Although the historical coral proxy measurements are not high resolution (1 year resolution available), they can provide substantiation for models of the modern day instrumental record. This post is a revisit of a previous analysis of the Universal ENSO Proxy (UEP).

The interval from 1881 to 1950 of the ENSO data was used to train the DiffEq ENSO model. This gives a higher correlation coefficient (~0.85) on the test interval (from 1950 to 2014) than the training interval (1881-1950) as shown below:

Since ENSO data shows stationarity and coherence over the interval of 70 years, this fit was re-applied to the UEP data over 4 different ranges 1650-1720, 1720-1790, 1790-1860, and 1860-1930. High correlation coefficients were found for each of these intervals (> 0.70) and compared against fits to a red noise model shown below:

Each of the ENSO fits lies within the 0.95 significance level, and only 1 out of 500 red noise simulations obtained a 0.8 correlation coefficient, which is what the 1720-1790 interval achieved.

Interval | CC |
---|---|

1650-1720 | 0.772 |

1720-1790 | 0.807 |

1790-1860 | 0.710 |

1860-1930 | 0.763 |

The significance of having each of these intervals at least 0.95 is 1-(1-0.95)^4 if these are all independent. That is a small number less than about (1/20)^4 in likelihood.

The caveat is that the ENSO is also not likely to be coherent over intervals much greater than 70 years, as the shift around 1980 in phase for the model demonstrates.

This substatntiates the finding of Hanson, Brier, Maul [1] that ENSO and El Nino frequencies may be relatively constant back to the year 1525.

Astudillo et al [2] also confirmed the ENSO shift after 1980 stating that *"the amplitude of the 1982-1983 event is unique"*. Further they concisely describe the ENSO behavior as being highly deterministic by stating:

"This is of crucial importance since if a system is deterministic, the vector field at every period of the state space is uniquely defined by a set of ordinary differential equations."

## References

[1] K. Hanson, G. W. Brier, and G. A. Maul, “Evidence of significant nonrandom behavior in the recurrence of strong El Niño between 1525 and 1988,” Geophysical Research Letters, vol. 16, no. 10, pp. 1181–1184, 1989.

[2] H. Astudillo, R. Abarca-del-Río, and F. Borotto, “Long-term potential nonlinear predictability of El Niño–La Niña events,” Climate Dynamics, pp. 1–11, 2016.

One of the issues in doing correlations of ENSO proxy data over long intervals is that the records themselves are not contiguous. The UEP data set is comprised of several individual records that span subintervals of the entire duration. Since the coral rings do not extend to the current data, getting the correct absolute date on an older data set would seem problematic. So, if the dating of the end of an individual set is even off by one year, then the phase coherence of a model fit is disrupted. I don't know how often this issue is raised in the research literature but it definitely contrasts to the modern ENSO instrumental record whereby the absolute dates are known precisely.

For this UEP data, I actually interpolated the yearly data points to linearly infill with monthly data. This allowed the second derivative to be approximated and the problems with the Nyquist sampling limit of periods > 2 years minimized. I also tried a 4-point LOESS filter to smooth out the linear interpolation and found that gave similar similar results. There may be coral proxy data with higher resolution as this paper indicates

Urban, Frank E., Julia E. Cole, and Jonathan T. Overpeck. "Influence of mean climate change on climate variability from a 155-year tropical Pacific coral record." Nature 407.6807 (2000): 989-993.

A bimonthly data set from 1840-1994 for this paper is here

ftp://ftp.ncdc.noaa.gov/pub/data/paleo/coral/west_pacific/maiana_d18o.txt

May look at this sometime as it provides higher resolution information from 1840 to 1880 which can be used to further substantiate the ENSO model.

Also going way back one can see that the biennial component is very strong forthousands of years. This is a model :

(I think they mean biennial and not biannual here)

Evolution and forcing mechanisms of El Niño over the past 21,000 years

Zhengyu Liu, Zhengyao Lu, Xinyu Wen, B. L. Otto-Bliesner, A. Timmermann & K. M. Cobb, Nature 515, 550–553 (27 November 2014) doi:10.1038/nature13963