Observation of a Lunar Signal in Solar Irradiation Data

Late last Friday evening as I wasted a couple of hours trying in vain to buy 2 tickets from the London  Olympics website, I filled my time looking further at the SORCE TIM solar irradiation data [1]. The olympics website turned out to be broken but all was not in vain because instead, I had a brainwave about what causes the apparent regular small oscillations in the data. It is the Moon of course ! In reality the Moon and  the Earth orbit each other around  their common centre of mass. This is located about 4000 km outside the center of the Earth so as a result the Sun-Earth distance also  changes in phase to the lunar month. The exact monthly  variation in distance (D) will depend on  orbital parameters but could be as much as 8000km.   The data clearly show a monthly variation of about 0.2 watts/m2  (figure 1) during 2008-2009 which turns out to be  in  phase with the lunar cycle. There is a negligible probability that this occurs by pure chance – see below.

Fig 1: The left axis shows the TIM data and the theoretical data for Earth-Sun orbit. The difference between the two curves is plotted as the black signal scaled to the right y-axis. The red curve is a calculation of the lunar phases based on a siderial month of 29.53 days using an arbitrary scale for comparison. At full moon the Earth is approximately 4000km nearer the sun.

As far as I am aware this is the first time this effect has been seen as  I cannot  find any other reference to  in the literature. Apologies if I am mistaken.

My original aim in studying the TIM data was to try to isolate a possible (annual)  signal as the Earth passes through plane of the interplanetary dust cloud. Could ice ages be really  caused by  an oscillation in dust density lying between the Earth and the Sun in phase with the eccentricity of the earth’s orbit ? But that is another story…


[1] http://lasp.colorado.edu/sorce/index.htm

About Clive Best

PhD High Energy Physics Worked at CERN, Rutherford Lab, JET, JRC, OSVision
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9 Responses to Observation of a Lunar Signal in Solar Irradiation Data

  1. Chaeremon beyond Alexandria says:

    Thanks for posting this picture, very interesting for my work (in astronomy). I’ve also read the discussion in the tallbloke blog, also interesting your climate research. In case you or your peers look for actual sunearth distance measurements, perhaps http://www.aip.de/groups/gregor/ can give them (solar telescopes are rare on planet earth 😉

    But one can also use computations (by numerical integration) based on the most recent DE421 ephemerides, they are reviewed constantly by practically every amateur / professional astronomer, and any discrepancy would result in sensational news and the astronomer would get his/her rightful place in the hall of fame 🙂

    In the tallbloke blog there was also discussion about using the barycenter: this is just a fictitious mathematically-dynamic point, and of no relevance when gravitational aspects do not play any dominant role. Instead, all distance measurements between bodies are made and documented between their geocenters (which b.t.w. are physical locations).


  2. Greg Goodman says:

    Just picked up you link on WUWT. Very interesting.

    Any idea why the annual peak is near 1st November ?? I thought perihelion was the annual max. This seems to be almost in quadrature here.

    Does that phase change after a few years?

    Thanks, Greg.

    • Clive Best says:

      To be honest I don’t understand this signal. It is particularly strong during this two year period as if it is in phase or something. The official TSI data filters this out because it is normalized to 1AU and uses the JPL ephemeris to do this. I simply subtracted out the earth’s eliptical orbit and out poped the lunar signal. If you look in the comments you’ll see a response from Knopf who is lead scientist on TRIM.

  3. greg says:

    Make backup of the SORCE data you have , apparently the goalposts are in movement (see WUWT)

    I have corrected Willis’ R code to add full and new moons as you suggested and plotted the spectrum: Looks more credible:


    • Clive Best says:

      Thanks !

      I have been driving all day to Lucca in Italy – so missed a lot of this.

      In my code I simply took 3 vectors earth(3) moon(3) and sun(3) from the JPL ephemeris coordinate system.

      moon-earth is the lunar tide vector
      sun-earth is the solar tide
      (moon-earth) dot (sun-earth) gives you the cosine between them

      I will eventually write up a derivation of the tidal force as it is very confusing.

      • greg says:

        I’m trying to work out the direction of the resultant vector but don’t seem to be able to find a clear definition of the Geo (500) coordinate system produced by JPL.

        Origin is clearly Earth centre but is z-axis earth rotational axis or norm of orbital plane?

        Do you know?

        I tried adding the z-components on the basis that it was axis of rotation but the spectrum seems far too simple and the time series was modulated by a pattern of 3 year bumps.

        tideforce_z=( abs(sunforce/sundist*sunz)+ abs(moonforce/moondist*moonz) )

        The result seems far too simple considering the complexity of the orbit.

        Any comment?


  4. Greg says:

    Clive, I have tried to lay out what I think is a correct description of the tidal forces from the perspective of an inertial frame.


    I think this shows that there is no need to use a rotating frame and fictitious forces.

    I know this is contrary to what you suggested earlier so I’d like to know if you can see a fault in this description.

    • Greg Goodman says:

      I don’t know what treatise you are working from but it seems to be quite complex mathematically and thus may well be correct.

      You mentioned other terms that increased towards the poles but to simplify the discussion you leave them out. That sounds like it maybe a coreolis term. If you want to work in a rotational frame you need both centrifugal and coreolis fictitious forces.

      If that is the case it may lead to an erroneous conclusion that there is a centrifugal component to the bulge. I really don’t think you can have one without the other.

      If that kind of approach is done correctly, it should be mathematically identical to an inertial frame treatment however, when we start chopping out certain terms to simplify the equation there is a risk of inducing an error.

      I’ve made simplifications too , so maybe I’m missing something out, but in principal it should be possible to reconcile the rotational and inertial approaches to arrive a the same conclusions.

      Feel free to point out if you think I’ve missed something.


  5. climategrog says:

    Clive, I just came across this post again and re-read it.

    I think this may related to Scaffeta’s work. He showed via JPL output that there is a 9.1y periodicity in Earth’s motion which is not present in EMB motion, thus proving that this component of Earth’s motion is due to the moon. He goes on to suggest that this is probably an unresolved mixture of two frequencies corresponding to 8.85y and 9.3y.

    Scaffeta shows this also exists in some climate records such as Aurora data. Curry was involved in a BEST paper which finding 9.2 +/- 0.2 ( IRCC ).

    I also find 9.07y in cross-correlation of ACE and SST:


    This is probably long term modulation of what you are noting here.

    Greg Goodman

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