: 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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There are many great answers here, I just wanted to show what does a “chaotic system” mean. A [double pendulum](https://en.m.wikipedia.org/wiki/Double_pendulum) is probably the simplest chaotic system.
[Here](https://youtube.com/watch?v=-Fo4ZZfvcTE) is the visualisation of 1,000,000 identical double pendulums released from the same position with very slight variations – about one billionth (10^-9 ) of the circle between the two adjacent ones. Notice how wildly do they deviate after only a couple of rotations. The weather on Earth exhibits the same behaviour but on a larger scale. No matter how precise our measurements are, we will always be some pendulums away from the “real” position, so our calculations will start to deviate from the actual weather after a while.
ELI5: It’s too much information and needs to be processed too quickly.We barely understand all the forces at play in pouring out a bucket of water.
Some guesstimates on the numbers involved……
In air, we have density, humidity, charge, speed, direction (in 3D), temperature, etc.I’ve listed 8 numbers there.It is further impacted by sun activity, moon, tides, surface materials etc.Then we have to measure that every hour. Or every minute?
It’s no good calculating these things 1km apart. In 1km, the air is going in different directions at different speeds and temperatures. The more detail the better so let’s measure every metre.
So for 1 cubic kilometre of measurements, we have 1000m x 1000m x 1000m x 8 measures x 60 times per hour. That is 480,000,000,000 numbers for 1 cubic meter of air for 1 hour.
So a town of 5km x 5km, and measuring 10km up, we have 5000 x 5000 x 10000 x 8 x 60.120,000,000,000,000 of numbers in 1 hour.
To cover a day, that is 2,880,000,000,000,000 numbers (2880 Trillion).
To cover the USA that is approx 50,350,080,000,000,000,000. For 1 hour.
For 1 day, 1,208,401,920,000,000,000,000 numbers. 1.2 Billion Trillion.
Now calculate the interactions of these numbers for 7 days.
And add in the impact of the ground shape with mountains and buildings.
To be really accurate we should calculate every 0.5m but that is 8 times the data.
This doesn’t even mention the complexity of HOW we calculate the interactions of the air. That in itself is not ELI5.
I work in tech and I find this question really interesting. 30 yrs ago we prob asked this same question, 30 yrs before that .. same, 30 yrs before that … and 30 yrs before that .. and …
But it seems we all think technology stops here. But sure as the wind will blow, in 30yrs time we’ll ask the same question .. and 30 yrs after that .. and 30 yrs …
I had the same question yesterday when I have gone to work in shorts, because they said it will get sunny. And came home in heavy rain with like 12°C
To predict the behaviour of a system you must know all the variables that influence this system, how this variables change along time, the initial status of these variables and how are they related with each other. Simple systems have few variables and we know how they are related but with the atmosphere it is almost impossible. It is known as a chaotic system, a very little variation in the initial states of the variables that we know can change completely the prediction. As you can see we can measure the weather quite well in a 3-5 day range but further than that is almost completely random. Guessing the next 2 month weather and trying to calculate have the same probabilites to be right (or wrong).
Take a look at this video that explains chaotic systems:
[https://www.youtube.com/watch?v=PDeN3iCtyNY](https://www.youtube.com/watch?v=PDeN3iCtyNY)
simple answer? not enough computing power.
fluid dynamics – because gasses can be treated as fluids for purpose of calculation – would require you to input characteristics of ~every gas particle~ contained in the atmosphere in order to predict their behavior with 100% accuracy. and there is also chaotic behavior that has to be taken into account – very small change in initial conditions, can produce greatly variable outcomes. yes, this is the famous “butterfly effect”, and it does happen in the atmosphere. maybe not in such spectacular way, but surely the atmosphere is a chaotic environment.
Basically, some things (even some very simple things) are “chaotic” – they can behave vastly differently over time if their starting conditions are changed by even the *tiniest* amount. That makes them inherently unpredictable. And weather is one of them.
Here’s [a computer model of three double pendulums](https://www.youtube.com/watch?v=pEjZd-AvPco). They start within a degree of each other, but just 20 seconds in they’re starting to do very different things. If you build an actual double pendulum, and try to make it do the same things repeatedly by starting it “in the same position” each time – you’ll fail, simple as that.
(Don’t fall into the trap of thinking that, well, it’s just a question of getting the start positions “close enough”. It’s tempting to think that, but it’s not true. Chaotic systems simply don’t work like that. Make THE smallest change you can conceive of to a chaotic system, and it is perfectly capable of behaving radically differently.)
Here’s [a TED video of another chaotic system](https://www.youtube.com/watch?v=vFdZ9t4Y5hQ), this time a (real) pendulum and magnets.
Those are *really* simple things. The weather, by contrast, is huge and massively complex. And it, too, is chaotic. To predict it perfectly, we’d have to have full, perfectly accurate data on every last thing that comprises it – every molecule of air, every photon arriving from the sun, whether or not you choose to slightly stir the air around you by scratching that itch on your nose…). Oh, and a perfect model of how it all fits together, of course. We have neither. What should actually be astonishing is just how well we manage to do with the very limited amount of actual data we gather.
Our technologies are always grounded in a mathematical understanding of the natural laws around us. In physics we have equations to accurately describe a great many natural phenoma like electricity, gravity, kinematics, quantum mechanics, etc.
The trouble with weather is that to accurately model it, you would have to be accounting for billions upon billions of particles in the air of all different shapes and sizes, and all of their interactions with the surface of the earth and each other. To do so with conventional physics is obviously impractical and probably will never be practical, it’s just too much processing power required.
We do have equations that give us approximations for how fluids behave over large areas which we can use to generally describe things like weather patterns, but it’s never going to be an exact science using these methods. As a result, we are left with very short term forecasts that are oft changing, giving the appearance that we don’t know how to predict the weather.
It’s not that we don’t, it’s that it’s literally impossible to do it perfectly
because you only have limited precision. now, don’t get me wrong, modern computer systems can have very high, even arbitrary precision arithmetic. but in practice, colloquially speaking, you only simulate with numbers that have a fixed-size representation, and therefore a fixed maximum precision. in a chaotic system like the global weather system even the smallest imperfections will quickly escalate into major computation inaccuracies to the point where eventually you can’t be confident in the results anymore. if you want to understand just how massive such an effect can be look up double-pendulum simulations online as an example for a very simple, highly chaotic system. watch how the smallest deviation from the start configuration is quickly amplified into behaviour that has absolutely no resemblance to the original behaviour. and now think about the infinite and complex interactions of the weather system on a global scale
100%? Dude I’d settle for 25%. The number of days a month where the CURRENT weather is completely wrong, things like saying it’s clear blue sky when it is raining, is bad enough let alone the predicted weather.
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