# : With the incredible technology that we have today, why is it still impossible to have 100% accuracy on predicting the weather?

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: With the incredible technology that we have today, why is it still impossible to have 100% accuracy on predicting the weather?

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The weather models use non-linear partial differential equations. This leads to a host of problems. First of all, they are really sensitive to initial conditions. Secondly, we only have so many places taking measurements as input, but in theory we would need an infinite number of measurements. Thirdly, most have no closed form solution, so you to grind through them one little bit of volume at a time. So computationally, they are expensive.

Plus, some of the behavior is chaotic, meaning that small changes in inputs can have really large changes in outputs.

Bottom line, modeling the weather is a very difficult problem, both theoretically, and practically.

Because unless you have the technology to fully and completely simulate the *entire world and everyone/everything in it*, it’s functionally impossible to accurately predict the weather something like a few months into the future.

This is because weather is something called a “chaotic system”, or colloquially called “the butterfly effect”, where every tiny gust of wind bumps into every other tiny gust of wind, which keep bumping into each other, over and over, eventually reaching a point where you can’t say much about where the air is moving. So if you missed one tiny gust of wind in your calculation, one eddy current off an airplane, even something as small as the wingbeat of a butterfly, (this is why it’s called the butterfly effect) then you’ll lose accuracy on your prediction within a month or two.

Keep in mind a 50% chance of rain does not mean you have a 50/50 chance it will rain. It means 50% of the reported area will get rain

There was a book about 35 years ago called Chaos by James Gleick that explains it well. Weather systems demonstrate a classic feature of chaotic systems: sensitive dependence on initial conditions. What that means is that tiny variations in the initial conditions can greatly change the outcomes over time. This is commonly referred to as the butterfly effect. The butterfly effect is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier.

The problem with chaotic systems is that they are so sensitive to tiny changes in initial conditions that making predictive models becomes extremely difficult. They are difficult because they become less
and less accurate when you attempt to simplify them. All models are by definition simplifications of real world system. You must simplify them because your datasets don’t contain everything weather systems react to and you can’t factor in all the tiny seemingly insignificant variables that affect outcomes.

This idea of chaotic systems does have some somewhat stunning implications. For example, it’s easier to predict where mars will be relative to the Earth and Sun in 100 years than the exact path a single rain drop will take as runs down a pane of glass.

Because weather is chaotic (in a mathematical sense).

In a well behaved system, if you change the inputs a little bit, the outputs also change a little bit. Think about bouncing a ball. If you drop the ball onto a flat surface from one height, then drop it from a slightly different height, it’s going to do roughly the same thing. It’s going to bounce back up, almost but not quite to the height you dropped it from. If you drop it a few inches to the right or left, it’s going to do basically the same thing. A tiny change in how or where you bounce the ball isn’t going to make a huge change to the outcome. You can pretty easily bounce and catch the ball.

Weather does not do this. It’s more like dropping a ball onto an uneven surface, with bumps and dips in an irregular pattern. If you drop it in one place, the ball will bounce straight up, but if you drop it just a little way away, where the floor is angled in a different direction, it’s going to go off in a totally different direction. Bouncing and catching the ball is going to be a lot harder in this scenario.

To catch a ball, you need to predict where it’s going to go. That’s hard if you’re bouncing the ball on an irregular surface. The irregular surface is going to make small changes in where you drop the ball into big changes in where it ends up. Weather is like this- small changes get magnified into big changes, in a way that’s hard to predict. You would need extremely precise measurements of all the variables like temperature, air pressure, humidity, and so on to predict what it’s going to do tomorrow. If you get your measurements wrong by a tiny bit (and remember, no measurement can be perfect), you can be way off in your prediction of what’s going to happen.