I haven't ran across any post about storm spells and how they work but last night I was in mire with my LS and we were killing monsters waiting for people to gather for ZNM. I was SCH/BLM playing with nukes, It was Waterday, thunder weather and I had Thunderstorm effect on myself. First Thunder IV I did about 1.2k to a fly. We grabbed another one and under the same effects of the first nuke, my Thunder IV landed for about 1.6k+. Which was a surprise to me because it was a 400DMG+ difference between the first and this nuke has done.
So it seems that no weather + storm spell = single weather, Weather + Matching Storm spell will = effect of double weather.
I haven't been able to do more testing if more needed to be done. I am real curious to know if storm spells are combined with weather or counted alone and could even stack up with double weather alone. Though it is kind of hard to test it because of how rare double weather is and I never seen double water from Nyzul Isle kick in on my Water IVs.