Singular, countable nouns are not used without a determiner. 'Desert' and 'rainbow' are both countable nouns and, in the above cases, they are singular. Therefore they should be preceded by a determiner. A determiner might be an article - 'a' or 'the'. Or it might be 'this', 'that', 'my', 'some', 'every', etc. You can generalise by making the noun plural. In this case, no determiner is needed.

The zero article rule doesn’t work with singular nouns. So it should be “The desert is hot” and “The rainbow is colorful.” If you were to make them plural (“deserts are hot” or “rainbows are colorful”) the zero article rule would work. Hope this helps.

When you talk about rainbows, you might have in mind one specific rainbow (like the one that is outside your window at this moment) or you might have in mind many specific rainbows (like the three rainbows you saw last week), or you might have in mind all rainbows that ever have been or ever will be. To talk about specific rainbows, you must always use an article, whether you are thinking of just one rainbow or three rainbows: "The rainbow outside my window is colorful." "The rainbows I saw last week are colorful." When you talk about nonspecific rainbows (all rainbows that have ever existed or ever will exist), you have a choice. You can say "Rainbows are colorful" or "The rainbow is colorful". Only the last one is confusing. What logic allows us to say "the rainbow" (which sounds like one rainbow) when we are actually talking about all rainbows? It is the same logic that allows you to say "The human being is a smart animal" when you are actually talking about all human beings. Nouns are names for things, but they are also names for the class the thing represents. For example, consider these two sentences. One uses "telephone" to name a specific thing and the other uses "telephone" to name the class the thing represents: "I have a telephone" "Alexander Graham Bell invented the telephone"

Requires using "the".