was studying a simple mathematical model of flow in the atmosphere, and a model like that holds no randomness at all: the same starting conditions always lead to the same outcome. Then he entered a slightly rounded number. What happened?
An entirely different weather. He published it in 1963: even with full in the equations and no randomness in them anywhere, there is . The gap between the two runs grew exponentially, doubling over each fixed interval, until the two had nothing in common. Which sets a hard limit, since every improvement in measurement buys only a little more forecast horizon.
The background is the assumption that held until then: if the laws are known and there is no randomness, then given a good measurement you can forecast. Weather counted as hard only because there were not enough stations and not enough computing power.
Lorenz was working on a drastically simplified model of air flow, three equations, entirely deterministic. And on the telling, when he retyped a starting value that had been rounded slightly, he got a completely different weather.
That is not a fault but a property. The minute gap between the two trajectories grew exponentially, which is to say it doubled over each fixed interval, until the two were nothing alike. From which follows a hard limit: every improvement in measurement precision buys only a little more forecast horizon.
What turned up alongside it is no less beautiful. The trajectory neither escapes to infinity nor settles into a cycle, but moves forever inside , one shape resembling a pair of butterfly wings. There is clear order and no predictability, together. The model itself is an extreme simplification of the atmosphere, and it explains a principle rather than replacing full meteorological models.
wat. A world with no dice in it can still be hard to predict, if it is sensitive enough to where it started.
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It explains why a long-range forecast is hard even with good computers. The problem is not only missing information but the amplification of small errors.
How do we know?
The paper set out a system of nonlinear equations and analyzed numerical solutions of it. The trajectories stayed bounded inside a strange attractor, and never settled into a simple cycle.
What is still unknown
The Lorenz model is an extreme simplification of the atmosphere. It explains a principle; it does not replace full meteorological models.
Learn something?
Where to next
Does cloud seeding actually work?weather
Why is flying east harder on the body than flying west?models
Who was allowed to tell the public what tomorrow’s weather would be?weather