Some Simple Questions

UC (whose comments should always be read attentively) wondered the other day about the effect of taking monthly normals – a step that is routine in much climate analysis as a preliminary to analysis. In the case of Dessler v Spencer, both parties to the litigation work after-taking monthly normals ( “post-normal” statistics, so to speak 🙂 )

I’ve spent a couple of days looking at CERES data without taking normals and present a couple of questions for readers to think about. (I know the answers.) I’d like readers to answer according to their general knowledge and not by looking up or researching.

The first question: the “solar constant” (as measured by CERES) is approximately 340.5 wm-2 (1362/4). What is the variation in average annual incoming solar as measured by CERES?

I’ve temporarily shut off comments on this thread so that you have an opportunity to make your answer without being affected by the answers from other readers. Update: Open now.

Answer: the difference between the annual max and annual min is about 23 wm-2, or about 5 times the 3.8 wm-2 anticipated from doubled CO2, as readers quickly observed. Some people instinctively think about solar variability, but it’s the eccentricity that matters.

Question 2: What is the approximate annual variability in global tropospheric temperature (pick an AMSU lower troposphere level) ? Does the annual temperature maximum coincide with the annual forcing maximum? If not, how much is the phase difference?


  1. Steve McIntyre
    Posted Sep 13, 2011 at 7:14 PM | Permalink

    Comments open now.

  2. Steve Fitzpatrick
    Posted Sep 13, 2011 at 7:18 PM | Permalink

    About 23 watts/M^2, that is, +/- ~3.3% of the mean value.

  3. MikeN
    Posted Sep 13, 2011 at 7:23 PM | Permalink

    What are the other questions?

  4. Posted Sep 13, 2011 at 7:28 PM | Permalink

    As SteveF says, 3.3%. And the eccentricity of Earth’s orbit is 1.67%. Put that together with inverse square and …

  5. BarryW
    Posted Sep 13, 2011 at 7:33 PM | Permalink

    Without knowing the distribution how could you know? That’s assuming there’s more than one year of data involved which would give you just one data point. Or am I missing something?

  6. commieBob
    Posted Sep 13, 2011 at 7:37 PM | Permalink

    I thought we were receiving about 1300 watts per square meter at the top of the atmosphere. I also thought it didn’t change enough to worry about.

    ??? (I obviously didn’t cheat by looking anything up.)

  7. Steve McIntyre
    Posted Sep 13, 2011 at 7:38 PM | Permalink

    Yup.. the difference between the annual max and annual min is about 23 wm-2, or about 5 times the 3.8 wm-2 anticipated from doubled CO2. Also not a small amount in Dessler v Spencer terms.

    Some people’s instinctive reaction is to think in terms of solar variability… which is negligible in comparison to the effect of eccentricity.

    The max is around 350 wm-2,. the min around 330 wm-2. While the percentage change isn’t much, the absolute variation in solar forcing is definitely noticeable from a TOA perspective.

    See post for next question.

    • David L. Hagen
      Posted Sep 14, 2011 at 9:40 AM | Permalink

      For reviews of TSI variations see: “Total Solar Irradiance Satellite Composites and their Phenomenological Effect on Climate,” ch 12, pp 289-316. (In “Evidence-Based Climate Science: Data opposing CO2 emissions as the primary source of global warming” Don Easterbrook, Ed. Elsevier) (2011).
      Periodicity of Total Solar Irradiance K.J. Li et al. Solar Physics V267, N.2, 295-303, DOI: 10.1007/s11207-010-9655-8

    • Scott Brim
      Posted Sep 14, 2011 at 12:50 PM | Permalink

      Now that Question 1 of Steve’s pop quiz has been officially answered, the following snippet of information from Wikipedia might be cause for raising some further corollary questions:

      “The eccentricity of the Earth’s orbit is currently about 0.0167, meaning that the Earth’s orbit is nearly circular, the semiminor axis is 99.98% of the semimajor axis. Over thousands of years, the eccentricity of the Earth’s orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets (see graph).”

    • Geoff Sherrington
      Posted Sep 17, 2011 at 6:45 PM | Permalink

      Before a variation can be assigned to a mean, there has to be agreement about the value of the mean. This is probably dependent on choice of model+assumptions, but one prominent author, Normal Loeb form NASA, 2011, notes (and it’s worth reading to the last line) –

      The uncertainty in 1°x1° regional LW clear-sky TOA flux is determined from calibration
      uncertainty, error in narrow-to-broadband conversion, ADM error, time-space averaging, and
      scene identification. For CERES, calibration uncertainty is 0.5% (1σ), which for a typical global
      mean clear-sky LW flux corresponds to ≈1 Wm-2. Figs. 2a and 2b show the regional distribution
      of the correction used to correct for regional narrow-to-broadband error. This is derived by
      applying narrow-to-broadband regressions to MODIS infrared radiances for completely cloud3
      free CERES footprints and then comparing the estimated broadband flux with CERES. The
      overall bias is -0.5 Wm-2 and the regional RMS difference is 2.5 Wm-2. Assuming a 50% error in
      the correction, the narrowband-to-broadband contribution to regional uncertainty becomes 1.74
      Wm-2. For clear-sky LW TOA flux, ADM error contributes 0.7 Wm-2 to regional RMS error
      (Loeb et al., 2007), and time-space averaging adds 1 Wm-2 uncertainty. The latter assumes zero
      error over ocean (i.e., no diurnal appreciable diurnal cycle in clear-sky LW) and a 3 Wm-2 error
      in the half-sine fit over land and desert (Young et al., 1998). In EBAF, “clear-sky” is defined as
      cloud-free at the MODIS pixel scale (1 km). A pixel is identified as clear using spectral MODIS
      channel information and a cloud mask algorithm (Minnis et al., 2011). Based upon a comparison
      of LW TOA fluxes for CERES footprints identified as clear according to MODIS but cloudy
      according to CALIPSO, and TOA fluxes from footprints identified as clear according to both
      MODIS and CALIPSO, Sun et al. (2011) found that footprints with undetected subvisible clouds
      emit 5.5 Wm-2 less LW radiation compared to completely cloud-free footprints, and occur in
      approximately 50% of footprints identified as clear by MODIS. This implies an error of 2.75
      Wm-2 due to misclassification of clear scenes. The total error in TOA outgoing clear-sky LW
      radiation in a region is sqrt(12+1.742+0.72+12+2.752) or approximately 3.6 Wm-2.

      Click to access Tech-Note_rlutcs_CERES-EBAF_L4_Ed2-6_20110809.pdf

      So at least part of the figure is assumed, through choice of one of several ADM errors (Angular Distribution Model). Will be interesting to see this reference Loeb, N.G., S. Kato, W. Su, T. Wong, F.G. Rose, D.R. Doelling, and J. Norris, 2011: Advances
      in understanding top-of-atmosphere radiation variability from satellite observations. Surveys
      Geophys. (submitted).

  8. Jiri Moudry
    Posted Sep 13, 2011 at 7:41 PM | Permalink

    I’ve seen somewhere +- 5%, mostly due to the Earth orbit’s eccentricity.

  9. Steve McIntyre
    Posted Sep 13, 2011 at 7:45 PM | Permalink

    Question 2: What is the approximate annual variability in global tropospheric temperature (pick an AMSU lower troposphere level) ? Does the annual temperature maximum coincide with the annual forcing maximum? If not, how much is the phase difference?

    Again – try to give an answer as a reaction, rather than researching. If you don’t know, guess based on what you think you know or what you think makes sense.

    • Posted Sep 15, 2011 at 5:53 PM | Permalink

      I’m fairly pleased that my 3 years of climate science have allowed an answer to two of the important questions, the phase is outside of my experience.

      As far as global variance, I think Roman’s method provide the best answers.

    • Tom Gray
      Posted Sep 15, 2011 at 6:10 PM | Permalink

      There must be a form of thermal capacitance. So there will be a lag in temperature relative to forcing

      • DeWitt Payne
        Posted Sep 15, 2011 at 7:51 PM | Permalink

        Yes, it’s called heat capacity. Because the surface layer of sea water is mixed to a depth of as much as 100 feet, the heat capacity of the ocean surface is large. Not only is there a phase lag, but also, as expected when the frequency is high compared to the characteristic frequency, a reduction in the magnitude of diurnal and seasonal temperature range compared to land. In electrical circuit terminology, heat content in Joules is similar to charge and temperature to voltage.

  10. Steve McIntyre
    Posted Sep 13, 2011 at 7:53 PM | Permalink

    Question 3: Average outgoing shortwave flux at the TOA is about 99 wm-2. what is the annual variability in outgoing shortwave flux at the TOA? What is its phase relationship to annual incoming solar flux?

    • Posted Sep 14, 2011 at 7:19 PM | Permalink

      The altitude is irrelevant.

      Question 3: Average outgoing shortwave flux is about 99 wm-2. what is the annual variability in outgoing shortwave flux? What is its phase relationship to annual incoming solar flux?

      My point is pedantic. 😀

      • curious
        Posted Sep 15, 2011 at 6:57 AM | Permalink

        Doesn’t the altitude determine the area of the integral surface and hence the denominator for the flux density in W/m2?

  11. Posted Sep 13, 2011 at 8:18 PM | Permalink

    Answering according to my general knowledge, the answer can only be 42.

    • P. Solar
      Posted Sep 16, 2011 at 12:09 PM | Permalink

      No, it’s more like 4.2

      Arthur Dent tore up the bit of paper with the answer to “the fundamental question of life the universe and everything” on it. When they patched it back together, they apparently failed to notice the decimal point.

      The white mice presumably were well aware of all this but continue to observe the human race running round in circles trying to work out for themselves.

      If they read the peer-review literature, they must be pissing themselves laughing.

  12. David L. Hagen
    Posted Sep 13, 2011 at 8:52 PM | Permalink

    Phase relationship: From thermal inertia (~capacitance), the ocean temperature lags the solar forcing by 3 months (25% of 12 months from Pi/2 or 90 deg lag) ignoring diffusion, (having recently read models by Nir Shaviv and David Stockwell.) The outgoing radiation is in phase with the temperature and consequently lags the solar variation by 3 months.

    • David L. Hagen
      Posted Sep 14, 2011 at 7:26 AM | Permalink

      For the 11 year solar cycle, Stockwell’s 25% phase lag was 2.75 years.

  13. Brian Macker
    Posted Sep 13, 2011 at 9:55 PM | Permalink

    If I remember correctly the earth has an eliptical orbit and sweeps out equal areas inside the ellipse in equal intervals. It spends more time further from the sun than closer. Despite this it will need to spend half it’s time warming and half cooling, otherwise it would not have an average stable temperature. Solar influx and orbital speed is bilaterally symmetrical (with regards to a line running from min and max distance). Therefore the temporal periods of warming and cooling will also be symmetrical. The boundaries between both being exactly at the temporal half way points between the min and max distance.

    Temperature will continue to rise just so long as the planet is in the warming half, and will continue to fall just so long it is in the cooling half.

    Therefore there would be a 25% lag in max and min temperature in phase from max and min distance. But only assuming a uniform surface and an untilted axis.

    The earth has both a tilted axis and a non-uniform temperature. I know the earths tilt is about 23 degrees but do not know the tilt to phase. I also do not know the difference in reflectance of the different hemispheres. There would also be effects caused by rotation, and radition effects cause by temperature differences between the equator and poles.

    Of course it would also depend on the variations in surface water, wind patterns, evaporation and all kinds of other factors.

    I haven’t a clue how to easily adjust for any of the other stuff and have no idea by what percentage they have an effect.

    So I’ll just go with 25%.

  14. Steve Fitzpatrick
    Posted Sep 13, 2011 at 10:39 PM | Permalink

    Steve McIntyre,

    The annual cycle is, I imagine, mainly related to the relative thermal capacities of the north and south hemispheres (south is much greater!) The questions are interesting, at least somewhat. However, the fact that the thermal inertia of the oceans is very substantial means that most all short term variations are not going to be going to be observable above the background noise. Which is why I think suggestions of “instantaneous” reactions by the climate to variations of any kind of forcing are almost certainly incorrect, except over land. In reality, the biggest variation is (of course) the seasonal one…. which reaches on the order of 200 watts per square meter far from the equator. Toronto in July vs January is a good demonstration.
    This is why I think Bart’s frequency domain analysis is interesting… 4-5 years sounds like a very reasonable global response time to changes in radiative forcing.

  15. timetochooseagain
    Posted Sep 13, 2011 at 10:45 PM | Permalink

    For phase difference of global atmospheric temperatures, I’m gonna go with being out of phase quite a bit, something near 180 degrees: The reason is that the main source of there being an annual cycle in incident radiation is different from the reason for a difference in cycle of temperature. The reason for a cycle in temperature is asymmetry between the hemispheres: The Northern Hemisphere has the larger cycle (due to stronger seasonal variation of landmasses, and landmass dominance of the Northern Hemisphere), however, it is during Northern Hemisphere Winter that the global incident radiation is at it’s peak, IIRC.

    As for the magnitude of the annual temperature cycle, I can’t think what it would be at the moment. I probably couldn’t guess anyway.

  16. Steve Fitzpatrick
    Posted Sep 13, 2011 at 10:46 PM | Permalink

    Sorry, I forgot to directly answer… The annual variation in outgoing is probably (I am guessing) on the order of 10 watts/M^2. The phase difference is slightly less than 90 degrees, as it must be for any system where the forcing frequency is much faster than the response time.

  17. David Smith
    Posted Sep 13, 2011 at 10:53 PM | Permalink

    Here’s a post I made earlier today in my new sandbox, by coincidence:

  18. Geoff Sherrington
    Posted Sep 13, 2011 at 11:24 PM | Permalink

    Re the first question with its divide by 4 (presumably to convert a hemisphere to a disc and then to account for half daytime, half nighttime). If you include twilight, the lit time of the surface is more than 50% so the 4 cannot be absolutely accurate for the task in hand.

    • Duster
      Posted Sep 14, 2011 at 3:19 PM | Permalink

      I think that if you consider the geometry of a sphere, an adjustment would be necessary to deal the fact that the area occluded by the sphere, and the surface area that actually intercepts incoming radiation are different animals entirely. As incoming watts/m^2 is measured, if the sensor were moved away from the central portion of the area occluded by sphere, the amount of energy intercepted per square meter will decrease as proportionate to longitudinal distance from the solar noon position; it’s why evenings and dawns are dimmer than noons. Also, possibly, why maximum daily temperatures lag maximum insolation. Would the divide-by-four be correcting for that?

    • simon abingdon
      Posted Sep 15, 2011 at 12:22 PM | Permalink

      Geoff, since the surface area of a hemisphere is twice that of a flat disc of the same diameter I still can’t see why we should divide by four. Also does not the quoted solar watts/sqm apply only where the sun is directly overhead, which it is for just one position at any moment during daylight, and then only within the tropics?

  19. John Ritson
    Posted Sep 13, 2011 at 11:36 PM | Permalink

    I think the lag is a few months at most. I remember being told we’re at perihilion around June and I recall seeing AMSU anomoloies peaking in August. So I’m going for 2 months.

    I think I see where Steve is going with this one.

  20. dlb
    Posted Sep 13, 2011 at 11:59 PM | Permalink

    I agree with “Timetochoose” for the phase difference between global temps and incoming shortwave radiation for the reasons given.

    However question (3)is really interesting, if the earth was a homogenous surface and atmosphere then the out going SW radiation would be in phase with the incoming solar flux. It all depends on which hemisphere has a greater albedo. In June there is probably more surface reflecting than in December, though Antarctica could well have an influence then. Also I have no idea which hemisphere produces the most cloud, at a guess I think it might be the NH. So in that case outgoing SW would be roughly in phase with the northern solstice.

  21. Bruce Cunningham
    Posted Sep 14, 2011 at 12:12 AM | Permalink

    The Earth’s average daily temperature (according to amsu data) peaks during the summer months of the northern hemisphere (during July I think). This is when the Earth is at aphelion, and is at its farthest distance from the Sun!

  22. Curt
    Posted Sep 14, 2011 at 12:50 AM | Permalink

    I have read a couple of times, including once from Leif Svalgaard on this or a similar blog, that the main global climate models do not include the variations in insolation due to the earth’s elliptical orbit. Rather they simply use the average insolation value all the time. I find this hard to believe. Can anyone confirm or disprove?

  23. Steven Mosher
    Posted Sep 14, 2011 at 1:40 AM | Permalink


    Since I’m working in that… as we speak

    I believe I’ve looked this up several time for folks.. ModelE belwo

    !@sum ORBPAR calculates the three orbital parameters as a function of
    !@+ YEAR. The source of these calculations is: Andre L. Berger,
    !@+ 1978, “Long-Term Variations of Daily Insolation and Quaternary
    !@+ Climatic Changes”, JAS, v.35, p.2362. Also useful is: Andre L.
    !@+ Berger, May 1978, “A Simple Algorithm to Compute Long Term
    !@+ Variations of Daily Insolation”, published by Institut
    !@+ D’Astronomie de Geophysique, Universite Catholique de Louvain,
    !@+ Louvain-la Neuve, No. 18.
    !@auth Gary Russell (with extra terms from D. Thresher)
    C**** Tables and equations refer to the first reference (JAS). The
    C**** corresponding table or equation in the second reference is
    C**** enclosed in parentheses.
    USE CONSTANT, only : twopi,PI180=>radian
    C**** Input:
    !@var YEAR = years C.E. are positive, B.C.E are -ve (i.e 4BCE = -3)
    C**** Output:
    !@var ECCEN = eccentricity of orbital ellipse
    !@var OBLIQ = latitude of Tropic of Cancer in degrees
    !@var OMEGVP = longitude of perihelion =
    !@+ = spatial angle from vernal equinox to perihelion
    !@+ in degrees with sun as angle vertex
    C**** Table 1 (2). Obliquity relative to mean ecliptic of date: OBLIQD

    • David L. Hagen
      Posted Sep 14, 2011 at 8:29 AM | Permalink

      Compliments. For +/-0.0003 deg accuracy, see: Solar Position Algorithm for Solar Radiation Applications, Ibrahim Reda and Afshin Andreas Jan. 2008 NREL/TP-560-34302 which includes orbital calculations.

      • Posted Sep 14, 2011 at 10:13 PM | Permalink

        This is code from modelE.. just to answer Curt’s question

        • Curt
          Posted Sep 15, 2011 at 3:20 PM | Permalink


          Thanks for the quick response. While there may be many issues with models, I was hoping something that basic wouldn’t be one of them.

    • Posted Sep 15, 2011 at 2:29 AM | Permalink

      @ Steven Mosher

      Some years ago I coded Berger series into Java and excel, together with some applets for visualization of past insolation and differences with current values.
      I have put them here.
      There is also a link to a more detailed insolation calculator for current conditions.

      If anybody feels like coding the series in R, it would be quite welcome.

  24. Steven Mosher
    Posted Sep 14, 2011 at 1:41 AM | Permalink


  25. Geoff Sherrington
    Posted Sep 14, 2011 at 2:44 AM | Permalink

    Question 3. It is not automatic to assume that there is a single phase difference. I’d expect that observations combined a number of phase differences because of the many paths before outgoing is measured at TOA, in the sense of tracking a photon through its whole cycle. The gross maximum amplitude of the combination might be a complex, time-dependent combination of smaller parts and it might not have strong physical significance. Also, one way to discern between a lag, lead and harmonic is to examine the effect of a shock. While a lag of several months is graphed in some papers, there is less dicussion of variations like whether it is n years + those several months. I wish it was possible to work at finer resolution than monthly, increasing the ease of finding shocks, so that some of these variations can be more confidently excluded as unlikely.

  26. simon abingdon
    Posted Sep 14, 2011 at 3:31 AM | Permalink

    Perihelion is at southern hemisphere midsummer (early January).
    Southern hemisphere maximum insolation greater than northern but (from Kepler) of shorter duration. Annual insolation variation greater in southern hemisphere.

  27. Ron Cram
    Posted Sep 14, 2011 at 7:46 AM | Permalink

    Great post, as always. A minor nit. 23 wm-2 is about 6 times the 3.8 wm-2 anticipated from doubled CO2, not 5 times. I’m eager to see your answers for the other questions.

    David Smith, very nice post. I think I have a question or two for you, which I will leave on your site.

  28. EdeF
    Posted Sep 14, 2011 at 8:14 AM | Permalink

    The earth not only is tilted but precesses like a spiinning top so that the orientation
    towards the sun is different now than it was 2000 or 4000 yrs ago. This complicates
    making comparisons of the earth’s climate with past climates. My guess for Q2 is
    15 deg C and 2 months.

  29. P. Solar
    Posted Sep 14, 2011 at 8:14 AM | Permalink

    Looking at evidence for a radiation driven relationship, this may be relevant:

    Following Spencer’s lag regression approach and using the data linked in the “Dessler” thread, I noticed the extracted long term trend given by R.slr had a heavy signature of ENSO in it. I focused on the period 2006-2010 where this was the strongest and got the above linked plot.

    Now the correlation of the trend does not show causation, it just shows correlation. However, looking at the lag regression shows that this relationship is oscillatory and radiation driven. If the forcing was non radiative in nature (energy from upswelling of deep ocean currents) it would have a strong spike at lag=0.

    This fundamental difference that allows us to differentiate the origin of the forcing seems to have been overlooked until now.

    Looking at the OLS estimator , rather than just the correlation will probably allow an estimation of the feedback response.

    • Paul_K
      Posted Sep 14, 2011 at 9:59 AM | Permalink

      “If the forcing was non radiative in nature (energy from upswelling of deep ocean currents) it would have a strong spike at lag=0.”
      This was postulated by Spencer based on his simple model, but is yet to be proved. If you examine Figure 2 from Dessler 2011, these GCM runs come from the pre-industrial control suite of Meehl et al 2007. These runs have NO radiative forcing, only “non-radiative forcing”, and yet, apart from two models, do NOT show the signature response at zero lag-time anticipated by Spencer. Until this is explained, I don’t believe that you can rely on Spencer’s postulate.

  30. P. Solar
    Posted Sep 14, 2011 at 8:33 AM | Permalink

    Here is the overlay of ENSO data on the “trend” section of the srl decomposition of hadSTT

    Over the period 2006-2010 , ENSO seems to correlate almost perfectly with SST trend. If ENSO was the cause the lag plot would be strong around zero.

    Dessler seemed to be trying to bait Spencer (in their email discussion last December) into saying that ENSO was driven by cloud variation. It seemed he thought the idea so ludicrous that Spencer would blow his credibility by saying yes. (He largely avoided the issue).

    Unless I’m misreading this it would indeed seem that it is radiation driving ENSO changes.

    If that can is the case , it’s going to make some waves.

  31. P. Solar
    Posted Sep 14, 2011 at 8:40 AM | Permalink

    Apologies, that is hadCRUT3 global not SST.

    • Bernie
      Posted Sep 14, 2011 at 8:58 AM | Permalink

      Which changes things, I would think?

  32. Paul_K
    Posted Sep 14, 2011 at 9:37 AM | Permalink

    Question 2. I believe that the amplitude of the annual GMT variation is between 2 and 4 degrees. However, if one examines temperature variation by latitude, you can see that this rather sedate GMT variation represents the RESOLUTION of huge temperature swings by latitude, with each latitude cycling slightly out of phase with the one above and below. If we start the clock with the emergence of the arctic from permament night, we observe that this starts a temperature gain of order 50 degrees in the extreme northern latitudes. A little later the northern mid-latitudes start to warm up with a temperature-cycle amplitude of about 30 degrees. Eventually the warming cycle reaches the tropics with a humble 2 degree temperature amplitude, approximately pi/2 out of phase with the start of arctic warming. And so on through the Southern mid latitudes and down to the Antarctic, which is close to pi degrees out of phase with the Arctic. The big changes in each SH latitude therefore largely offset the big temperature changes in the corresponding NH latitude in the calculation of GMT. We can speculate that, because of temperature amplitude dampening by ocean heat uptake, the different land/ocean ratios in the NH and SH have some effects on both the observed phasing and amplitude of GMT variation.

    • Paul_K
      Posted Sep 14, 2011 at 10:23 AM | Permalink

      I forgot to address the second part of Question 2. The answer depends on the definition of forcing. I think that solar insolation peaks at perihelion – early January, and I am fairly sure that GMT peaks in late July/early August, so I would guess 6 months for the difference between peak solar forcing and peak GMT. This answer treats all seasonal albedo change as a feedback to the change in solar insolation.

      If, on the other hand, you consider the forcing to be net incident radiation (change in received SW after accounting for albedo), then I suspect the difference between the peaks should be around three months, and I would guess April for peak net incident radiation.

  33. Tim Sorenson
    Posted Sep 14, 2011 at 9:55 AM | Permalink

    Don’t know if someone asked (and someone answered) but why is CERES using 1362/4 instead of 1362?

    • Paul_K
      Posted Sep 14, 2011 at 10:04 AM | Permalink

      Basically because solar radiation strikes a disc of area pi*r^2, but for energy balance, the flux is averaged over the surface of the globe – 4pi*r^2.

      • Posted Sep 14, 2011 at 11:22 AM | Permalink

        In case anyone is wondering whether it “matters” that this assumes the Earth is a perfect sphere: it would appear not:

        From Wiki, the Earth’s surface area is:

        510,072,000 km^2

        it has a mean radius of:

        6,371.0 km

        this translates to a sphere of area

        510,064,472 km^2 (rounded up slightly)

        which is about 99.999% of the actual surface area. Pretty dang close!

        • P. Solar
          Posted Sep 14, 2011 at 11:48 AM | Permalink

          Even school kids get told : don’t trust WP as source of reliable information 😉

          Maybe the mean radius is defined in terms of the surface or vice versa. What is the surface of a mountain? The difference maybe your PI versus theirs.

          BTW “wiki” is software, wikipedia is what you are refering to.

        • Posted Sep 14, 2011 at 12:11 PM | Permalink

          Always check wiki’s source, in this case it’s:

          Various (2000). David R. Lide. ed. Handbook of Chemistry and Physics (81st ed.). CRC. ISBN 0-8493-0481-4.

          for radius and

          Pidwirny, Michael (2006-02-02). Surface area of our planet covered by oceans and continents.(Table 8o-1). University of British Columbia, Okanagan. Retrieved 2007-11-26.


          Staff (2008-07-24). “World”. The World Factbook. Central Intelligence Agency. Retrieved 2008-08-05.

          for surface area.

          Pretty good references, no reason to think they are fudging anything. If the figures had agreed more closely, I would be more tempted to believe that perhaps the radius was being “defined” by the surface area: it appears not, however, since they are different in that respect by about 8000 square kilometers in terms of actual and implied area. This is a small percentage, but quite measurable. It’s too large to be because they used a different approximation for pi, I think (I just used that on the computer calculator).

          Wiki is indeed software. However, that didn’t stop you from immediately knowing what I was making shorthand reference to, did it? 😉

        • Posted Sep 14, 2011 at 12:41 PM | Permalink

          Hm, you may be right, actually, that they are just using a different value for pi. The value of pi implied if they are doing what you suggest would be correct within 3 decimal places. Still, just how big a difference does the fact that the Earth is not perfectly spherical actually make, anyway? I suspect it is still very small.

        • JamesW
          Posted Sep 14, 2011 at 4:28 PM | Permalink

          If you take the area you quote of 510,072,000, and divide by 4 pi, and then take the square root, you get 6371.047. When rounded to 5 digits results in 6371.0.

          So the numbers given on Wikipedia are self consistent.

        • timetochooseagain
          Posted Sep 14, 2011 at 6:25 PM | Permalink

          So they are just rounding? Hm, okay, so the question, then, is does the non-perfectly-spherical shape of the Earth have a significant impact on it’s surface area?

  34. P. Solar
    Posted Sep 14, 2011 at 10:10 AM | Permalink

    Q2. Does the annual temperature maximum coincide with the annual forcing maximum? If not, how much is the phase difference?

    To answer that you would have to define what “annual forcing” term is. This would seem to be the cause of some debate.

    Nothing with a finite heat capacity can have max/min of temp coincide with the forcing causing it.

    Probably the only way to answer that kind of question without attributing a specific physical cause is to look at the lag regression , like I posted on the Dessler thread. That shows (for surface temps) a slightly asymmetrical situation. 4-5 months on a lead , about -10 months on the lag side.

    This may be due to the asymmetry of convection in the oceans : cold water sinks whereas warm water spreads.

  35. Noblesse Oblige
    Posted Sep 14, 2011 at 10:19 AM | Permalink

    See Scafetta, J. Atmospheric and Solar-Terrestrial Physics for some interesting correlations between terrestrial temperature and solar system motion.

  36. P. Solar
    Posted Sep 14, 2011 at 11:41 AM | Permalink

    Hopefully this will more answer Q2 more directly :

    lag plot of CERES vs UAH global , which I believe is TLT.
    period 2006-2010 which has max signal/noise ratio.

    Plots from 2000 are a bit muddy and don’t show a clear character.

    If Q2 is seeking the phase relationship, this way may be more informative that looking for the max temp and “forcing” (whoever he may be).

    I would take the kink at zero crossing to indicate the “true” zero of the phase relation. Not sure what this offset represents.

  37. TomL
    Posted Sep 14, 2011 at 2:45 PM | Permalink

    The ellipticity of the earth is about 1 part in 300, due to centrifugal force. That translates to about a 20 km difference between the polar and the equatorial radius.

  38. Noblesse Oblige
    Posted Sep 14, 2011 at 5:25 PM | Permalink

    Q#2. As a guess, roughly two months lag on average. It will depend on altitude and humidity. In Colorado at 7100 ft. where we spend much time, the lag is near zero. Temperature follows forcing very closely. In the Northeast US, the warmest month is August and the coldest is February, about 6 weeks lag. Since most surface is water, I’ll guess two months.

  39. Geoff Sherrington
    Posted Sep 14, 2011 at 8:07 PM | Permalink

    Don’t really want to split hairs, but whereas the Elementary charge is known to 10 sig figs, 1.602176487×10^-19C, Newton’s Gravitational constant big G is measured to only 5-6 sig figs. There has been discussion whether it is indeed constant from whence “The two most accurate measurements of Newton’s gravitational constant, from Sevres and Wuhan are:
    6.675 59 (27) x 10^-11 m3kg-1s-2 and, 6.669 9 (7) x 10^-11 m^3kg^-1s^-2, respectively. The calculated value is, 2.08% and 2.00% lower than these values, respectively.”
    Also debate on whether little g, related to the mass of the Earth, is constant. Wegener lead Carey et al (plate tectonics gelology) to propose an expanding earth, whose definitive test probably would rely on satellite sophistication. We seem to be reaching that level now, but interpretation seems more weighted to ocean level change than to earth expansion.
    Both G and g could be effects to consider in geological time extrapolations. For orbital calculations of the effect of varying Earth mass, see and scroll down.

  40. Tim Channon
    Posted Sep 14, 2011 at 9:56 PM | Permalink

    An observation. Going to keep this brief.

    For what it’s worth the figure I came up with for temperature leading sea level was something like 4 years. (can look it up if needed)

    In addition temperature lags asymmetric solar by a few months. I assume this is about magnetics.

    Looks like I did make something available, if crude and doesn’t tell all, done that way to be visually compelling.

    Click to access solar-sea-temperature-lags.pdf

    I faded out on this stuff, probably return sometime.
    Plenty I could say if anyone wants to have a go.
    Solar came from nasa/greenwich data.
    Sea level is sat record.
    Tropical temperature rss/uah is fine, hadcrut much the same. Need to do this from gridded.
    There is a common term.

  41. Jeff Norman
    Posted Sep 15, 2011 at 12:10 AM | Permalink

    This is one of those nightmares where I forgot to drop out of the course at the beginning of the semester, I did not attend any classes and here we are at exam time… so please excuse my ignorance.

    “The first question: the “solar constant” (as measured by CERES) is approximately 340.5 wm-2 (1362/4). What is the variation in average annual incoming solar as measured by CERES?”

    According to the NASA CERES Brochure:

    “Each CERES instrument has three channels — a shortwave channel to measure reflected sunlight, a longwave channel to measure Earth-emitted thermal radiation in the 8-12 μm “window” region, and a total channel to measure all wavelengths of radiation”

    Does it actually measure “incoming solar”?

    According to this NASA CERES website:

    “The incoming solar radiation can easily be derived by dividing the SW by the albedo. CERES uses a solar constant of 1365 Wm-2”

    Does CERES actually measure “incoming solar”?

    And to make things so much clearer, NASA GISS tells grade 9 to 12 students “S = solar “constant” = 1370 W/m^-2/K^4″
    when they do the Earth energy balance calculation, a rounding difference that is greater than the 3.8 W/m² attributed to a doubling of CO2.

    Steve: Hmmmm. Good question. I don’t know the answer for sure. Until I know for sure, I’ll allow for the possibility that it’s a calculated number.

    • TAC
      Posted Sep 15, 2011 at 8:24 AM | Permalink

      …one of those nightmares where I forgot to drop out of the course at the beginning of the semester, I did not attend any classes and here we are at exam time…

      I agree that I ought to know the answers to these questions.

    • David L. Hagen
      Posted Sep 15, 2011 at 8:37 AM | Permalink

      Jeff Re: “1370 W/m^2/K^4”. Drop the “K^4”. For the latest, see “A new, lower value of total solar irradiance: Evidence and climate significance Greg Kopp, Judith Lean Geophys. Res. Lett., 38, L01706, doi:10.1029/2010GL045777. 30 Nov 2010

      The most accurate value of total solar irradiance during the 2008 solar minimum period is 1360.8 ± 0.5 W m−2 according to measurements from the Total Irradiance Monitor (TIM) on NASA’s Solar Radiation and Climate Experiment (SORCE) and a series of new radiometric laboratory tests. This value is significantly lower than the canonical value of 1365.4 ± 1.3 W m−2 established in the 1990s

      • Jeff Norman
        Posted Sep 15, 2011 at 7:58 PM | Permalink

        David L. Hagen

        I agree, drop the K^4, but I put the whole thing in quotes for a reason. Unfortunately I forgot the link:

        Click to access CERES_litho.pdf

        It looks like the GISS people are walking high school students through a basic calculation of the radiative heat balance. What message are they sending by overstating the solar “constant”?

        • David L. Hagen
          Posted Sep 15, 2011 at 9:05 PM | Permalink

          Per Steve’s post on variations, the most important yet unasked question is “what happens with a 5% change in albedo” i.e., clouds vary with temperature and/or solar/cosmic changes. IPCC AR4 Table 2.11 categorized “solar” and “cloud albedo” as “low” “level of scientific understanding”, and “cosmic rays” as “very low” – as evidence by sensitivity estimates varying from ~0.3 deg C to ~9 deg C.
          Re K^4 is properly in the Stefan Boltzman constant. Please bug NASA ’till they correct that error – especially since that was posted in 2001! Re “overstating” – probably just rounded up to “3” (2.5) significant figures. Ask them to update to 1360.8.

    • Geoff Sherrington
      Posted Sep 16, 2011 at 12:12 AM | Permalink

      Jeff Norman, Like you, more homework to do. The sum of the short wave and medium IR channels you quote would be less than the total. I do not know the spectral range of the “total” and whether it is clipped at either end. If a single figure is used for total, there is a risk that its components (as wavelength bands) do not vary in unison, as in some days there might be more UV-vis than usual, hence the inclusion of the 2 other channels. Presumably the spectrometry is solid, but it’s worth a check. Will try.

  42. imarcus
    Posted Sep 15, 2011 at 2:57 AM | Permalink

    An interesting slant on the response times of the lower troposphere to a solar perturbation, is given by Dragi’c et al, who have linked Forbush events to NST responses in the order of days. As I understand it, the Forbush event induces an increase in earth system shielding from GCRs followed by a Svensmark drop in cloud cover and this is correlated with ~0.4ºC rise visible in the NST trace.

    Reference to the paper below

    Astrophys. Space Sci. Trans., 7, 315–318, 2011
    © Author(s) 2011. CC Attribution 3.0 License. Astrophysics and Space Sciences
    Forbush decreases – clouds relation in the neutron monitor era
    A. Dragi´c1, I. Aniˇcin1, R. Banjanac1, V. Udoviˇci´c1, D. Jokovi´c1, D. Maleti´c1, and J. Puzovi´c2
    1Institute of Physics, University of Belgrade, Pregrevica 118, Belgrade, Serbia
    2Faculty of Physics, University of Belgrade, Studentski trg 16, Belgrade, Serbia
    Received: 15 November 2010 – Revised: 15 February 2011 – Accepted: 23 March 2011 – Published: 31 August 2011

  43. Posted Sep 15, 2011 at 3:14 AM | Permalink

    Exercise 1.

    Let T be a monthly anomaly time series. Show that the sum of Jan-Dec (*) trends in the reference period is zero.

    *) Or Dec-Nov, depending on the anomaly definition

    Steve: very nice. 🙂

    • Posted Sep 15, 2011 at 11:28 AM | Permalink


    • Posted Sep 15, 2011 at 1:39 PM | Permalink

      ‘trends’ in the LS-sense:


      • David L. Hagen
        Posted Sep 15, 2011 at 3:18 PM | Permalink

        Similar statistical analysis: Stockwell asks: Is the Atmosphere Still Warming?

        • Posted Sep 16, 2011 at 2:03 AM | Permalink

          Interesting, are those monthly anomalies as well? This link

          is even more relevant. I used HadCRUT just as an example, any time series will lead to the same result.

        • Paul_K
          Posted Sep 16, 2011 at 6:53 AM | Permalink

          Roman’s work suggests that the effect is small but interesting for the temperature series alone. I suspect that the effect should be larger when one considers statistics derived from cross-plots of anomalies derived from net-flux vs Temperature anomalies when a low correlation offers little compensation, as is the case for Dessler’s Rcloud vs Temp. Should be easy to check.

        • Posted Sep 16, 2011 at 6:56 AM | Permalink

          That is Exercise 2., I didn’t have time to write it down yet 🙂

        • John Whitman
          Posted Sep 19, 2011 at 3:33 PM | Permalink


          That was an educational link. Thanks. I might turn from nuclear engineer to statistician yet (give or take a decade).

          More of those educationa statistical links, please.


        • Posted Sep 20, 2011 at 2:27 PM | Permalink

          If we have linear trend + weather noise, then the Feb to Dec anomalies are just noise? That should be taken into account if one wants to predict monthly values.

        • Posted Sep 21, 2011 at 4:52 AM | Permalink

          Farmer et al. 1989 mentions sine curve phase+amplitude least squares fitting. Maybe that should be preferred in the blogosphere gambling. Not fair for the warmers that they have to wait until January call to place their bets.

  44. Posted Sep 15, 2011 at 4:43 AM | Permalink

    Q2: At a given place north of the Tropic of Cancer the maximum annual solar forcing due to solar daily maximum ALTITUDE occurs at the summer solstice on 21 June. The maximum temperature in a continental location typical occurs about 5 weeks later. In a maritime place the lag is longer, about two months.

    The question here is how much the lag is for the entire earth due to variation in ECCENTRICITY solar forcing. Different cause but probably rather similar lags. Since the earth as a whole is quite a maritime place the expected lag should be about two months or perhaps even a bit more.

  45. Coldish
    Posted Sep 15, 2011 at 7:34 AM | Permalink

    Slightly OT, but possibly relevant to this discussion is an early paper by Ellis, Vonder Haar, Levitus and Oort (1978) entitled ‘The annual variation in the global heat balance of the earth'(JGR, Vol 83, pp. 1958-1962).
    Using monthly averages, Ellis et al found an annual range of about 31 watts per meter squared.
    The value they used for global albedo was at a minimum at the equinoctial months (March and September)and at a maximum at the solstice months (June and December), with the overall range being about 10% of the mean annual value.
    Ellis et al had only a limited number of oceanic sampling stations and their observations only covered a period of 29 months, so it is likely that better estimates are available in more recent literature.

  46. edrowland
    Posted Sep 15, 2011 at 8:15 AM | Permalink

    But isn’t that exactly what you would expect? A 25% lag. Global temperature would be the integral of energy input. Assuming the solar forcing is K+sin(phi) to very rough approximation, where phi is the position in the orbit, global average temperature would be the integral of that: cos(phi)+C. To very rough approximation.

    • P. Solar
      Posted Sep 15, 2011 at 9:27 AM | Permalink

      edrowland: no, that would be the case for a loss-less system. The earth is radiating to space so the peak will be sooner, though what you say does put an upper limit on the possible range of lag.

  47. Doug Proctor
    Posted Sep 15, 2011 at 10:40 AM | Permalink


    The least discussed and yet the initiating radiative driver is the sunshine we get. Least discussed by warmists, that is.

    The elliptical nature of our orbit changes the TOA by 6% summer to winter, yet the perihelion position – January – is about 2C cooler than the aphelion position – July – due, it is said, to the greater landmasses in the Northern Hemisphere. Somewhere in there would be the cloud cover difference, as well, but that is in the albedo-by-land-mass explanation. Trying to work out the thermal heating power of the differing geometry of land, sea and ice in the Northern Hemisphere would appear to be the first, obvious step in understanding the energy balance of the Earth. But this issue gets lost when 1362+/-11.5 W/m2 gets dumbed down to 340.5 W/m2 averaged over the year and over the day.

    The use of grossly averaged numbers – including the “global” temperature – is a convenience for computers and statisticians. Yet we all know that statistics don’t truly reflect reality, but an abstracted reality that even with the “19 out of 20 times” caveat doesn’t accurately reflect the nuances that embed the physical activity.

    Our lives are governed not by means, averages or running trends, but by exceptions from all these things. It is the natural variation from trends etc. that count. The statistical treatment of climate to deduce weather is spurious at best, but as Gore knows, that is how people perceive. “Normal” is what we had experienced as kids.

    We love number crunching the way accountants do: it gives us a feeling of security and power over our lives in its sweet simplicity. A statistical analysis is required to find underlying patterns that we can later explain (or not), but the patterns do not help us very well in anticipating what is happening next year. Even the simplest of statistics here – the insolation of TOA – doesn’t help us if we think there is a direct link between temperatures and sunshine power on even an annual basis.

    • P. Solar
      Posted Sep 15, 2011 at 10:54 AM | Permalink

      What you say is true and there are many more variations. This is why Spencer’s simple model includes by a generalised “non feedback, radiative forcing” term to avoid endlessly analysing detailed mechanics of it all.

      This Dessler has *inaccurately* paraphrased as R-cloud and gone off on his own merry way as though it somehow “refutes” Spencer’s work.

      Spencer is now keen for Dessler to (really) publish , I imagine so that he has something he can argue against. He can’t refute a now publicised but unpublished paper.

      • Paul_K
        Posted Sep 16, 2011 at 6:56 AM | Permalink

        Not quite. Dessler equates Rcloud to Spencer total RADIATIVE forcing term, implying all other forcings are zero. Still a wrong thing to do, but not quite what you are suggesting.

        • Paul_K
          Posted Sep 16, 2011 at 6:59 AM | Permalink

          Damn. Ignore my previous comment. I misread what you wrote. Sorry.

  48. DeWitt Payne
    Posted Sep 15, 2011 at 12:23 PM | Permalink

    Global temperature peaks in July. Ocean heat content peaks in March. There’s more land in the NH than the SH so the temperature range is larger and thus dominates the global average. The lag between the solstices and peak temperature in the SH and NH is less than 90 days because the response time for the land is shorter than 1 year. There’s more ocean in the SH so it dominates the global ocean heat content. The response time of the ocean is much longer than 1 year so the phase lag in heat content from the solstice is closer to 90 days. The effect of orbital eccentricity is pretty much lost in the noise.

    • timetochooseagain
      Posted Sep 15, 2011 at 5:30 PM | Permalink

      “The lag between the solstices and peak temperature in the SH and NH is less than 90 days because the response time for the land is shorter than 1 year.”

      This appears to be actually understating the shortness of the lag for insolation and temperature. Douglass Blackman and Knox found phase lags for surface temperature cycle on the order of just one month for most of the Northern Hemisphere and 45 days for most of the Southern:

      Click to access DBK%20Physics%20Letters%20A%20.pdf

      So it is not merely less than 90 days, it appears to be half that

  49. Posted Sep 15, 2011 at 11:35 PM | Permalink

    As guest on a radio program a couple of years ago I raised the point that the IPCC models did not include the Milankovitch Effect. Andrew Weaver, climate modeller, and lead author of the model chapters in three of the IPCC Reports including those for 2001 and 2007 and listed as participant in the next Report, phoned in to say the Effect was precluded because the time scale was too large.

  50. Colin Davidson
    Posted Sep 16, 2011 at 8:50 AM | Permalink

    By coincidence I have been looking at Tropopause heights recently. Still not finished, but initial impression is that Tropopause height varies enormously day-to-day. See for example Guam radiosonde data on the 14th and 15th of September, where the Tropopause is respecively at 17.7 and 15.5km.
    I haven’t looked at variation through the year yet.
    I use the data from

    It may be worth remembering that IPCC AR4 (2007) WG1 Chapter 2 emphasises that “Radiative Forcing” is NOT the same as “Surface Forcing”, and that variations in absorbed sunlight are the latter. From a simple model of the Surface Energy Balance (derived from the diagram in AR4 WG1 Chapter 1) the sensitivity of the Surface to a change in Surface Forcing is between 0.1 and 0.15 DegC/W/m^2.

    I live in Canberra. At that latitude, the difference in average insolation summer to winter is approx 150W/m^2. The difference in mean temp Jan to July is 15DegC. Looks to me as if Surface Forcing determines Surface Temperature.

    But I’m far from being an expert!

  51. Colin Davidson
    Posted Sep 16, 2011 at 9:18 AM | Permalink

    The trouble with rushing in is that you make mistakes.
    My Tropopause figures above are wrong, should be 15.9, 15.5km.
    A more illustrative sequence is 7,8,9 September, with Tropopause heights 16.6, 15.5, 16.0 km.

  52. P. Solar
    Posted Sep 16, 2011 at 10:35 AM | Permalink

    Here is another graph which may help to answer Qu.2 (as well as a whole lot more about response)

    +ve lag shows radiation leading temperature and the oscillatory nature is what would be produced by -lambda.dT negative feedback.

    zero lag corresponds to the in phase (plank) response of radiation to temperature. Don’t be fooled by the regression “slope” being 1.5 . The error in doing that is incorrectly calling the ols regression estimate “slope”. OLS estimator will be attenuated by the non linear signal, in this case roughly equal to it in amplitude and contaminated by non-zero correlation of the oscillatory component.

    The negative side shows rad lagging temp , the zero crossing probably answers Qu2.

    There could be some discussion about lags between SST and the UAH measured temps seen here. There seems to be too much crud affecting surface temperature records to get this kind of clear result.

    So Steve, does that tie in with what you have found?


  53. P. Solar
    Posted Sep 16, 2011 at 11:04 AM | Permalink

    BTW, the period of the fit I got for decaying sine wave was 36.061 months.

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