There is a discussion going on at the Moyhu blog concerning chaos in climate modeling and how well GCMs work.

[Nick rightly says](https://moyhu.blogspot.com/2016/10/chaos-cfd-and-gcms.html#comment-form):

> "The key word there is work. They do."

Yet the bigger question concerns why we can't easily map out the silly oscillations of ENSO like we can with tides. For heaven's sakes, ENSO is just a standing wave dipole of ocean sloshing and should have been figured out long ago, maybe not as long ago as the last Cubbies championship but certainly by now.

What makes it that hard to figure out? The key is that it isn't necessarily a chaotic system but one that is defined more by metastability. Everything about ENSO points to an underlying periodicity governed by a period doubling of the annual cycle. Yet period doubling from 1 to 2 years implies that something has to set the bifurcation parity to either an odd-year cycle or an even-year cycle. Energetically, there is nothing that obviously determines the even vs odd cycle ... except perhaps how tidal gravitational forcing interact with the seasonal cycle. In fact, as I have [shown on my blog](http://contextearth.com/2016/04/21/biennial-mode-of-sst-and-enso/) there is a distinct biennial parity for each of the three classes of lunar tides (nodal, anomalistic, and tropical), which occurs after a nonlinear mixing with the seasonal cycle.

$sin(\pi t) \cdot sin(\omega_m t) = \frac{1}{2} ( cos(\pi t - \omega_m t) - cos(\pi t + \omega_m t) ) $

If you [expand all the terms with this biennial factor](http://contextearth.com/2015/11/17/the-math-of-seasonal-aliasing/), then you can reconstruct a strongly aliased lunar tide cycle.

The metastability revolves around how easily this balance is tipped. From what I have been able to discern this metastability has only flipped once, and that was during the 1980 to 1996 time interval. This can explain why standard signal processing techniques have not uncovered the metastability but the one described recently by Astudillo has detected the disturbance at 1980 as well:

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.

Cubs finally win, and perhaps we are nearing an understanding of ENSO

Here is the latest analysis:

http://contextearth.com/2016/11/03/short-training-intervals-for-enso/

[Nick rightly says](https://moyhu.blogspot.com/2016/10/chaos-cfd-and-gcms.html#comment-form):

> "The key word there is work. They do."

Yet the bigger question concerns why we can't easily map out the silly oscillations of ENSO like we can with tides. For heaven's sakes, ENSO is just a standing wave dipole of ocean sloshing and should have been figured out long ago, maybe not as long ago as the last Cubbies championship but certainly by now.

What makes it that hard to figure out? The key is that it isn't necessarily a chaotic system but one that is defined more by metastability. Everything about ENSO points to an underlying periodicity governed by a period doubling of the annual cycle. Yet period doubling from 1 to 2 years implies that something has to set the bifurcation parity to either an odd-year cycle or an even-year cycle. Energetically, there is nothing that obviously determines the even vs odd cycle ... except perhaps how tidal gravitational forcing interact with the seasonal cycle. In fact, as I have [shown on my blog](http://contextearth.com/2016/04/21/biennial-mode-of-sst-and-enso/) there is a distinct biennial parity for each of the three classes of lunar tides (nodal, anomalistic, and tropical), which occurs after a nonlinear mixing with the seasonal cycle.

$sin(\pi t) \cdot sin(\omega_m t) = \frac{1}{2} ( cos(\pi t - \omega_m t) - cos(\pi t + \omega_m t) ) $

If you [expand all the terms with this biennial factor](http://contextearth.com/2015/11/17/the-math-of-seasonal-aliasing/), then you can reconstruct a strongly aliased lunar tide cycle.

The metastability revolves around how easily this balance is tipped. From what I have been able to discern this metastability has only flipped once, and that was during the 1980 to 1996 time interval. This can explain why standard signal processing techniques have not uncovered the metastability but the one described recently by Astudillo has detected the disturbance at 1980 as well:

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.

Cubs finally win, and perhaps we are nearing an understanding of ENSO

Here is the latest analysis:

http://contextearth.com/2016/11/03/short-training-intervals-for-enso/