What did meteorologists have to learn to be able to reliably predict the weather accurately?
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Thermodynamics and Differential Equations.
Thermodynamics takes the pressure, temperature, composition (how much water vapor, carbon dioxide is present), energy input from the Sun, energy output from the Earth.
The differential equations start off with the initial conditions, (temp, humidity, cloud cover) as a function of altitude for many places on the Earth and see how they’ll change based on energy from the sun and conditions in neighboring areas.
The basics of how the weather works have been known for decades, but to get accurate predictions, you need the initial conditions for many points and computer power to model many closely spaced points. A halving the distance between points means you need 4 to 8 times the amount of computing power needed.
We won’t ever be able to predict the weather accurately many weeks in the future, because the equations that govern the weather are non-linear, meaning a small change in initial conditions will amplify and yield drastically different results in the future. This is the butterfly effect.
That is not the same as predicting the climate. With reasonable certainty I can tell you it will be 80s or 90s with a chance of thunderstorms in Chicago in July, but I won’t be able to tell you what day it will rain or what the high will be more than a week in advance. Climate change models are basically saying, the average July temp will move from 80 F today to 85 F in 50 years.
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