Tidal gauge sea-level height (SLH) readings can reveal the impact of ENSO if analyzed properly.

If the two are compared directly, there is a faster cycle in the SLH readings (taken from [Sydney harbor](http://www.psmsl.org/data/obtaining/stations/196.php)) than in the ENSO SOI measure:

![un](http://imageshack.com/a/img922/2552/m2mRSm.png)


If we apply an optimal Finite Impulse Response ([FIR](https://en.wikipedia.org/wiki/Finite_impulse_response)) filter to the SLH then we get a better fit:

![third](http://imageshack.com/a/img922/1765/wiIjUE.png)

The FIR is shown in the upper left inset, which has units of lagged **month**.

From that, one can see that harmonics of ~1/4 year combined as a lagged FIR window generate a much better approximation to the ENSO time-series.

But even more interesting, is that this very intriguing FIR of a 2-year lagged differential impulse window gives an equivalent fit!

![two](http://imageshack.com/a/img922/5033/PFmH57.png)

This is predicted based on the biennial modulation model of ENSO that I presented at AGU. The nonlinear sloshing interaction of external forcing (lunar and annual) with the Pacific ocean leads to this subharmonic. Intriguingly, the 2-year lag tells us that ENSO can be predicted effectively 2 years in advance just from SLH readings!

This is not the first time [I have observed this effect](http://contextearth.com/2016/04/13/seasonal-aliasing-of-tidal-forcing-in-mean-sea-level-height/), but I will likely explore this further because it gives an alternative perspective to the biennial and lunisolar contributions to ENSO.