Common advice in Sweden regarding alkalinity and calcium hardness is:
Alkalinity somewhere between 60 and 125
Calcium hardness somewhere between 100 and 400, but always higher than the alkalinity.

Just out of curiosity, what could be the reason for the advice to keep calciumhardness higher than the alkalinity?

Basically, the Total Alkalinity is determined to have enough to give pH buffering but not too much that would lead to a pH rise over time due to carbon dioxide outgassing. So the TA range is somewhat narrower. Once that is set and once one wants a pH near 7.5, then the Calcium Hardness (CH) is the variable left to adjust to have saturation of calcium carbonate. It turns out that in ppm units this is higher than TA.

Thank´s for your reply, chem geek.

I think I understand the basics of the CSI, and that it turns out that Calcium Hardness for most cases need to be at least >150 for calcium saturation.

But, some recommendations in Sweden states that CH should always be higher than TA (not mentioning SI at all), leading to for example:
1) TA 80 and CH 100 is Ok
2) TA 120 and CH 100 is not ok

If you have vinyl liner pool, using trichlor, and soft fill water, situation 2 should be Ok. But, according to some recommendations, it is not good simply because TA is higher than CH. What reason could there be for recommending keeping CH higher than TA?

Just to clarify, here´s a typical recommendation (in swedish, but I think you can follow)

Ideala vattenvärden för poolen:
pH 7,2-7,6
Klor (totalt) 0,7-2,0 ppm
Fritt klor 0,7-2,0 ppm
Bundet klor 0-0,5 ppm
Alkalinitet 80-120 ppm
Kalkhalt minst 100 ppm (alltid högre än alkalinitet)
Cyanursyra 0-50 ppm endast utomhuspooler)

Putting in the values from the low end ranges (pH 7,2, TA 80, CH 100, cyan 0) in the pool calculator, with salt at 100 and temp at 90F, gives CSI = - 0,62., which should be almost ok. If you raise TA to 120, and keep CH at 100, the CSI would improve, but it is not ok because CH < TA. Is there a logical reason for recommending specifically that CH > TA?

That doesn't make any sense to me. CH will almost always be higher than TA, but I can't think of anything that would go wrong if CH was lower.

Ditto. I don't understand why CH would have to be higher than TA in a vinyl pool. Also, your example in Sweedish with the low CSI is not something I would recommend at all for a plaster pool -- the CH should be much higher.

Now in practice to prevent foaming or for fiberglass pools you're going to want at least 120 ppm CH anyway so in practice the CH will usually be higher than the TA, but I don't see why that has to be on first principles.