I previously wrote about the Quasi-Biennial Oscillation (QBO) and its periodic behavior, and in particular how it interacts with ENSO -- tentatively as a forcing. The ability of QBO to recreate the details of the ENSO behavior is remarkable. The possibility exists however that the forcing connection may be more intimately related to tidal torques which force QBO and ENSO simultaneously. Over a year ago, I first showed how the lunar tidal periods can be pulled from the QBO time series. See Figure 1 here, where the synodic month of 29.53 days is found precisely.
An interesting hypothesis is that the draconic lunar month of duration 27.2122 days may also be a common underlying significant driver. Unfortunately, the QBO and ENSO data are sampled at only a monthly rate, so we can’t do much to pull out the signal intact from our data ... Or can we?
What’s intriguing is that the driving force isn’t at this monthly level anyways, but likely is the result of a beat of the monthly tidal signal with the yearly signal. It is expected that strong tidal forces will interact with seasonal behavior in such a situation and that we should be able to see the effects of the oscillating tidal signal where it constructively interferes during specific times of the year. For example, a strong tidal force during the hottest part of the year, or an interaction of the lunar signal with the solar tide (a precisely 6 month period) can pull out a constructively interfering signal.
To analyze the effect, we need to find the tidal frequency and un-alias the signal by multiples of 2π
So that the draconic frequency of 2π/(27.212/365.25) = 84.33 rads/year becomes 2.65 rads/year after removing 13 × 2π worth of folded signal. This then has an apparent period of 2.368 years.
This post will go into more detail and show how a combination of the synodic tide and draconic tide cycles are the primary forcers for QBO.
After reviewing some old Eureqa machine learning experiments on QBO, prompted by Graham at the Azimuth Project forum, I realized once again the significance of what it found. This is the learning recipe in 5 easy steps.
1. Started with raw QBO data
2. Next targeted a solution with sinusoidal factors
Set the fit criteria to maximize the correlation coefficient
3. Then let Eureqa crank away
After 20 hours it looked like it wasn't coming up with a better solution.
4. Picked a high complexity solution
The high complexity doesn't really matter as the other solutions have similar common components.
5. Focused on the two strongest factors that Eureqa found
These were sinusoids with an obviously folded or aliased frequency of between 2 and 3 years (i.e. quasi-biennial). The aliasing was obvious because it also selected high frequency components that, when folded, came out to the same 2 to 3 year period.
strength aliased freq period in days actual % error 78
2.663410332.359075219 27.20894362 27.212=draconic 0.011233004 35 2.29753386 2.734751989 29.53743558 29.531=synodic -0.021787874
6. The two factors have periods when un-aliased, match the Draconic and Synodic lunar month, with errors 0.01% and 0.02% respectively
What are the chances of that?
The results of the QBO characterization should not be surprising. The Wikipedia entry says that
" The precise nature of the waves responsible for this effect was heavily debated; in recent years, however, gravity waves have come to be seen as a major contributor and the QBO is now simulated in a growing number of climate models (Takahashi 1996, Scaife et al. 2000, Giorgetta et al. 2002)"
One form of gravity waves are the lunar tides, which happen to oscillate with the same frequency as QBO once the QBO signal is unaliased.
And that is likely the exact same mechanism for ENSO. The two behaviors, QBO and ENSO just happen to have the same underlying forcing mechanism. The numbers match up too well. The Baby D model of ENSO described in the previous post essentially includes the QBO as a forcing, but transitively this can be considered identically to applying the same synodic and draconic tidal forcing factor instead of the QBO !
Below is a simple model fit of the wave equation transformed SOI data. It uses the same strong Draconic and Synodic aliased periods as the QBO contains. I also included a periodic forcing of 2.9 years, which is the spin-orbit coupling oscillation of the Earth with the Moon .
I will try to automate this process and apply a least-squares fit ala the CSALT model and place it online via the Entroplet server.
I am currently thinking that perhaps the ENSO and QBO are being forced by the same underlying factors, and what we are seeing with respect to the difference in the two responses results from the characteristics of the medium that generates the response. So that the QBO, characterized by a low density medium (thin air), is able to respond quickly and thus has a very high characteristic frequency. But the ENSO, characterized by the sluggish response of a huge volume of water operating on a thermocline, must have a much lower characteristic frequency. This lower characteristic frequency allows other factors, such as the Chandler Wobble and long-term tidal factors cycles to gain importance (essentially resonate more easily) and thus make the ENSO waveform much more erratic than the QBO. The latter essentially only responds to a narrow window of forcing between 2 and 3 years, so that that is why it looks much more periodic.
Please also read the commentary at the Azimuth Project Forum on evaluating the predictability of QBO.
As I said in a previous post, I was anticipating that the models for ENSO (and QBO) would be much more complex than they may have turned out to be. The mystery is why this simple forcing by tidal factors has escaped the notice of so many researchers over the years.
Perhaps they had seen it but thought it a coincidence. For me the plausibility (i.e. gravity waves as a common forcing) and parsimony (i.e..importance of precise lunar months for both QBO and ENSO) of the model and its fit to the data is too good to pass up.