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)
hadcru4 is data?? I don’t think so. Contaminated and manipulated. The 1930s were warmer than current temps. Simply plot realistic temps on a realistic Y-scale.
http://www.woodfortrees.org/plot/best/scale:4/plot/rss-land
Post 1979 RSS satellite data plotted overl BEST data shows the discrepancy
Matthew R Marler says:
Your model result contrasts nicely with Vaughan Pratt’s model result. At least one of you will soon be proved wrong.
Pratt’s “sawtooth” ocean oscillation curve fit comports very closely to the SSA’s non-trend major modes (k=3,4,5,6}. See http://wp.me/a2xhN5-4u
I have a number of problem with Pratt’s analysis. Note the divergence of the residue after 1950. Compare that to figure 10a above. Also his model fails after 1995 due to the wide filter he is using. Thus he makes no predictions regarding the so called pause.
@Vukcevic:
On another thread (several, but one recently) you have pointed out the correlation between geomagnetic variation and weather changes. I’ve often wondered “How?”….
A speculation:
I’ve seen many correlations between lunar / tidal effects and weather cycles. Might not tides in the molten earth where the magnetic field is generated cause variations in the geomagnetic field?
You might want to do a correlation comparison of geomagnetic data with tide data and lunar tidal forces and see if there’s a match.
http://chiefio.wordpress.com/2013/01/24/why-weather-has-a-60-year-lunar-beat/
http://www.pnas.org/content/97/8/3814.full does a great job of laying out the case for lunar tidal driving of ocean currents / weather. (peer reviewed paper too…)
referenced in:
http://chiefio.wordpress.com/2011/11/03/lunar-resonance-and-taurid-storms/
@Leif:
You continue to speak to TSI as relatively invariant, but make no mention of the drop in UV that happens as the sun goes quiet. It looks like a redistribution of WHERE the components of TSI end up as they shift more “red-ward” matters to how the climate system reacts.
Add in synchronous tidal effects from lunar activities (all kept coordinated via orbital resonance effects) and “things add up”. Yet no one thing will be demonstrably the whole thing.
It resolves the “sun did it with planet cycles” vs “TSI is not enough” via “the Earth does it as the spectrum shifts while the moon stirs the oceans in sync with the planet orbits” and can end some of the “does so / does not” bickering…
Endlessly saying “TSI doesn’t change enough” is not very enlightening. Rather like saying “The fall didn’t kill him” when it was the sudden stop at the end… The two are very different, but driven by the same initial events… It would be more helpful to understanding to cast a broader net. IMHO.
Per “What happened in 1878?”, it looks to my eye like it is rather near point “b” in this graph:
http://www.pnas.org/content/97/8/3814/F1.expansion.html
from the above paper. One of the marked “cold maximum” points. 1974 marked as “C” being another one (as is 1787 “B”). FWIW, point “c” in about 2040 is also so marked.
“A time-series plot of Wood’s values of γ (Fig. 1) reveals a complex cyclic pattern. On the decadal time-scale the most important periodicity is the Saros cycle, seen as sequences of events, spaced 18.03 years apart. Prominent sequences are made obvious in the plot by connected line-segments that form a series of overlapping arcs. The maxima, labeled A, B, C, D, of the most prominent sequences, all at full moon, are spaced about 180 years apart. The maxima, labeled a, b, c, of the next most prominent sequences, all at new moon, are also spaced about 180 years apart. The two sets of maxima together produce strong tidal forcing at approximately 90-year intervals. ”
So it looks to me like it was an inflection point in the lunar / tidal forces changing how the oceans flow and mix cold water to the surface. At a new moon, being a lower case letter, so we ought to expect something similar to happen in about 2040 (after a long period of cooling that started in about 2000 (not labeled in the graph, but at the bottom of a dark “V” shaped of the plotted lines, at the ‘hot inflection’ point). 1920-30 is also near the bottom of one of those dark hot “V”s…
These changes in cold ocean mixing to the surface then drive changes in ENSO / La Nina / El Nino (vis Tisdale) that lead to all the meridional / zonal changes and shifts of cloud bands pointed out by Stephen Wilde and all the rest.
It is a “natural ocean cycle” but driven by a lunar metronome… that is itself moving in time to a planetary orchestra via orbital resonance. (That also stirs the sun and causes it to change output… but not via TSI, via color shifts; that might only correlate, or might be a partial additive driver along with GCR et. al.) It all beats together, so correlation can not be used to prove causality nor can “not enough” be used to disprove partial causality in a chorus of synchronized actions. It will be very hard to prove how much each part matters.
Personally, I think the lunar / tidal is most direct (and likely tides in the spinning interior of the Earth explains the magnetic correlation) and the sun just a ‘bit player’, but with some impact. Then much of the rest being “elaboration” of the basic changes. But that, too, is speculation.
But: that 1878 is near to on top of point “b” on the graph is not speculation.
It’s a fact.
E.M.Smith says:
October 4, 2013 at 10:48 pm
You continue to speak to TSI as relatively invariant, but make no mention of the drop in UV that happens as the sun goes quiet.
The UV varies simply with the sunspot number. Figure 9 of http://www.leif.org/research/Rudolf%20Wolf%20Was%20Right.pdf shows how UV varies. You can’t tell that apart from the sunspot number, so UV does not vary in a mysterious way, it simply varies like TSI, like F10.7, like sunspots, or inversely like cosmic rays.
@Leif:
And as that UV fades and blues diminish with more reds and infrareds; more of the TSI causes prompt evaporation of the ocean surface and less goes meters into the deep. That change in where the energy is deposited and how much evaporation it promptly causes matters to weather. Similarly, NASA saw a shrinking of the total atmospheric height as less UV caused a cooler stratosphere; that then is closer to the poles when it starts to descend in the Night Jets (and, IMHO, is part of the cause of the more “loopy” jet stream in this mode and colder polar weather).
In short, just saying “TSI” ignores where on Earth the different spectra end up and what they do when they get there. Distribution of energy can be as important as how much of it. (Though I still think Lunar Tidal ocean mixing is the lions share. But with no numbers measured on that it becomes speculative wishing…)
Jeffrey, I like the method, though like RC Saumarez, I’m a little mistrusting of all the SSA/EOF craze.
Damped 2nd order is interesting. Also note that it is clearer in SST. I would further suggest that you try running the analysis on ICOADS SST as well as HadleySST based ‘products’.
I looked at their processing and found the ‘corrections’ to be speculative at best. That does not necessarily mean wrong but removing more than half of the variability from more than half the record makes me baulk at it.
http://judithcurry.com/2012/03/15/on-the-adjustments-to-the-hadsst3-data-set-2
There is a problematic glitch in ICOADS around WWII but your method will be little disturbed by that.I think. I suspect Hadley’s correction to that adds as big an error as the one it aims to remove.
Someone else mentioned Krakatoa which was my first thought.
http://legacy.earlham.edu/~bubbmi/krakatoa.htm
Apparently most of the island disappeared into a 6km under water caldera. This was a volcanically active era so it may have included considerable under-water activity too. In fact that would be “very likely” TM.
It is clear that temperature records show an acceleration rather than a linear rise. Much of that acceleration is to negate the later 19th c. cooling trend. This is the bit Hadley felt was ‘bias’ in the data and set about removing 67% of it’s amplitude.
I would be interesting to see how this affects you fitted 2nd order response. Does it move the starting date?
To reduce the possibility that this is just an artefact of the SSA, you should try fitting to the least processed data possible. Assume you have correctly identified the 60 cycle and subtract it from the original dataset. Then fit your 2nd order to what’s left.
The regression should take care of the noise. Do you get parameter values that are close to what you found fitting to the SSA model?
BTW, there are several errors in your text where you describe the data in the right hand plot as “de-trended” when it isn’t.
How much of what ‘kicked in’ in 1880 was Hadley ‘bias corrections’?
This is what the overall adjustment looks like for hadSST3.
http://curryja.files.wordpress.com/2012/03/hadsst3-cosine-fit1.png
Maybe the fit will be enhanced , I don’t know. But since those adjustments have a very similar scale and form to what you’re fitting, I think your need to check .
ICOADS is available for KNMI, it should be easy to repeat using icoads sst. It should be interesting.
E.M.Smith
Thanks for the links. No doubt that tidal movements have an impact but papers I have looked at (e.g. Keeling and Ray) come to opposite conclusions, and my knowledge in the area is (and elsewhere) limited.
Regarding the magnetic field, probability of solar connection appears to be strong, based on analysis of raw geomagnetic data (illustration 2 for the AMO & 3 for LOD in http://www.vukcevic.talktalk.net/EarthNV.htm )
However when the smoothed version of the same data are used, most of the information is lost.
Assumption is that the Earth’s field changes slowly so smoothing is used to eliminate short term changes which are mostly induced by the geomagnetic storms. Often these are not negligible e.g. 2nd Oct2013, effect lasts from few days up to 2-3 months (see here), it is registered by the geomagnetic stations, with the signal deviating from the slow trend of the earth’s core field.
Dr. S may dispute above, but the indisputable evidence is there.
CaligulaJones says:
October 4, 2013 at 11:14 am
A point I’ve tried to make to environmentalists for years: if millions of cattle farting now are a danger, you have to at least “back out” the millions of slaughtered bison to get a net, not a (pardon the pun) gross figure…
Don’t forget the 7,000,000,000 humans farting. I blame the fast food and the cola companies!
Nice to see you here EM, Leif gaurds the solar blogs to correct what he feels is wrong thinking.
Have you read the stuff put out by the Russian scientists on the International space station, they have been doing some serious solar watching and measuring. Abdussamaton is the main man I think. Regards Wayne
No Wayne I haven’t , have you? …
Maybe we now know the time-lag of the Earth’s climate response to an event of this type.
E.M.Smith says:
October 4, 2013 at 11:09 pm
And as that UV fades and blues diminish with more reds and infrareds; more of the TSI causes prompt evaporation of the ocean surface and less goes meters into the deep. That change in where the energy is deposited and how much evaporation it promptly causes matters to weather.
All that is good and well, but completely irrelevant because the variation of UV over time simply follows that of the sunspot number and TSI.
E M Smith said:
“Similarly, NASA saw a shrinking of the total atmospheric height as less UV caused a cooler stratosphere; that then is closer to the poles when it starts to descend in the Night Jets (and, IMHO, is part of the cause of the more “loopy” jet stream in this mode and colder polar weather).”
Recent observations suggest that the stratosphere warms above 45km and towards the poles when the sun is less active.
Also that it cools above 45km and towards the poles when the sun is more active.
Conventional climatology (and Leif Svalgaard) claims that the entire atmosphere warms when the sun is active and cools when it is inactive but that doesn’t seem to apply to the mesosphere (above about 45km) where the response seems to be reversed.
The reason must be that an active sun actually destroys ozone rather than creating it above 45km and towards the poles.
The reverse sign change in the mesosphere then seems to influence the sign of the stratosphere response as a whole with the main effect towards the poles.
We need that reverse sign response to explain the equatorward surges of cold surface air when the sun is less active because to push surface air equatorward from the poles the height of the tropopause above or around the poles must fall and that implies a warming stratosphere rather than a cooling stratosphere above the poles.
If a quiet sun were to reduce ozone above the poles to cool the stratosphere there then the tropopause height would increase above the poles and the jets would become less loopy and more zonal as the air circulation was pulled poleward.
That is not what actually happens.
That is a feature of my New Climate Model which appears to have ‘gone over the heads’ of most readers.
E M Smith said:
“And as that UV fades and blues diminish with more reds and infrareds; more of the TSI causes prompt evaporation of the ocean surface and less goes meters into the deep.”
So less UV and more longer wavelengths at a time of less active sun would provoke more evaporation but then that evaporation create a more buoyant equatorial troposphere which would push tropopause heights up and force the jets and climate zones poleward.
That results in less loopy more zonal jets whereas in fact we see the opposite.
Therefore I have to conclude that it is the top down effect on tropopause heights near the poles that is dominant and not the equatorial evaporative response to less UV and more of other wavelengths.
Jeff Patterson: “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."
Thank you for your response. My lack of familiarity with the SSA technique and the press of other matters have conspired to prevent me from yet providing an adequate reply. Against the possibility of returning to this again, I'll lay away this summary of what I understand you to say.
If we're looking in the data for evidence of anthropogenic effects, that evidence must lie in some difference between the way data acted after the human activity and the way they did before. For the "way they did before," you use SSA–of which I don't profess to have anywhere near an intuitive picture–to tease a set of orthogonal basis functions from the detrended temperature record and retain the pair that, with the trend, explains most of the record. This is the way you look at "what they did before" (my words, not yours). I might add that I don't think you are uncomfortable with the proposition that this "way they did before" may be descriptive only of a relatively small swatch of more-secular behaviors.
Now, you've observed a spike in the solar-activity data and hypothesize that its effect can be modeled as the response, to an impulse occurring at the time t = tau of the spike, of the linear time-invariant system characterized by q4 dy^4 / dt^4 + q3 dy^3 / dt^3 + q2 dy^2 / dt^2 + q1 dy / dt + p0 y = p3 dx^3 / dt^3 + p2 dx^2 / dt^2 + p1 dx / dt + p0 x, where dy^3 / dt^3 and dy^2 / dt^2 are both zero at t = tau, q1 = q0 = p2 = p1 = 0, and q1 / p0 equals your a-b, i.e., equals the difference between the trends before and well after the spike. This leaves only q3/q1 and q2/q1 as free parameters. (I know I've imposed a change of variables on you, but my experience is that stating my understanding in different but what I think are equivalent terms is more likely to betray any misapprehensions under which I may be laboring than a mere repetition of the words a concept's discloser has used.)
As a test of whether finding a such a system would be mathematically likely, you suggest attempting it repeatedly on random data. But I'm not sure what random data I'd use. Specifically, your assumptions suggest to me that you propose superimposing (presumably, red) noise on the sum of at least an initial-trend ramp b t u(t) and some oscillatory component. But, to throw out one of the parameters, you imposed the constraint of a terminal trend, so I think the signal upon which the noise should be superimposed is the sum of the oscillatory component and not just the initial ramp but also the ramp (a-b) t u(t – tau). And the noise's variance should equal that of the signal that results from subtracting that sum from the real-world data, right?
Also, I would need to reflect on the justification for so many constraints on the type of (time-invariant linear) system assumed.
I re-emphasize here that I'm not really implying anything, because I haven't had a chance really to think things through. But if I do get a chance, these are questions that I still need to ponder.
***
Stephen Wilde says:
October 5, 2013 at 5:24 am
Therefore I have to conclude that it is the top down effect on tropopause heights near the poles that is dominant and not the equatorial evaporative response to less UV and more of other wavelengths.
***
The amount of watts in UV variance is insignificant compared to the overall watts in TSI, and TSI energy manifests itself as heat almost entirely at the surface. The sparse stratosphere does not “drive” weather — weather is driven by convection from the surface upward. The stratosphere height changing altitude (it does that because it is so sparse) doesn’t affect the troposphere significantly.
***
E.M.Smith says:
October 4, 2013 at 11:09 pm
***
EM, I don’t accept that solar magnetic cycles have any significant effect on climate — the amounts of energy variance are just too small.
However, there was something you posted on your site that explained an interesting graph I saw many yrs ago. The graph showed the outgoing IR spectrum from orbit at 3 sites. The tropical & extratropical spots showed what one would expect — a decided, cold “notch” at the CO2 absorbing/emitting frequency. However, the same notch for the Antarctic site was the opposite — it was a “warm” notch! Didn’t make sense.
However, when you pointed out that polar regions are often under temp inversions, it made sense. There, the radiating layer of CO2 (~40,000 ft altitude) was actually warmer than the surface due to the inversion! In that situation, CO2 is actually operating as an anti-GHG, radiating at a higher temp (& thus cooling) than it would without CO2.
Wonder if the models take that into account? (rhetorical)
beng
The height of the tropopause and especially the gradient of tropopause height between equator and poles is critical to the pattern of convective overturning beneath it.
There would be no tropopause if there were no direct interaction between ozone and sunlight creating the temperature inversion.
Changes in the temperature of the stratosphere immediately above the tropopause are enough to alter the entire global air circulation pattern in the troposphere.
Stephen Wilde says:
October 5, 2013 at 8:51 am
Changes in the temperature of the stratosphere immediately above the tropopause are enough to alter the entire global air circulation pattern in the troposphere.
since you never mention actual data [numbers[ I keep forgetting what your grand thesis is. Observations show that the temperature in the lower stratosphere just above the tropopause is lowest at solar maximum [when we have most UV and most warming] and highest at solar minimum [when we have least UV and least warming]: http://www,leif.org/research/Temp-Strat-30hPa-1979-2011.png
From your past comments I predict you will claim that this is just what you expected and that all data always confirm your ideas.
lsvalgaard says:
October 5, 2013 at 9:01 am
http://www.leif.org/research/Temp-Strat-30hPa-1979-2011.png
Leif,
I don’t mention numbers because the data is not available. I do however refer to direction of trend which is good enough for diagnostic and falsification purposes.
You have previously asserted that an active sun warms the entire atmospheric column whilst a less active sun cools it. That is the established viewpoint.
Now you confirm that an active sun cools the relevant region and an inactive sun warms it.
Whether you like it or not that is indeed part of my proposition, as you well know.
Thank you.
And, Leif, your chart shows that the cooling stratospheric trend stopped around 2000 which is exactly when I first noticed the jets start to become more meridional as I have been stating in public since 2008.