Processing Rainfall Data

I am working with raw rainfall data, directly from the files retrieved from a tipping bucket rain gauge.

I have two columns, one is the time log for each tip and at that time the read of 0.5mm of rainfall. Since it is not a continuous time series, I cannot identify whether it is a dry period or a missing value. (Refer to the attached file for an example of the retreived data).

I am using R to convert those readings to a continuous time series; of course, so far I am filling with zeros the time where there are no readings. I am not sure if that is correct. The code just sums up the readings between a time step, say for example 5, 10 and 15 minutes. 

I would much appreciate any further readings or reference on processing rainfall data. Any advice is welcome!