@ToivoSäwén Ah, makes sense. Didn’t know it is done like this though, so thanks for adding this info.

That's what I essentially meant. Thanks, I think I've understood.

If I want to put it into less-mathematical more intuitive phrasing, can one simply say: "Many (slightly) different situations would evolve to the same/similar weather situation (and the maths "smooths" over this) - so reverting doesn't get you to one of them (and the maths exaggerates the error)" ?

Thanks a lot for filling in the mathematical details for me.

@gerrit 99% the answer I want (-I agree to the practical point, still would be curious if there is mathematical forking point in the alogirthm which would prevents it from working or not. Or rather: Can one - given the current system - compute the previouse system (f.e. if some planet atmosphere on a remote planet would be 'snap-shot' visited, could one compute "backwards"?. but can you make your comment into an answer so that I can accept and close?

@JeopardyTempest Sure, but some mathematical algorithms are reversible, some within limits and some simply aren’t. I don’t know into which category the ones used for weather predictions fall - hence me asking.

@Communisty No, but from a programmers/mathematicians perspective that would be an interesting idea to validate forecast methods, I think. And I was also interested if these methods are invertible or not. So, I assumed somebody else might have had this idea as well (for sure) and at least tried it. Unless, of course, it is not doable. Which would be the other answer...

Thanks a lot, this is very much what I was looking for but wouldnt have known how to achieve. (The now obviouse didn't occur to me: Staring out with the appropriately projected 2D map.)