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Solar Cycle Model fails to predict the recent warming

Posted on 19 December 2012 by Hans Petter Jacobsen

Jan-Erik Solheim, Kjell Stordahl and Ole Humlum have recently published two papers supporting the myth that the sun is behind the recent climate changes. They make a model based on variations in the lengths of the solar cycles. The model predicts that we are now in a decade with sharply falling temperatures.

However, as will be shown in this post, the model fails to keep up with the recent global warming. Temperatures fitted well with the model until the mid-1970s, but not later. It is therefore extremely unlikely that the prediction about sharply falling temperatures in this decade will be right.

The solar intensity varies by approximately 0.1% over a solar cycle. Both the variations and the average value of the intensity differ a little from one cycle to the next. These variations are a solar radiative forcing that affects the energy balance of the Earth. A solar cycle lasts on average for just over 11 years. The previous solar cycle, number 23, ended in November 2008 after having lasted for an unusually long time, well over 12 years. The current solar cycle 24 will probably last for the rest of the decade.

Jan-Erik Solheim, Kjell Stordahl and Ole Humlum (hereafter SSH) find a relationship between the mean temperature in a solar cycle and the length of the previous solar cycle [1, 2], which we will refer to as the Solar Cycle Model: A long solar cycle is followed by a solar cycle with a low temperature, and a short solar cycle is followed by a solar cycle with a high temperature.

When a solar cycle has ended, its length is known, and the model can predict the temperature in the next solar cycle. Due to the long solar cycle 23, the model predicts that we are now in a solar cycle with sharply falling temperatures.

In this blog post, observed mean temperature is the average of the observed global surface temperatures in a solar cycle, and predicted temperature is the prediction by the Solar Cycle Model for the mean temperature in a solar cycle. A prediction is calculated based on the observed mean temperatures in the previous solar cycles and the lengths of the previous solar cycles.

Results based on temperatures in the northern hemisphere

SSH concentrate on some local temperature series from the northern hemisphere. The HadCRUT3 NH temperature series contains the combined land and sea surface temperatures for the entire northern hemisphere. We first examine how this series matches the Solar Cycle Model.

Figure 1 shows the observed mean temperatures in solar cycles 10 to 23 as blue circles, and the mean temperature observed so far in the current solar cycle 24 as a blue star. It also shows the predicted temperatures in solar cycles 14 to 24 as red stars. The horizontal positions of the temperatures are in the middle of the solar cycles that they represent.

Solar cycle model fails - blog post - Figure 1

Figure 1. The observed and predicted temperatures up to now. 

Figure 1 shows that the observed mean temperatures in solar cycles 21 to 23 are much higher than predicted.

SSH predict sharply falling temperatures in the current solar cycle 24. But the mean temperature observed so far in solar cycle 24 is much higher than predicted. Solar cycle 24 still has many years to go, and the situation may of course change. But given the failures of the predictions for cycles 21 to 23, and the high mean temperature observed so far in cycle 24, the model's prediction for cycle 24 is extremely unlikely to be right.

Figure 2 shows the temperatures in solar cycles 10 to 21 as a function of the length of the previous solar cycle. Solar cycle 21 ended in October 1986.

Solar cycle model fails - blog post - Figure 2

Figure 2. The observed mean temperatures up to and including solar cycle 21, and the prediction for cycle 21, as a function of the length of the previous solar cycle.

The blue trend line sloping downwards in Figure 2 is the best fit to the blue circles, which show the observed mean temperatures in solar cycles 10 to 20. The trend is calculated with linear regression analysis. The observed mean temperatures fit well with the Solar Cycle Model when they are close to the trend line, and they do not fit well when they are far away from it.

Solar cycle 20 lasted for 11.6 years, and the prediction for solar cycle 21 is therefore on the trend line at the horizontal value 11.6 years. The dotted red lines show the 95% confidence interval (uncertainty range) for the prediction.

The observed mean temperature in solar cycle 21 is displayed as a blue star in Figure 2. It is far above the upper limit of the 95% confidence interval around its prediction. According to the model, there is only a 0.41% probability of measuring such a high mean temperature in solar cycle 21.

Solar cycle 20 ended in June 1976. Figure 2 shows that the temperatures measured before the mid-1970s fit very well with the Solar Cycle Model, but that temperatures in the first solar cycle after the mid-1970s do not. Figure 2 shows when the Solar Cycle Model collapsed with respect to the ability to predict future temperatures.

The current solar cycle 24 started in December 2008, and it will probably last for the rest of the decade. Figure 3 shows how the Solar Cycle Model predicts its temperature, just as Figure 2 did for cycle 21.

Solar cycle model fails - blog post - Figure 3

Figure 3. The observed mean temperatures up to now, and the prediction for cycle 24, as a function of the length of the previous solar cycle.

Due to the high temperatures in solar cycles 21 to 23, the blue circles in Figure 3 are no longer close to the blue trend line. The observed mean temperatures in solar cycles 10 to 23 as a whole do not fit with the Solar Cycle Model, causing the uncertainty of the model to increase and thereby the confidence intervall around the prediction to expand. Despite the greatly expanded confidence interval, the mean temperature observed so far in solar cycle 24 is far above the upper limit of the 95% confidence interval around its prediction. 

Results based on other temperature series

This blog post concentrates on the temperatures in the northern hemisphere, and it therefore shows results based on the HadCRUT3 NH temperature series. Results based on the global HadCRUT3, NASA GISS and NCDC temperature series are about the same as the results based on HadCRUT3 NH; i.e. the observed mean temperatures match the predictions until the mid-1970s, but not later. SSH also use the HadCRUT3 NH temperature series, but they place more emphasis on some local temperature series.

This blog post is a basic version of a longer article. It shows that the median of the results based on the local temperature series also diverges from the Solar Cycle Model predictions after the 1970s, in about the same way as does the results based on the HadCRUT3 NH temperature series. The longer article also contains more explanations, plots and statistics.


If there is a real, physical reason why temperatures fitted so well with the Solar Cycle Model until the mid-1970s, that reason must be a solar radiative forcing. If so, this forcing must still be present after the mid-1970s, although it no longer dominates. Another forcing, or several, must have become dominant. My analysis says nothing about what the new dominant forcing(s) may be. But it is natural to think of the human-induced forcings, which many scientists claim became dominant in the 1970s.

Skeie et al [3] show that the sum of the various human-induced forcings first became positive in the 1970s. Before 1970, the sum was small and the sign varied. After 1970, the sum has increased steadily up to a substantial positive value in 2010. This is the probable explanation why there is an increasing gap between the Solar Cycle Model's predictions and the observed mean temperatures after the middle of the 1970s.


A special thanks to Christian Moe for valuable comments and for language editing.


1. Solar Activity and Svalbard Temperatures  
Jan-Erik Solheim, Kjell Stordahl and Ole Humlum.

2. The long sunspot cycle 23 predicts a significant temperature decrease in cycle 24 
Jan-Erik Solheim, Kjell Stordahl and Ole Humlum.

3. Anthropogenic radiative forcing time series from pre-industrial times until 2010
Skeie et. al.

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Comments 1 to 21:

  1. Nice, thank you!
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  2. Excellent work, Hans Petter! Great to see some sensible stuff coming out of Norway, pretty rare these days. I remember seeing a presentation of SSH's work in an article in the newspaper Aftenposten last year. I emailed the journalist and told her to do a follow up interview with SSH in 2014. We'll see if that happens. Could be interesting. A record warm 2013 or 2014 (depending on ENSO) could mean big trouble for the deniers. I say could, because the science side has not been nearly good enough at highlighting the failed cooling predictions of the denial movement (going back to at least 2007) A failed prediction is something the average Joe understands, but so far, the deniers have been allowed to fail time after time without the public getting informed.
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  3. It seems that if you just number the dots by cycle number in their diagrams, the increasing failure of the model after cycle 20 is blatantly obvious. How can they have failed to think of this?
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  4. Very nice post, thanks for looking into this. I wonder, how would this look using data from HadCRUT4?
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  5. Thanks for the feedbacks. It is great that Esop asked the newspaper to do a follow up inteview with SSH in 2014. When I downloaded the temperatures from the internet in May/June 2012, the HadCRUT3 NH temperature anomalies were available up to and including March 2012. The model's prediction for solar cycle 24 (SC 24) is -0.381°C. The mean temperature in SC24 up to and including March 2012 is +0.505°C, which is plotted in Figure 1 and 2. Now the HadCRUT3 NH temperatures are available up to and including October 2012, and the mean temperature observed so far in SC24 has risen to +0.525°C. This makes it even less likely that the temperature in SC 24 will be as low as predicted by SSH.
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  6. These two papers by Solheima Stordahlb & Humlum are classics of the genre - nonsense presented to look like scientific argument. The graph-fest presented in The long sunspot cycle 23 predicts a significant temperature decrease in cycle 24 was the first to be written although the last to be published (allowing both papers to reference each other). As yet, the authors haven't quite perfected their style. In this first paper they are quite insistant that just "looking at" their graph of sun cycle lengths "tells us that we can expect several long cycles in the next decades" which their analysis says is indicative of very low NH temperatures. What is remarkable by its absence in these two papers is intelligent comment about the temperature records since Sun Cycle 23 ended. These are the ones that will contribute to the low average temperatures they are predicting for Sun Cycle 24. The nearest they get to such a comment is in their second paper Solar Activity and Svalbard Temperatures where they suggest a small drop in Winter temperatures in 2009 &10 may point the way to their predicted freeze up. Yet this 2009/10 Winter record is hardily even a straw to grab onto. These jokers are predicting Svalbard temperatures will drop "from −4.2°C in SC23 to −7.8°C, with a 95% confidence interval [−5.8 to −9.6]°C in SC24." This is their grand finding, the whole reason for the paper. And why not? Svalbard's annual and winter mean temperatures "are completely described by the PSCL-model" that they created. To achieve this lower annual mean, given the 2009-2011 mean at −3.76°C is even higher than the mean for SC23 (also noting the all-time record high for winter 2011-12) and also given the last 12 months could be taken as a reasonable value for the 2012 mean temperature (−1.87°C which would be the second highest annual mean on record), then the average over the remaining years of Sun Cycle 24 to achieve the temperature drop forecast by our trickster trio would have to be −10.4°C, with a 95% confidence interval [−7.6 to −13.2]°C. If you bear in mind the coldest single year on record for Svalbard (from 1912) is −10.4°C, never mind "even less likely," can we really take these jokers seriously?
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  7. #6: Agreed. Their prediction for Svalbard is so far off that it beggars belief: The remarkable thing is that (as far as I have seen) nobody in the scientific community has taken them to task for this failure regarding Svalbard temperatures. Ie, they can continue this nonsense and get away with it, duping the ignorant masses in the process. Very few in the scientific community take these guys seriously, but that does not mean they don't have an impact. They get quoted in the Norwegian press all the time, geting more coverage and having more impact than those doing real science.
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  8. Philip @3, I agree that the failure of the model after cycle 20 is obvious when the dots are numbered with their solar cycle numbers. I don't know why SSH don't show the numbers. Without the numbers it is very difficult for the reader to see the failure. I did not see it myself before I had downloaded the temperatures, written the programs and examined my plots with the numbers. In [2] SSH show many plots with many local temperature series and with the HadCRUT3 NH temperature series, but without the solar cycle numbers. In this post on my google blog I show many of the same plots, with the numbers. I did this to check that the dots are in the same positions. They are, so there is no disagreement betwen SSH and myself on that. Alex @4, on this website we can download the HadCRUT3 (and the CRUTEM4) temperatures in a simple ascii format, but not the HadCRUT4 temperatures. Therefore I have not executed the programs with the HadCRUT4 temperatures. Do you know of a website where I can download the HadCRUT4 temperatures in the same simple format ?
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  9. It's unfortunate that the real utility of the SSH study was missed in the SSH paper, but fortunately was clearly presented in this article and the longer version. Until cycle 20 there is somewhat of a correlation and a plausible physical mechanism to conclude that the solar cycle is a detectable forcing for the climate system. That forcing presumably continues after cycle 20 but is small compared to some new forcing that is not correlated with the solar cycle and really kicks in in the 1970s (hmmm...what could it be?). This post very nicely explains what the SSH paper could have explained if only they had applied high quality scientific analysis as effectively as Hans Petter Jacobsen. Would you consider submitting your analysis to the journal as either a Comment on SSH or a separate paper that challenges the SSH conclusions?
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  10. Hans Petter Jacobsen @8 Is this HadCRUT4 page of use?
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  11. Thanks to MA Rodger @6 for his discussion of the Longyearbyen temperature series. The local temperature series vary considerably with respect to how well they fit with the Solar Cycle Model. Longyearbyen is a short series, starting in 1912. The other local series in [2] cover a longer period of time. I therefore think it is wrong to place special emphasis on Longyearbyen, as SSH do in [1]. I think it makes thing even worse to do separate analyses for the four seasons in the Longyearbyen series, as SSH also do. The Longyearbyen temperature series contains monthly absolute temperatures. I convert them to monthly temperature anomalies to be able to use monthly resolution for the start and end of both the solar cycles and the temperature series. The Longyearbyen temperatures at is now available up to and including November 2012, covering the first four years of SC24. I just repeated the analysis with the updated temperatures. The observed mean temperature in these four years is 4.6°C higher than the model's prediction for SC24. I played a little with that number, and concluded approximately as MA Rodger does at the end of his comment @6. Thanks also to MA Rodger @10 for the link to the HadCRUT4 temperatures. That is what I need to answer Alex's question in his @4. I see that the file format is a little different from the formats that I have programmed so far, so I need some time to update the programs.
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  12. Thanks to Larry for the feedback in @9. The first time I processed the temperatures I was surprised to see how well the temperatures up to and including solar cycle 20 fitted with the model. So I agree with Larry that SSH should have concentrated on this instead of trying to predict the temperatures in SC24. I am satisfied that my analysis is published here at SKS, and I don't know if it is necessary to write it up as a comment to the journal.
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  13. for those who are into cycles presents two cycles, of 60 + c.317 years that look to fit somewhat into recent behavior of temperatures. Of course if this was true one would have to throw out MWP and LIA, proxies of the past 1000 years, accept that there can be a cycle of almost 320 years (that's longer than Pluto's but shorter than Eris' period) within a fusion rector (sun) and dismiss some archeological finds (just for the heck of it) Anyway, it's cool to know what sort of periodical phenomena we should be looking if there's some overestimate in the equilibrium and other sensitivities.
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  14. HPJ @11 What kind of formatting would you need the hadcrut4 data to be in? Or alternatively which hadcrut3 data format did you use? I can help you convert it to pretty much any input format you want, don't bother modifying the programs. Just drop me a note at at
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  15. Thanks to Tommi for his kind offer in @14. But I had already programmed the library function for reading the HadCRUT4 ascii format when I read his comment. The HadCRUT4 webpage that MA Rodger provided a hyperlink to, gives the possibility to download the temperatures in a simple ascii format. I follow the monthly Northern hemisphere link to download the temperatures for the NH. There are some differences between the HadCRUT3 and 4 NH temperatures. But the HadCRUT4 NH temperatures seem to fit with the model approximately as the HadCRUT3 NH temperatures do, i.e. OK until the mid 1970s, but not after that. That is not surprising, because I have earlier seen that the NASA GISS NH temperatures also fit with the model in approximately the same way as the HadCRUT3 NH temperatures do. I have generated the same plots as in Figure 2 and 3, but now based on the HadCRUT4 NH temperatures. I show these plots in this google blog spot. Those interested in more details can follow that hyperlink.
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  16. HPJ@12, I hope it's not amiss to ask a question about scientific publication protocol rather than climate: Why not send a comment to the journal? Granted, the information is now out in the world, but it's not right in front of the people who saw the original article. And it doesn't seem to me that it would need to be anything elaborate, just 'Adding solar cycle numbers to the dots in their figure X (see figure Y) shows that their model fails increasingly badly after solar cycle 20.' And a reference to this posting. At worst you waste a couple of hours. At best you can point out to deniers and journalists that SSH have been shot down where they were originally published. Granted, I may completely underestimate the difficulties, but that's why I'm asking.
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  17. Philip: comments in journals are actually a fairly rare thing, and a lot of journals don't really like them much. Some may not allow them at all. It can also be a lot of work to prepare one, and you don't get much credit as an academic for them. To advance a career, time is better spent on full articles - but for that to be a "response" to a bad paper, it has to have enough new stuff in it to merit publication on its own (but then can also be submitted to any journal you want, not just the one with the bad paper). For a bad paper in an odd journal, the editors may not want to publicly acknowledge that they let utter crap through their peer review process - which may mean that the subject was one they didn't really know much about to begin with (and therefore can't judge the merits of the comment, either). You'll see frequent mention here at SkS by dana1981 to the paper discussed in the post Nuccitelli et al. (2012) Show that Global Warming Continues. That was published as a comment, but the original idea was (I think) to submit it as a stand-alone paper, and the journal/editor decided it was more suited as a comment. Dana may wish to weigh in on the difficulties of the process.
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  18. Interesting, but aren't you beating the wrong dead horse? The question currently being asked is whether Sunspot cycles and variations in cosmic rays that accompany them are influencing the Earth's temperature and climate.
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  19. @ JRT256 #18 The answer to the question, “What's the link between cosmic rays and climate change?”, is the SkS rebuttal article to the denier myth, “It’s Cosmic Rays”. To access the Intermediate version of the rebuttal article, click here To access the Advanced version of the article, click here If you have any follow-up questions about the contents of either of these two articles, please post them on the common comment thread to the articles.
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  20. JRT256, Your comment is puzzling. Did you actually read the post? Sunspot cycles and variations and cosmic rays are definitively not currently warming the Earth's climate, since those factors have been on the decline for the past thirty years. As such, while there is some chance that they have a small influence on climate, this influence must be negative, and yet is clearly being vastly overwhelmed by CO2. Why is it that you think the above post does not answer "the question currently being asked?"
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  21. SSH mention briefly that both total solar irradiance, ultraviolett light and cosmic rays change during a solar cycle. They do not highlight any of these processes in particular. The calculations within SSH's Solar Cycle Model are independent of which of these processes that is the strongest. The bottom line is that SSH's model cannot explain the global warming since the mid-1970s, regardless of the relativ strength between these processes.
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