TSI, SORCE and a signature

Posted: December 2, 2012 by tchannon in Analysis, Solar physics

Figure 1

Couple of days ago someone mentioned TSI variation significantly varies during earth orbit, no news in this, it did though trip me having another look at SORCE data, see if I agreed with the figure.

For some reason I decided to look more closely whereupon something which had never occurred to me popped out, obvious in hindsight.

The lunar orbit modulates sun-earth distance too which leads to an idea.

Since this is such a precise signal can it be demodulated out of earth data and therefore give a useful measure of earth TSI sensitivity for the earth dataset being used. I don’t know whether this has been done or how feasible it is.

I am using the daily SORCE data, runs from Feb 2003.


Figure 2

The dataset includes values at earth distance and at 1AU

This examination is looking closely at the earth distance data.

Figure 2 show raw SORCE and with earth orbit one year subtracted, no surprises.


Figure 3

Figure 3 shows the second stage of subtracting out earth orbit, plot is offset zero now. Blue trace is red trace figure 2.


Figure 4

Figure 4 blue trace is figure 3 red trace. This is close to the SORCE 1AU data, note the detail, the fast wave. That is lunar.


Figure 5

Figure 5 subtracts out the lunar signal, shown separately to scale. Software here says it is 29.49 days assuming 365.2422 days per year. (we are into la-la land trying to get numbers exact)

Question is whether that can be unearthed from terrestrial data. Reported as 0.102595 watts/sqm rms, which is tiny, nevertheless synchronous working is the most extreme.

What else?

Figure 1 shows the final result of subtracting out earth and lunar data, plus an approximation to the underlying slow variation. the extrapolation is very uncertain but I’ve shown it anyway.

There is a disagreement between the result and the official 1AU values, too little to be concerned about. I note a long pattern in the residual, perhaps from earth orbit perturbations.

Given the TSI has an extreme crest factor there are a number of crocodiles lurking to do with handling data, just the kind of thing which messes up inadequate instrumentation. CF is most known in the mains power field but is general.

Sorry about the poor post format, WordPress is being awkward as usual with unknown CSS fighting default HTML and secret specials. Only practical way to put images right there is tables, another cantankerous item. If your browser misrenders awkwardly please speak up, see what I can do.

Post by Tim Channon

  1. Tim Cullen says:

    Very interesting subject…

    Clive Best also picked up on this “lunar” signature…
    The signature shows increased TSI at Full Moon:


    Personally, I am very interested in trying to understanding “cause and effect”.

    One dataset I haven’t stumbled across is a detailed [i.e. km specific] Sun-Earth distance ephemeris – similar to the Earth-Moon apogee-perigee distance tables.

    This level of detail should clearly show the Earth distance varying [in step with the Lunar cycle] as the Earth rotates around the Earth-Moon barycentre.

    Personally, I have very grave doubts about the whole barycentre “bag of tricks”:

    Therefore, I think it is really interesting [important] to clearly demonstrate that the TSI “lunar signature” is related to the Earth’s distance from the Sun because there are other possibilities like:
    Increased solar wind penetration into the atmosphere at Full Moon.
    Increased Zodiacal Light at Full Moon.

    Question: Have you been able to specifically pin down the Sun-Earth distance?

    Another of my outstanding “dig here” queries relates to the concept of the Solar System Barycentre [SSB] which should also affect Sun-Earth distance and TSI.

    Question: Have you found any detectable SSB signal in the raw TSI data?

  2. wayne says:

    “One dataset I haven’t stumbled across is a detailed [i.e. km specific] Sun-Earth distance ephemeris – similar to the Earth-Moon apogee-perigee distance tables.”

    Tim, have you tried the NASA Horizon system or are you looking specifically for actual measurement data? That system will give you a very precise ephemeris of any time spans you want. The precision is to at least 15 digits if you choose vector output.

  3. Tim Cullen says:

    wayne says: December 2, 2012 at 9:52 am
    Tim, have you tried the NASA Horizon system or are you looking specifically for actual measurement data?

    Thanks for the pointer :-) but it would be great to see some real measurements.

    What I have stumbled across doesn’t show any “lunar” signature:


  4. tchannon says:

    Answer from me is no I haven’t looking into ephemeris or measurement of lunar distance.

    I assume this is so deeply studied for so many years on a lunatic would not know *but* there is danger in everyone knows, the subtle everyone assumes everyone knows about some critical detail.

    Lunar range data probably exists online. No doubt amateurs have done this and shown but as I recall Apollo left prisms on the lunar surface.

    Simple, bung this into a search engine, refine as needed

    lunar ranging

    Actually this has been going on for years, predates manned space flight

    On the moon

    (from http://www.nasa.gov/mission_pages/LRO/multimedia/lroimages/lroc-20100413-apollo15-LRRR.html)

  5. Tim Cullen says:

    tchannon says: December 2, 2012 at 2:30 pm

    It’s real Sun-Earth distance observations that I trying to pin down.
    It seems to be one of those areas where everybody “knows” but can’t find the references…
    I’ll keep my fingers crossed and keep looking…
    Many thanks…

  6. tchannon says:

    Ah, I see.

    I suspect there are only old measurements because it can be calculated far more accurately yet as you say that is not confirmation by measurement.

    There are recent works trying to figure out change in solar diameter, without so far as I could find any reliable result. Simply defining the “surface” is too hard.

  7. Clivebest says:

    I emailed Greg Kopp (lead scientist on SORCE-TIM) last January about the lunar signal that pops out once the Earth’s elliptic orbital effects have been subtracted. He was kind enough to reply, explaining their analysis, thus both earning my deep respect for his scientific integrity and the professionalism of the TIM group’s data analysis. His reply helps explain the TSI data processing.

    The residual you show does not appear in our ‘tsi_1au’ value because we correct for the lunar effect on the Earth’s orbit (and many others). We produce the 1-AU corrected TSI for people studying the Sun’s output; and we produce the ‘tsi_true_earth’ value for those, such as climate modelers, wanting direct radiative inputs to the Earth’s system. Thus the ‘tsi_true_earth’ appropriately does not remove the effect of the lunar tug on the Earth, since that does affect the at-Earth radiative inputs.

    In our orbital corrections, we use the JPL ephemeris VSOP87, which accounts for the positions of all the planets in the solar system as well as the Moon to make our Sun-Earth distance corrections to a fixed 1-AU; so you shouldn’t see any lunar signal in the ‘tsi_1au’, but you should (as you do) in the ‘tsi_true_earth’. This ephemeris also includes effects such as that the Sun itself rotates around the center of mass of the solar system, which, thanks to Jupiter, is close to the Sun’s surface and has a ~12-year period.

    We also correct for spacecraft effects, which include Sun-instrument distance changes due to the spacecraft’s low Earth orbit. These are comparable to the lunar effects (+/- 14000 km) and occur on 95-minute orbital time scales. And we apply Doppler corrections, as the instrument collects blue-shifted photons depending on its radial velocity toward the Sun, whether due to the spacecraft’s or the Earth’s orbital motions. These are ~50 ppm corrections over the spacecraft’s 95-minute orbital period.

    If I’m understanding your lunar calculation correctly, you’re starting to apply some of the neat physics subtleties in these data — and now hopefully also starting to appreciate some of the many other corrections that we apply to make the accurate 1 AU data.

    He also pointed out that their latest value of TSI is 1360.8 W/m^2 at solar minimum (ref. Kopp & Lean 2011), which is considerably lower than the older 1367 W/m^2 value adopted by most IPCC models

    I am pretty sure that as a consequence of this GCM models are overestimating climate sensitivity by about 20%. – see http://clivebest.com/blog/?p=3681 independently of the physics assumptions made.

  8. Berényi Péter says:

    This barycenter thing is a funny one. Distance between center of Earth and the barycenter of Earh-Moon system is very small compared to the Earth-Sun distance, so it does not have much effect on TSI.

    On the other hand, the Earth-Moon sytem does not orbit the Sun, but the barycenter of the solar system. The Sun does the same thing, just in a much smaller orbit and a quite complex one, because more than one planet have significant effect (Jupiter & Saturn being the top players).

    Because of this the Earth-Sun distance varies rather haphazardly. As TSI flux is inversely proportional to the square of this distance, TSI is modulated by the relative position of the major giant planets. The effect is not negligible. Difference in TSI between Jupiter being in conjunction or opposition at the same date of the year is 27 W/m², that is, it’s huge (compared to the supposed 3.7 W/m² direct forcing of CO₂ doubling). Excursions in annual averages due to Jupiter are much smaller of course, still, distribution of insolation along the calendar year can have a considerable effect on climate, it’s only common sense. The same kind of effect is supposed to bring about ice ages after all (via Milankovitch cycles).

    Now, here comes the unbelievable blunder. NASA (the National Aeronautics and Space Administration of the U.S. of America) has an Atmosphere-Ocean Model page. A small part of this project is a Monthly Latitude Insolation calculator utility. It is written in Fortran (on 2002 September 25), source code is downloadable, it compiles fine with any reasonable Fortran compiler (I have used gcc-gfortran 4.4.6).

    However, on closer examination it turns out Sun’s wobbles around the barycenter of the solar system are not taken into account by the author, Gary L. Russell. He even boasts proudly (in a comment found in source): “Existence of Moon and heavenly bodies other than Earth and Sun are ignored.”

    Indeed. Why not?

    After all astronomical calculations are about the only tiny part of a climate model that can be done correctly, from first principles, using data known to astronomers to many decimal places since the 19th century. And it is apparently enough reason for modellers to get it absolutely wrong.

    The model is maintained by GISS (the Goddard Institute for Space Studies), whose head is who else? James E. Hansen (of Hockey Stick fame).


  9. tchannon says:

    Good one Clive.

    Mention of VSOP87 is interesting and means they are using the venerable French works, JPL is not the only route. I mention this stuff some time ago in connection with very long term orbit changes. Might be worth doing a revisit.

    1360.8 is the value showing in figure 1.

    I don’t believe SORCE is absolute accurate as close as often claimed.

  10. tallbloke says:

    Péter: beware, here be dragons. The reason Russell doesn’t bother calculating the motion of the Sun WRT to the solar system barycentre is because Earth orbits the Sun, not the solar system barycentre. Why would it? The barycentre doesn’t weigh anything. It has no mass. So as the Sun wobbles around the barycentre, the Earth goes with it, except for the extent to which it is pulled away from the Sun directly by Jupiter (mostly) or towards the Sun by Venus.

    These secondary motions are small compared to the 1.5M km the Earth gets pulled by the Sun as it careens around. There are some even smaller secondary perturbations introduced by Jupiter’s orbital eccentricity and conjunction cycle with Saturn. Gradual changes in these and their interaction with the other two gas giants motion change the shape of Earth’s orbit over tens of thousands of years – the Milankovitch cycles.

    You can confirm this with the JPL horizons ephemeris system online.

  11. Berényi Péter says:

    Well, I must have been sleepy and you are right. I will come back to you with accurate calculations.

  12. Clivebest says:

    In reality the solar energy received by the Earth is the true measurement ‘tsi_true_earth’ and NOT the astronomically corrected values usually shown ‘tsi_1au’. TSI is defined as the solar energy flux at a distance of 1 Astronomical Unit. One AU is only approximately the “average” distance of the Earth from the Sun over a full year. However the actual average distance is always changing depending on the other planets and especially variations in the Moon’s orbit. The precession of the lunar orbit is just 18.6 years.

    So the sine wave in http://clivebest.com/blog/wp-content/uploads/2012/01/moons.png is the full ‘tsi_true_earth’ signal showing beautifully how the solar input varies during the year as the Earth follows its elliptical orbit. The lunar signal shows up once you subtract the prediction of the elliptical orbit from the data. So the solar energy received by the earth really does vary each month.

  13. So if I’m reading this correctly, in *measured* TSI data there is a lunar signal, in phase with the full moon.

    Some people have postulated that this is due to the Earth getting closer to the Sun due to orbit about the Earth-moon barycenter.

    However, that variation is negligible compared to an astronomical unit, so I doubt that the source.

    If the TSI signal is from measured data, where is the data measured? From the ground?

    I think they’re just getting moon-shine into the measurement station. The moon is kinda bright, and it reflects short wave solar radiation. Obviously the variation would be sinusoidal in phase with the full moon.

  14. Clivebest says:

    Correct. The “raw” measurement is from a satellite in orbit around the Earth. It measures daily average total solar radiance. There is a lunar signal present in phase with the full moon.

    The monthly change in distance to the sun is about 8000km – so small compared to 149600km. However the radiance falls as 1/r^2 so this means the lunar effect causes a proportional change in radiance of about 10**-4 – or only about 0.2 watts/m2. The observed signal agrees with that during 2008. Look at the right hand scale in the figure.

    Moonshine I think should be even smaller. I estimate it to be about 5 times smaller or only 0.04 watts/m2.

    I strongly suspect though that moonshine and lunar atmospheric tides are important effects during the polar winter, when TSI = 0.0.

  15. tchannon says:


    One of the lesser realised solar system features is the path of the earth moon through space.

    The moon orbits the sun (ignore barycentre here) where the path through space is a wiggle impressed on the 1 year orbit because it is concurrently in earth orbit.

    The moon is small but nevertheless it’s mass is sufficient to wiggle the earth in it’s orbit, hence sun earth distance varies too.

    I’ve seen an animation of this but finding one is hard.

  16. tchannon,

    Yes I am certainly aware of barycenters and all that as I am an astronomer. But the Earth-moon wobble is negligible compared to an astronomical unit.

    The moon is bright enough to see-by at night, and that has got to be on the order of a few Watts or so. The first plot in the comments shows a variation of about 20 Watts in phase with the moon, correct? That’s way too large for the Earth-barycenter-moon orbit.

  17. Berényi Péter says:

    One can get Sun-Earth distance (and many more solar system data) tabulated with high precision at the Jet Propulsion laboratory HORIZONS Web-Interface.

    Deviations from a true Keplerian orbit are indeed small.

  18. tchannon says:

    Joseph, see figure 5 green trace, that is the lunar caused wobble, 0.1W rms, ~0.282W peak to peak.

  19. Brian H says:

    Does not using the barycenter as the orbit origin take into account exactly the same tugs as calculating planets’ influence individually, and adding them? If not, what’s a barycenter for?

  20. tallbloke says:

    Short answer is No. The solar system barycentre is the centre of mass of the entire system and is the point that the Sun dances around (the word ‘orbit’ gives a false impression – see my avatar for an example of a ‘harmonious motion phase of ~50 years).

    It predominantly reflects the gravitational effect between the gas giants and the Sun. The Earth is much smaller and much closer to the Sun than the gas giants, and is forced to follow the Sun as the focus of its orbit very closely.

    The barycentre “is for” determining the position of the Sun within the system as a whole.

  21. tchannon says:

    I’m not sure I follow either of you.

    Gravitationally everything orbits the solar system barycentre.

    In addition each body is to varying degrees affected by every other body but much more than that starts to fall apart.

    Perhaps it is better to realise there are barycentres for of everything. One classic that gets mentioned often is the earth/moon as a pair and the barycentre of the pair.

    I think a problem is the assumptions popularly made which lead to misconception, in this case by failing to clearly state the exact contexts. The moon for example follows what path through space?
    Answer is it is in orbit around the solar system barycentre and very strongly affected by a close by body, together with which it tumbles through space.

    I seem to recall high board divers can somersault whilst diving, perhaps initially travelling upwards some of the time but as gravity accelerates them all motion is forwards.

    You are in orbit around the solar system barycentre… which itself is moving in orbit.

    Be cogs in cogs. Some incognito ;-)

  22. tallbloke says:

    It’s very hard to explain clearly in a few words in a way which enables people to visualize what is going on. Tim is right that the Earth (and everything else in the solar system) orbits the barycentre; BUT, it take the Sun varying amounts of time to ‘go around’ the barycentre, often 12 years or so, whereas the Earth orbits the Sun every year. The Sun-Earth barycentre is a lot closer to the Sun’s centre than the solar system barycentre (except when they coincide). So in effect, the Earth is orbiting the Sun, not the Solar system barycentre at the timescale it orbits in.

  23. tchannon says:

    I”ve seen various planetarium style computer programs but none seem to allow exploration or visualisation outside of the popular conceptions. The nuts and bolts are hidden.

    Maybe this needs a way to selectively magnify motion and leave trails, all done in 3D.

  24. Berényi Péter says:
    December 2, 2012 at 11:52 pm

    “This barycenter thing is a funny one. Distance between…….”

    We (at http://www.solarchords.com) absolutely agree, the whole of Solar Chord Science is based upon this, Newton’s basic laws of motion and the very fundamental formulae e.g. F=ma, the inverse square law etc. are just that, simple and basic, as far as I can see people overcomplicate the calculations and do not appreciate the significance of the basic math involved, I see comments like; ‘a barycentre doesn’t weigh anything’ and similar nonsense, the Barycentre is a mathematical construct to enable calculations to be made, just like any constructed formula, including Newton’s laws.

    The biggest single mistake I see in the quest to understand orbital motions, is the insistence upon looking at the problem in a purely 2D model, the massive kinetic energy of celestial bodies given by their enormous forward velocity, about 250km/sec along the Galactic path, is a fundamental element in understanding the motions. Have a look at the image on the following link;


    Newton’s First Law
    An object remains in constant straight line motion unless an unbalanced force acts on it. An object at rest remains at rest unless an unbalanced force acts on it.
    The first law is also known as the Law of Inertia. Unbalanced forces produce a NET force that is NOT zero. IMPORTANT- when there is a NET force on an objects, the object changes its motion- it accelerates!

    Newton’s Second Law
    Newton’s second law is the primary law when calculating motion quantities. In words it states that the acceleration of an object is proportional to the ratio of force to mass.
    i.e. F=ma – Force equals mass times acceleration.

    The first law tells us that the body wants to travel in a straight line but gravity acts upon it to bend it around the Barycentre position, the amount of bending or deviation from a straight line is dependant upon the gravitational strength (the combined masses) and the forward velocity, the greater the forward velocity the less the bending or deviation for a given gravitational (mass) pull.

    This does NOT mean that the methods used in SCS (Solar Chord Science) is the answer to the N body problem, i.e how to predict the future positions of celestial bodies, that is currently impossible,
    BUT, because in a moderate time scale of about 400years, due to the periodic nature of orbits and accurate measurement, the relative positions of the planets are very predictable and, if you take an instantaneous snapshot of any configuration of the planets, by taking moments about the solar system barycentre, you can determine the relative position of the sun in relation to the earth and hence the true earth to sun distance at any time. As Berényi Péter stated this is ignored in TSI calculations.

    All our basic calculations, methods and quoted figures has been submitted to and verified by, various Professors of Astrophysics in several top universities.

  25. [...] thanks to Lawrence Wilson, who has taken the time and trouble to continue investigating the controversy around the question of the focus of Earth’s orbit. This has an important bearing on the [...]

  26. tallbloke says:

    Howard Bailey says:
    The first law tells us that the body wants to travel in a straight line but gravity acts upon it to bend it around the Barycentre position

    I don’t think so. The first law tells us what you said before you got to the word ‘but’.
    The second half of your sentence begs the question of what the ‘centre of attraction’ for Earth is. We’re about to run some calcs to answer that question. My engineering estimate plucked from the eye of the mind is that it will be much closer to the Sun-Earth barycentre than the solar system barycentre for most of the time. Stand by for results.

    the greater the forward velocity the less the bending or deviation for a given gravitational (mass) pull.

    The gravitational force is (on average throughout the orbit) perpendicular to the forward motion in the direction of the orbit of the solar system around the galaxy and so will not affect the degree to which the gravity of the Sun and other planets acts on the mass of the Earth to create its centre of attraction or orbital focus.

  27. tallbloke says:

    OK, I’ve plotted the distance in AU to the SSB and the Sun at perihelion from 1900 to 2100. Earth-Sun distance is stable, Earth-SSB distance isn’t. My plot is consistent with Geoff’s. The Earth pretty much orbits the Sun, with small perturbations caused by other planets. That settles the argument for me, though your mileage may vary. The data is from JPL Horizons DE 405 ephemeris. Any questions or counter-arguments?

  28. tchannon says:

    One way of considering this is the earth orbits the gravitational elephant but is taken for an SSB wobble along the way by the sun. The SSB has no gravity.