Dear Emily,

Depends on your purpose different strategies are possible:

(i) If you are interested by short-term climate variations you should work with anomalies (i.e. deviations of climatic parameters from some mean - stationary or evolving with time).

(ii) If you are interested by the long-term variations of climate parameters (30 years or more) then it is better to work with actual measurements, not with their deviations from the mean.

The next step (what you question is related for) is what mean we should use if decide to work with anomalies?

(a) Choosing a stationary mean (i.e. average over several decades) you will have anomalies with some non-linear trend - because of the non-linear character of climate evolution with time. So your first duty will be to remove it in other to determine existence of some other periodicities.

(b) If you choose, however, non-stationary mean - for example running average with time window of ~ 22 years, them you will have more realistic short-term deviations, because the long-term variability will remain in you dynamically evolving mean.

Miss-understanding of this point is one of the problems of the "alarmistics" climate analyses, which overload the short-term variations of climate system with its long-term variability. Thus the higher "stationary" anomalies are attributed to the anthropogenic forcing, nevertheless that part of them are due to the long-term variations of climate system - driving factors of which are still not well understood.

This paper directly compares PRISM with the ANUSPLIN algorithm, which is what was used to create the WORLDCLIM layers:

Parra, J.L. and W.B. Monahan. 2008. Variability in 20th century climate change reconstructions and its consequences for predicting geographic responses of California mammals. Global Change Biology 14:2215-2231.

I have my aproach that diverges from the rest, I have writen and documented and detailed described that, and discovered the mechanisms involved

https://www.researchgate.net/profile/Dimis_Poulos