As I indicated in this post, lots of good information is available in “unpublished” NASA memorandum.
Returning to the mystery of an inferred phase reversal in the biennial forcing, the best description of the interaction of the Chandler wobble with ENSO is this NASA technical memorandum.
Fig 1: From B.F.Chao, NASA Technical Memorandum 86231
So Chao essentially reports that the Chandler wobble is in-phase with ENSO from 1900-1979, but it flips phase starting around 1980. This is precisely in line with what I am finding.
Here’s an example of how you can gain confidence that you are on the right track. I configured the multiple linear regression to train on the ENSO time series applying the wave equation transform from 1880-1940, and then looked at the correlation coefficient over the interval 1940-2013 — which is completely outside the training interval.
Fig 2: Training from 1880-1940, correlation outside. The ENSO signal is phase reversed from 1980 to 1996.
The in=inside cc is 0.725 and the out=outside cc is 0.758. It is rare that you can get a correlation higher outside of the training interval, but because of the stronger noise in the earliest ENSO measurements this is not out of the question. In terms of variance contributions, the reduced noise promotes the real underlying signal.
Next, we generate a set of several synthesized red-noise random walks that have similar variance to the actual ENSO data. This is essentially the Ornstein-Uhlenbeck algorithm, describing a random walk with a reversion-to-the-mean potential well factor. Ten runs were combined into an animated GIF shown below:
Fig 3: A set of O-U random walk profiles.
Note that although the correlation coefficient is moderate within the training interval (anywhere from 0.4 to 0.6), it is insignificant outside of the training interval, and a few times it actually goes negative. In other words, there is no phase coherence outside of the interval, and any apparent agreement within the training interval is likely the result of over-fitting.
Alas, research is still being published [1] arguing whether or not ENSO is red noise. This is actually a moot point since what the GCMs generate (as far as I can tell) are invariably reported as sets of time series with random outcomes. If ENSO is actually deterministic — apart from the rare metastable phase reversal and volcanic activity — the GCMs should be slight variations of Figure 2 and not Figure 3.
[1] Chen, Xianyao, and John M. Wallace. “Orthogonal PDO and ENSO indexes.” Journal of Climate 2016 (2016).
You don’t need a weatherman to know which way the wind blows.
GeoEnergy Math 
Paul,
I am wondering if you have considered the possibility that the “sloshing” motion of the Pacific Ocean that you require for you ENSO model is produced by the changing ratio of the strength of consecutive periodic slow downs in the Earth rotation rate once every 13.66 days as the Moon crosses the Earth’s equator.
Please see:
1. http://astroclimateconnection.blogspot.com.au/2016/03/there-is-natural-gleissberg-like-cycle.html
2. http://astroclimateconnection.blogspot.com.au/2014/11/evidence-that-strong-el-nino-events-are_13.html
3. http://astroclimateconnection.blogspot.com.au/2016/05/moderate-to-strong-el-nino-events-are.html
[N.B. Consecutive periodic increases in the Earth’s LOD once every 13.66 days are produced when the Moon crosses the Earth’s equator from north to south and then from south to north.]
As you can see from the first reference there is a slow cycling in the relative strength of consecutive periodic slow downs in the Earth’s rotation rate over a period of 9.01900 anomalistic (perihelion to perihelion) years. The 9.01900 year period is just 8 x Full Moon Cycle of 1.1274 years
This means that there are two periods of 4.5096 years where:
Period
0.0000 to 4.5096 years_________NSC > SNC
4.5096 to 9.0019 years_________SNC > NSC
Key
Strength of slowdown due to North to South Crossing = NSC
Strength of slowdown due to South to North Crossing = SNC
The difference in the strength of consecutive slow downs in the Earth’s rotation rate would amount an “agitation” of the Pacific ocean that could produce a “sloshing” motion.
Just wondering….
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Ian, The numbers don’t quite work out for that mode. I will double check but when I tried a close-to 9 year forcing, the model response was not correlated with the data and below significance. A value of 9.3 was at least 3 times more strongly correlated with the data.
But that was still smaller than the strongest forcings at 6.45 and 14 year periods.
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Regarding the ENSO phase reversal. Here is another piece of evidence showing something happening in 1980:
Note the strong uniformity up to 1980. By 2000, it may be back to the original.
Roundy, P.E. “On the interpretation of EOF analysis of ENSO, atmospheric Kelvin waves, and the MJO.” Journal of Climate 28.3 (2015): 1148-1165.
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If you look closely at the chart by Roundy, there appears another phase reversal that ends around 1880. Although the data for ENSO SOI is progressively poorer the further one goes back before 1930-1940, there is data available. And a strong EL Nino is documented in 1878 [1].
For training of 1909 onward, and a flip of the biennial forcing prior to 1880, the SOI model does nail this strong El Nino rather precisely. See the yellow highlight below.
[1] Aceituno, Patricio, et al. “The 1877–1878 El Niño episode: associated impacts in South America.” Climatic Change 92.3-4 (2009): 389-416. link
This 1878 El Nino was also associated with a yellow fever outbreak in the USA!
[2] Diaz, Henry F., and Gregory J. McCabe. “A possible connection between the 1878 yellow fever epidemic in the southern United States and the 1877-78 El Nino episode.” Bulletin of the American Meteorological Society 80.1 (1999): 21. link
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