First of all, one 0f my concerns was shifting seasonality in the data, so when I did my smoothing process (described here) I repeated it ten times on each month as a timeseries separately. This did indeed suggest there were changes in the seasonal structure of the SOI. These were then rescaled by a factor of approximately 1.4, as suggested by a simultaneous linear regression. I then renormalized each month to a mean (1876-2013) of zero and standard deviation of 10 (that is, I divided by their standard deviations and multiplied them by 10). I then took that data, took the absolute value of each data point, and repeated by smoothing procedure 10 times on that, which gave me a sort of index of the variations in the variance, over the long term. I took that, divided it by it’s average value so it would scale to a mean of 1, and then divided my normalized timeseries by that variance factor. For comparison purposes I also renormalized the original SOI data to a long term mean and standard deviation of 10. Here is what they look like in comparison to one another:
Red is the original SOI, black the IEI. The main difference appears to be that the variance of ENSO in the middle of the record is increased, and near the beginning and end it is reduced. Specifically, there seems to have been reduced ENSO variance from the 1920’s to the 1970’s, a period of relative ENSO quiescence. However the greatest variance was, originally, at the beginning of the record, indicating that ENSO variance has tended to decrease. But the purpose of isolating the trends of these kinds and removing them is to judge ENSO events themselves, as to how “abnormal” they are relative to typical background climate. This is the “background” we are removing:
There isn’t really much of a trend in this data (or in the SOI data to begin with) and it is not at all obvious how these changes in the SOI “background” might relate to global warming or anything else. They appear, instead, to simply be slow variations in the ENSO phenomenon that have heretofore gone unrecognized. For easier visualization and connection with ENSO events, I also divided the indices by 10, multiplied by negative one, and took the average of 11 and 13 month centered averages:
Similarly I can take that index (ie divided by 10 and multiplied by -1), but instead of annually smoothing, I can take calendar year averages, and then rank the years from most negative, to most positive. The 20 strongest La Niña years, in order from strongest to weakest:
The same for El Niño years:
It should be interesting to examine various data for evidence of weather differences in such years. Because they are distributed the way they are, they should be essentially orthogonal to any long term trends.