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)
lsvalgaard says:
October 4, 2013 at 11:15 am
Max Hugoson says:
October 4, 2013 at 10:59 am
Can we REALLY SAY OUR RECORDS begin with large cycles 200 years before the DALTON, based on sparse, “cottage industry/hobby” observations of sunspot numbers with no uniform basis to measure them?
Yes we can, as Galileo was a very careful observer: http://galileo.rice.edu/sci/observations/sunspot_drawings.html
animation: http://academo.org/demos/galileos-sunspots/
Modern sunspots are also counted with small telescopes, e.g. http://www.leif.org/research/Wolf-37mm.png
Perhaps two counts should be published, one using small telescopes similar to Galileo and the other using modern high res scopes.
SPOT OF BOTHER
Wolf widely traveled between the 1860`s until his death in 1893 using his small telescope with which he saw on average of 40% fewer sun spots compared to the large telescope in Zurich.
Leif re your 12:02 comment – you say
” Would you say that solar activity and TSI, and temperatures were larger during the Maunder Minimum than during the 20th century”
You seem to have misunderstood my earlier comment in some way. I’m saying exactly the opposite
I say that the various high cosmic ray counts during the various temperature minimums in Steinhilber -shown in Fig 9 the http://climatesensenorpag.blogspot.com post referred to earlier reflect minimums in the solar magnetic field strength. Looks pretty obvious to me.
Echoing CaliguaJones earlier commnet the appeal of the WUWT is the open mindness and reasonalble and informed discussion.
What happende din 1878?
Carrington event too early 1859
Krakatoa too late 1883
The influences on the Earths climate are numerous.
The predominant factor is the Sun. But the sun travels through space. There are no obvious siginficant meteor showers or comets around this period. The contribution made by cosmic rays in cloud formation ( as has been pointed out previously by more eminent informed contributors) is siginficant. ( it is the basic principle of the cloud chamber – no dust to form water droplets).
So is the cause celestial, Solar or terrestial? Or a combination of factors ? This is the issue I have with the IPCC attributing all climate change to a single trace gas. It is a lot more complicated than they believe or can model.
My only observation that is that in the 1870’s steamships were beginning to supplant sail ( sorry Willis) and smoke particles over the oceans had a signficant effect. However this theory requires a negative feedback( as soot particles would create more clouds, increasing albedo) so unlikely.
obnoxious – what wonderful word. Now why did that come to mind ?
Joe Born says:
October 4, 2013 at 1:20 pm
In that connection, my count has now risen to ten
There are five parameters w,z,tau,a,b. b is independent and is simply the mean for t<tau. The final value is also independent and is equal to a-b. That leaves w,z to control the transient behavior.
Joe:But surely it’s an overstatement to say that with the remaining parameters you “match the data at every [one of 120 points]”
Well yes, a slight exaggeration but the point is that the fit is with-in the experimental accuracy of the data involved and highly constrained, not under-constrained as you post implied. Try it out on some random data, you won't get close unless the data comes from a second-order process whose parameters match your fit.
Edit: “clearly tracts Solanki” tracks
Robuk;
So the step change was an equipment change?
Steven Devijver says: “Earth was hit by a ginormous coronal mass ejection in 1859 that did not deflect: http://en.wikipedia.org/wiki/Solar_storm_of_1859 ”
Where would this affect the Earth? Primarily from the eastern US to asia? And at what level? How would the effect (if any) be distributed between land and sea? Would the ionosphere bear the brunt of the CME? What effect would this have on tropospherical temperatures?
@leif, when you say there is ‘no clear’… how can you say this? Even you have cited http://www.geo.umass.edu/faculty/bradley/lean1995.pdf which provides empircal evidence of a underlying approx 60 year 5 w/m^2 variation cycle.
I have to say, I have a real problem with you using HadCrut 4 pre-1979 to analyse or to extract data or patterns from !
We KNOW its been highly adjusted, and is most certainly not representative of real temperatures.
Terry Oldberg says:
October 4, 2013 at 11:19 am
There is a question about the usefulness of a model which, like this one, is not predictive. For the purpose of controlling a system, one needs a predictive model.
___
THe only people who want control the system (and make money trying to by taking it from us) are the alarmists.
Jim Brock says:
October 4, 2013 at 10:43 am
Simplified: In an interglacial period (like now) it keeps getting warmer….until it doesn’t, and we have another ice age.
>>>>>>>>>>>>>>
No it doesn’t the interglacial warming peaks after the solar insolation peaks and then declines gradually until it hits the circumstances that tip it into the cold climate regime. GRAPH
As Doctor R.G. Brown has been at pains to point out we are looking at a chaotic system with ‘Strange Attractors’
More on Strange Attractors
http://www.stsci.edu/~lbradley/seminar/attractors.html
The real question is what are the circumstances that tip us from glacial to interglacial and back and what causes bond and D-o abrupt climate change events. Instead politicians and bureaucrats have spent trillions on trying to hang the human race using a beneficial trace gas.
Bart, I’ve been thinking about Krakatoa as well. I’ve come up with a storyline. Not likely to be true, but an example of a plausible combination of events that demonstrates just how complex climate could get.
Let’s assume the planet was cooling when two separate events occurred. First, a slow buildup of a super volcano located around Krakatoa. Since most of the volcano was under water a lot of heat was transferred into the Pacific ocean during this growth. This slowed the growth of the volcano to centuries. At around the same time the Maunder minimum occurred sending global temperatures plunging. This might have led to the onset of the next glacial period except for the heat being added to the system through the super volcano. Due to its location the energy was added to the natural ENSO cycle causing an enhancement in amplitude This was just enough to prevent the glaciation.
This continued until the 1883 eruption. In fact, the 1878 super El Niño was probably due to the last throes of the buildup. With the eruption the heat being added to the PWP ended but with enough already in place to continue enhanced ENSO amplitudes and allowing the heat to be spread around the planet over the next 130 years. This could explain the following reconstruction.
http://iprc.soest.hawaii.edu/news/press_releases/2011/1100_years_ElNino.pdf
It would be difficult to determine whether something like this occurred after so many years.
Salvatore Del Prete says:
October 4, 2013 at 12:09 pm
Leif’s assertions about cosmic ray modulation during the Maunder Minimum are strictly his opinions and by no means the consensus.
Unfortunately, it is the current consensus that there is significant cosmic ray modulation during Grand Minima. I didn’t come up with that idea [wish that I did though].
Salvatore Del Prete says:
October 4, 2013 at 12:25 pm
Steinhilber F, Abreu-Castineira JA, Beer J, McCracken KG:
MORE PROVE OF MAJOR DIFFERENCES IN OPINIONS.
We just finished our workshop on this: http://www.leif.org/research/Svalgaard_ISSI_Proposal_Base.pdf
Note that Steinhilber, Beer, Solanki, and McCracken were participants. The general consensus [which we are writing up as we speak] is that there is no large long-term variation the past several hundred years. And that there was significant modulation during Grand Minima. Even the Berggren paper that was linked to says that: “Periodicity in 10Be during the Maunder minimum reconfirms that the solar dynamo retains cyclic behavior even during grand solar minima”
Robuk says:
October 4, 2013 at 1:34 pm
Wolf widely traveled between the 1860`s until his death in 1893 using his small telescope with which he saw on average of 40% fewer sun spots compared to the large telescope in Zurich.
The ‘large’ telescope in question is still small, with opening only 80 mm [3 inches].
Dr Norman Page says:
October 4, 2013 at 1:50 pm
referred to earlier reflect minimums in the solar magnetic field strength.
That is the point, there is no good evidence that the magnetic field strength was particularly low, in fact there is evidence that it was significant: http://www.leif.org/EOS/Eddy/2007SP_praire.pdf “The historical eclipse observations described here seem to require the presence of even the bright network structures, and thus of substantial solar photospheric magnetism during at least the last decade of the Maunder Minimum. Hence, the red-flash observations would argue against a climatologically important decrease in TSI during that period of time”.
And certainly not back to 1850s or even 1830s. Here is the best reconstruction we have of the field strength: http://www.leif.org/research/2009JA015069.pdf Figure 10.
Looks pretty obvious to me.
As Yogi Berra said: “if I hadn’t believed it, I wouldn’t have seen it.”
TImothy Sorenson says:
October 4, 2013 at 2:59 pm
Even you have cited http://www.geo.umass.edu/faculty/bradley/lean1995.pdf which provides empirical evidence of a underlying approx 60 year 5 w/m^2 variation cycle.
Not even Lean believes that old, obsolete reconstruction. Here is a more modern one: http://www.leif.org/research/Solar-Magn-Flux-Schrijver.png
“[1] Variations in the total solar irradiance (TSI) associated with solar activity have been argued to influence the Earth’s climate system, in particular when solar activity deviates from the average for a substantial period. One such example is the 17th Century Maunder Minimum during which sunspot numbers were extremely low, as Earth experienced the Little Ice Age. Estimation of the TSI during that period has relied on extrapolations of correlations with sunspot numbers or even more indirectly with modulations of galactic cosmic rays. We argue that there is a minimum state of solar magnetic activity associated with a population of relatively small magnetic bipoles which persists even when sunspots are absent, and that consequently estimates of TSI for the Little Ice Age that are based on scalings with sunspot numbers are generally too low. The minimal solar activity, which measurements show to be frequently observable between active region decay products regardless of the phase of the sunspot cycle, was approached globally after an unusually long lull in sunspot activity in 2008–2009. Therefore, the best estimate of magnetic activity, and presumably TSI, for the least active Maunder Minimum phases appears to be provided by direct measurement in 2008–2009. The implied marginally significant decrease in TSI during the least active phases of the Maunder Minimum by 140 to 360 ppm relative to 1996 suggests that drivers other than TSI dominate Earth’s long-term climate change. Citation: Schrijver, C. J., W. C. Livingston, T. N. Woods, and R. A. Mewaldt (2011), The minimal solar activity in 2008–2009 and its implications for long-term climate modeling, Geophys. Res. Lett. , 38, L06701”
@ur momisugly Lewis P Buckingham from October 4, 2013 at 2:00 pm, re American bison near-extinction.
” You would expect the pasture to rebound and absorb CO2 reducing atmospheric CO2 and causing cooling, if you think CO2 is the main driver of climate. But that did not happen”
I recognize that CO2 can absorb and emit radiant heat energy. I also maintain that physics must be consistent to be a real phenomenon. The arbitrariness of warming and non-warming between adjacent counties, and adjacent cities, cannot be explained if CO2 is the cause of atmospheric warming. How does CO2 know which cities are to warm, and which are to be ignored?
I’m no botanist, but it seems likely that the sudden absence of bison would allow the grasses to grow just so much, and then no more. It seems the bison’s grazing, and fertilizing with manure, would have stimulated grass growth. This is what happens in modern day ranching. However, it must also be realized that decomposition of millions of bison carcasses and gases produced from that process would have added a short-term burst of those gases into the atmosphere.
A fascinating post and much clearer that any IPCC efforts. Any proof pointing to a 50-70 year climate cycle affecting world production is most welcome.
My long term stock market analysis convinces me that there are external cyclical drivers. I have proved for investment grade shares the market is not random walk but price is a function of earnings, corporate size, liquidity and (insignificant) noise.Liquidity has both short term and long term components.
There appears to be a cycle of about 50-70 years period which drives general global economic activity. The simplest mechanism I have proposed for years is more sun yielding better agricultural production and general prosperity.
The economic boom and bust affect may be explained by the initial prosperity boost fueling natural aspirations which ultimately exhaust ability and resources, with a succeeding generation without the memory of the past failed attempt, retrying again on the next cycle.
Leif
Don’t you think that the Cosmic Ray peaks shown in the Fig9 C.D referred to earlier and associated with temperature minimums are de facto evidence of reduced solar field strength.?
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.
Do those modes represent physical processes that will continue into the future?
Figure 3 – First difference of extracted trend
I am happy to see more estimation of derivatives. Murry Salby has done interesting work with derivatives (wrt time) of CO2 and global mean temperature.
As before, the big unknown is whether any of the model results tell us anything about the physical processes or make reliable predictions about the near future.
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,
That should stimulate someone to find out what it was.
If you have a large enough parameterized family of functions (and we have zillions now, more than anybody can count), and an extant data set that has been repeatedly analyzed, then you can find a function that fits the low-frequency variation (long term trend) and another that fits the residual (short-term oscillations). Your model result contrasts nicely with Vaughan Pratt’s model result. At least one of you will soon be proved wrong.
Dr Norman Page says:
October 4, 2013 at 6:57 pm
Don’t you think that the Cosmic Ray peaks shown in the Fig9 C.D referred to earlier and associated with temperature minimums are de facto evidence of reduced solar field strength.?
Give the link again.
Dr Norman Page says:
October 4, 2013 at 6:57 pm
Don’t you think that the Cosmic Ray peaks shown in the Fig9 C.D referred to earlier
Your blog does not exist:
“Sorry, the blog you were looking for does not exist”
lsvalgaard says:
October 4, 2013 at 7:54 pm
Dr Norman Page says:
October 4, 2013 at 6:57 pm
Don’t you think that the Cosmic Ray peaks shown in the Fig9 C.D referred to earlier
Your blog does not exist:
“Sorry, the blog you were looking for does not exist”
=============================================
I’m getting it OK, Dr. Svalgaard. Try this :
http://climatesense-norpag.blogspot.co.uk/
Anything is possible says:
October 4, 2013 at 8:40 pm
http://climatesense-norpag.blogspot.co.uk/
Thank you. wonder what was wrong with the link.
Anyway, the answer is ‘no, Fig. 9 C and D do not correctly depict the solar magnetic field [nor the actual cosmic ray intensity’
Figure 2 of http://www.leif.org/research/Svalgaard_ISSI_Proposal_Base.pdf and Figure 10 of http://www.leif.org/research/2009JA015069.pdf are better representations of the field. Or even http://www.leif.org/research/Solar-Magn.Flux-Schrijver.png
The salient point is that in each century 18th, 19h, and 20th the field rises to about the same level:The 1870 maximum on par with the 1958 maximum and with the 1780 maximum. Plus that the dominant period the past 300 years has been about 100 years, not 60 years, so whatever periods are found in climate do not match what the sun has been doing.
Anything is possible says:
October 4, 2013 at 8:40 pm
I’m getting it OK, Dr. Svalgaard. Try this :
http://climatesense-norpag.blogspot.co.uk/
The link given was
http://climatesensenorpag.blogspot.com
I often mistype my links, so I have several copies of the file with slightly different names matching my most common mistakes 🙂
Leif Just came back- sorry the link was typed incorrectly it should be
http://climatesense-norpag.blogspot.com