Simple Subject: "Rain"
Complete Subject: "Rain"
The Simple Subject of a sentence is nearly always one word. In fact, I cannot think of a time when it would be more. This word is the word that the sentence is about.
It is a noun, but there can be more than one noun in a sentence. Therefore, identifying a noun is not an effective method in itself.
"South Australian Wombats are notoriously fuzzy beasts."
In this sentence, wombats and beasts are both nouns. The Simple Subject is the noun that comes before the verb. In my example, this is "Wombats." In your question, it is "Rain."
The Complete Subject of a sentence is the entire phrase that precedes the verb. In my example, this is "South Australian Wombats." In your question, this is still just "Rain" because it is the only word before the verb "is."
In addition, the Predicate and Complete Predicate function much the same. The only difference is the fact that they lie on the other side of the verb.
In our example, the Predicate is "are." In your's, it is "is."
The Complete Predicates are "are notoriously fuzzy beasts" and "is one kind of precipitation."