All zones in the kingdom have a 'water depth', which among other things effect wandering monster.
At depth 6 in each of the three zone types (indoor, outdoor, basement), the wandering monster that shows up gives an item that can be used to get a skill. There are three sets of 7 skills in Heavy rain. For Thunder, Rain, and Lightning.
*edit* It looks like there is some mechanic which lets you aquire some skills in later runs. So the requirement/timing of getting skills won't actually be as strict of an issue later on...
You need the +1 depth buff from Thunder skills to get Rain skills.
You need the +1 depth buff from Rain skills, And the previous Thunder skill to get Lightning skills
The earliest you can see 6th depth basement is Hobo Sewers (basement) or Crypt.
The earliest you can see 6th depth indoor is 2nd floor spooky raven with Thunder Cloud Buff.
Once you get both the Rain and Thunder Buff, you can probably see depth 6 outdoor at goat, airship, level 9 quest.
The most relevant skills are:
Thunder Clap: All day Banisher (1 wandering monster investment)
Rain Man: Fax anything from your Manuel. (2 wandering monster investment)
Ball Lightning: 100 turn Yellow ray. (3 wandering monster... no wait. just use Golden light instead.)
You can expect to hit your wandering monsters on turn 9-11, 44-56, 79-101 for the first three. I've found a 34 turn timer to be relatively reliable for the start of the 'window'. Meaning if you want the skills you'd have to survive sewers at turn 10, and unlock spooky raven before your 2nd or 3rd.
Thunder Clap - 40 dB combat skill, appears to be a banisher
Thundercloud - 20 dB non-combat skill, gives 100 turns of increased water level
Thunder Bird - 1 dB combat skill, delevels ~15% of atk/def
Thunderheart - 20 dB non-combat skill, gives 100 turns of +100% Max HP
Thunderstrike - 5 dB combat skill, once per fight and seems to be a stunner
Thunder Down Underwear - 60 dB non-combat skill, summons an accessory described earlier in the thread
Thunder Thighs - Passive, increases thunder regeneration.
Rain Man - 50 drops - make monsters out of rain.
Rainy Day - 20 drops - make weather bleaker (+1 depth).
Make it Rain - 10 drops - Once per fight combat. Increase meat drops by 100%
Rain Dance - 10 drops - 100 turns 20% item.
Rainbow: - 3 drops - Combat.
Rain coat: - 40 drops - Summons rain coat item.
Rain delay: passive 3 elemental resistance all
lightning strike - 20 bolts - Combat.
Clean Hair - 10 bolts - Buff (100) +100% MP.
Ball Lightning - 5 bolts - Combat. Yellow ray (100)
Sheet lightning- 10 bolts - Buff (100) Spell damage 100%, damage opponents
Lightning Bolt - 1 bolt - Combat. Deals 5000 damage on third cast in same combat. 1 damage otherwise.
Lightning Rod: - 20 bolts - Summons: Can make a staff out of lightning
Riding the Lighting: Passive. +100% MP
Summoned items disappear at end of day:
Thunder down underwear: DA +100, HP +100, 10-20 HP/MP regen
Famous blue raincoat: So-So Resistance to All Elements (+2), +10% Item Drops from Monsters, Combat Initiative +40%
Lightning rod: 200% spell damage, +50 MP, 5-10 Mp regen