The Köppen–Geiger climate classification made simpler (I hope so)

[Pixie]

We have that formula: Precipitation= temperature/2 (+something)
So, every time you move by 2 temperature categories, the minimum rain required move by one

It doesn't. It is a linear relationship, it changes the scale (temperature and precipitation are measured in different units anyway), but not the progression. The graphs you showed earlier (temperature vs. precipitation) had that straight line. Twice as much temperature requires twice as much precipitation for the same level of "wetness".

In photoshop, this could translate in having another layer. (...) . The first serves only as a reference representing total precipitations and the second represent the ''wetness level'' or ''relative precipitation''?

That's what I was trying with the "available humidity" map and the column called "humidity" in that reference table. Still, I admit having only arid/semi-arid/humid is too short to accurately classify climates - it's well enough to determine deserts but insufficient for anything else.

What should we use for precipitation level?

if I use the holdridge precipitation on the right combine with a possible equivalent on the left.
very wet/ super humid
wet/ per humid
moderate/ humid
steppe?/ sub humid
steppe/ semi arid
steppe/ arid
desert/ per arid
desert/ super arid

I'll try to come up with a second 2-entry table adding up mean temperature and precipitation pattern. I mean, if I understand your idea (and if this is it I am for it), we will have three maps:
1. mean temperature
2. precipitation pattern
3. "wetness level" / "available humidity" / "humidity" (pick your preferred denomination, I vote for "humidity")

Climate regions would then be determined by finding particular combos of mean temperature and humidity.