I've been thinking about the word 「大雨」and can't seem to ignore the kanji「大」in it. Why does 「大雨」mean 「大量に降る雨」 (a great quantity of rain)? Wouldn't something like 「多雨」be more appropriate?
When I was first studying Japanese, and I saw the word 「大雨」my first impression was that it meant "the rain drops were large". Is there any reason why 「大」 in 「大雨」 was chosen to represent that "there is a lot of rain"?
The 大 is probably used here to mean 大【おお】いに which means 非常に, たくさん, or はなはだ. So it's more like "a great rain", where "great" could either mean 大量に降る雨 or perhaps "big in scope".
Your logic with 多【た】雨【う】 makes sense, but I've never seen that word until now. However, the definitions I see for it say "heavy rainfall" or "much rainfall". The "-fall" in those to me would indicate rain over a longer period of time, as opposed to one "instance" (day, afternoon, etc.) of rain. In fact, another definition shows 雨の日が多いこと。また、雨量の多いこと。
大 can be used idiomatically to mean 'great' or 'super duper' or 'awesome' in addition to 'physical dimensions are quantitatively large'. If you compare 多雨 and 大雨, the first one looks more scientific and the second one has a more 'a whole ton of rain!' feeling.
I'd hazard a guess that 多 is used for countable objects/quantities, and 大 for uncountable ones. 多雨 seems to be a meteorological term so it makes sense when talking about measurable rainfall amounts. 大雨, on the other hand, looks to be less formal and indicates that the rain was greater than usual.
