Guest essay by Jeffery S. Patterson
My last post on WUWT demonstrated a detection technique that allows us to de-noise the climate data and extract the various natural modes which dominate the decadal scale variation in temperature. In a follow-up post on my blog, I extend the analysis back to 1850 and show why, to first-order, the detection method used is insensitive to amplitude variations in the primary mode. The result is reproduced here as figure 1.
Figure 1a – First-difference of primary mode Fig 1b – De-trended first-difference of primary mode
We see from Figure 1b that once de-trended, the slope of the primary mode has remained bounded within a range of ± 1.2 °C/century over the entire 163 year record.
The linear trend in slope evident in Figure 1a implies a parabolic temperature trend. The IPCC makes oblique reference to this in the recently releases AR-5 Summary for Policymakers:
“Each of the last three decades has been successively warmer at the Earth’s surface than any preceding decade since 1850 (see Figure SPM.1). In the Northern Hemisphere, 1983–2012 was likely the warmest 30-year period of the last 1400 years (medium confidence).”
True enough, but that has been true since at least the mid-1800s. The implication of the IPCC’s ominous statement is that anthropogenic effects on the climate have been present since that early time. Let’s examine that hypothesis.
Up to this point I have been using de-trended data in the singular spectrum analysis (SSA) because de-trending helps to isolate the oscillatory modes of the climate system from the low-frequency trend. We are now interested in the characteristics of the trend itself. Figure 2 shows the SSA trend extracted from the raw Hadcrut4 northern hemisphere data.
Figure 2 – SSA[L=82,k = 1,2] on Hadcrut4
We see the data oscillates about the extracted trend with approximately equal peak –to-peak amplitude until about the year 2000. More about this departure later. The really interesting characteristic of the trend is revealed when we look at the first-difference (time derivative of the red curve of figure 2), shown in figure 3.
Figure 3 – First difference of extracted trend
Any engineer will instantly recognize this shape as the step-response of a slightly under-damped 2nd order system as described by equation 1.
(1)
where a is the step-size, b the offset, w the natural frequency, z the damping factor and t the offset in time at which the input step occurs. 
is the unit step function which is zero when its argument is negative and unity elsewhere.
A parametric fit of (1) to the data of figure 3 is shown in figure 4.
Figure 4 – Parametric fit of (1) versus data 
I know what you are thinking. That fit is too perfect to be true. It must be an internal response of the SSA filter. We can test that hypothesis by integrating equation (1) and comparing it to the unfiltered data.
Figure 5 – Indefinite integral of (1) versus data
We see the resulting integral fits the unfiltered data, with the residual exhibiting the same oscillatory behaviors as before. The integral of (1) yields eqn. 2 below:
(2)
I know what you’re thinking. We’ve said all along that the AGW signature would show up as a step in in the slope of the de-noised temperature data, precisely what we see in figure 4. Is this the AGW smoking gun? If we plot figure 3 and the raw data on the same graph we see the real smoking gun.
Figure 6 – First-difference of extracted trend versus data
Around the year 1878, a dramatic shift in the climate occurred coincident with and perhaps triggered by an impulsive spike in temperature. As a result, the climate moved from a cooling phase of about -.7 °C/century to a warming phase of about +.5°C/century, which has remained constant to the present. We see that this period of time was coincident with a large spike in solar activity as shown in figure 7.
Figure 7 – Solanki et al, Nature 2004 Figure 2. Comparison between directly measured sunspot number (SN) and SN reconstructed from different cosmogenic isotopes. Plotted are SN reconstructed from D14C (blue), the 10-year averaged group sunspot number1 (GSN, red)
Virtually all of the climate of the last century and a half is explained by equation (2) and the primary 60+ year mode extracted earlier as shown in figure 8b.
Figure 8 – Primary mode SSA[L=82,k=3,5] vs. residual from eqn.(2) (left) Fig. 8b – eqn. (2) + primary mode vs. hadcrut4
As others have observed, this 60+ year mode plotted in figure 8a is highly correlated to solar irradiance.
Figure 9 – This image was created by Robert A. Rohde from the data sources listed below
1. Irradiance: http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant
2. International sunspot number: http://www.ngdc.noaa.gov/stp/SOLAR/ftpsunspotnumber.html
3. Flare index: http://www.koeri.boun.edu.tr/astronomy/readme.html
4. 10.7cm radio flux: http://www.drao-ofr.hia-iha.nrc-cnrc.gc.ca/icarus/www/sol_home.shtml
Note that the reconstruction due to Solanki et al shown in figure 7 disagrees with figure 9 in terms of present day solar activity. The temperature record clearly tracts Solanki, but I’ll leave that controversy to others.
The residual from Figure 8b, shown in Figure 10, shows no trend or other signs of anthropogenic effects.
Figure 10a – Residual from 
primary mode Figure 10b – Smoothed histogram of residual
A similar analysis was done on the sea-surface temperature record. The results as shown in Figure 11:
Figure 11 – SST (red) vs. Hadcrut4 (blue)
We see the land temperatures follow the ocean surface temperature with a 4-5 year lag.
Conclusion
The climate record of the past 163 years is well explained as the integral second-order response to a triggering event that occurred in the mid-to-late 1870s, plus an oscillatory mode regulated by solar irradiance. There is no evidence in the temperature records analyzed here supporting the hypothesis that mankind has had a measurable effect on the global climate.
Related articles
- Detecting the AGW Needle in the SST Haystack (wattsupwiththat.com)
Salvatore Del Prete says:
October 5, 2013 at 11:13 am
Leif not convincing, because even the article you sent suggest no one really knows. which is my point.
Because of the diverse views earlier, I called for the workshop [involving all actors] to re-examine the issue. As a result we have now come to a new realization with much closer agreement [of course along the lines I suggested some time ago], so although it is correct that nobody knows we have now a well-founded and reasoned idea of what has happened in the past and what will happen in the future, and I expect that when the Maunder-type minimum I and colleagues are predicting rolls around we will be able to solidify our conclusions.
Stephen you are on the correct path and again it is the realtive difference in temp in the stratosphere ,rather then if the stratodssphere has warmed or cooled overall that really counts.
Leif, your graph does agree with me. The blue line shows stratospheric cooling ceased at that level around 2000.
The pink line shows signs of levelling off.
The other source that I linked you to clearly shows the cessation of stratospheric cooling as per my hypothesis.
On your chart you just draw a straight line downward across the whole chart without paying attention to the inflection point. That is cherry picking and wholly misleading in the broader scheme of things.
Leif again this current solar grand minimum should clarify many things among them being a solar/climate connection or connectoins and just how variable or not the sun really is.
Time will tell, but as of now NOBODY REALLY KNOWS.
and studies that reach different conclusions over short periods of time make for more uncertainty not less.
Salvatore Del Prete says:
October 5, 2013 at 11:21 am
Leif the current quiet solar period in 2009-2010, (much more active then the Maunder Minimum in contrast) , has already produced a IMF field lower then your floor of 4.0 nt.
nonsense, the lowest valuer in 2009 was 3.93 nT with is well within the error bar on the 4.0+/-0.2 nT that we propose.
Stephen Wilde says:
October 5, 2013 at 11:23 am
Leif, your graph does agree with me.
As i say: every graph by anybody ALWAYS agrees with you.
Leif , many even if those you mention should change, still hold the view that the Maunder Minimum had a IMF around 2nt.
Time will tell.
Salvatore said:
“It is the relative difference in temp in the stratosphere ,rather than if the stratosphere has warmed or cooled overall that really counts.”
That is right.
What matters is the gradient of the slope of tropopause height between equator and poles. Changing that allows the jets and climate zones to slide latitudinally beneath the tropopause which alters total cloudiness and global albedo.
It is a matter of the net balance between solar creation of ozone above the equator and below 45km and the solar destruction of ozone above 45km above or around the poles.
That creates the necessary see-saw of tropopause height gradient between equator and poles depending on whether the sun is quiet or active.
And it is a matter of chemistry involving ozone rather than TSI.
Exactly my point 3.93 nt and the solar activity quiet period during that time was much less in duration then during the depths of the Maunder Minimum, suggesting a lower floor of 3.93 nt during the Maunder Minimum, was/is very possible, if not likely.
Leif, if your chart had showed the lower stratosphere at those latitudes warming at a time of active sun then that would have been a problem for me so your assertion is false.
Similarly if the stratosphere had continued cooling at the same rate or faster to date then your belief about the effect of CO2 would have held up.
Since neither happened my hypothesis is correct and yours is wrong.
Or don’t you believe in data?
Salvatore Del Prete says:
October 5, 2013 at 11:30 am
Leif , many even if those you mention should change, still hold the view that the Maunder Minimum had a IMF around 2nt.
The people on my team are the world experts on this [you quoted them], so if some other people still cling to the wrong notions, too bad for them [and for you if you cling with them]
Stephen Wilde says:
October 5, 2013 at 11:36 am
Or don’t you believe in data?
You believe that ANY data by ANYBODY ALWAYS supports your view, I take a less dogmatic approach.
Leif said:
“You believe that ANY data by ANYBODY ALWAYS supports your view, I take a less dogmatic approach.”
That is clearly a false and unworthy allegation.
My hypothesis is replete with opportunities for the real world to falsify it.
One of them would have been a warming stratosphere at high latitudes with an active sun but it didn’t happen.
I have listed some of them for you on more than one occasion previously but you persist in your defamations.
In contrast, you still think that our CO2 cools the stratosphere despite a cessation of stratospheric cooling at certain levels some 15 to 20 years ago whilst our emissions increased substantially.
Pots, kettles and the psychological strategy known as projection come to mind.
If it is a long Maunder instead of a shorter version, my hunch is that global climates will feel the affects of a colder cyclic weather pattern variation driven by intrinsic oscillatory convergence but it will again be blamed on a “cold” (sic) sun.
Unrelated oscillations can occur together and often do. Only the ones that were catastrophic led gullible people to kill virgins so the god of the [fill in the blank] would behave. The fact that modern people say that two events are linked by sciency-sounding causation does not make the unsupported link any better than when virgins were sacrificed to please an angry god.
I think my projection is extremely likely.
Stephen Wilde says:
October 5, 2013 at 11:59 am
I have listed some of them for you on more than one occasion previously but you persist in your defamations…
Pots, kettles and the psychological strategy known as projection come to mind.
Now, that I would call defamation, but I have a thick skin and have seen worse, perhaps you eventually will improve in the defamation-department.
Pamela Gray says:
October 5, 2013 at 12:04 pm
Unrelated oscillations can occur together and often do
Global temperatures have long been correlated with the price of a US postage stamp, so perhaps it is time to get rid of the Postal Service… to stop global warming and save the planet.
Isvalgaard, I must clearly have missed something since the text states:
“Virtually all of the climate of the last century and a half is explained by equation (2) and the primary 60+ year mode extracted earlier as shown in figure 8b.
Fig 8 – Primary mode SSA[L=82,k=3,5] vs. residual from eqn.(2) (left) Fig. 8b – eqn. (2) + primary mode vs. hadcrut4
As others have observed, this 60+ year mode plotted in figure 8a is highly correlated to solar irradiance. [fig 9]”
Hence, where is your 100yr cycle coming from, and do you have references to back it up?
david dohbro says:
October 5, 2013 at 12:25 pm
As others have observed, this 60+ year mode plotted in figure 8a is highly correlated to solar irradiance. [fig 9]”
Since fig.9 only covers 30 years it is hard to claim that the 60+ year mode is correlated. Furthermore we have no data for TSI before 1977, so any comparisons must be with an artificial reconstruction based on the sunspot number. The dominant ‘cycle’ of the sunspot number is 100+ years as is evident to the eye: http://sidc.be/sunspot-index-graphics/wolfaml.php
Hence, where is your 100yr cycle coming from, and do you have references to back it up?
One can also use more sophisticated signal processing to show that there is the 100-yr cycle so clearly visible to the naked eye, e.g. http://www.leif.org/EOS/Lomb-Sunspot-Cycle-Revisited.pdf
“the period around 100 years remains with the modulation by this period obvious in a visual
examination of a plot of the modified sunspot number data”. There are also smaller, less dramatic subharmonics at 67, 54, 170, and 44 yrs, but they only create small second-order effects. The one that matters is the 100+ year cycle. You can also see it here: http://www.leif.org/research/Solar-Magn-Flux-Schrijver.png
You don’t really need references to see something with your own eyes.
There does seem to be a 100 year ‘pulse’ in solar activity set within the millennial cycle that gave us the Roman Warm Period, Dark Ages, Mediaeval Warm Period, Little Ice Age and the Modern Warm Period.
Temperature matches quite well too with low solar activity and cool temperatures near the beginning of each century from the early 1700s followed by higher solar activity and warming up through the subsequentcentury.
So what we have is the basic millennial cycle containing 100 year ‘pulses’ of activity or ‘pauses’ if one prefers and then the 60 year internal ocean oscillation lying beneath those longer term solar variations.
The net effect is upward temperature stepping from one 30 year oceanic positive phase to the next when the sun is becoming more active across multiple cycles and downward temperature stepping from one 30 year oceanic negative phase to the next when solar activity is declining across multiple cycles.
Leif has previously pointed out that (according to his latest revised solar activity charts) the sun may have been as active or nearly as active during the 18th century as it has been recently and in fact the bulk of the 18th century was warm too but it cooled off towards the beginning of the 19th century as the sun became less active again. The 1812 disaster in Russia for Napoleon was during that cooler period of less active sun at the beginning of the 19th century.
So however much Leif manages to flatten the historical trend for solar activity the residual solar variations still correlate with temperature changes on Earth.
Stephen Wilde says:
October 5, 2013 at 1:05 pm
Leif has previously pointed out that (according to his latest revised solar activity charts) the sun may have been as active or nearly as active during the 18th century as it has been recently and in fact the bulk of the 18th century was warm too but it cooled off towards the beginning of the 19th century as the sun became less active again
the 1860-1870s were active years on par with the 1975-1995 high activity…We see this in sunspot numbers, geomagnetic activity, and cosmic ray modulation.
Stephen Wilde says:
October 5, 2013 at 1:05 pm
The 1812 disaster in Russia for Napoleon was during that cooler period of less active sun at the beginning of the 19th century.
and the 1942 disaster in Russia for Hitler was during that cooler period of less active sun in the middle of the 20th century…
Stephen Wilde says:
October 5, 2013 at 1:05 pm
in fact the bulk of the 18th century was warm too
No, the 18th century was brrr cold [colder than the 19th, 20th, and 21st].
http://wattsupwiththat.com/2010/09/28/loehle-vindication/
@Wayne Job:
Not followed it yet. Talked to Habibullo at Chicago and he said they were going to do measurements of solar diameter as he thinks changes in it are an important observable correlated with solar changes of output. I suppose that’s what they are doing “up there” now.
For the discussion of UV and stratospheric changes, I’ll be using bits / pointing at this paper:
http://www.nwra.com/resumes/baldwin/pubs/Baldwin_Dunkerton.pdf
It is “jargon rich” and not as explanatory as I’d like, but you work with what exists…
It claims to find and lay out a mechanism by which variation in solar output, in particular UV, modulates surface weather; via several intermediary steps that are a bit hard to follow (thanks to the jargon rich nature…). I “took the liberty” of condensing that to “stratosphere cools when UV drops” so as to not post an entire paper and a few dozen pages of commentary when desiring to really just say “UV through stratosphere and ocean interactions modulates weather”. Could that simplification be wrong? It certainly is. All simplifications are. But they are still useful. (Do we really need Einstein’s relativistic terms on the “wrong” simplification of Newtonian mechanics?)
What I think it is saying is that the more equatorial stratosphere cools but the polar descending zone can have some Sudden Stratospheric Warming events (due to descent / compression, not UV changes) as that global stratosphere descends at the poles. (That descent increasing Rossby Waves and doing other stuff to ground weather as well). Could I have the sign backward on stratospheric warming / cooling at some particular altitudes or latitudes? Almost certainly, since I think it goes in different directions in different places (though the jargon rich “explanation” is a bit hard to figure out for sure). I don’t think that matters in a blog post comment.
With that said: Anyone wishing “the full Monty”, read the paper. If you understand it, please, let me know where some of the more obtuse parts have something interesting to say. I’m going to put some of my attempts at understanding here, with small quotes, but I’m more than happy to have clarifications and corrections if I’ve got something wrong.
@Leif:
Those folks say UV variations cause weather variations. You say UV varies with sunspots and TSI. OK, so connect those two and it says variations in sunspots and TSI correlate with changes in weather on the surface. Thanks for confirming that… 😉
Now, as I read that, it is saying that UV decreases, so ozone decreases, so the ozone derived heating decreases, which implies to me a cooling stratosphere. It also says that ends up with the stratospheric layer headed off to the poles and descending faster, so I’d expect compression heating at the poles along with a push to a loopier jet stream.
There’s a lot more in that paper about other oscillations and all. How that relates to a simple “buoyancy” argument, I have no idea. My point on ocean surface heating was about prompt evaporation and the resultant increase in rain (which we have seen… it is raining a lot in many places around the planet). How to “correct out” that precipitation and turn that into a change in meridional vs zonal flow? Good luck with that…
Note, too, that “cooling” and “heating” are ambiguous to temperature. I can have a cooling stratosphere with increasing temperatures if that cooling (less energy due to less UV deposition) air is descending (having compression raising temperatures). So does cooling mean “less energy being delivered from absorption of UV” or does it mean “temperature dropping”? Unfortunately, English is often ambiguous on heat vs temperature and the article is not much better. Often avoiding direct references to temperatures or “heating” vs “cooling”.
So, in a Humpty Dumpty mood: Cooling, as I was using it, meant “less energy being absorbed from UV”. Less energy in, things are cooler. I was not addressing what might happen to a given parcel of air in the following hours, days, or weeks as it might descend and suffer compression heating. As I read that article, it seems to me to imply instantaneous lower temperature with statements like “Ozone variations have a direct radiative impact on the stratosphere and troposphere, and observations of temperatures are broadly consistent with the expected radiative forcing.” “Direct” usually meaning “same sign”. Then again, it isn’t clear about what “expected” is, so who knows…. (Frankly, while nice to know, my interest is just in the fact that there IS a “direct” connection from solar UV to surface weather. If it has sign inversion a few times along the way as various obscure things happen, so what? But it would be nice to have it fully elucidated.)
With statements like the following, it is pretty clear that ANY simplification put into a single sentence, or even a few, is going to be “wrong”, as things have many moving parts and lots of linkages.
But connect and link it does…
Now, to me, it looks like more UV gives more ozone and thus more “ozone heating” of the tropical upper stratosphere. Less UV then ought to give less “ozone heating” and a cooler tropical stratosphere. (Not talking about descending polar stratosphere here…)
The paper goes on into a whole lot of detail about how various waves and such interact and move the energy around (and change meridional or zonal patterns – and it isn’t just buoyancy…) One small (and more approachable) sample is:
I’ll leave off quoting more of it at this point.
So, my points are simply these:
Solar UV variation has a direct and measured impact on high altitude changes and surface weather. It is ozone mediated to some extent. It looks, to me, like it is “direct” with more UV and more ozone meaning more heating (in the tropics) but likely inverted with the stratospheric winds then causing descending air masses at the poles to heat (but blowing out some nice Rossby waves and making a more “loopy” jet stream when UV is low). The particular behaviours that lead to a “loopy” jet stream are way more complex than just “more down at the poles, more up at the equator”, but involve a lot of jargon that I’ve not waded through yet. (How a QBO enters into it? Equatorial waves vs planetary waves vs rawinsonde observations? This is stuff for Anthony and meteorologists to translate…) One example more, though:
And on it goes… Hard to decode, but it’s pretty clear that what happens is not adequately captured with descending air at the poles and rising at the equator as model drivers; nor with a simple “warms” or “cools” for the stratosphere as a whole.
OK, I’d tried to use a shortcut to avoid a diatribe, and ended up needing to post a diatribe anyway. Sometimes you just can’t win…
Hopefully this has not obscured the message / observation that:
1) Solar variations in TSI are much greater in UV.
2) UV variations changes Ozone, and through that, stratospheric heating.
3) That, then, changes surface weather with lower UV making more rain, more “loopy” jet stream, and overall cooling of the surface over time.
Exact mechanism far more complicated than can be put into a comment, so ALL comments about them will be too abbreviated and wrong on details. Yet can still illustrate what the ‘net effect’ would be.
In particular, which part of the stratosphere matters when saying “warms” or “cools” and disambiguating “gains net energy” from “temperature rises” matters. With LESS energy gain at the tropical stratosphere, the polar descending stratosphere can have compression heating, despite less total energy in the air and an over all lower atmospheric height from an overall lower energy (so lower temperature prior to any compression heating with loss of altitude).
Less UV, cooler surface weather. Lots of moving parts in between.
E.M.Smith says:
October 5, 2013 at 3:17 pm
Those folks say UV variations cause weather variations. You say UV varies with sunspots and TSI. OK, so connect those two and it says variations in sunspots and TSI correlate with changes in weather on the surface.
What is means is that if there is no good correlation of climate with sunspots or TSI, there is also no good correlation between UV and climate.
E M Smith says
“With statements like the following, it is pretty clear that ANY simplification put into a single sentence, or even a few, is going to be “wrong”, as things have many moving parts and lots of linkages.”
This is certainly true. I would suggest that any participant in this thread would do well to study carefully all the impressive amount of data and the arguments in Erl Happs various post and pdfs on this topic i e dissecting the very complicated relationship between climate and solar activity. In particular I would ask Stephen if his conclusions differ in any significant respects from Erls and would be interested to hear what comments Leif may care to make. In my opinion Happs has pretty well nailed it.
See for starters http://climatechange1.wordpress.com/
and then http://www.happs.com.au/images/stories/PDFarticles/TheCommonSenseOfClimateChange.pdf
@Beng:
I’m pretty sure the main “driver” is lunar / tidal modulation of ENSO / La Nina – El Nino. Solar just a small effect. (Though the cited paper does claim to find an effect and elucidates a mechanism).
IMHO, any time you see “driven by ENSO” or “ocean cycles”, one ought to prepend “driven by lunar tidal changes”…
That nobody much seems to take a look at that pnas paper cited in my first comment (complete with nice graphs / pictures 😉 is a bit sad. I think it explains so much, so easily, and so easily tested. But folks don’t want to think it could be as simple as “moon variation in tides” and certainly don’t want to hear “your favorite hobby horse moves in sync with this larger driver so isn’t as important as you think” even when one adds “but it still matters some…”
Oh Well…
The stratosphere gets down to near /at ground level during the dead of the polar night. I think that matters. Perhaps a lot… Lets a big IR window open in the dark…
Greg Goodman says:
October 5, 2013 at 12:07 am
Thank you for that and your other helpful suggestions. The re-analysis you suggested above can be found here: Followup: The Great Climate Shift of 1878
Best
JP