I’ve recently been exploring a new analysis technique for examining the the slow, long period variations in climate datasets, as distinguished from inter-annual variability. The approach I am working on involves “smoothing” the data in such a way that the length and time resolution of the data are preserved, while the short term fluctuations in the data are ironed out, revealing, I think, what is mainly a decadal and longer term signal, all using only actual data, no “padding” or extrapolation involved. I would simply like to offer an example of this approach here, without much further comment, except to explain the methodology.
First, this smoothing technique, which I carry out in Excel, involves successive three point averages, which taper off at the point at which only one or two such averages are possible. This is done mainly to determine how many such averages one can take. The next step is to take the first smooth, and at the end points, take the average of the last and first two points, double weighting the very endpoints. Now it is possible to carry out such averages indefinitely, however I have chosen to stop at the point at which the number of successive three point averages stop. At this point, with a hundred year or more monthly dataset, I have so many timeseries Excel is starting to strain and sometimes seizes up, but I’m not done yet. I have one more step I will take just to see if I can see what happens when I average at each point all the series I have just created, and the original data set. Doing so (and I have tried this on a few different time series) restores some of the amplitude of variability and a little of the more short term variation, but still emphasizes the “slow” variations. Today I am going to show you the results I have gotten from the Southern Oscillation Index [EDIT: for the purposes of this analysis, to examine the ENSO phenomena correlated, rather than anti-correlated with ENSO sea surface temperatures, the SOI values were multiplied by negative one.] with first the data with the greatest smoothing (Before averaging all generated timeseries and the original) then the version with averaging of all timeseries done to restore some of the variance.
I would like to hear people’s thoughts about this technique. I am prepared to be told how stupid or useless you think this is, and any other thoughts. Thanks!