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Generally at altitude the wind goes from west to east. During the Cold War the US would launch spy balloons to overfly Russia whilst the wind was blowing against the Russians reciprocating. This is generally true in the current Ukraine war too.

Some interesting links:

https://www.hisutton.com/US-Navy-CIA-Submarine-Launched-Spy-...

https://www.hisutton.com/Chinese-Navy-High-Altitude-Spy-Ball...

https://m.youtube.com/watch?v=iD6XaaO9bEo

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As I understand it, it's a combination of things: aircraft reports, atmospheric motion vectors (e.g. a cloud doesn't have any propulsion, so if a cloud moves 30 km in an hour, you have learned something about the wind), Doppler wind lidar, and satellite measurements.

The numerical predictions of weather models often have many vertical components as well, so solving it for ground level also requires extending the forecast to the air, depending on the model.

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To predict anything on the ground, you have to predict air temperature, humidity, wind speed and direction etc. for the entire troposphere. The output of the models in altitude are as relevant to the meteorologists as the output on the ground for manual expert analysis.
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Not just wind speed, but all kinds of weather data can be extracted from radiosonde recordings. The data output is called a Skew-T Log-P graph. Some examples of how to interpret them at https://www.weather.gov/source/zhu/ZHU_Training_Page/convect...

There are of course several different global weather models that predict the behavior of the atmosphere, and it is a lot more complicated than just interpolating past data. But they all do rely on radiosonde data for daily calibration of actual atmospheric conditions.

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