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)
Stephen Wilde says:
October 6, 2013 at 1:52 pm
But Leif forgets the effect of the negative PDO which started to cool the air a little before the start of low cycle 20 and which then amplified the cooling effect of low
A little? enough that people back then [I was there] worried about the looming ice age. So, you are saying that PDO overwhelms the Sun. Very likely, IMHO. The Sun does have an influence, all of 0.1 C, and the Sun never ‘cools’ anything, just warms a little less. But again we are lacking NUMBERS. How much did the PDO do and how much did the Sun do? Without numbers it is just hand waving.
Leif asked:
“But again we are lacking NUMBERS. How much did the PDO do and how much did the Sun do? Without numbers it is just hand waving.”
We have no current means of knowing.
But it isn’t CO2 to any significant degree.
I said:
“As evidenced by Leif”s contributions here he will not take ANY data inconsistent with his views.”
Leif replied:
“by definition that is so, as the data drives my views.”
Then why do you not seem to ‘see’ the data that is inconsistent?
Are you not currently the most dogmatic contributor here?
Leif said:
“A little? enough that people back then [I was there] worried about the looming ice age.”
I was there too.
The ice age scare developed by the mid 70s after a few years of negative PDO being supplemented by lower cycle 20.
The negative PDO on its own wouldn’t have caused much concern if it had been offset by a more lively cycle 20.
One way or another solar variations alter global air circulation and albedo. The effect is strongly modulated by the oceans but if the solar changes are maintained they feed through the ocean oscillations into a temperature step change from one positive or negative ocean phase to the next.
It is a complicated dance but it is there.
Stephen Wilde says:
October 6, 2013 at 2:02 pm
We have no current means of knowing.
Yet you draw conclusions and base speculation of something you don’t know.
But it isn’t CO2 to any significant degree.
Which is an irrelevant red herring [the fallacy known as ignoratio elenchi]. It is also not the Martians playing with our climate.
Are you not currently the most dogmatic contributor here?
When it comes to the data being king, I readily confess.
Stephen Wilde says:
October 6, 2013 at 2:08 pm
“A little? enough that people back then [I was there] worried about the looming ice age.”
I was there too.
But were you active in the Sun/Weather/Climate debate then? As I was [being part of the group that revived the field]: http://www.leif.org/EOS/Sun-Weather-Climate.pdf
“Yet you draw conclusions and base speculation of something you don’t know.”
Observations of trends and inflection points is sufficient for the basic diagnosis.
Detailed measurement and accurate apportionment needs more time and more data.
“But were you active in the Sun/Weather/Climate debate then?”
I’ve been in the field but not the debate since the 50’s when I first became a weather/climate enthusiast as a child.
I have however followed the debate and observed the data as a reality check.
Maybe, rather than reviving anything, you helped to divert and negate the progress that had been ongoing as a result of the work of H H Lamb and others.
We need to get back to that and consider it all afresh from first principles and observations.
Leif provided this link:
http://www.leif.org/EOS/Sun-Weather-Climate.pdf
which is a very interesting publication from the 70s which looks strangely familiar to me.
I might even have read it at the time.
So why was all that work apparently abandoned?
With new data and modern techniques we should be able to have a new look at the issues raised.
I think the main omission was a recognition that the jets and climate zones shift latitudinally as a negative system response to any forcing element that seeks to make system energy content diverge from that set by the strength of the gravitational field, atmospheric mass and ToA insolation.
But note that system energy content can be altered in the short term by internal ocean oscillations and by solar induced changes in global albedo. Both those influences mimic changes in ToA insolation by affecting the proportion of ToA insolation absorbed at the surface (especially by the oceans).
In the end however the jets and climate zones will shift to eliminate the effect.
At the time the book was written little was known of internal ocean oscillations or of long term latitudinal climate zone and jet stream shifting. Nor was much known about the different effects of solar changes at different levels in the atmospheric column and at different latitudes.
It is the effects of those phenomena interacting together that I now bring to the table.
I have incorporated them into my New Climate Model and if anyone has better ideas I’m happy to hear them.
Stephen Wilde says: “We have no current means of knowing.
But it isn’t CO2 to any significant degree.”
Blatant self-contradiction.
lsvalgaard says:
October 6, 2013 at 2:15 pm
http://www.leif.org/EOS/Sun-Weather-Climate.pdf
….
Chapter 3.4 Sunspot Cycle and Atmospheric Electric Parameters
is relevant to the thread above ‘Using a climate model to map global atmospheric conductivity’
Stephen Wilde says:
October 6, 2013 at 2:23 pm
Maybe, rather than reviving anything, you helped to divert and negate the progress
You are not paying attention. I was a reviewer [page vii] of that book and working [along with colleagues at Stanford] with the founder of NCAR [if you know what that is] Walter Orr Roberts. Our work on the Vorticity Area Index revived the whole field which had in the 1950-1960s been killed by the outstanding Soviet meteorologist Monin. Our papers form a significant input [e.g. section 4.3] to the book: http://www.leif.org/EOS/Sun-Weather-Climate.pdf
So why was all that work apparently abandoned?
Because, as so often is the case, with more and better data the correlations reported [and mostly accepted at the time] have turned out to be spurious.
lsvalgaard says:
October 5, 2013 at 10:53 am
Salvatore Del Prete says:
October 5, 2013 at 10:52 am
I SAY WRONG.
who cares what you say…
====
lsvalgaard cares apparently, He’s spent about half this thread arguing the toss with him. I long since stopped even reading posts that begin with “Salvatore Del….”
Jeffrey,
Your figure 3, the first difference trend, has a resemblance to a feature at Mt Coolum on the Sunshine Coast of Queensland, especially if you fill in the plain level that this photo misses. It was the first I found to show the shape.
http://www.geoffstuff.com/MtCoolum.jpg
The point is that we often invoke “correlation is not causation” when making criticisms of work by others. The topic seems to arise again when you talk of a response curve for an underdamped perturbation, as familiar to engineers. I know what you mean, many non-engineers might not, but I still felt moved to raise this because there are other possible shapes like it in nature.
The suggestion is that curve matching is a better story when there is some explanation of possible causation.
Please take this as a gentle reminder, one not meant to detract from the body of your work as blogged here.
I remember a group of signal analysis engineers doing this about twenty years ago and showing it to some climate scientists who told them more or less to F*** off and go back to fixing washing machines. The were not happy since they had given their time free of charge to get data for them for the acid rain which they got no credit for the work at all.
Greg said:
“Blatant self-contradiction.”
Not so because the first phrase related only to ascertaining the relative contributions of PDO and Solar.
Obviously neither of those influences involve CO2.
Leif said:
“with more and better data the correlations reported [and mostly accepted at the time] have turned out to be spurious.”
Then it is time to reopen the whole issue because what seemed spurious could well turn out not to be so in the light of oceanic oscillations, latitudinal climate zone shifting and differential heating of the atmospheric column from solar variations.
Those factors could not have been adequately explored at the time.
Only the darkest of dark agents of ignorance &/or deception aggressively deny what earth rotation and global atmospheric angular momentum records show. It’s a black & white observation, easily verifiable dozens of ways. It’s shameless political distortion and/or shameful functional innumeracy whenever anyone tries to paint an observation so simple and so crystal clear as a shade of grey. Dismissing this observation &/or trying to paint it uncertain grey untenably asserts violation of the law of large numbers &/or the law of conservation of angular momentum. The solar-climate discussion is so grievously corrupt that authority devilishly refuses to acknowledge 1+1=2. Sensible folks: Draw a line here. Anyone crossing this line is corrupt in the most egregious sense possible. This isn’t the kind of thing you discuss, negotiate, or argue about. When you say 1+1=2 and someone persistently disagrees, you know the person is f**d up &/or playing games and that you have on your hands an intractable scenario. The way you deal with the person changes fundamentally.
http://tinypic.com/view.php?pic=2jg5tvr&s=6#.UlKmVKKBwrQ
Nice pic. But of course totally meaningless in isolation and without the slightest attempt to say what it means beyond the vague title.
David Cage says:
I remember a group of signal analysis engineers doing this about twenty years ago and showing it to some climate scientists who told them more or less to F*** off and go back to fixing washing machines.
===
LOL, Yes, that was when most objective science seems to have stopped on climate.
Paul Interesting picture showing the great climate shift of 1978 (See Happs) Would appreciate more info re its origin and how and by whom it was it was constructed.
http://judithcurry.com/2013/10/02/spinning-the-climate-model-observation-comparison-part-ii/#comment-393011
All very mysterious. Would appreciate a plain English explanation of the patterns seen in the original link and the significance of the boundaries between them. Thanks.
Geoff Sherrington says:
October 7, 2013 at 12:17 am
Thanks for the gentle reminder which we all need from time to time but I think it is misplaced here. The observation is not as you say, that the perturbation is under-damped, but rather that the climate itself responded to some as yet unidentified perturbation in a way that is well-modeled by an under-damped, second-order system. That that normalized response can be reduced to equation form governed by just two parameters, and that that parameterized equation matches the observed data over a century time span, and that two separate forms of analysis performed on two separate data sets gives the similar result (see http://wp.me/p2xhN5-4C) makes mere coincidence dubious in my view. But in any case, the observation about the transient behavior is interesting and may provide a clue to mechanism but it is not really the main point.
Such a response requires a triggering mechanism and there happens to be a candidate event but I was careful to point out that the start of the observed step in slope was “coincident with and perhaps triggered by an impulsive spike in temperature.” We haven’t showed that that event was the cause (it is after all at the output out the system, not the input). Something may have caused them both, or they may be unrelated. Either way, it is an empirical fact that the slope of the temperature anomaly shifted in 1878. That the transient part of that shift seems to be second order may be a piece to the puzzle, or that too may be mere coincidence (although it is hard to ignore that match). But even if that shift isn’t related to the coincident impulsive event and was instead due completely to anthropogenic CO2 (that has doubled in concentration every 29 years since), the sensitivity to that forcing must be exceedingly small. In a hundred years (3 doublings) the trend (with the PDO+AMO oscillations removed) only went up by .5K giving a sensitivity of .16 K/per double- 1/20th of the IPCC’s “most likely” value.
My intent with these articles was not to provide a climate model. That fascinating work must be done by those trained in it’s dynamics. My intent is to show that the null hypothesis w.r.t. CAGW can not be rejected with anything close to the confidence the IPCC proclaims. They can’t have it both ways. If AGW was detectable at the turn of the last century, the climate sensitivity to it must be exceedingly small. If on the other hand, the climate sensitivity is as large as they claim but not detectable in the background variation until the middle of the last century, then it would be easily detectable now, as I showed in my previous article. see http://wattsupwiththat.com/2013/09/26/detecting-the-agw-needle-in-the-sst-haystack/
Best regards,
JP
The Greg’s and Leif’s of the world are always correct. Enough of that foolishness.
Stephen what you have to keep in mind are some have an agenda and are not interested in seeking the truth.
Stephen, Leif made specific solar predictions for the rest of this year for solar cycle 24, so far they are much to high. The upshot being his thoughts and predictions from solar variability to solar /climate lack of connections are nothing more then speculation on his part .
I have furnished many studies (very recent ) that run counter to what he keeps trying to convey.
For my part I am very confident that indeed solar rules the climate, and this will be proven before this decade ends.
https://www.google.com/#q=solar+brightness+of+other+sun+like+stars