d_s90, I'm not sure I understand your question. It appears as if you have rainfall data collected over 38 years(?) on a 141x71 spatial(?) grid. But then it looks like you are trying to compute the means for each location over the entire time span.
So time would go away at that point. Can you clarify what you want to do?
If you want to find means at each location, you don't need any loops, mean(rain,3) would compute means across your time dimension.
Also, meanprecip = nanmean(rain(141,71,38)) almost certainly doesn't do what you want, which I think is to pre-allocate. meanprecip = nan(size(rain)) maybe?