Updated: Low Climate Sensitivity Estimated from the 11-Year Cycle in Total Solar Irradiance
By Dr. Roy W. Spencer
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.
Discussion
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).
vukcevic says:(June 6, 2010 at 8:43 am)
“You can use this until you come across something better.
http://www.vukcevic.talktalk.net/SSCsl.htm
Cheers.”
Thanks. Just a follow-up observation of cycle lengths. Yes, the average cycle length is a tiny bit over 11 years. But, if the cycles are divided into 3 groups:
a. less than 10.5 years
b. 10.5 to 11.5 years
c greater than 11.5 years
it shows that there were only 6 cycles in the b group, 8 cycles in group a and 9 cycles in group c. So maybe that citing the “11 year average” is a bit misleading.
Also, cycles appear to randomly vary in lengths, some substantially cycle to cycle, but cycles 15 – 19 are very close to the same length. Is there a reason for that?
[stumpy says:
June 5, 2010 at 11:49 pm
Obviously if the sun does influence global albedo in some way, the earths sensitivty to changes in TSI could be considerably different to the earths sensitivity to other factors such as green house gasses, and the GCR theory would add an amplification. There is little to support the amplification with co2. We could be comparing apples with oranges!]
Total solar iradiance cancels itself out during the cycle from solar min to solar max back to solar min.
http://www.skepticalscience.com/solar-activity-sunspots-global-warming.htm
In the last 35 years of global warming, the sun has shown a slight cooling trend. Sun and climate have been going in opposite directions.
The rest of the article goes into the detailed explanation of the effect of the sun upon climate sensitivity.
The sun is radiating slightly less and yet we are warming. co2 is like a one way valve letting the sun’s radiation in and reradiating back to earth some of the energy on its way back out to space. This is the whole crux of climate change theory. By observations the scientific community is observing 3 degrees centigrade increase in temperature with a doubling of co2
[Martin Lewitt says:
June 5, 2010 at 9:26 pm
I not sure what comfort the skeptic can derive from Camp and Tung’s estimate of climate sensitivity, for one, it is an estimate of climate sensitivity to solar forcing, and there is no reason to assume that the climate sensitivity to CO2 forcing is the same, given how differently the forcings are coupled to the climate system.]
http://en.wikipedia.org/wiki/Climate_sensitivity
We have a climate sensitivity to the really small changes in the sun and the sun has mildly decreased over the last 35 years. Add on to that a world temp record might occur this year depending on how strong the La Nina is. During solar minima. What will happen during solar maxima?
[S.E. Hendriksen says:
June 6, 2010 at 7:54 am
@Charles Higley
Hi Charles
>>With the 50 to 1 partitioning between sea and air, we would be hard put to raise CO2 by 20% if we tried by burning all our available carbon.<<
Prof. Tom V. Segalstad (Oslo Norway) made that calculation long time ago when the CO2 level in the atmosphere was 380 PPMv… if you burn all known fossil fuel, it will end up with 456 PPMv in the atmosphere (a rise of 20 %), so a doubling of the CO2 in the atmosphere is not possible due burning fossil fuel.]
I disagree with your statement.
http://www.globalwarmingart.com/wiki/File:Carbon_Stabilization_Scenarios_png
This figure shows a range of simulated trajectories for carbon dioxide (CO2) that would result in stabilization of the atmospheric carbon dioxide concentration at between 450 and 1000 parts per million by volume (ppmv), and the variations in industrial emissions (expressed in gigatonnes carbon per year [GtC/yr]) that would be required to realize those trajectories.
As is illustrated here, stabilization at 1000 ppmv or less is likely to require that CO2 emissions reach a maximum during the course of this century and are subsequently reduced to levels below present day. The oceans and atmosphere are presently able to absorb ~40% of modern emissions made each year, so immediate stabilization at present day levels (380 ppmv) would require an immediate 60% reduction in emissions.
If you choose to read the article, the scientists seem to agree we can reach 1000 parts per million. Our oceans only absorb 40% of our co2 emissions. In one of my postings above 2006 was 28 gigatons of co2. Approximately 17 gigatons per year will go into the atmosphere. The 50 to 1 ratio just doesn't hold up.
[tallbloke says:
June 6, 2010 at 10:53 am
Arno Arrak says:
June 6, 2010 at 9:53 am
Climate sensitivity to doubling of CO2 is big on the agenda of true believers in AWG. But it is a dead issue because the work of Ferenc Mikolczi has shown that it may not even exist. He worked for NASA but his work first appeared in an obscure Hungarian journal in 2007. When his supervisors realized what he had done he was told not to talk about it, so he quit.]
Spencer has shown he believes in climate sensitivity, giving it a 1.75.
http://en.wikipedia.org/wiki/Climate_sensitivity
Spencer was also at the Unipcc for the fourth publishing.
Jeff Green says @2:43 pm:
“By observations the scientific community is observing 3 degrees centigrade increase in temperature with a doubling of co2.”
You have my attention.
Please provide a reference/citation of those observations showing a 3°C temperature rise from a doubling of CO2.
Omit anything resorting to models or to adjusted numbers, as that is conjecture. Show empirically that the rise in temperature has been observed to be caused by CO2; and that the rise in temperature and CO2 are not coincidental anomalies, and that CO2 is not rising as the effect of increasing temperature, but is the observed cause of increasing global temperature.
You stated that this is the whole crux of climate change theory. Please provide testable evidence that CO2 is the driver of the climate. Thanks.
wayne says:
June 6, 2010 at 1:55 pm
Indeed, every time people get excited about returning sunspots and activity, the sun turns off again for a few days. This cycle looks like it will be much reduced in amplitude and the next should be lower still. Nick Scafetta predicted this in a previous post:
http://wattsupwiththat.com/2010/03/14/dr-nicolas-scaffeta-summarizes-why-the-anthropogenic-theory-proposed-by-the-ipcc-should-be-questioned/
where he superimposed the last few solar cycles on the solar wavetrain prior to one of the previous minima (dont remember which).
The climate establishment is still in denial of this decline – perhaps subconsciously some of them know what it spells for the future.
[Nicola Scafetta says:
June 5, 2010 at 9:52 pm
… Therefore the climate sensitivity to doubling of CO2 cannot be calculated by simply using a regression model between the 11-year TSI cycle and the equivalent cycle found in the temperature. The two things are apples and oranges.]
From what I can gather from reading the first paragraph, there has been a great deal of work going on on just that.
http://www.amath.washington.edu/research/articles/Tung/journals/solar-jgr.pdf
1. Introduction
Although previously attention has been focused on the UV part of the solar cycle and its absorption by ozone in the stratosphere, the amount of the total solar irradiance (TSI) reaching the earth’s surface is not negligible. The observed 0.90 Wm-2 variation of the solar constant from solar min to solar max in the last three solar cycles translates into a net radiative heating of the lower troposphere of 0.900.85 Q=4δi~0.19 Wm-2. The factor of 4 is to account for the difference between a unit area on the spherical earth and the circular disk on which the solar constant is measured, while 0.85 is to account for the 15% of the TSI variability that lies in the UV wavelength and is absorbed by ozone in the stratosphere with the remaining reaching the lower troposphere, the surface and the upper ocean [Lean, et al., 2005; White, et al., 1997]. This solar radiative forcing is about 1/20 that for doubling CO2 (δQ~3.7 Wm-2). Thus the annual rate of increase in radiative forcing of the lower atmosphere from solar min to solar max happens to be equivalent to that from a 1% per year increase in greenhouse gases, a rate commonly used in greenhouse-gas emission scenarios [Houghton and et al., 2001]. So it is interesting to compare the magnitude and pattern of the observed solar-cycle response to the transient warming expected due to increasing greenhouse gases in five years.
The
{Arno Arrak says:
June 6, 2010 at 9:53 am
Climate sensitivity to doubling of CO2 is big on the agenda of true believers in AWG. But it is a dead issue because the work of Ferenc Mikolczi has shown that it may not even exist. He worked for NASA but his work first appeared in an obscure Hungarian journal in 2007. When his supervisors realized what he had done he was told not to talk about it, so he quit. His latest work is in E&E, Volume 21, No. 4 (2010). He shows that IPCC method of determining the water vapor feedback mechanism is error-prone and uses empirical data from sixty one years of radiosonde measurements to prove that feedback of water vapor effect on greenhouse-gas optical thickness is strongly negative, thoroughly contradicting the IPCC doctrine of it being positive. What this means is that computer models used by IPCC in predicting warming are all in error. In fact, if his theory stands there is no AGW now and there never was any. Warming, yes, but only of the natural kind.}
The ice cores from the last 800,000 years show a really strong correlation between co2 and temperature. Calculations are done to give the example that the earth would be an ice ball without GHG. So going the opposite direction, too much ghg’s will make us warmer no matter what the source human or the natural cycle of earth.
Jeff Green says:
June 6, 2010 at 3:01 pm
the sun has mildly decreased over the last 35 years.
Cobblers.
It had well above average TSI and sunspot numbers from the late 70’s to 2003.
The Global temperature has on average fallen since 2003.
Smokey says:
June 6, 2010 at 3:23 pm
Jeff Green says @2:43 pm:
http://www.pik-potsdam.de/~stefan/Publications/Book_chapters/Rahmstorf_Zedillo_2008.pdf
What you are asking for is pretty detailed. This is a readable article by one of the more experienced scientists in the field.
Jeff Green,
Wikipedia is not an authority on climate science. It promotes an incredible, one-sided alarmist view that hand-waves pro-CAGW opinion through, while repeatedly interfering with and deleting authoritative skeptical responses. William Connolley moderates Wikipedia and RealClimate. Please use credible references, there are plenty out there. Thanks.
Prof Don Easterbrook states:
And Prof Richard Lindzen states that the CO2 sensitivity number might be 2°F — not 2°C — and that negative feedbacks may well negate even this small number. Even without negative feedbacks, a 2°F rise in global temperatures is to be desired, not feared.
Regarding your assertion that “ice cores from the last 800,000 years show a really strong correlation between co2 and temperature”, correlation is not causation. Note that those ice core samples consistently show that CO2 rises as an effect of rising temperature. Effect can not precede cause, therefore using the ice core data to support the CO2=CAGW hypothesis fails.
Jeff Green says:(June 6, 2010 at 3:46 pm)
“The ice cores from the last 800,000 years show a really strong correlation between co2 and temperature. Calculations are done to give the example that the earth would be an ice ball without GHG. ”
It is quite annoying when you first refer to CO2 and then morph into GHG.
Water vapor, as we all know, is the dominant GHG. You are not fooling anyone with your subtle switch in mid paragraph. Furthermore, we are all aware what GHGs do to keep the Earth from freezing but that is not the argument.
Anthony,
Have you seen this?
http://www.rocketscientistsjournal.com/2010/03/sgw.html
IPCC hoisted on it’s own data.
Would you be interested in getting people to discuss this in a separate post. It seems another point of view on TSI.
[Smokey says:
June 6, 2010 at 4:01 pm
Jeff Green,
Wikipedia is not an authority on climate science. It promotes an incredible, one-sided alarmist view that hand-waves pro-CAGW opinion through, while repeatedly interfering with and deleting authoritative skeptical responses. William Connolley moderates Wikipedia and RealClimate. Please use credible references, there are plenty out there. Thanks.]
This is an article written by Stefan Rahmsdorf, one of the leading climatologists in the world. He has a few pages refuting Richard Lindzen in his assertion that climate sensitivity is small. Which means Richard LIndzen recognizes climate sensitivity and the effect of co2 reflecting infrared back to the earth.
[Smokey says
Regarding your assertion that “ice cores from the last 800,000 years show a really strong correlation between co2 and temperature”, correlation is not causation. Note that those ice core samples consistently show that CO2 rises as an effect of rising temperature. Effect can not precede cause, therefore using the ice core data to support the CO2=CAGW hypothesis fails]
I don’t expect to reach your absolute proof. CO2 is a postive feedback to the orbital and axial forcing. There is causal relationship to the temperature of the past. CO2 is a clearly proven GHG. It will never be disproven by anyone. If co2 increases we reflect more heat back to the earth. Hence temperature increase.
Well I’ll be: I just learned from watching a story on “Need to Know”, that the FTC requires those who blog for pay, to disclose their paid status.
Don’t look at me. Nary a penny has graced my mailbox.
The use of “HadCRUT3 global surface temperature anomalies”, while better in
quality than GISS temp anomalies, still leaves a lot of arbitrary modeling
assumptions lurking within Dr. Spencer’s commentary that aren’t accounted
for, compensated for, or even documented within the study. (See P.G. Sharrow’s
comment, above.)
A HadCRUT3 dataset stripped of all the accumulated “adjustments” save for
faulty equipment would add to the credibility of any paper looking at the
“relationship between TSI variations and temperature”.
[tallbloke says:
June 6, 2010 at 3:47 pm
Jeff Green says:
June 6, 2010 at 3:01 pm
the sun has mildly decreased over the last 35 years.
Cobblers.
It had well above average TSI and sunspot numbers from the late 70′s to 2003.
The Global temperature has on average fallen since 2003.]
http://www.skepticalscience.com/solar-activity-sunspots-global-warming.htm
Figure 1: Annual global temperature change (thin light red) with 11 year moving average of temperature (thick dark red). Temperature from NASA GISS. Annual Total Solar Irradiance (thin light blue) with 11 year moving average of TSI (thick dark blue). TSI from 1880 to 1978 from Solanki. TSI from 1979 to 2009 from PMOD.
Other studies on solar influence on climate
If you choose to read the rest of the article there are several papers based in science showing the point I’m making.
[Tom in Florida says:
June 6, 2010 at 4:14 pm
Jeff Green says:(June 6, 2010 at 3:46 pm)
“The ice cores from the last 800,000 years show a really strong correlation between co2 and temperature. Calculations are done to give the example that the earth would be an ice ball without GHG. ”
It is quite annoying when you first refer to CO2 and then morph into GHG.
Water vapor, as we all know, is the dominant GHG. You are not fooling anyone with your subtle switch in mid paragraph. Furthermore, we are all aware what GHGs do to keep the Earth from freezing but that is not the argument.]
H2O will become a positive feedback to co2. From an increase in co2 more H2O will be in the atmosphere increasing the total GHG effect due to higher temperature.
@Jeff Green
“By observations … 3.0 degrees… per doubling”
What observations? This has been forecast based on tweaking tuning constants in models based on the asumption that all of the temperature increase in the past cyclical upswing was anthropogenic because Mann said it was. He lied. Also, it is not nearly as warn now compared to prior peak periods as Hansen would have us believe.
Bill Hunter says:
June 6, 2010 at 12:59 pm
The well mixed layer ends at the point where the thermocline begins, and is where the temperature falls with increasing depth instead of being almost perfectly constant. Here are ten randomly grabbed values for the depths (in meters) of the well mixed layer from ARGO floats currently located in the tropical Atlantic, Pacific, and Indian oceans: 92, 80, 91, 25, 50, 30, 75, 125, 70, 51. The average for these ten is 68.9 meters (if I have done the math right). An average value of 25 meters for the well mixed layer seems too low. Oceanographer Josh Willis (at NASA JPL), has suggested an average value for the well mixed layer of 50 meters.
Jeff Green,
Your link to Dr Stefan Rahmsdorf expresses his opinion. He is an oceanographer who calls himself a climatologist. [Maybe that’s all it takes these days.]
In your link Dr Rahmsdorf argues that Dr Lindzen is wrong, and he is right. Why would he feel the need to do that, if the sensitivity number was clearly established? From the 1st IPCC Assessment Report onward the sensitivity number has declined.
In your link, Rahmsdorf bases much of his argument on an appeal to the authority of Svante Arrhenius, who made the first estimate of climate sensitivity to CO2 in 1896 as a hobby, when he estimated up to 6°C warming for a doubling of atmospheric CO2.
But Rahmsdorf omits the fact that in his 1906 paper, Arrhenius had recalculated, and greatly reduced his sensitivity estimate to only 1.6°C. This is a much lower number than Rahmsdorf claims. But it doesn’t fit the CO2 alarmism upon which so much grant income depends, so Rahmsdorf never mentions the 1906 paper.
Rahmsdorf also hand-waves away Lindzen’s methodology, saying that the sensitivity number simply must be high, and that unknown factors support his conclusion: “….there is no viable alternative explanation. In the scientific literature, no serious alternative hypothesis has been proposed to explain the observed global warming.”
Do you see what Rahmsdorf is doing here? He is basing his conclusion on an argumentum ad ignorantiam: the fallacy of assuming that something is true, simply because it hasn’t been proven false. A major part of the catastrophic global warming scare employs this same fallacy.
The climate’s sensitivity to CO2 is 1°C or less. Rahmsdorf admits that. But then he argues that various positive feedbacks make the sensitivity several times higher. That kind of conjecture is fine, as long as you understand that it is simply a conjecture, and not backed by any testable, empirical evidence.
Further, there must be, a priori, many more negative feedbacks than positive feedbacks. Feedbacks cancel when the signs are opposite. We do not know nearly all the climate feedbacks with any precision. It is entirely possible, and in fact seems likely, that water vapor feedback is canceled by one or more negative feedbacks; the planet is clearly not warming as predicted.
What I had originally responded to was your assertion that “…the scientific community is observing 3 degrees centigrade increase in temperature with a doubling of co2.” That is not correct. There has been no such empirical ‘observation.’ If there had been, Prof Lindzen and others would not destroy their hard earned credibility by continuing to debate a settled issue.
Jeff Green says:(June 6, 2010 at 6:06 pm)
” From an increase in co2 more H2O will be in the atmosphere increasing the total GHG effect due to higher temperature.”
You have no clue do you. Now I know how Leif feels.
Several years back Willis E. demonstrated in the comments section of a posting at this website that the direct effect of a change in TSI and that of an equivalent forcing in W/m2 by CO2 are not the same. A change in TSI adds or reduces heat input into the entire climate system. However, an equivalent change in forcing from CO2 suffers from losses due to convection etc. If my memory serves me correctly the effect of a globaly averaged change in TSI is 1.6 times greater than the equivalent forcing by CO2. Perhaps another reader has a clearer memory of that exchange than I do. It related to the “spherical iron greenhouse” hypothesis.
I suspect Roy Spencer might need to consider this lack of equivalence in his assessment of the sensitivity of climate to forcing by CO2