"Over 40 centimeters of snow has fallen." is the correct way to say this sentence.

The correct answer to your question has nothing to do with tense. "Has fallen" and "have fallen" are both in the same tense (present perfect), but "has" is used with a singular subject and "have" is used with a plural subject. What you are trying to determine is whether "40 centimeters of snow" is a plural or singular construction so that you can use the correct form of the verb with it. I found the following at http://englishplus.com/grammar/00000039.htm : Nouns Expressing Measurement A noun expressing an amount or measurement is normally singular. If the unit of measurement refers to a number of individual items, then it treated as a plural. Examples: Two spoons of sugar is too much for me. (A single measurement) Twelve dollars is less than what I want to sell it for. (A single sum of money) Four-fifths of the country is satisfied with its health insurance. (One part of a whole) Four-fifths of the people are satisfied with their health insurance. (Four-fifths refers to many individuals.) Your question is like the first example: Snow can't be counted; therefore, it is a singular concept and requires a singular form of the verb when being measured, i.e., "Over 40cm of snow HAS fallen." But if instead of snow it was snowflakes, because snowflakes are individual and countable, you would say, "Over 40cm of snowflakes HAVE fallen." Now, that's a fairly nonsensical sentence, because we measure snow, not snowflakes, but I wanted to give you a direct and comparable example. It would be the same answer whether you were measuring sand (singular) or grains of sand (plural), rain (singular) or raindrops (plural), money (singular) or British pounds (plural).

Over 40cm of snow have/has fallen. You can use either. Strange as it may seem, but expressions of measurement can take the singular form of the verb. Two dollars isn't enough. Three litres gives you lots of mileage. 190cm is quite tall.

"Over 40cm of snow has fallen." The question is, "how much snow has fallen?" You're asking about the snow, not the centimetres. "Has/have fallen" is present perfect tense. It In this case, it means 40cm of snow fell last night, and is still there now. A past event is used to describe the present.