A forecaster reads surface maps and satellite images, but the backbone of every modern forecast is a computer model. Its strengths and limits come from one of the deepest ideas in science: chaos.
Key idea
A numerical weather prediction model divides the atmosphere into a 3-D grid, starts from the observed state, and steps the laws of physics (motion, energy, water and gas laws) forward a few minutes at a time. Because tiny errors in the starting state grow over time (chaos), forecasts lose skill after several days. Forecasters run an ensemble: many runs from slightly different starting states. Where the runs agree, confidence is high; where they spread apart, it is low.
Why it works
In 1963 Edward Lorenz found that a simple model of convection, restarted from numbers rounded in the fourth decimal place, soon gave a completely different "weather." Small differences grew, roughly doubling every so often, until they were as big as the weather itself. The real atmosphere behaves this way: no thermometer network can measure every gust, and even a perfect model would start from a slightly wrong picture. So instead of one forecast, models make many, and the share of runs that do something (say, rain) becomes a probability.
Worked example: How many grid points?
A model covers the contiguous United States, about 8,000,000 km², with grid columns 10 km apart and 50 levels. About how many grid points is that?
- Each column covers $10 \times 10 = 100$ km², so there are $8{,}000{,}000 \div 100 = 80{,}000$ columns.
- Times 50 levels: $80{,}000 \times 50 = 4{,}000{,}000$ grid points, each stepped forward thousands of times.
Answer: About 4 million
Worked example: Errors that double
A forecast starts with a temperature error of 0.1 °C that doubles every 2 days. How big is it after 10 days?
- 10 days is 5 doublings.
- $0.1 \times 2^5 = 0.1 \times 32 = 3.2$ °C, about as big as a real day-to-day change.
Answer: 3.2 °C
Common mistake
Thinking a missed forecast means forecasting doesn't work. Small errors grow with time, so forecasts are very good a day or two ahead, useful for about a week, and lose most of their skill beyond about 10 days. NOAA puts it this way: a 5-day forecast is right about 90% of the time and a 7-day forecast about 80%, while forecasts of 10 days or more are right only about half the time. Check: compare a 1-day forecast's record with a 10-day forecast's.