Guest Post by Willis Eschenbach
I was pointed to a 2010 post by Dr. Roy Spencer over at his always interesting blog. In it, he says that he can show a relationship between total solar irradiance (TSI) and the HadCRUT3 global surface temperature anomalies. TSI is the strength of the sun’s energy at a specified distance from the sun (average earth distance). What Dr. Roy has done is to “composite” the variations in TSI. This means to stack them one on top of another … and here is where I ran into trouble.
I couldn’t figure out how he split up the TSI data to stack them, because the cycles have different lengths. So how would you make an 11-year composite stack when the cycles are longer and shorter than that? And unfortunately, the comments are closed. Yes, I know I could write and ask Dr. Roy, he’s a good guy and would answer me, but that’s sooo 20th century … this illustrates the importance of publishing your code along with your analysis. His analysis may indeed be 100% correct—but I can’t confirm that because I can’t figure out exactly how he did it.
Since I couldn’t confirm Dr. Roy’s interesting approach, I figured I’d take an independent look at the data to see for myself if there is a visible ~ 11 year solar signal in the various temperature records. I started by investigating the cycle in the solar variations themselves. The TSI data is here. Figure 1 shows the variations in TSI since 1880
Figure 1. Monthly reconstructed total solar irradiance in watts per square metre (W/m2). As with many such datasets this one has its detractors and adherents. I use it because Dr. Roy used it, and he used it for the same reason, because the study he was investigating used it. For the purposes of my analysis the differences between this and other variations are minimal. See the underlying Lean study (GRL 2000) for details. Note also that this is very similar to the sunspot cycle, from which it was reconstructed.
If I’m looking for a correlation with a periodic signal like the ~ 11-year variations in TSI, I often use what is called a “periodicity analysis“. While this is somewhat similar to a Fourier analysis, it has some advantages in certain situations, including this one.
One of the advantages of periodicity analysis is that the resolution is the same as the resolution of the data. If you have monthly data, you get monthly results. Another advantage is that periodicity analysis doesn’t decompose a signal into sine waves. It decomposes a signal into waves with the actual shape of the wave of that length in that particular dataset. Let me start with the periodicity analysis of the TSI, shown in Figure 2.
Figure 2. Periodicity analysis of the Lean total solar irradiance (TSI) data, looking at all cycles with periods from 2 months to 18 years. As mentioned above, there is a datapoint for every month-by-month length of cycle.
As you can see, there is a large peak in the data, showing the preponderance of the ~ 11 year cycle lengths. It has the greatest value at 127 months (10 years 7 month).However, the peak is quite broad, reflecting the variable nature of the length of the underlying sunspot cycles.
As I mentioned, with periodicity analysis we can look at the actual 127 month cycle. Note that this is most definitely NOT a sine wave. The build-up and decay of the sunspots/TSI occur at different speeds. Figure 3 shows the main cycle in the TSI data:
Figure 3. This is the shape of the main cycle for TSI, with a length of 10 years 7 months.
Let me stop here and make a comment. The average cyclical swing in TSI over the period of record is 0.6 W/m2. Note that to calculate the equivalent 24/7 average insolation on the earth’s surface you need to divide the W/m2 values by 4. This means that Dr. Roy and others are looking for a temperature signal from a fluctuation in downwelling solar of .15 W/m2 over a decade … and the signal-to-noise ratio on that is frankly depressing. This is the reason for all of the interest in “amplifying” mechanisms such as cosmic ray variations, since the change in TSI itself is too small to do much of anything.
There are some other interesting aspects to Figure 3. As has long been observed, the increase in TSI is faster than the decrease. This leads to the peak occurring early in the cycle. In addition we can see the somewhat flat-topped nature of the cycle, with a shoulder in the red curve occurring a few years after the peak.
Looking back to Figure 2, there is a secondary peak at 147 months (12 years 3 months). Here’s what that longer cycle looks:
Figure 4. The shape of the 147-month cycle (12 years 3 months) in the Lean TSI data
Here we can see an advantage of the periodicity analysis. We can investigate the difference between the average shapes of the 10+ and the 12+ year cycles. The longer cycles are not just stretched versions of the shorter cycles. Instead, they are double-peaked and have a fairly flat section at the bottom of the cycle.
Now, while that is interesting, my main point in doing the periodicity analysis is this—anything which is driven by variations in TSI will be expected to show a clear periodicity peak at around ten years seven months.
So let me continue by looking at the periodicity analysis of the HadCRUT4 temperature data. We have that temperature data in monthly form back to 1880. Figure 5 shows the periodicity analysis for the global average temperature:
Figure 5. Periodicity analysis, HadCRUT4 global mean surface air temperatures.
Bad news … there’s no peak at the 127 month period (10 year 7 month, heavy dashed red line) of the variation in solar irradiance. In fact, there’s very little in the way of significant periods at all, except one small peak at about 44 months … go figure.
Next, I thought maybe there would be a signal in the Berkeley Earth land temperature data. The land should be more responsive than the globe, because of the huge heat capacity of the ocean. However, here’s the periodicity analysis of the Berkeley Earth data.
Figure 6. Periodicity analysis, Berkeley Earth global land surface air temperatures. As above, heavy and light red lines show main and secondary TSI periods.
There’s no more of a signal there than there was in the HadCRUT4 data, and in fact they are very similar. Not only do we not see the 10 year 7 month TSI signal or something like it. There is no real cycle of any power at any frequency.
Well, how about the satellite temperatures? Back to the computer … hang on … OK, here’s the periodicity analysis of the global UAH MSU T2LT lower tropospheric temperatures:
Figure 7. Periodicity analysis, MSU satellite global lower troposphere temperature data, 1979-2013.
Now, at first glance it looks like there is a peak at about 10 years 7 months as in the TSI. However, there’s an oddity of the periodicity analysis. In addition to showing the cycles, periodicity analysis shows the harmonics of the cycles. In this example, it shows the fundamental cycle with a period of 44 months (3 years 8 months). Then it shows the first harmonic (two cycles) of a 44-month cycle as an 88 month cycle. It is lower and broader than the fundamental. It also shows the second harmonic, in this case with a period of 3 * 44 =132 months, and once again this third peak is lower and broader than the second peak. We can confirm the 132 month cycle shown above is an overtone composed of three 44-month cycles by taking a look at the actual shape of the 132 month cycle in the MSU data:
Figure 8. 132 month cycle in the MSU satellite global lower troposphere temperature data.
This pattern, of a series of three decreasing peaks, is diagnostic of a second overtone (three periods) in a periodicity analysis. As you can see, it is composed of three 44-month cycles of diminishing size.
So the 132-month peak in the T2LT lower troposphere temperature periodicity analysis is just an overtone of the 44 month cycle, and once again, I can’t find any signal at 10 years 7 months or anything like it. It does make me curious about the nature of the 44-month cycle in the lower tropospheric temperature … particularly since you can see the same 44-month cycle (at a much lower level) in the HadCRUT4 data. However, it’s not visible in the Berkeley Earth data … go figure. But I digress …
I’m sure you can see the problem in all of this. I’m just not finding anything at 10 years 7 months or anything like that in either surface or satellite lower troposphere temperatures.
I make no claims of exhausting the possibilities by using just these three analyses, of the HadCRUT4, the Berkeley Earth, and the UAH MSU T2LT temperatures. Instead, I use them to make a simple point.
If there is an approximately 11 year solar signal in the temperature records, it is so small that it does not rise above the noise.
My best wishes to everyone,
w.
PERIODICITY THEORY: The underlying IEEE Transactions paper “Periodicity Transforms” is here.
DATA: As listed in the text
CODE: All the code necessary for this is in a zipped folder here. At least, I think it’s all there …
USUAL REQUEST: If you disagree with something I said, and yes, hard as it is to believe it’s been known to happen … if so, please quote the exact words you disagree with. That way, everyone can understand your point of reference and your objections.
Willis Eschenbach says:
April 11, 2014 at 11:08 am
“Folks, “science by assertion” doesn’t work with me. If you want to make some claim like Rob’s claim, that the climate changes if sunspots go above or below a certain (unspecified) limit, you need more than your mouth to back that claim up.”
Wow, rereading it does seems I was making the assertion, but I didn’t mean to. I meant to state it as a plausibility. The Maunder minimum which likely had few sunspots occurred during the middle of the LIA. Some have attributed recent warming to above normal sun activity for the last few cycles. So I think the possibility exists and is plausible. Detailed observations really only exist from after the LIA, so proof is unlikely but its seems the plausibility might temper concluding (not putting words in anyone’s mouth) sunspot activity has little effect on climate.
steverichards1984 —-
Steve: I went and read the IEEE paper. It’s PRIMO! Written so that someone with a 30 year old, EE signal theory background, could really understand it. The implications of this are ASTOUNDING in many ways. It says MANY THINGS identified as NOISE could have intelligence in them.
Holy Cow! The right band spread signal, injected…say on “Heavy Metal Music” and you could have Beethoven’s 9th..Or, better yet, you could extract value from “Nightly News”.
The possibilities (and the satire) are endless!
Willis
I said others, in that case Svalgaard and Scafetta. From the pdf:
Svalgaard Scafetta (Years)
10.04 9.99 Figure 3
10.92 10.91 Figure 3
11.92 11.87 Figure 3
RobR
We do have pretty good records back to 1659 with Central England Temperature which I have extended to 1538 here;
http://curryja.files.wordpress.com/2011/12/11.jpg
I remain an agnostic about sunspots but it is plausible as some of the solar minimums do coincide with low temperatures. I am currently reconstructing the record to 1200AD and initial indications appear to be that we can infill the period 1500 to 1538 as being pretty warm with the fifty years before that being more unsettled and colder. This century long period overlaps with the Sporer minimum so it would appear to contain a notably warm AND a notably cold period!
Solar activity is not my field but its an interesting subject and hopefully the extended record might give us some more clues as to how the climate is affected by sunspots.
Incidentally it is quite noticeable in the historic record that at times the Aurora Borealis is seen a lot even in Southern Britain, whilst for the vast majority of the time it can’t be seen from this latitude. Presumably that would correlate with solar activity.
I am very dubious about the long term effect of volcanos though. The big ones appear to have an impact for a season or two, other than that the historic record shows their emissions as being lost in the noise
tonyb
Don Easterbrook says:
April 11, 2014 at 9:57 am
Not sure what you mean. Are you talking about a scatterplot of HadCRUt4 temperature vs. sunspot count? If so …
Is there a relationship between HadCRUT4 temperature and sunspots? Most definitely. Is it statistically significant? Yes, the p-value is less than 0.0001.
But does it make any difference? Well, the mean sunspot number is about 50. So when there are no sunspots at all, we can expect the earth to be cooler by 0.0001 * 50 = 0.005°C … five thousandths of a degree.
Like I said, the signal is lost in the noise.
w.
PS—I note that the peak-to-peak swing in the mean TSI values is about 0.6 W/m2, corresponding to the swing in the sunspot numbers of about 70 spots from peak to quiet. This would imply that a swing of 0.6 W/m2 in TSI would give us a swing of 70 * 0.0001 = .007°C … lost in the noise.
It also implies a climate sensitivity of 0.04°C per doubling of CO2, for what that’s worth.
tonyb says:
April 11, 2014 at 12:03 pm
………..
Your “long thaw from LIA to year 2000” axiom appears to be remarkably appropriate to the CET winter temperatures (see link in my graph, post further above).
Solar is in there, but indirectly and a way around, so it gets lost in the noisy crowd of ‘wannabes’.
Bart says:
April 11, 2014 at 11:31 am
T2 = 11*9.3/(11-9.3) = 60 years
Ahh, yes as Dr. Svalgaard would say “numerology”
60 year cycle in the AMO and in the N. Hemisphere, is what one might call an illusion, due to the short length of the data set. In the much longer CET records, which well correlate with NHT, there are two distinct periodicities of about 55 and 68 and possibly 90 years. Spectral analysis can’t separate them clearly in the shorter data sets such as the AMO, but produces a spectral envelope of these frequencies (see link in my post above – magenta line).
In addition, the spectrum of the NA. tectonics data appears to correlate closely.
It is rather premature to announce death of the 60 year cycle, but from here it looks to be in very poor health.
Sorry if someone has already mentioned this but there was a recent claim of sunspot integral correlating well with temp record: http://hockeyschtick.blogspot.com/2014/04/the-time-integral-of-solar-activity.html
Willis Eschenbach says:
April 11, 2014 at 12:09 pm
“Are you talking about a scatterplot of HadCRUt4 temperature vs. sunspot count? ”
What about http://www.giss.nasa.gov/research/news/20070208/2006_temp_anom.gif
or earlier
With this: http://www.leif.org/research/New-Sunspot-Series-21yr-Run-Avg.png
“Thanks, Steven. I dealt with the “volcanoes caused the Little Ice Age” claim in my post “Dronning Maud Meets the Little Ice Age“. Short answer? Ice core data says volcanoes had nothing to do with it.”
Sorry Willis, not buying anything you wrote.
Steven Mosher says:
April 11, 2014 at 11:11 am
Thanks, Steven. Indeed something else modulates forcing. By a couple orders of magnitude, the largest factor in modulating the forcing is how much of the sun is allowed into the system. You keep ignoring the fact that there is a throttle on the system controlling the amount of energy which makes it into the earth’s climate system.
This throttle is the tropical clouds. They change the amount of incoming energy by hundreds of watts per square metre, not the pansy-arsed 0.6 W/m2 variation we get from TSI or the wimpy 1.2 W/m2 increase we’ve seen over the 20th century from CO2.
And the tropical clouds in turn are thermally regulated, meaning that the warmer it gets the more clouds you get. A few moments reflection shows that this kind of throttle linkage is theoretically sufficient to keep the temperature of the earth within narrow bounds (e.g. a temperature variation of only ± 0.3°C over the 20th century).
Finally, notice that the balance point of this cloud-based thermal regulation system is set by temperature. Tropical clouds form when the temperature is sufficiently high, not when the forcing (whether from solar or CO2) is high. They don’t care a fig for the forcing levels. They form wherever there is a local hot spot, not where there is a spot of increased forcing.
As a result, the system is largely immune to changes in the total forcing.
So you’re almost there, Steven. You just need to stop focusing on what changes forcing by 2 W/m2, and notice the clouds changing the forcing by 200 W/m2 …
w.
vukcevic says:
April 11, 2014 at 12:28 pm
‘Ahh, yes as Dr. Svalgaard would say “numerology”’
He probably would. But, that would be incorrect. Here, there is an actual, plausible physical mechanism involved.
Steven says:
April 11, 2014 at 12:38 pm
.. a recent claim of sunspot integral correlating well with temp record: http://hockeyschtick.blogspot.com/2014/04/the-time-integral-of-solar-activity.html
Interesting
vukcevic says:
April 11, 2014 at 11:03 am
Steven Mosher says (elsewhere):
……… magic undetectable fairy dust (that) controls the temperature?
Not exactly, but close enough, it’s the flutter of its wings ; see bottom right hand corner,
http://solarscience.msfc.nasa.gov/images/bfly.gif
RobR says:
April 11, 2014 at 11:40 am
Thanks for replying, Rob. Is it plausible that the variations in TSI/heliomagnetism/cosmic rays somehow cause variations in the climate? Absolutely. That’s the reason that so much energy has been expended in trying to demonstrate some such link, including my own.
However, the problem is that there is no such clear or convincing evidence. What I show above is my latest attempt to find such evidence. I thought, well, regardless of whether there are lags in the effect (likely), and regardless of of what the mechanism linking the sun to the earth might be, the one thing I could depend on was that the effect would have a cycle length of right around eleven years. So a few days ago I set out to see what I could find in the way of that cycle in some of the major temperature datasets.
As with all of my previous attempts to find such evidence, this one showed that the effect was so small it didn’t raise above the noise.
Now, I do show above that there is in fact a statistically significant relationship between sunspots and temperature … but it is extremely small. Above, I implied the TSI relationship from the sunspot numbers. Hang on, let me re-do the analysis using the actual TSI numbers versus the temperature.
…
…
Nope, just tested it. There’s no significant relationship between TSI and HadCRUT4, the p-value is .278.
Ah well. You see my problem. While as you point out it is plausible that 11-year solar variations can have an effect on the global temperature, repeated attempts to find evidence for such a relationship have generally failed. And when they haven’t failed, as in my analysis above, the effect is vanishingly small.
To me, this supports my contention that the temperature is thermally regulated by emergent climate phenomena like thunderstorms, El Nino, dust devils, and the PDO. One feature of the system I hypothesize is that it is robust against variations in forcing.
w.
lgl says:
April 11, 2014 at 12:01 pm
Sorry, lgl, but I simply don’t know or don’t remember what you are talking about.
Folks, QUOTE WHAT YOU ARE DISCUSSING. What “pdf”? What “others” What “Figure 3”? I deal with hundreds of comments every day, new people are always joining the discussion, and I simply can’t be bothered to search for your previous pearl of wisdom.
Quote it or forget it.
w.
Bart says:
April 11, 2014 at 12:51 pm
Makes no sense, lack of foundation. Which “here” and which “plausible physical mechanism” are you referring to?
w.
Willis Eschenbach says:
April 11, 2014 at 12:51 pm
This throttle is the tropical clouds. They change the amount of incoming energy by hundreds of watts per square metre, not the pansy-arsed 0.6 W/m2 variation we get from TSI or the wimpy 1.2 W/m2 increase we’ve seen over the 20th century from CO2.
And the tropical clouds in turn are thermally regulated, meaning that the warmer it gets the more clouds you get. A few moments reflection shows that this kind of throttle linkage is theoretically sufficient to keep the temperature of the earth within narrow bounds (e.g. a temperature variation of only ± 0.3°C over the 20th century).
Willis Eschenbach says:
April 11, 2014 at 1:19 pm
..One feature of the system I hypothesize is that it is robust against variations in forcing.
While it maybe robust against warming, it may not be equally robust against cooling.
Richard says:
April 11, 2014 at 1:00 pm
I read the start and couldn’t make heads or tails of it. For example, perhaps one or the other of you gentlemen could shed some light on this statement:
“Averaging-out the uncertainties”? I’d love to do that, but how?
And how does removing uncertainties “produce the average global temperature oscillation”? What does that mean?
Finally, he says that the “average global temperature oscillation” is the result of the “net” oscillation of the surface of the ocean … sorry, but that statement doesn’t seem to touch bottom anywhere. I don’t even know what a “net oscillation” might look like as opposed to say a “gross oscillation”.
Like I said, I couldn’t make sense of it, so I let it go. So many drummers … so little time …
w.
http://wattsupwiththat.com/2011/04/05/courtillot-on-the-solar-uv-climate-connection/
Dr. Vincent Courtillot points out that total solar irradiance only varies by about .1% over a solar cycle, the solar UV varies by about 10% & that secondary effects on cloud formation may vary up to 30% over solar cycles. Hence the variation in UV is 100 times greater than in TSI. Dr. Svalgaard counters that this is still not much energy relative to TSI & adds that he doesn’t like Courtillot’s data handling.
As some have argued on this blog, the small variation in UV could have outsized effects high in the atmosphere in ways not adequately studied yet, such as creating CCNs. Ways in which such a possible influence ultimately affects the climate system might not be immediately obvious in climatic data, without more & better data & the breakdown & analysis thereof, such as effects in regions or at times typically low in CCNs.
Maybe a better place to make this comment might have been in the recent post on Svensmark’s solar magentism modulated GCR-CCN hypothesis, but IMO it applies here as well.
Richard says:
April 11, 2014 at 1:33 pm
While it is clearly not robust against a regime shift to ice-age temperatures, it is robust against normal cooling.
The reason is that there is plenty of heat for the system to draw on. So for example, in the tropics when it is cooler than normal, the clouds form later in the day or not at all.
This means that at noon the tropical surface may be getting as much as a kilowatt of solar energy per square metre … which is a very robust response to cooling, enough to give the planet a bad sunburn if the clouds didn’t return.
w.
Willis Eschenbach says:
April 11, 2014 at 1:26 pm
“Here” refers to the post above, in which the plausible physical mechanism was put forward.
milodonharlani says:
April 11, 2014 at 1:39 pm
Thanks, [s]milodon. That is exactly why I did this type of analysis. It doesn’t matter for my purposes whether the hypothesized connection is a direct TSI effect, or an effect modulated by cosmic rays, or an effect from UV. They all vary on the same ~ 11-year cycle, in line with the sunspots. As a result, if any or all of them had a significant effect, it would show up in the periodicity analysis … but it doesn’t.
w.
Willis Eschenbach says:
April 11, 2014 at 1:45 pm
Which is why more data are needed. IMO only then can solar UV & magnetic flux be ruled out as important influences on climate. The required data are lacking.
PS: Courtillot’s analysis does show a strong solar influence, although as noted Svalgaard thinks that his data handling exaggerates the correlation.
Willis,
Sorry—I should have been more specific. I wasn’t thinking of a scatterplot of HadCRUt4 temperature vs. sunspot count. I was thinking of plotting temperature data older than HadCrut4 against time, then plotting sunspot incidence for the same time period, and overlaying the two plots to see if they correlate. This has been done in a general way (e.g., the Maunder and Dalton), but the time scales aren’t very detailed or don’t go back far enough in time (at least not the ones I’ve seen). In order to get better temperature/time resolution I used the original oxygen isotope data from the GISP2 Greenland core and temperatures from the CET record. The original data has plenty of data points so you can choose your own level of detail. Both the GISP2 ice core and the CET show times of significant cooling that correspond to the historical record. Overlaying these plots on a sunspot/time plot for the same time periods shows a remarkable correlation, even for less pronounced temperature variations. The same is true for the Hoyt/Shatten TSI data. Others have published a variety of correlations (see for example, the one by Dan Pangburn referred to in comments), but don’t go back far enough in time.
So why am I asking you this question? What I’m looking for is better resolution than what you see in the published literature and with your phenomenal knack for digging up data, thought you might have a better handle on this.
Don