Weather forecasting was invented by a guy in a trench in WW1, as I recall. He had the idea that if he knew the temp and air pressure of every cubic foot of the earth's atmosphere, he could predict the temperature and pressure in the next moment in each cubic foot. In practical reality, we don't have that, but we can come close enough for some useful approximation that is not 100% perfect, but way better than pure chance. Data processing power is also a limiting factor. At UCLA in 1970s, we had one of 10 IBM 360 Model 91 computers, for a brief moment, biggest in the world, certainly on the west coast. It had 4 MB of memory when 8 KB was common and 64 KB was big. You had to finish your programming lab by midnight, because then they used it to run the next day's weather forecast.
It also depends on where you live. I live on the west coast where our weather comes from the pacific ocean, thousands of miles of similar moderate temperature and no mountains. You can watch storms come in, they lok like multiple waves of commas or parenthesis moving in slowly changing formations. Very well organized. They break up somewhat at the coast, but after the storm crosses the continental divide, it whacks into the swirl of weather from north pole, atlantic, gulf of Mexico, and swirls. East coast is harder to be accurate.
They called the storm of the last 2 weeks here, pretty much nailed it, predicted record snow in the sierra, happened just when they said. Weather reports are not always accurate, but way better than wild guess. Weather in Tahoe is the weather from San Francisco, 12 hours later.
The forecast here is almost always close, often right on. The rain might be an hour early or an hour late, it night be a little less or more than predicted. If they spent the money to grid the pacific ocean with weather ships and spent much more supercomputer time running the model, it would be more accurate. Not done because $$$$$$. And the money gets bigger with more accuracy, diminishing returns.
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https://en.wikipedia.org/wiki/Antarctic_Automatic_Weather_Stations_ProjectWeather forecasters need to look at the weather around them and make global weather maps, using satellite photos, and matching that up with earthbound data. This extends everywhere in every direction, there is no edge.
If you postulate FE with an edge, either the weather forecasting system is part of a conspiracy, or they are actually complete morons, or there is a giant industry of faking data, which has to be continuous 24/7/365. The Antarctic weather stations and their data must be faked in a way that matches up with the fake satellite pics. The storm coming onto one side of the disk would have to match one leaving the other side. Weather forcasters fundamentally have to know the shape of the earth. Or they are either genius frauds, or morons making occasional lucky guesses.
That would be something, wish I could know more about how this works on FE. Perhaps a new branch of weather studies, what happens with weather up against the dome. We know only one thing - weather at the south pole works very differently on FE vs RE.