"Today is a cloudy day."
Translation:He lā ʻōmalumalu kēia lā.
Sometimes we use time-based terms to give a context for the sentence. These "time stamps" are not part of the basic subject-verb-object action of the sentence, but extra information tagged on to give us a setting for the action of that sentence. So we might say, in English, "Tomorrow, the weather will be nice." Or, "Yesterday, it was rainy."
We also have the option to treat those time words as things in their own rights and use them as the subject of the verb. We can say things like "Tomorrow will be nice," and, "Yesterday was rainy."
The difference in meaning between those two grammatical structures is negligible, but there is a significant difference in the grammar itself. One uses the time word as a setting, as a "time stamp", and has to use something else (like the weather) as the subject of the sentence. The other, uses the time frame itself as the subject and does not need any additional subject.
Hawaiian also has these two different methods of including time references, though the specific grammar is a little different than English. To mark the time reference as the context for the sentence, as a "time stamp", you mark it with "i" and you must find another subject for your verb:
‘Ōmalumalu ka lā i kēia lā.
"Today, the day is cloudy."
To use the time reference directly as the subject, you place it immediately after the verb and don't mark it in any way:
‘Ōmalumalu kēia lā.
Today is cloudy.
Similarly, in equivalence sentences, if the time reference is acting as one of the two things being equated, it is not marked:
He lā ‘ōmalumalu kēia lā.
Today = a cloudy day.
I suppose one could say: He lā ‘ōmalumalu ka lā i kēia lā. Today, the day = a cloudy day.
The rule is whether you are using it as a time stamp or a grammatical subject. "It is cold today" would use i because "it is cold" is a complete sentence and "today" is being added on to identify when you are talking about. "Today is cold" would not get i because today is actually being used as the grammatical subject of the sentence. In this exercise, "today" is being used as one of the noun phrases in an equivalence sentence and those noun phrases don't get marked with i.