Monday, November 25, 2013

The Sun explains 95% of climate change over the past 400 years; CO2 had no significant influence

A new post by Dan Pangburn shows that solar activity explains 95% of global temperature change over the past 403 years since 1610, including the recovery from the Little Ice Age. Change to the level of atmospheric carbon dioxide was found to have no significant influence.

Calculated Mean Global Temperatures 1610-2012

Guest post by Dan Pangburn


This monograph is a clarification and further refinement of Reference 10 which also considers only average global temperature. It does not discuss weather, which is a complex study of energy moving about the planet. It does not even address local climate, which includes precipitation. It does, however, consider the issue of Global Warming and the mistaken perception that human activity has a significant influence on it.

The word ‘trend’ is used here for measured temperatures in two different contexts. To differentiate, α-trend applies to averaging-out the uncertainties in reported average global temperature measurements to produce the average global temperature oscillation resulting from the net ocean surface oscillation. The term β-trend applies to averaging-out the average global temperature oscillation to produce the slower average temperature change of the planet which is associated with change to the temperature of the bulk volume of the water involved.

The first paper to suggest the hypothesis that the sunspot number time-integral is a proxy for a substantial driver of average global temperature change was made public 6/1/2009. The discovery started with application of the first law of thermodynamics, conservation of energy, and the hypothesis that the energy acquired, above or below breakeven (appropriately accounting for energy radiated from the planet), is proportional to the time-integral of sunspot numbers. The derived equation revealed a rapid and sustained global energy rise starting in about 1941. The average global temperature anomaly change β-trend is proportional to global energy change.

Measured temperature anomaly α-trends oscillate above and below the temperature anomaly trend calculated using only the sunspot number time-integral. The existence of ocean oscillations, especially the Pacific Decadal Oscillation, led to the perception that there must be an effective net surface temperature oscillation with all named and unnamed ocean oscillations as participants. Plots of measured average global temperatures indicate that the net surface temperature oscillation must have a period of 64 years with the most recent maximum in 2005.

Combination of the effects results in the effect of the ocean surface temperature oscillation (α-trend) decline 1941-1973 being slightly stronger than the effect of the rapid rise from sunspots (β-trend) resulting in a slight decline of the trend of reported average global temperatures. The steep rise 1973-2005 occurred because the effects added. A high coefficient of determination, R2, demonstrates that the hypothesis is true.

Several refinements to this work slightly improved the accuracy and led to the equations and figures in this paper.

Prior work

The law of conservation of energy is applied as described in Reference 1 in the development of the equations that calculate temperature anomalies.
Change to the level of atmospheric carbon dioxide has no significant effect on average global temperature. This was demonstrated in 2008 at Reference 6 and is corroborated at Reference 2.

As determined in Reference 3, reported average global temperature anomaly measurements have a random uncertainty with equivalent standard deviation ≈ 0.09 K.

Global Warming ended more than a decade ago as shown in Reference 4 and Reference 2.

Average global temperature is very sensitive to cloud change as shown in Reference 5.

The parameter for average sunspot number was 43.97 (average 1850-1940) in Ref. 1, 42 (average 1895-1940) in Ref. 9, and 40 (average 1610-2012) in Ref. 10. It is set at 34 (average 1610-1940) in this paper. The procession of values for average sunspot number produces slight but steady improvement in R2 for the period of measured temperatures and progressively greater credibility of average global temperature estimates for the period prior to direct measurements becoming available. A graph of R2 vs. average sunspot number indicates that further lowering of the number would not significantly increase R2 and might even reduce it.

Initial work is presented at

The sunspot number time-integral drives the temperature anomaly trend

It is axiomatic that change to the average temperature trend of the planet is due to change from break-even to the net energy retained by the planet.

Table 1 in reference 2 shows the influence of atmospheric CO2 to be insignificant (tiny change in R2 if considering CO2 or not) so it can be removed from the equation by setting coefficient ‘C’ to zero. With ‘C’ set to zero, Equation 1 in Reference 2 calculates average global temperature anomalies (AGT) since 1895 with 89.82% accuracy (R2 = 0.898220).

The current analysis determined that 34, the approximate average of sunspot numbers from 1610-1940, provides a slightly better fit to the measured temperature data than did 43.97 and other values 9,10. The approximate AGT during 1610-1940 is 286.2 K. With these refinements to Equation (1) in Reference 1 the coefficients become A = 0.3596, B = 0.003503 and D = ‑ 0.4475. R2 increases slightly to 0.904839 and the calculated anomaly in 2005 is 0.5046 K. Also with these refinements the equation calculates lower early anomalies and projects slightly higher future anomalies. The excellent match of the up and down trends since before 1900 of calculated and measured anomalies, shown here in Figure 1, corroborates the usefulness and validity of the calculations.

Projections until 2020 use the expected sunspot number trend for the remainder of solar cycle 24 as provided 11 by NASA. After 2020 the limiting cases are either assuming sunspots like from 1925 to 1941 or for the case of no sunspots which is similar to the Maunder Minimum.

Some noteworthy volcanos and the year they occurred are also shown on Figure 1. No consistent AGT response is observed to be associated with these. Any global temperature perturbation that might have been caused by volcanos of this size is lost in the temperature measurement uncertainty. Much larger volcanoes can cause significant temporary global cooling from the added reflectivity of aerosols and airborne particulates. The Tambora eruption, which started on April 10, 1815 and continued to erupt for at least 6 months, was approximately ten times the magnitude of the next largest in recorded history and led to 1816 which has been referred to as ‘the year without a summer’. The cooling effect of that volcano exacerbated the already cool temperatures associated with the Dalton Minimum.

(Click on image or equation to enlarge)

Figure 1: Measured average global temperature anomalies with calculated prior and future trends using 34 as the average daily sunspot number.

As discussed in Reference 2, ocean oscillations produce oscillations of the surface temperature with no significant change to the average temperature of the bulk volume of water involved. The effect on AGT of the full range of surface temperature oscillation is given by the coefficient ‘A’.

The influence of ocean surface temperature oscillations can be removed from the equation by setting ‘A’ to zero. To use all regularly recorded sunspot numbers, the integration starts in 1610. The offset, ‘D’ must be changed to -0.2223 to account for the different integration start point and setting ‘A’ to zero. Setting ‘A’ to zero requires that the anomaly in 2005 be 0.5046 - 0.3596/2 = 0.3248 K. The result, Equation (1) here, then calculates the trend 1610-2012 resulting from just the sunspot number time-integral.


Trend3anom(y) = calculated temperature anomaly trend in year y, K degrees.

0.003503 = the proxy factor, B, W yr m-2.

17 = effective thermal capacitance of the planet, W Yr m-2 K-1

s(i) = average daily Brussels International sunspot number in year i

34 ≈ average sunspot number for 1610-1940.

286.2 ≈ global mean surface temperature for 1610-1940, K.

T(i) = average global absolute temperature of year i, K,

-0.2223 is merely an offset that shifts the calculated trajectory vertically on the graph, without changing its shape, so that the calculated temperature anomaly in 2005 is 0.3248 K which is the calculated anomaly for 2005 if the ocean oscillation is not included.

Sunspot numbers back to 1610 are shown in Reference 1 Figure 2.

Applying Equation (1) to the sunspot numbers of Reference 1 Figure 2, produces the trace shown in Figure 2 below.

Figure 2: Anomaly trend from just the sunspot number time-integral using Equation (1).

Combined Sunspot Effect and Ocean Oscillation Effect

Average global temperatures were not directly measured in 1610 (thermometers had not been invented yet) or even estimated very accurately using proxies. The anomaly trend that Equation (1) calculates for that time is roughly consistent with other estimates but cannot be verified. Also, there is no way to determine for sure how much and which way the ocean surface temperature cycles would influence the values.

As a possibility, the period and amplitude of oscillations attributed to ocean cycles demonstrated to be valid after 1895 are assumed to maintain back to 1610. Equation (1) is modified as shown in Equation (2) to account for including the effects of ocean oscillations. Since the expression for the oscillations calculates values from zero to the full range but oscillations must be centered on zero, it must be reduced by half the oscillation range.


The ocean oscillation factor, (0.3596,y) – 0.1798, is applied prior to the start of temperature measurements as a possibility.

Applying Equation (2) to the sunspot numbers from Figure 2 of Reference 1 produces the trend shown in Figure 3 next below. Available measured average global temperatures from Reference 3 are superimposed on the calculated values.

Figure 3: Trend from the sunspot number time-integral plus ocean oscillation using Equation (2) with superimposed available measured data.

Figure 3 shows that temperature anomalies calculated using Equation (2) estimate possible trends since 1610 and actual trends of reported temperatures since they have been accurately measured world wide. The match from 1895 on has R2 = 0.9048 which means that 90.48% of average global temperature anomaly measurements are explained. All factors not explicitly considered must find room in that unexplained 9.52%. Note that a coefficient of determination, R2 = 0.9048 means a correlation coefficient of 0.95.

Calculated anomalies look reasonable back to 1700 but indicate higher temps prior to that than most proxy estimates. They qualitatively agree with Vostok, Antarctica ice core data but decidedly differ from Sargasso Sea estimates during that time (see the graph for the last 1000 years in Reference 6). Credible accurate assessments of average global temperature that far back were not found. Perhaps solar output was a bit lower for a period prior to 1700 which would allow lower average global temperatures in spite of more sunspots. Ocean oscillations might also have been different from assumed.

Other assessments

Other assessments are discussed in Reference 1.


Others that have looked at only amplitude or only time factors for solar cycles got poor correlations with average global temperature. The good correlation comes by combining the two, which is what the time-integral of sunspot numbers does. As shown in Figure 2, the anomaly trend determined using the sunspot number time-integral has experienced substantial change over the recorded period. Prediction of future sunspot numbers more than a decade or so into the future has not yet been confidently done although assessments using planetary synodic periods appear to be relevant 7,8.

If the temperature of the bulk volume of water participating in the ocean oscillation is used in place of the surface temperature of the water, the time-integral of sunspot numbers alone appears to correlate with the estimated true average global temperature trend after approximately 1700.

The net effect of ocean oscillations is to cause the surface temperature trend to oscillate above and below the trend calculated using only the sunspot number time-integral. Equation (2) accounts for both and also, since it matches measurements so well, shows that rational change to the level of atmospheric carbon dioxide can have no significant influence.












Graphical sunspot number prediction for the remainder of solar cycle 24


  1. It would have been interesting to show / calculate the temperature back to 1810 in graph 1 perhaps.

    1. The global temperature observations only go back to 1850 in the HADCRU record. Only a few individual station records exist before 1850.



  4. Dan You might like to compare your cooling forecast with mine at
    -here's a summary of the conclusions of the latest post.
    "I have combined the PDO, ,Millennial cycle and neutron trends to estimate the timing and extent of the coming cooling in both the Northern Hemisphere and Globally.

    Here are the conclusions of those posts.

    1/22/13 (NH)

    1) The millennial peak is sharp - perhaps 18 years +/-. We have now had 16 years since 1997 with no net warming - and so might expect a sharp drop in a year or two - 2014/16 -with a net cooling by 2035 of about 0.35.Within that time frame however there could well be some exceptional years with NH temperatures +/- 0.25 degrees colder than that.
    2) The cooling gradient might be fairly steep down to the Oort minimum equivalent which would occur about 2100. (about 1100 on Fig 5) ( Fig 3 here) with a total cooling in 2100 from the present estimated at about 1.2 +/-
    3) From 2100 on through the Wolf and Sporer minima equivalents with intervening highs to the Maunder Minimum equivalent which could occur from about 2600 - 2700 a further net cooling of about 0.7 degrees could occur for a total drop of 1.9 +/- degrees
    4)The time frame for the significant cooling in 2014 - 16 is strengthened by recent developments already seen in solar activity. With a time lag of about 12 years between the solar driver proxy and climate we should see the effects of the sharp drop in the Ap Index which took place in 2004/5 in 2016-17.

    4/02/13 ( Global)

    1 Significant temperature drop at about 2016-17
    2 Possible unusual cold snap 2021-22
    3 Built in cooling trend until at least 2024
    4 Temperature Hadsst3 moving average anomaly 2035 - 0.15
    5 Temperature Hadsst3 moving average anomaly 2100 - 0.5
    6 General Conclusion - by 2100 all the 20th century temperature rise will have been reversed,
    7 By 2650 earth could possibly be back to the depths of the little ice age.
    8 The effect of increasing CO2 emissions will be minor but beneficial - they may slightly ameliorate the forecast cooling and help maintain crop yields .
    9 Warning !! There are some signs in the Livingston and Penn Solar data that a sudden drop to the Maunder Minimum Little Ice Age temperatures could be imminent - with a much more rapid and economically disruptive cooling than that forecast above which may turn out to be a best case scenario.


  6. Hansen 1988: Sun controls climate

  7. plot for yourself at WoodforTrees:

  8. From a comment at WUWT:

    Greg says: December 28, 2013 at 11:58 pm lsvalgaard says: >> geologyjim says:”does not answer my question about the RATE OF CHANGE.” Becasue the Rate of Change is not important. The amount of energy output is. Indeed , so “activity” probably needs to be integrated in some fashion to get energy. Simply integrating some measure of activity over all time would not be reasonable since as the Earth warms or cools in response to a changing input there will be tendency to return once the perturbation ends. If climate has linear relaxation response to such perturbations the Laplace response will be convolution with a decaying exponential. That is basically a weighted integration. As an illustration SSN is integrated with 20 year time constant response and compared to low-pass filtered SST.

  9. I look forward to this work being submitted to a peer reviewed journal.

  10. This is very interesting and makes sense.

    I have one question. How shall I interpret the factor "(0.3596,y)"? What does the comma mean?

  11. Has this amazing finding been submitted to a peer reviewed journal? It will overturn 150 years of climate science, and make the author world famous. What is he waiting for??

    1. David, it would be nice if, for a change, you would instead contribute a constructive comment that is scientific in nature, rather than a troll drive-by shooting.

  12. Sun more important in late 20th century warming that previously believed


  14. This is an interesting exercise but using SST to explain SST is not ideal ( especially if you use it 3 times: T^4, PDO,AMO ).

    Here is an alternative but similar idea:

    The continuous integral with T^4 cooling can be replaced with a simple relaxation response.

    Instead of adding a T^4 feedback term that reduces the integrand, this approach assumes that SSN is a proxy for some aspect of solar activity that influences surface temps.It further assumes that there is a simple relaxation to equilibrium which implies a decaying exponential response to any change in SSN.

    This is just like a pot of hot water cooling. once the flame is cut.

    The way to calculate this is like a running average with exponential weighting.

    It is probably the simplest physical model.

    The last script on this page can be used or any convolution type filter adapted.

    This has several theoretical advantages.

    It only has 3 parameters. scaling and time-constant and offset
    It does not use SST to explain SST.
    It does not assume a specific feedback ( Plank T^4 f/b ) is the only climate reaction
    It matches changes around 1850 - 1950 much better than what you show above.

    Notable differences between the relaxation and SST :

    Residual of "11y" cycle does not match the circa 9y variability in SST.
    Relaxation starts to drop just before 1990, not 2005.

    The latter is probably explained by the long term effects of volcanoes which has not yet been "noticed" my mainstream:

  15. Does your "effective weighted integration" of sunspots correlate better to temperature than a simple "cumulative departure from the mean"

    If you would be willing to write this up as a guest post for a lay audience, I would be happy to post it here at The Hockey Stick. Thanks

  16. Dan Pangburn said...

    ‘Other molecules’ outnumber CO2 molecules by approximately 2500 to 1.

    When a molecule of CO2 absorbs a photon of terrestrial EMR it immediately (less than 0.1 microsecond, hyperphysics calc is about 0.1 nanosecond) bumps into other molecules handing off the added energy in a process called thermalization (some spell it thermalisation). Once it has handed off the energy it cannot emit a photon.

    Thus the only influence that added CO2 can have is to cause the absorption/thermalization process to move slightly closer to the emitting surface.

    Why isn’t thermalization (or thermalisation) mentioned in IPCC reports?

    Two natural drivers have been identified that explain measured average global temperatures since before 1900 with R^2>0.9 (95% correlation) and credible values back to 1610. Global Warming ended before 2001 The current trend (from a graph for longer than a century) is down.

    The method, equation, data sources, history (hind cast to 1610) and predictions (to 2037) are provided at and references.

  17. As a layman I have always wondered how the CAGW believers can put so much faith in the power of the trace gas CO2 to drive global temperatures. It has always seemed to defy logic and I have never seen anything written that shows the "proof" of the hypothesis. It is nice to see a scientific study that concludes that CO2 is not, nor ever has been, a "control knob" for global temperatures.
    Again, as a layman, it seem so much more logical that the sun and its fluctuations in released energy would be the most powerful controlling force for temperatures on earth.
    Thanks for putting together this study.

  18. This is probably closer to the truth than the Al Gore crowd wants to hear. If you add the weakening earth's magnetic field and reduction in algae and plankton along with drilling releasing hidden methane pockets the basis for targeting CO2 is nothing but a Ponzi scheme.

  19. Hi MS,

    I wasn't sure if this is the best method by which I can contact you, or if there is a more applicable place, but I had a question.

    I'm involved in a climate debate online and was wondering if you could provide me with scientific studies pertaining to the time lag associated with solar forcing upon climate. I have found several studies, but a couple are inadequate in demonstrating the point. Any studies concerning the thermal inertia of the system, climate response time lags following variations in solar forcing, etc., would be greatly appreciated.