically transformed the whole pattern his program produced, over two months of simulated weather.”²

In 1963, Lorenz published a scientific paper in the Journal of Atmospheric Sciences. “Deterministic Nonperiodic Flow” was a highly technical study that triggered a scientific revolution.³ The subject of the article was not specifically weather predicting. Instead, Lorenz focused on using finite systems of deterministic ordinary nonlinear differential equations to analyze hydrodynamical flow patterns. Cascading water has been problematic to describe in mathematical equations. Water cascades typically “vary in an irregular, seemingly haphazard manner, and, even when observed for long periods, do not appear to repeat their previous history.”⁴

Nonlinear differential equations are notoriously difficult to solve because a change in one variable does not produce the exact difference or reaction in related variables. But Lorenz felt utilizing nonlinear differential equations was appropriate for the dynamic system of water cascades he was trying to model mathematically. In a dynamic system, a change in one variable may not produce the exact change every time in other variables.⁵ In his book The Essence of Chaos, Lorenz discussed why differential equations are the appropriate mathematical tool for handling flows, including water oscillations or the action of a pinball machine. “A system of differential equations amounts to a set of formulas that together express the rates at which all of the variables are currently changing, in terms of the current values of the variables,” he explained.⁶

What he found out was that slight variations in the variables produced drastic changes in the results. He found that “slightly differing initial states can evolve into considerably different states.”⁷ He concluded the article by applying his findings to the atmosphere. “In view of the inevitable inaccuracy and incompleteness of weather observations, precise very long-range forecasting would seem to be non-existent,” he noted.⁸ Lorenz had concluded that the problem with long-range weather forecasting is that the variety of weather possibilities are so immense that even small changes can drastically affect weather outcomes.

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Lorenz’s conclusion challenged the classical understanding of nature. Sir Isaac Newton published laws in 1687 that suggested a highly “predictable mechanical system—the ‘clockwork universe.’”⁹ Though Lorenz had just developed a mathematical proof that weather is unpredictable, his 1963 paper went largely unnoticed. Yet, the importance of Lorenz’s work was enormous. “By showing that certain deterministic systems have formal predictability limits, Ed put the last nail in the coffin of the Cartesian universe and fomented what some have called the third scientific revolution of the 20th century, following on the heels of relativity and quantum physics,” said Kerry Emanuel, a professor of atmospheric science at MIT.¹⁰

But the scant two-week-long accuracy of weather forecasts reflects a fundamental problem described by Ed Lorenz at MIT in 1961. The weather is chaotic—small changes in how we start the model can lead to very different predictions after a few weeks. So no matter how precisely we might specify current conditions, the uncertainty in our predictions grows exponentially as they extend into the future. More computer power cannot overcome this basic uncertainty.

Steven E. Koonin, former undersecretary for science, U.S. Department of Energy under the Obama administration, Unsettled: What Climate Science Tells Us and What It Doesn’t and Why It Matters, 2021¹¹

On December 29, 1972, Lorenz presented a paper at a meeting of the American Association for the Advancement of Science. The paper was entitled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”¹² In the paper, Lorenz questioned whether a single flap of a butterfly’s wings could generate a tornado somewhere else in the world. He was equivocal in that he also noted that a single flap of a butterfly’s wing would have no more effect on the weather than any flap of any other butterfly’s wings, not to mention the activities of other species, including our own.

The fact that the large computer models indicate such a temperature rise as a consequence of increased carbon dioxide cannot be taken as evidence of truth; for any such model is merely a formal statement of the modeller’s opinion of how the atmospheric system works.

Reid A. Bryson, “Simulating Past and Forecasting Future Climates,” 1993¹³

The term “Butterfly Effect” gained notoriety in 1987 when science historian James Gleick published his book entitled Chaos: Making a New Science.¹⁴ Gleick’s first chapter, “The Butterfly Effect,” was dedicated to giving Lorenz credit for discovering a new branch of mathematics now deemed “Chaos Theory.” In his book The Essence of Chaos, Lorenz admitted he did not develop the Butterfly Effect name for chaos theory. He mused that the name might have come from “A Sound of Thunder,” a short story written by science-fiction writer Ray Bradbury. Lorenz considered the reference appropriate. He noted that in the story the death of a prehistoric butterfly and its consequent failure to reproduce changed the outcome of a present-day election. “Perhaps the butterfly, with its seeming frailty and lack of power, is a natural choice for a symbol of the small that can produce the great,” Lorenz wrote.¹⁵

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