Around 1960 at MIT, Edward Lorenz ran a tiny weather model on a desk-sized computer. To rerun a stretch, he typed in numbers it had printed earlier and went for coffee. An hour later the machine had simulated two months of weather, and the new run looked nothing like the first. He suspected a broken vacuum tube.

Nothing was broken. The machine kept six decimals; the printout showed three. That tiny gap doubled about every four simulated days until the two runs were strangers. Real air is never measured that exactly, so a perfect forecast far ahead is impossible.

In 1963 he quoted a meteorologist who said one flap of a seagull's wings could change the weather forever. In 1972 an organiser, Philip Merilees, gave his talk a butterfly instead. Today's best estimate of the limit is about two weeks, and data ten times better buys up to five more days. So forecasters run 51 versions and count.

The numbers and curves on screen are examples and illustrations. The butterfly-shaped curve is drawn from Lorenz's 1963 equations.

How far ahead do you trust a forecast?

Sources: Edward N. Lorenz, The Essence of Chaos, 1993; Lorenz, "Deterministic Nonperiodic Flow", Journal of the Atmospheric Sciences, 1963; Lorenz, "The Predictability of Hydrodynamic Flow", Transactions of the New York Academy of Sciences, 1963; Lorenz, "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?", AAAS, 1972; Zhang et al., "What Is the Predictability Limit of Midlatitude Weather?", Journal of the Atmospheric Sciences, 2019; ECMWF, ensemble forecasting fact sheet.
Sounds: Freesound, CC0 (ikomlino, kikuchiyo, tt_runscript, steaq, nickmaysoundmusic); Apple iMovie sound effects.