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I would like to simulate the trajectory of a weather balloon in an altitude of 12 to 20 km. For this I would like to know how the velocity-field (i.e. wind-speed and direction as a function of position and time) looks like and how constant it is in the time and space domain.

Is there some publicly available data about air-circulation in the stratosphere? Or do you have an idea how to generate test-data for my simulation?

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This presentation mentions "Atmospheric Motion Vectors (AMVs)", and specifically mentions a number of AMVs, which separately cover the globe (GOES AMVs ±60N, plus polar AMVs from MODIS/AVHRR/VIIRS, and a combined product from UW CIMSS) but says that are all only 3 layers. That presentation is talking about producing a more global, higher resolution product, but it's only a year old, so I'd guess the data isn't available yet.

However, the UW CIMSS AMV page says that their datasets have 13 layers, so maybe it is suited for what you need. The data is gap-filled with modelled data.

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I have also found these maps: http://earth.nullschool.net/

It is a nice visualization of winds at different elevations (from surface up to 10hPa).

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