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).
Jeff Green says: “Data sets are showing in temperature change that the north polar reigion is increasing in temperature faster than the rest of the earth. About 2 to 3 times more. The melting of the artic ice which is one the most visible sensitive changes to observe, is loosing multi year ice every year. Part of the climate sensitivty measurement is a projected loss of ice and a warmig of the artic north waters. This is big. From there we get an ever northward moving of the thawing tundra. Which is another feedback that is postive for increasing the temperature of the earth.”
You are confusing the effect and the cause. There is no doubt that Arctic warming is real. But you immediately jump to the conclusion that it must be greenhouse warming. For your information, greenhouse warming is ruled out because Arctic warming started suddenly at the beginning of the twentieth century, after a two thousand year old steady, linear cooling trend. You ought to check your physics sometime. It is impossible for carbon dioxide to start a sudden warming without its partial pressure simultaneously taking a jump, and this did not happen. It is highly probable that the abrupt start of the warming was caused by a rearrangement of the North Atlantic current system at the turn of the century which directed the Gulf Stream unto its present northerly course.
The warming was interrupted from 1940 to 1960, then resumed, and continues to this day. It is impossible to explain this interruption by any carbon dioxide theory but variability of ocean currents makes it easily comprehensible. The Gulf Stream keeps the Russian Arctic ice free in the summer and has eaten away approximately one third of the Arctic sea ice that would otherwise exist. A smaller amount of warm water enters the Arctic through the Bering Strait. It is usually sufficient to keep the Chukchi Sea, just north of the strait, ice free.
But thanks to winds in 2007 more than the usual amount of warm water came through and created a large ice free bubble on the Bering Strait side of the Arctic while the Gulf Stream side of it changed only a little.These currents are sufficient to explain all past and present Arctic warming. No greenhouse effect or some magical arctic amplification needed.
Jeff Green says:
June 6, 2010 at 6:06 pm
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.
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Huh?
Circular reasoning at its best…and in its own negative feedback cycle.
Chris
Norfolk, VA, USA
Steve F. says:
“Oceanographer Josh Willis (at NASA JPL), has suggested an average value for the well mixed layer of 50 meters.”
Keep in mind the term “well mixed” implies a body of water with uniform temperatures which is not the case. It is always dangerous to deal with averages spread over a range of conditions that may for certain purposes be considered well mixed but in fact is not. Fact is even the “well mixed” zone is heavily stratified under normal weather conditions.
Jeff Green says:”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.”
This is quite confusing. First, correlation does not equal causality. He does not even mention that in those ice core data temperature rise precedes rise in CO2 values by as much as six hundred years. If you are looking for a cause and effect relationship, the cause is the one that comes first. Hence it was the temperature rise that caused the increase in CO2 and not the other way around. That calculation he cites is trivial and leads nowhere. I guess he means increase in GHG will make us warmer. That is just the point at issue: IPCC claims it does and Mikolczi has proven them wrong.
Arno Arrak says:
June 6, 2010 at 8:12 pm
@Jeff Green
This is quite confusing.
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You bet it is!
What I have read so far, every single one of Mr. Green’s posts are an encyclopedia of logical fallacies.
As I said before, anyone who “reasons” in a circular manner, entraps themselves [unless they work hard to set themselves free]…in their own, personal negative feedback cycle of cognitive dissonance.
Those that know little…or worse…those who argue with manipulation…should be quiet and listen more.
They might learn something.
Chris
Norfolk, VA, USA
Jeff Green,
“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?”
Solar activity was still unusually high during most of those 35 years. A solar maximum like we just experienced is unlikely to recur during the next century, but if it does presumably it may be as warm or warmer than last time, depending upon what the phases of the PDO and the NAO are. See Solanki’s work for perspective on how unusual the recent solar activity was.
Unless there is significant net positive feedback to CO2 forcing. Global temperatures will naturally vary up and down over the next century and possibly average on the order of a degree C higher towards the end of the century. Record high and record low years will probably occur during the mean time, given the short historical temperature record.
savethesharks says:
June 6, 2010 at 8:00 pm
Somebody forgot to clue Mr. Green in on Carbon Dioxide being a replacement gas in the atmosphere, with plenty of hungry plants competing for it.
Bill Hunter,
“Correct me if I am wrong but isn’t SW radiation less likely to be perturbed by the climate system than LW radiation? If so, and there is a difference in sensitivity, would it not be more likely that solar forcing would be more likely to have high sensitivity?”
SW radiation penetrates much deeper into the ocean’s mixing layer (10s of meters) than the CO2 infrared wavelengths which penetrate mere microns. That makes CO2’s coupling to the ocean a skin effect at a complex interface that is not properly captured in todays models. Yes, I would expect a higher sensitivity to solar radiative forcing than for CO2 forcing due to the lag caused by immediate dispersal in the thermal mass of the ocean, by corollary to Hansen’s understanding:
“The lag in the climate response to a forcing is a sensitive function of equilibrium climate sensitivity, varying approximately as the square of the sensitivity (1), and it depends on the rate of heat exchange between the ocean_s surface mixed layer and the deeper ocean (2–4). The lag could be as short as a decade, if climate sensitivity is as small as 0.25-C per W/m2 of forcing, but it is a century or longer if climate sensitivity is 1-C perW/m2 or larger.”
http://wattsupwiththat.com/2010/06/05/spencer-on-climate-sensitivity-and-solar-irradiance/#comment-404377
Any energy imbalance has to eventually end up in the oceans where most of the thermal mass of the climate system is. Solar energy’s route there is more direct. CO2 has to slow the loss of heat by the ocean, another surface effect, so is more likely end up in the latent heat of water vapor. This is without considering the possible non-radiative solar couplings to the climate.
An aptly named Green wrote :
If co2 increases we reflect more heat back to the earth
Even if there was much more other noise and nonsense in the post , this above quote is enough to show that the Green has no clue about pysics in general and CO2 in particular .
CO2 reflects nothing and certainly not heat .
Reflection has nothing to do here . Back to school .
I suspect that the Green is just another of the CAGW gang’s employees who had been given a set of links and predetermined sentences to post on blogs but who has no real understanding about the issues .
Set Green on ignore .
Since CO2 accumulates 90% to the 1900 foot off the planets surface, would not the CO2 theory reflect more solar radiation back out in space? After all, the higher you go up in the atmosphere, the less atmosphere there is.
Jeff Green says:
June 6, 2010 at 5:57 pm
TSI from 1880 to 1978 from Solanki. TSI from 1979 to 2009 from PMOD.
Colour me uimpressed. A proxy derived curve spliced to a model driven record whose chief investigator stands accused by the original data gathering mission scientists of applying inappropriate adjustments.
How about looking at the 17yr coronal hole cycle. We all know that one winter to the next can be many degrees different in temperature, so the big variable output of the sun would be the likely cause. This being the solar wind. If world temp`s followed SSN or radio flux, they would up and down like a roller coaster.
Joe Lalonde said on June 6, 2010 at 5:01 am:
“Have and hold” may require some closer defining to get a proper answer. I’ll try anyway.
Much of what is called water’s ability to “have and hold” is due to it being a polar molecule. Stuff dissolves in it, the result being called an aqueous solution. When common salt (NaCl) dissolves in water, it separates into Na+ and Cl- ions. CO2 in water becomes carbonic acid. Water can form other mixtures like suspensions and colloids.
CO2 is a non-polar molecule so that limits its ability to “have and hold” other molecules. It also is not found under normal Earth conditions in solid and liquid forms, another limitation. As a gas it doesn’t do much. Chemically speaking, in solutions the substance present in the greatest amount is generally called the solvent, thus normal Earth atmosphere can be called a solution of gases dissolved in nitrogen which is the predominant gas. Likewise you could have a solution of other gases dissolved in CO2. But generally molecular interactions between gases are so rare that such are just referred to as mixtures, plain and simple.
So CO2’s ability to “have and hold” trace elements and other molecules is effectively nil in any real sense, especially when considered relative to water.
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Joe Lalonde said on June 7, 2010 at 3:14 am
CO2 does not “reflect” solar radiation. It absorbs radiation of a certain few wavelengths, then radiates the energy outwards, which a CO2 molecule can do in any direction. For what makes it a “greenhouse gas,” it absorbs infrared light coming from the ground in those wavelengths, then emits the energy. About half of that energy goes back towards the ground, half outwards to space.
Charles Higley says:
June 5, 2010 at 9:03 pm
I greatly appreciate the discussion on climate sensitivity, but it should be included every now and then, for the reading public, that the doubling of atmospheric CO2 regularly mentioned in climate sensitivity does not mean that it will be doubling in the future.
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.”
Would appreciate comments and references on this.
Jeff Green says:
June 6, 2010 at 2:27 pm
Data sets are showing in temperature change that the north polar reigion is increasing in temperature faster than the rest of the earth. About 2 to 3 times more. The melting of the artic ice which is one the most visible sensitive changes to observe, is loosing multi year ice every year.
Hi Mr. Green.
Let me declare my view: Lately I come to like the global warming Anthropo – Genic or not, and further more I would like it to be Anthropo rather than anything else Genic, since we could keep it going, god forbid another Little Ice Age.
However my hope may be somewhat forlorn. As far as the Arctic is concerned the old Gaia may have another answer, her two shaking magnetic arms appear keep warming the Arctic ocean as shown here:
http://www.vukcevic.talktalk.net/NFC1.htm
So may we declare it Geogenic Global Warming or GGW and hope for the best .
Thank you kadaka (KD Knoebel).
Interestly enough, if our planet had 100 times more pressure, then we would have liquid CO2 pools.
The research I have been doing has been showing that trace elements actually play a role in our planets evolution.
http://www.skepticalscience.com/climate-sensitivity.htm
Climate sensitivity from models
The first estimates of climate sensitivity came from climate models.
•In the 1979 Charney report, two models from Suki Manabe and Jim Hansen estimated a sensitivity range between 1.5 to 4.5°C.
•Forest 2002 uses a fingerprinting approach on modern temperature records and finds a range 1.4 to 7.7°C.
•Knutti 2005 uses modelling (entering different sensitivities then comparing to seasonal responses) to find a climate sensitivity range 1.5 to 6.5°C – with 3 to 3.5 most likely
•Hegerl 2006 looks at paleontological data over the past 6 centuries to calculates a range 1.5 to 6.2°C.
•Annan 2006 combines results from a variety of independent methods to narrow climate sensitivity to around 2.5 to 3.5°C.
•Royer 2007 examines temperature response to CO2 over the past 420 million years and determines climate sensitivity cannot be lower than 1.5°C (with a best fit of 2.8°C).
Climate sensitivity from empirical observations
There have been a number of studies that calculate climate sensitivity directly from empirical observations, independent of models.
•Lorius 1990 examined Vostok ice core data and calculates a range of 3 to 4°C.
•Hoffert 1992 reconstructs two paleoclimate records (one colder, one warmer) to yield a range 1.4 to 3.2°C.
•Hansen 1993 looks at the last 20,000 years when the last ice age ended and empirically calculates a climate sensitivity of 3 ± 1°C.
•Gregory 2002 used observations of ocean heat uptake to calculate a minimum climate sensitivity of 1.5.
•Chylek 2007 examines the period from the Last Glacial Maximum to Holocene transition. They calculate a climate sensitivy range of 1.3°C and 2.3°C.
•Tung 2007 performs statistical analysis on 20th century temperature response to the solar cycle to calculate a range 2.3 to 4.1°C.
•Bender 2010 looks at the climate response to the 1991 Mount Pinatubo eruption to constrain climate sensitivity to 1.7 to 4.1°C.
Here are papers discussing climate sensitivity. With fast feedbacks combined with slow feedbacks 3.0 degrees centigrade is the agreed upon.
Schwartz did a paper of 1.1 c sensitivity over five years for different perturbations. With different comments on his paper he extended his time period out to 8.5 years to get 1.9 c sensitivity. It does appear that climate sensitivity over time gets higher due to feedbacks.
[tallbloke says:
June 7, 2010 at 3:28 am
Jeff Green says:
June 6, 2010 at 5:57 pm
TSI from 1880 to 1978 from Solanki. TSI from 1979 to 2009 from PMOD.
Colour me uimpressed. A proxy derived curve spliced to a model driven record whose chief investigator stands accused by the original data gathering mission scientists of applying inappropriate adjustments.]
http://www.globalwarmingart.com/wiki/File:65_Myr_Climate_Change_Rev_png
The PETM is all proxy. What we have learned is that the earth rapidly gained co2 in that time period in which one the great extinctions took place. We are emitting into our atmosphere co2 faster than that period.
Bob Tisdale says:
June 6, 2010 at 2:52 am
…
“So the one-year ocean lag is closer than the multiyear lags suggested in other papers.”
Isn’t the lag in relation to the cycle length more important than the absolute lag. When I looked at mid latitude SST’s, I found the lag to be about 80 days from solstice. For inland mid-latitude temps, I found the shortest lags to be about 30 days. Converting this to an 11 year cycle, we should see a lag of between 1 to 2.5 years, presumably weighted towards the 2.5 value. I think Dr. Spencer’s calculated lag is too short.
Interestingly the Willis paper you cite has a lag that is > 1/4th of a cycle. Assuming clear sky/sinusoidal irradiance cycle and a Newton Model of Cooling, the lag should be less than 1/4th of a cycle. But then again we actually have real sky irradiance and the tropics have two solar irradiance peaks per year. Also, Newton’s Model might not be appropriate for modeling ocean heat transfer. But I still find it interesting that your SST lag is shorter than Willis’s steric lag. How can the SST be cooling and the column still be expanding?
AJ
AJ says:(June 8, 2010 at 8:56 am)
“Isn’t the lag in relation to the cycle length more important than the absolute lag. When I looked at mid latitude SST’s, I found the lag to be about 80 days from solstice. For inland mid-latitude temps, I found the shortest lags to be about 30 days. Converting this to an 11 year cycle, we should see a lag of between 1 to 2.5 years, presumably weighted towards the 2.5 value.”
But cycle lengths AVERAGE 11 years. Only one was exactly 11 years (cycle 1) and the majority of cycles have lengths outside the 10.5 to 11.5 range. Wouldn’t those variances skew any results based on using an 11 year fixed cycle?
Jeff Green,
In comment-405285 you paste in a list of climate sensitivity studies from another site, the most recent ones have probably been discussed previously. Since you just cut and pasted without discriminating I can’t tell how prepared you are to discuss them. Did you just expect us to be impressed by the length of the list?
Did you notice that Camp and Tung had already been discussed up above and that there are articles that approximately halve their results. Bender 2010 is misclassified and should actually be considered model based.
Knutti and Hegerl is a better summary, but is already out of date:
http://www.iac.ethz.ch/people/knuttir/papers/knutti08natgeo.pdf
We can dismiss the model based studies until they have a couple more generations under their belt addressing correlated and other diagnostic errors. The paleo estimates usually have the problems are large uncertainties in the forcings and temperatures, cover longer time frames and cross climate modes or tipping points. Volcanic aerosol and solar sensitivity estimates from the current climate should not be assumed to be the same as the CO2 sensitivity.