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Regarding the first half of your question: your broad understanding seems to be correct. To answer your question about how to tell if there is fluid in a given cell, consider what the mass density $m(x,y,t)$ is in an empty cell. It's just zero. This is seamlessly handled by your system of equations already. Regarding the second half of your question, this ...


Kp is not really supposed to be a real-time index. The definitive Kp is calculated by GFZ Potsdam, often several weeks after the fact, based on data from 13 fixed magnetic observatories. These do not all report their data in real time. I believe the wing_kp data you linked to is a model based on ACE solar wind data: not actual geomagnetic measurements. ...

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