Unified ENSO Proxy

This is a check of the ENSO model by back-extrapolating against the Unified ENSO Proxy (UEP) records. The UE proxy is averaged together from various data sets and only has a resolution of one year, with a distinct possibility that the absolute yearly alignment could be off.  The alignment is easy to determine for the modern instrumental era as one can calibrate against SOI and NINO data, but for coral proxy data before 1880, the calibration becomes more difficult to verify.  This is important because a tidal forcing model is critically dependent on keeping absolute orbital phase relationships over all times. According to the recurring alignment of eclipses this period can be checked only after 372 years [1]. The UEP goes back to 1650, providing a the time series about 330 years long, so not long enough to detect a repeat pattern in the ENSO behavior.

With that said, the pre-1880 ENSO behavior can be captured effectively by slightly relaxing the fit to the SOI data that the model was initially based on.  In the multi-panel figure below, the last panel features monthly data (after 1880 with the modern-era SOI fit) and all others are yearly (from 1650 to 1880).

So the temporal lunisolar forcing pattern was essentially the same before and after 1880, but a slight temporal shift (at least partly due to the yearly to month transition)  and an independent spatial scaling (impacting the amplitude) was applied prior to 1880. Recall that only three lunar periods are involved in the fit, along with the annual harmonics. From 1650 to 1880 the correlation coefficient is 0.80

Before ~1900, the variance of the UEP appears to be significantly reduced as shown below. This indicates the possibility that the standing wave boundary conditions changed around that time. The stationary model of ENSO has a more stable variance over the 300 year time span than found from the coral proxy data, so we are forced to parameterize the model into two separate intervals.

 

References

[1] J. N. Stockwell, “On the law of recurrence of eclipses on the same day of the tropical year,” The Astronomical Journal, vol. 15, pp. 73–75, 1895.