Suppose a data file consists of a sequence of time averages of an observation, with an averaging interval dt (dt = 7 days, for weekly averaging). The averaged data have a timestamp, which could correspond to the beginning of the interval, the middle of the interval, or the end of the interval. I prefer the middle of the interval--then it would be a centered average, which has some advantages. If we have a model which uses the data in the file for a forcing as a continuous function of model time, then we interpolate from the data (which is averaged over interval dt).