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).
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Very clever indeed! However, is the detrended temperature immune from the heat island effects, such as sun on pavement.. Would that not influence the sensitivity you calculate?
Spencer:
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)
The 0.1K change is what we would expect from the variation of TSI, but explain what that has to do with the sensitivity to a doubling of CO2…
Sorry, but as you yourself admit, I find it hard to believe that you can pull any reliable conclusions out of such a small change in forcing. What are the uncertainties associated with the data being used? What are the uncertainties in the result achieved?
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.
With the recent realization that the alarmists really do not know how much we emit and appear to use speculation and opinion, it is not reasonable to assume that we are having a great effect on atmospheric CO2.
Unfortunately, the undiscriminating browser, who we want to become well informed, could mistake these discussions of climate sensitivity as discussions of an eventuality, which they are not.
Just a thought. I cannot wait to get out on those cold Maine waters next month. ‘Haven’t had my boat cruising the coast for many moons and have the fun of refitting for the first time in 38 years – time to update a few systems, I guess. There appears to be a bit of fog this year, which is what we had a lot of back in the early 70s.
Your note re the cloud albedo effect makes the rest of the calculations completely useless. It is not possible to calculate real world CO2 sensitivity without resolving this matter. Look at the AR4 WG1 report which is supposedly the basis for the Summary for Policy Makers but which in fact contradicts the latters scary projections. Look at WG-1 fig 2-20 ( page 203) this first wrongly allots all cloud albedo effect to anthropogenic factors when most of it is very likely a GCR forcing effect based on the suns magnetic field strength. Look at the error bars, ie uncertainty, of this effect then multiply that uncertainty by 2 as indicated as possible in the climate efficiency column . This would give an uncertainty factor of 3+- watts /meter which would completely obscure any CO2 effect. The notion that the projections of IPCC Temperature are 95% certain is completely unfounded based on its own science section. At this point we simply don’t know enough to make any convincing estimate of the sensitivity of the earths temperature to anthropogenic CO2.It is about time that the mainstream climate scientists acknowledged this.
Norman Page says:
June 5, 2010 at 9:19 pm
it is very likely a GCR forcing effect based on the suns magnetic field strength.
The Sun’s magnetic field right now is what it was 108 years ago. So, based on your ‘logic’ the climate should be the same today as back then…
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.
Secondly, if Camp and Tung are
wrongright, then the model attributions and projections are seriously under-representing a competing hypothesis for the source of recent warming:“Currently no GCM has succeeded in simulating a solar-cycle response of the observed amplitude near the surface. Clearly a correct simulation of a global-scale warming on decadal time scale is needed before predictions into the future on multi-decadal scale can be accepted with confidence.”
I’ve wondered about the implications of Lean and Rinds subsequent article since they find an amplitude of the signature of the solar cycle about half that of Camp and Tung. If they followed through with an estimate of observationally based climate sensitivity by the same method, would their estimate also be half as high?
“The 0.1 K (13-month mean) global solar cycle increase with modest warming at high latitudes (Figure 3) differs markedly from the 0.2 K solar cycle global increase dominated by significant high latitude warming that Camp and Tung [2007] derived by differencing solar cycle maximum and minimum epochs in the NCEP data. Their larger estimates of the solar cycle amplitude may be erroneous because of uncorrected volcanic cooling.”
http://yang.gmu.edu/eos754/paper/Lean2008GL034864-marked-attached.pdf
And this is based on the HadCRUT3 global surface temperature data? Sorry if I find this conclusion hard to believe. Before CO2 forcings are determined for sure maybe we need a solid temperature data set. pg
The eleven year cycle brings up another aspect that should probably be addressed by a post that goes up late on a Saturday night.
Does anyone else find it odd that whereas most stars only go to ten, ours goes all the way to eleven?
Anyone?
Correction:
“Secondly, if Camp and Tung are wrong …” should have been “Secondly, if Camp and Tung are RIGHT …”
Added note .The same figure also shows that the uncertainties in the Albedo effect completely overwhelm the effect of the small change in TSI during the solar cycle which is the commonly used by the AGW crowd to minimise the solar influence and enhance the GHG effect by comparison.
A much better analysis of the solar contribution to global mean surface temperature change is here:
N. Scafetta, “Empirical analysis of the solar contribution to global mean air surface temperature change,” Journal of Atmospheric and Solar-Terrestrial Physics 71 1916–1923 (2009), doi:10.1016/j.jastp.2009.07.007.
The 0.2 K found by Camp and Tung is too large for the 11-year solar signature signature on the surface record . The real value cannot go above 0.1 K, as found by numerous authors.
Moreover, everytime the climate sensitivity to solar irradiance or to anything the sun does is increased, the climate sensitivity to CO2 must be decreased because if not a model would nor reproduce the observed warming any more.
Moreover, as I explain many times in my works, the climate sensitivity calculated with empirical methods such as mine and those of Camp and Tung use TSI records as “proxy” model for the 11-year cycle. The 11-year solar signature on climate is not produced just by TSI alone, there are several other factors including cosmic ray effects, UV effects etc.
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.
The climate sensitivity to doubling of CO2 must be inferred indirectly by looking at other patterns. For example, in my paper just published it is argued that the climate sensitivity to CO2 doubling is 1/3 of what the IPCC has estimated. That is, something between 0.5 and 1.5 C.
Leif – don’t be disingenuous you know quite well that the earths climate – temperature – is the result of the complex interaction of many quasi cyclical processes of differing wavelengths . My point here was to show the IPCC reported uncertainty of the albedo effect . This applies whether the source of the change in albedo is GCRs or something else.
Doesn’t it all boil down to one thing?
Adjust here, homogenise there, assume that, this idea is mirrored by reality except when it isn’t, that idea isn’t mirrored by reality except when it is; we know this therefore that will occur but we can’t explain why that doesn’t always occur. It’s the sun. No, it’s the oceans. No, it’s the wobble of the planet around its variable axis. No its … add to the list as you will.
There is plainly and obviously no current authoritative answer. Draft the question how you will, the truthful answer is an unequivocal “who knows?”.
Leif Svalgaard says:
June 5, 2010 at 9:25 pm
I hope you are correct and it’s 1902, not 1802.
I don’t have any spot area data for 1802, but I have 1902 up and running:
http://www.robertb.darkhorizons.org/TempGr/SC24vs13_14.GIF
Changes made were
1.) Align solar minimums of SC13/14 & 14/15 to 2008.8
2.) Added the corrected flux
3.) divided Debrecen SC23/4 data by 1.1 (note from Tunde Baranyi) to fit with Greenwich data.
I’ll try another later on with umbral area data and see if a better fit to Flux results.
If it is 1902, then the rollup/rolldown of the last 7 months is a prelude to imminent ramp.
Almost the same thing happened with SC14/15.
🙂
You analysis still makes an assumption which constrains it, that of a first order lag model. I would advise you perform a cross correlation analysis, from which you can derive a more reliable system model. This is a fundamental reference. This is the one that really taught me how to do it many years ago. There may be a better reference on digital signal processing available today. MATLAB has routines for spectral analysis available in their Signal Processing Toolbox. There’ve have got to be rocket scientists on staff at UAH, or nearby at NASA, who might have their own canned routines for carrying this out, but at the very least might be valuable resources with whom to consult. Control systems people do this kind of stuff all the time.
I’ve been meaning to do this with the data you presented in your book, but just haven’t had the time. A cross correlation analysis might show definitively whether water vapor is a positive or negative feedback, irrespective of radiative or non-radiative forcing. All you should need to do is look for either a positive or negative phase slope in the frequency band of interest.
The above was addressed to Dr. Spencer.
who is lying?
http://weather.unisys.com/surface/sst_anom.html
or
http://www.osdpd.noaa.gov/data/sst/anomaly/2010/anomnight.6.3.2010.gif
George Turner says:
June 5, 2010 at 9:27 pm
Most Sun-like stars only go to ten.
They go down from zero, down through a minimum, then up through zero to maximum again, then down again – at ten, they are at zero.
What we do is, if we need that extra push down the cliff, you know what we do ?
Put it up to eleven years.
Eleven. Exactly. One longer.
It appears that they use both the 11 year cycle, and a small increase in TSI over the period, as signals in their analysis…..then go through a series of statistical acrobatics
If that’s all you have to do to get global warming grant money I could made my fortune
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!
Re: Bart on June 5, 2010 at 10:54 pm
Did you read Dr. Spencer’s article “How the UAH Global Temperatures are Produced“?
Did you read the About page on his site?
Have you done that, yet still are here providing your selections for basic digital signal processing references, mentioning freely-available tools, and suggesting he can check with the smart guys, the “rocket scientists,” at UAH, or perhaps NASA, for help like canned routines and additional info, so he can properly do a certain type of analysis?
stephan says:
June 5, 2010 at 11:32 pm
who is lying?
http://weather.unisys.com/surface/sst_anom.html
or
http://www.osdpd.noaa.gov/data/sst/anomaly/2010/anomnight.6.3.2010.gif
They both show the same thing but use different color scales. The NOAA one uses yellow (a warm color) starting at 0 degrees, while the Unisys one has green (a cooler color). The end result is that the NOAA map “looks” warmer than the Unisys map.
In a way the NOAA map tries to fool the reader into thinking there is warming going on where it is not, so in that sense is not entirely honest.
I wouldn’t go so far though as to say they are lying. All one has to do is look at the color scale to see which colors mean warming. But if one doesn’t look at the scale (most people?) one would get the impression of a world on fire.
stephan asked, “who is lying?” with respect to the differences between the Unisys and NESDIS SST maps.
They’re likely different datasets. The NESDIS “corral watch” uses nighttime satellite data only. They also don’t adjust for biases at high latitudes. Discussed here:
http://bobtisdale.blogspot.com/2009/09/note-about-sst-anomaly-maps.html
Dr Roy said:
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).
I think you missed the decimal point here Roy. Shouldn’t it be 0.6W/m^2 not 6?
On a more general note about the depth to which the ocean warms, the steric component of global sea level increase would indicate that heat-energy gets pushed down a lot futher below the well mixed layer, too as much as 1000m in some parts of the world. Quite how this energy transfer occurs is a bit of a mystery, but logic dictates that it must occur. It is worth remembering that sensible heat isn’t the only kind of energy storage in the ocean. I remember you were taken to task by Raymond Pierre-Humbug for your previous model which used the 1000m figure. My calcs show you were right!
The upshot of this is that the ocean stores and releases energy on longer timescales than previously thought, and that makes the effect of small multidecadal variations in TSI more effective in terms of global temperature change. My calcs showed that the steric component of sea level rise 1992-2002 indicated a thermal expansion of around 5200km^3 in the worlds oceans. The energy required to do that showed that the oceans were absorbing around an extra 4W/m^2 during that decade. This is way beyond anything co2 can do, so it must be down to the sun, amplified by cloud cover variation IMO.
It also proves that the variation in global temperature over the solar cycle is damped by energy absorption in the ocean, and thus that centennial variation in TSI has more effect on global temperature than generally accepted.