Inconsistent documentation about arts HOT 1 OPEN

@riclarsson @m-brath @stefanbuehler @olemke @j-petersen
This time it is I that decides to broaden the discussion, as non-existing/active dimensions continue to create confusion. I brought up aa_grid for DOIT some time ago, and now Richard asks about lat_grid and lon_grid. We have not been consistent in ARTS around how to look at grids not actively used. I think user and coding perspectives clash here, and that is why things are inconsistent. So we need to sort this out once for all. And I think the solution is to agree on how we look at "extra" dimensions, and in particular, if the associated grid should have length 0 or 1.

Let's assume that we have a case where the variation in the "extra" dimension is totally undefined. I would say that for such cases, the natural choice (from a user perspective) is to expect an empty grid. Because if asking for a length 1 grid, what does it mean?

But do we actually have any cases as above? A 1D atmosphere in fact implies that things are constant with latitude and longitude. With 1D and no sun, the radiation field is constant with azimuth (i.e. not being undefined).

Because if things are constant, it makes more sense to say that the associated grid should have length 1. In fact, this is already used here and there in ARTS. The retrieval grids work in this way. And the same when defining sensor characteristics.

As Richard explained, having empty grids cause problems for the documentation and coding. While I argue that it could make more sense for the user. But the question is if we actually will have a case where we have basically undefined dimensions. We have gradually gone from 1D with unpolarised emission, to 3D with Sun and polarisation, so it is not strange if old sins exist. My new ppath scheme will imply a full 3D view on the atmosphere in all cases. Will it be the same thing for calculations of radiation fields, that there is a clear view on the azimuth direction in all cases? Or undefined dimensions elsewhere?

That is, for me a length 1 grid implies constant data in that dimension, while length 0 flags undefined. And I would prefer to keep it like this. But on the same time ask if we have reached the state where we always have a clear view on the missing dimensions and could consistently treat length-1 grid in all of ARTS (i.e. implying constant data)?

from arts.