This is an attempt to understand via the numbers the concept proposed by Russian researcher Sidorenkov of a lunar year interacting with the terrestrial year to produce an effect of a ‘quasi-35 year’ climate cycle.
Sidorenkov in his paper ON THE SEPARATION OF SOLAR AND LUNAR CYCLES says:
The lunisolar tides repeat with a period of 355 days,
which is known as the tidal year. This period is also
manifested as a cycle of repeated eclipses. Meteorological
characteristics (pressure, temperature, cloudiness, etc.)
vary with a period of 355 days. The interference of these
tidal oscillations and the usual annual 365-day oscillations
generates beats in the annual amplitude of meteorological
characteristics with a period of about 35 years (Sidorenkov
and Sumerova, 2012b). The quasi 35-year variations in
cloudiness lead to oscillations of the radiation balance
over terrestrial regions. As a result of these quasi-
35-year beats, the climate, for example, over European
Russia alternates between “continental” with dominant
cold winters and hot summers (such as from 1963 to 1975
and from 1995 to 2014) and “maritime” with frequent
warm winters and cool summers (such as from 1956 to
1962 and from 1976 to 1994)
In a 2015 paper Sidorenkov explains:
Taking into account all these findings, we believe
that Rossby, Kelvin, and Yanai waves are visual
manifestations of tidal waves in the atmosphere.
From year to year, they repeat not with a tropical-year
period of 365.24 days, but with a period of 13 tropical
months, which is equal to 355.16 days ≈ 0.97.
It is called the tidal or lunar year.
Leaving aside the climate question, let’s borrow the
concept of the tidal year (13 tropical months) and go
from there. This is the nearest period to Earth’s
tropical year that is a whole number of lunar orbits.
Note: the Carrington rotation period of the Sun (27.2753 days)
nearly coincides with the rotation period of the Moon
The lunar numbers needed for this exercise are:
Tropical month = 27.321582 days
Synodic month = 29.530589 days
The solar numbers are:
Sidereal rotation = 25.38 days
Carrington rotation = 27.2753 days
The Earth number is: tropical year = 365.24219 days
First let’s find Sidorenkov’s quasi-35-year beats.
This has been done by others before on the Talkshop
e.g. Paul Vaughan who calculated a 35.3 year period.
(Tropical year (TY) x Tidal year (LY)) / TY – LY) = 35.3005 TY
Pushing this further i.e. by a factor of 10 we find:
353 tropical years = 363 ‘tidal years’
If the difference of 10 is the number of beats we get:
353 / 10 = 35.3 tropical years (TY) as calculated above.
Since a tidal year is 13 lunar months, the number of
those in 353 TY must be: 363 x 13 = 4719 LM
Since the difference between synodic months and
tropical months is by definition the number of TY:
4719 – 353 = 4366 synodic months (SM)
Turning to the solar numbers, we already saw that
the Carrington rotation period is very close to a lunar
month, in fact: 4719 LM = 4727 CR
The number of solar sidereal rotations (SSR) is 5080.
4719 LM = 128930.54 days
4366 SM = 128930.55 days
4727 CR = 128930.34 days
5080 SSR = 128930.40 days
353 TY = 128930.49 days
4719 – 4366 = 353
5080 – 4727 = 353
As stated the lunar months number is 363 x 13.
The synodic months number is 363 x 12, plus 10.
Tidal years minus tropical years is also 10 i.e. 363 – 353.
Therefore, if the SM number was just 10 less we would have:
363 x 12 (4356) SM = 363 x 13 (4719) LM
i.e. 12 SM = 13 LM but of course we don’t find that.
Now a check for other multiples of 363.
The solar sidereal rotations number is 363 x 14, minus 2 (5080).
The Carrington rotations number is 363 x 13, plus 8 (4727).
The difference between -2 and +8 is 10, the same as 363 – 353.
So this is the same result as the lunar synodic numbers i.e.
a difference of 10 from an exact multiple of 363.
The underlying pattern of the solar, lunar and terrestrial
numbers here is a very slight variation to a model where:
12 SM = 13 LM = 13 CR = 14 SSR
Of these, the only one where this model matches reality
exactly is the lunar month, but the others are close and
show a recognizable pattern using whole numbers only.
The difference of 10 is the number of ‘beats’ in 353 TY.
353 / 10 = 35.3 TY = Sidorenkov’s ‘quasi-35 year’ period.