Previously established facts about the lunar influence upon the Quasi-Biennial Oscillation (QBO).

Pukite [1] has identified four spectral peaks that contribute the greatest power to his QBO model.

These are:

Period________Relative Strength____________Pukite's Attribution

2.370 years________54.6________________Draconic month annually aliased
2.528 years________25.3________________Mf' annually aliased
2.715 years________22.1________________Tropical month annually aliased
1.960 years________21.6________________half x (the anomalistic cycle annually aliased)

These have been previously identified by Vaughan [2] who has attributed their discovery to Piers Corbyn on or before the 29th November 2009.

[N.B. Mean Parameters used (J2000) in this analysis are:
Synodic month = 29.5305889 days
anomalistic month = 27.554550 days
Draconic month = 27.212221 days
Tropical month = 27.321582 days

Tropical year = 365.242189 days]

Vaughan[3], himself has shown that:

a) 1.960 tropical years  - half x (the anomalistic lunar monthly cycle annually aliased).

anomalistic month = 27.554550 days
nearest harmonic of tropical year:
(365.242189) / 13 = 28.095553 days

physical aliasing:
0.5 * (28.095553)*(27.554550) / (28.095553 – 27.554550) = 715.486162 days
(865.5210016) / 365.242189 = 1.958936 tropical years which rounds to 1.959 tropical years.

b) 2.37 tropical years - the Draconic lunar monthly cycle annually aliased

Draconic month = 27.212221 days
nearest harmonic of tropical year:
(365.242189) / 13 = 28.095553 days

physical aliasing:
(28.095553)*(27.212221) / (28.095553 – 27.212221) = 865.5210016 days
(865.5210016) / 365.242189 = 2.369718 tropical years which rounds to 2.37 tropical years.

[N.B. this almost exactly twice the nominal mean period for the Earth's Chandler wobble
of 432.8 days i.e. 2 x 432.8 days = 2.370 tropical years]

c) 2.528 tropical years [This is my little contribution]

This very close to the harmonic mean of 2.715 and 2.370 i.e. 

2 (2.369718 x 2.715425) /(2.369718 + 2.715425) = 2.530930 tropical years
which rounds to 2.531 tropical years  

d) 2.715 tropical years - the Synodic or the Tropical lunar monthly cycles annually aliased.

Synodic month = 29.5305889 days
nearest harmonic of tropical year:
(365.242189) / 12 = 30.43684908 days

physical aliasing:
(30.43684908)*(29.5305889) / (30.43684908 – 29.5305889) = 991.7881136 days
(991.78821136) / 365.242189 = 2.715426 tropical years which rounds to 2.715 tropical years.

OR 

Tropical month = 27.321582 days
nearest harmonic of tropical year:
(365.242189) / 13 = 28.095553 days

physical aliasing:
(28.095553)*(27.321582) / (28.095553 – 27.321582) = 991.7877480 days
(991.7877480) / 365.242189 = 2.715425 tropical years which rounds to 2.715 tropical years.


CHECK:

As an added check, the above analysis indicates that if we take the beat period between the 2.370 tropical year aliased QBO Draconic period by the 2.715 tropical year aliased QBO Synodic period i.e.

2.715426 x 2.369718 / (2.715426 - 2.369718) = 18.61338 tropical years

we should get the same period as beat of the Draconic year (=346.62007589 days) with the tropical year i.e.

(365.242189 x 346.62007588) / (365.242189 - 346.62007589) = 6798.383967 days
__________________________________________________= 18.61336 tropical years.

References:

[1] http://contextearth.com/2015/11/07/more-refined-fit-of-qbo/#comment-174237

[2] https://tallbloke.wordpress.com/suggestions-14/comment-page-1/#comment-109035

[3] https://tallbloke.wordpress.com/suggestions-15/comment-page-1/#comment-109392