COUNTIF: dynamic range

I want to perform a COUNTIF in a column where data is added regularly. The COUNTIF range is to be the last 100 rows of data: so if yesterday that range was a2:a102 then today it should be a3:a103, tomorrow it will be a4:a104 and so on.

How can I get COUNTIF to change the range as new data is added? I can generate a string with the changing range ("a2:a102", "a3:a103", and so on) but how do I put that into COUNTIF?