Updated: Low Climate Sensitivity Estimated from the 11-Year Cycle in Total Solar Irradiance

June 4th, 2010 by Roy W. Spencer, Ph. D.

NOTE: This has been revised since finding an error in my analysis, so it replaces what was first published about an hour ago.

As part of an e-mail discussion on climate sensitivity I been having with a skeptic of my skepticism, he pointed me to a paper by Tung & Camp entitled Solar-Cycle Warming at the Earth’s Surface and an Observational Determination of Climate Sensitivity.

The authors try to determine just how much warming has occurred as a result of changing solar irradiance over the period 1959-2004. It appears that they use both the 11 year cycle, and a small increase in TSI over the period, as signals in their analysis. The paper purports to come up with a fairly high climate sensitivity that supports the IPCC’s estimated range, which then supports forecasts of substantial global warming from increasing greenhouse gas concentrations.

The authors start out in their first illustration with a straight comparison between yearly averages of TSI and global surface temperatures during 1959 through 2004. But rather than do a straightforward analysis of the average solar cycle to the average temperature cycle, the authors then go through a series of statistical acrobatics, focusing on those regions of the Earth which showed the greatest relationship between TSI variations and temperature.

I’m not sure, but I think this qualifies as cherry picking — only using those data that support your preconceived notion. They finally end up with a fairly high climate sensitivity, equivalent to about 3 deg. C of warming from a doubling of atmospheric CO2.

Tung and Camp claim their estimate is observationally based, free of any model assumptions. But this is wrong: they DO make assumptions based upon theory. For instance, it appears that they assume the temperature change is an equilibrium response to the forcing. Just because they used a calculator rather than a computer program to get their numbers does not mean their analysis is free of modeling assumptions.

But what bothers me the most is that there was a much simpler, and more defensible way to do the analysis than they presented.

A Simpler, More Physically-Based Analysis

The most obvious way I see to do such an analysis is to do a composite 11-year cycle in TSI (there were 4.5 solar cycles in their period of analysis, 1959 through 2004) and then compare it to a similarly composited 11-year cycle in surface temperatures. I took the TSI variations in their paper, and then used the HadCRUT3 global surface temperature anomalies. I detrended both time series first since it is the 11 year cycle which should be a robust solar signature…any long term temperature trends in the data could potentially be due to many things, and so it should not be included in such an analysis.

The following plot shows in the top panel my composited 11-year cycle in global average solar flux, after applying their correction for the surface area of the Earth (divide by 4), and correct for UV absorption by the stratosphere (multiply by 0.85). The bottom panel shows the corresponding 11-year cycle in global average surface temperatures. I have done a 3-year smoothing of the temperature data to help smooth out El Nino and La Nina related variations, which usually occur in adjacent years. I also took out the post-Pinatubo cooling years of 1992 and 1993, and interpolated back in values from the bounding years, 1991 and 1994.

Note there is a time lag of about 1 year between the solar forcing and the temperature response, as would be expected since it takes time for the upper ocean to warm.

It turns out this is a perfect opportunity to use the simple forcing-feedback model I have described before to see which value for the climate sensitivity provides the best fit to the observed temperature response to the 11-year cycle in solar forcing. The model can be expressed as:

Cp[dT/dt] = TSI – lambda*T,

Where Cp is the heat capacity of the climate system (dominated by the upper ocean), dT/dt is the change in temperature of the system with time, TSI represents the 11 year cycle in energy imbalance forcing of the system, and lambda*T is the net feedback upon temperature. It is the feedback parameter, lambda, that determines the climate sensitivity, so our goal is to find a value for a best value for lambda.

I ran the above model for a variety of ocean depths over which the heating/cooling is assumed to occur, and a variety of feedback parameters. The best fits between the observed and model-predicted temperature cycle (an example of which is shown in the lower panel of the above figure) occur for assumed ocean mixing depths around 25 meters, and a feedback parameter (lambda) of around 2.2 Watts per sq. meter per deg. C. Note the correlation of 0.97; the standard deviation of the difference between the modeled and observed temperature cycle is 0.012 deg. C

My best fit feedback (2.2 Watts per sq. meter per degree) produces a higher climate sensitivity (about 1.7 deg. C for a doubling of CO2) than what we have been finding from the satellite-derived feedback, which runs around 6 Watts per sq. meter per degree (corresponding to about 0.55 deg. C of warming).

Can High Climate Sensitivity Explain the Data, Too?

If I instead run the model with the lambda value Tung and Camp get (1.25), the modeled temperature exhibits too much time lag between the solar forcing and temperature response….about double that produced with a feedback of 2.2.


The results of this experiment are pretty sensitive to errors in the observed temperatures, since we are talking about the response to a very small forcing — less than 0.2 Watts per sq. meter from solar max to solar min. This is an extremely small forcing to expect a robust global-average temperature response from.

If someone else has published an analysis similar to what I have just presented, please let me know…I find it hard to believe someone has not done this before. I would be nice if someone else went through the same exercise and got the same answers. Similarly, let me know if you think I have made an error.

I think the methodology I have presented is the most physically-based and easiest way to estimate climate sensitivity from the 11-year cycle in solar flux averaged over the Earth, and the resulting 11-year cycle in global surface temperatures. It conserves energy, and makes no assumptions about the temperature being in equilibrium with the forcing.

I have ignored the possibility of any Svensmark-type mechanism of cloud modulation by the solar cycle…this will have to remain a source of uncertainty for now.

The bottom line is that my analysis supports a best-estimate 2XCO2 climate sensitivity of 1.7 deg. C, which is little more than half of that obtained by Tung & Camp (3.0 deg. C), and approaches the lower limit of what the IPCC claims is likely (1.5 deg. C).

20 Responses to “Updated: Low Climate Sensitivity Estimated from the 11-Year Cycle in Total Solar Irradiance”

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  1. John Lohman says:

    Excellent work! (and I suspect we could explain 90% of HadCRUT variation using TSI, its impact on cloud cover, and ocean circulation).

  2. Andrew says:

    There have been different types of analyses done on the solar cycle signal. One approach has been to try and use ENSO and aerosol indeces to estimate the temperatrue changes unrelated to the TSI variations by multiple regression, EG Douglass and Calder:

    Determination of the Climate Sensitivity of the Earth to Solar Irradiance David H. Douglass, B. David Clader Geophysical Research Letters 10.1029/2002GL015345. 2002

    What seems to be the first major problem with the Camp and Tung analysis is that if it were true that the amplitude of the solar cycle signal supported climate model sensitivities, then climate models would presumably show the same amplitude of a cycle. This is not the case, as the variability of the solar cycle is extremely damped by the long response time of sensitive climate models. Somehow, Camp and Tung think that the response time is very short but the sensitivity is very high. That is physically unreasonable.

    The second problem is that they essentially assume that the apparent solar cycle component is caused by the TSI alone. This leaves out the possibility of a coincidence (spurious correlation) or some amplifier of the solar cycle variations. I don’t want to start a debate about the controversial cosmic ray hypothesis, but Camp and Tung do implicitly exclude it from their analysis, and anything which is not known.

    Also, just a gripe: There were no measurements of TSI in the 50’s and 60’s! That part of the TSI data is proxy based and may not be reliable. There is even debate about how to stitch the measured satellite data together, see acrim . com for example.

  3. Carl Chapman says:

    I think I’ve figured out how this AGW nonsense started.

    Someone calculated the feedback factor to be 3 or 4, so an initial change of 1 degree would be magnified to give a final change of 3 or 4 degrees. But they left out a “/”. It should have been 1/3 or 1/4, so doubling CO2 to give an initial change of 1.2 degrees Celsius would give an insignificant final rise of about 0.3 or 0.4 degrees Celsius.

    I’m joking, but if any of the scammers want to use that excuse rather than admitting they were part of a huge grant driven scam, that’s ok.

  4. christopher Game says:

    Dear Roy, \

    I am away from home, just glancing at things in an internet cafe.

    This is is really the right stuff. I am surprised that the errors are not made too great by the smallness of the signal, but I think this is really sound stuff.

    It is, however, a serious methodological error to simply average out the el Nino kind of thing, since you know it exists. To average it out is to greatly weaken the accuracy of the method. The correct thing is to estimate it explicitly and remove the estimated effect perhaps by subtracting the estimate. We may say, in the language of E.T. Jaynes, that the el Nino kinds of things are “nuisance variables”, and should be integrated over to remove their irrelevant interfering effects. Larry Bretthorst is a top expert who would know with great skill how to do this.

    But using the sunspot cycle is a very very good way to go because it is NOT SRICTLY PERIODIC, and this means that every cycle contains information not present in other cycles.

    And this is really using an external driver. It is of course ENTIRELY DIFFERENT from thinking about the balance between absorbed solar radiation and OLR, which are both internal variables. The present method has no direct information about the degree of absorption and should be combined with an analysis of the reflected solar radiation and the OLR, which can both be measured, I think, and are both internal state variables. If their noise level of measurement is low enough, this should provide you with really hard-core dynamical information, the real stuff. There are standard methods for this kind of analysis.

    The point is that the feedback from earth to sunspot cycle is entirely negligible.

    Great Stuff.

    Yours sincerely,


  5. Craig Goodrich says:

    There is a (relatively) new Scafetta paper linked at WUWT which shows a strong correlation between planetary orbits (principally Jupiter and Saturn, the Big Boys) and the 60-year cycle identified with the PDO. Would backing out PDO effects from your model change the sensitivity?

    Off topic: I’m really not sure that the terms “forcing” and “feedback” are useful in a system as complex as climate, as long as we keep the causality arrows pointing in the right direction.

    For example, suppose Svensmark’s cosmic ray > cloud formation hypothesis is true. (I personally like it.) Then when the solar wind reduces low-level high-energy rays, the rays are a feedback, but when we pass through the galactic plane or a spiral arm, where cosmic rays greatly increase in density, the flux is a forcing.

    Moreover, given the complexity of climate processes, it is likely that we will find that Process A affects Process B, but B has consequences that affect A after a certain lag. Which is the feedback?

    So perhaps it would be better to simply talk about interrelated processes, rather than using the forcing-feedback technobabble.

    • Anonymous says:

      Very likely there is NO direct link between the 20 and 60-70 year PDO cycles and the orbital periods of Jupiter and Saturn. What you are seeing is a dierct link between the PDO and the 20.3 and 62 year Lunar/solar tidal cycles. The

      It just happens that the Lunar/solar tidal cycles are indirectly linked with the orbital periods of the Jovian planets (primarily Jupiter and Saturn).

  6. Andrew says:

    Craig Goodrich-“when the solar wind reduces low-level high-energy rays, the rays are a feedback”

    How so? Feedback refers to changes that are caused by the temperature change initially caused by something else that reinforce or dampen it. The solar wind is not caused by the Earth’s temperature changes.

  7. maxwell says:


    thanks for the analysis. It seems physically reasonable, though I have to admit I have not yet checked out the Tang paper.

    Quick note. Do you think you could plot the results of running more physically-intuitive model with a high climate sensitivity? It would be nice to visualize how they differ from the results with a low climate sensitivity.

    Also, as the sensitivity gets higher, does the lag time between the solar and temperature change get smaller?

    Thanks for the explanation.

  8. Andrew says:

    Maxwell-Roy will probably want to answer this himself, but I just want to say regarding the question:

    “Also, as the sensitivity gets higher, does the lag time between the solar and temperature change get smaller?”

    I would say that based on my knowledge of the physics of these models, this is almost the opposite of how it would be expected to work. A more sensitive system normally responds more slowly to perturbation.

  9. […] Spencer on climate sensitivity and solar irradiance Posted on June 5, 2010 by Anthony Watts Updated: Low Climate Sensitivity Estimated from the 11-Year Cycle in Total Solar Irradiance […]

  10. Anonymous says:

    This paper also got a value close to 1.7, or 1.9 +/- 1


    Given the multitude of papers that put the value higher that 1.5, that statement in the IPCC report seems to be jsutified.

  11. Guy says:

    It seems like coming up with the increase in degrees celsius per doubling of CO2 levels is the type of thing that could be done in a laboratory setting.