Modern weather forecasts are by powerful computers. Meteorologists collect of temperature, pressure, wind, and humidity from of weather stations, balloons, and satellites. Computers then use the of physics to calculate how the is likely to change. Today, a five-day forecast is about as as a one-day forecast was around 1980. , small errors in the starting data over time, so forecasts less reliable the ahead they look.

In 1961, the American meteorologist Edward Lorenz was running a simple computer model of the weather. Wanting to repeat part of a calculation, he typed in a number from a printout, 0.506, instead of the more precise value stored in the computer, 0.506127. He expected the tiny difference to have almost no effect. Instead, after a short time, the new weather pattern was completely different from the original.

Lorenz realized that in some systems, extremely small differences in starting conditions can grow into enormous differences later. In a famous 1972 talk, he asked whether the flap of a butterfly’s wings in Brazil could set off a tornado in Texas, and the idea became known as the butterfly effect.

The discovery helped found the field of chaos theory. It also explains why weather can never be predicted perfectly far into the future: we can never measure the atmosphere with complete precision.

Forecasters respond by running a model many times with slightly different starting data. If most of these runs agree, they can be more confident in the forecast. This approach, called ensemble forecasting, is now standard around the world.