Yeah I think that works better. Probably including both combos as Am will work best, I think, though that's something that will just have to be tested out (maybe the light one should still be Af, not sure). Though one thing that I realised from those more detailed precipitation maps you posted is that actually Am doesn't always have to be a transitional climate. Sometimes it can be just a rainier version of Aw. For example, the Am areas in India (the Western Ghats) have as long a dry season as the rest of the subcontinent, they just receive over 2500 mm rain during the monsoon season, so they're still classified as Am even if the driest month has close to 0 mm. But with our precipitation categories we're going to totally miss these cases (mainly occurring in SE Asia), unless we introduce an "above 500 mm" category for extreme monsoon rains or something.
The classification of the A climates is a bit weird in the sense that both Aw and As use the criteria that they are classified based on which season the "below 60 mm" month belongs to. But what if it's below 60 mm in both January and July? If it's 50+50 for example, the annual precipitation would be 600 mm. If we consider that an A climate has at least 18 °C annual mean (because the coolest month must be at least 18 °C), the min. F threshold would be 500 mm (=20*Tann+140). So that would technically not be dry enough to be considered BS, but neither does it receive more than 60 mm in either season. There just doesn't seem to be a climate category for this climate. Personally I did the same thing as you and just classified it as Aw because it's more common. But I'm not sure if this is an ideal solution.
Edit:
One solution that comes to mind is to modify the criteria for B in the case of A climates. I'm not even sure if the usual F, W, S thresholds make much sense for tropical climates to begin with, because the temperature just doesn't vary that much between the seasons in tropical areas. In some cases winter can even be the hotter season in the tropics because it's the dry season (so no clouds to reflect sunlight back to space).
Maybe use the following:
If coldest month > 18 °C:
- At least 2/3 of rain occurs in winter: Pth=20*Tann+140 (this is normally the F threshold)
- otherwise: Pth=20*Tann+280 (the normal W threshold)
That way the precipitation thresholds for Tann 18 °C would be 500 mm (if at least 2x rain in winter compared to summer) and 640 mm (all other cases). This should ensure that all areas that don't receive more than 60 mm in at least one season are always classified as arid.
Edit2:
Although I don't think this comes into effect using your categories, since all combos that don't have 50-100mm or above in at least one season seem to fall below the threshold in any case. Here's the "A sheet" with those categories that will always be considered arid (since the minimum Tann is 18 °C with A climates) marked out:
A_sheet_modified.png