Sidorenkov and the lunar or tidal year

Posted: November 27, 2016 by oldbrew in climate, Cycles, Maths, moon
Tags: ,



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.


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
(27.321582 days).

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.

  1. oldbrew says:

    Since the number of solar sidereal rotations (5080) is a multiple of 10, the quasi-cycle of Sidorenkov would average 508 of them.

    508 x 25.38 days = 12893.04 days = 35.3 tropical years

    ‘Richard Christopher Carrington determined the solar rotation rate from low latitude sunspots in the 1850s and arrived at 25.38 days for the sidereal rotation period. Sidereal rotation is measured relative to the stars, but because the Earth is orbiting the Sun, we see this period as 27.2753 days.’

  2. oldbrew says:

    This looks interesting – authors say ‘To the best of our knowledge this is the first reported detection of the horizontal tides with a pendulum.’

    Detection of Solar and Lunar Tidal Forces via Non-resonant Oscillations of A Pendulum

  3. Paul Vaughan says:

    “e.g. Paul Vaughan who calculated a 35.3 year period”

    Clarification for the second time (since I keep getting misunderstood on this):

    I showed how Sidorenkov got 35.3. I did NOT endorse it. On the contrary I CORRECTED it (and please do not misquote me on this a third time — thank you):

    I would suggest a simpler origin for 35:

    Harmonic of 6.409527865 nearest semiannual:
    (6.409527865) / 13 = 0.493040605

    (0.5)*(0.493040605) / (0.5 – 0.493040605) = 35.42266293 tropical years

    Failure (unwillingness) to appreciate the fundamental importance of the semi-annual oscillation KILLED the climate discussion. Climate discussion is dead.

  4. Chaeremon says:

    Using factor 5 instead of 10, this has 13 x Saros – 2 x Inex (eclipse series length is 882.50 years) with interesting characteristics at interval ends & all near opposite: perigee / apogee, opposite equinoces [and therefore perihelion / aphelion], opposite lunar declination [merely sign flip at same ° degree value].

    I’d say this is concerted advance like a metronome; one such pendulum swing is 176.50 years.

  5. Paul Vaughan says:

    Never mind subharmonics OB. Do division, not multiplication.

  6. Paul Vaughan says:

    “Intense desire to keep the discussion divided along political party lines in the US is corrupting the whole international climate discussion.”

    Nothing has changed fundamentally in the US. There’s just an optic ruse. The optic ruse won’t fix the 2 keys to ethical integrity (outlined elsewhere in recent Talkshop discussion).

    The only sensible leadership available comes from elsewhere — e.g. Russia & China. The EU is hanging itself with red tape. It’s killing itself. For awhile it seemed Australia & UK were cluing in to the US deception, but in recent weeks there has been a transparent spike in drunkenly obsequious naivety. If you’re too timid to call the Americans on their obsessive-compulsive deception you’re part of the problem.

  7. oldbrew says:

    I offer numbers, interpretation is open to anyone.

    Sidorenkov’s ‘tidal waves in the atmosphere’ is an interesting concept though.

    PV: sorry if I quoted you out of context.

  8. Paul Vaughan says:


    4D circulatory architecture cycling simplified to assist Ed’s vision:

    In a later suggestions thread I reminded that the volatility envelopes (e.g. 96 years) differ from the triggering series (e.g. 79.5 years) they contain. (People missed this point I’m quite sure.)

    I see no scope for discussion to advance anytime soon. I anticipate that it could be many decades before there’s a sufficient pool of luminaries sufficiently free of harassment and political interference.

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