There have been coolings in between warming stages in the past. The modern warming is no different from the Medieval, Roman or Minoan warm periods, except it hasn’t been as warm as any of those. The LIA might however have been colder than the previous cool periods.
The long-term (3000 to 5000 years) trend in temperature is still down.

Well to be fair the main reason for the shortage of timber in the UK and its increasing need for iron was the series of wars against the French from 1700 to 1815. These may have been influenced by the cooler climate but the main driver was geopolitical rivalry
The conflicts were in the form of periods of open warfare interspersed with the sort of cold war we were familiar with between the USA and USSR. Battles were fought on almost every continent with major campaigns fought in North America ,Europe and India with skirmishes in Australasia and Africa.
This required the felling of most of the forests in England to build ships and produce the charcoal to smelt iron. Coal had been mined on a small scale since at least the time of Queen Elizabeth 1st. It was shipped to London for domestic use. James Cook learned his trade on just such a vessel and the ships he used for his explorations were converted coal carriers. They were built with a wide beam and flat bottom so they could load and discharge coal from the beach without needing a port.

The two biggest signals are from c. 425 BC and AD 1260 (Table 2).
From 769 BC to AD 1 there were nine eruptions rated M & L (I didn’t count those rated S). Between then and AD 770, there were 12 Ms and Ls. From that year to AD 1540, there were eight Ms and Ls. Since AD 1540 (only 475 years), there have been seven Ms and Ls, which scales up to 11 (rounded to nearest whole integer) for 770 years.
So, if size matters, the most active such periods were AD 1 to 770 and from AD 1540 to now. It might be a more meaningful comparison to go by total sulfate load per century.

Cool immediately after? Compared to what? The other noise and oscillation clearly visible in the global anomaly? And what do you mean by “immediately”?
You need to play “hunt the volcano”. All it takes is a good friend who goes here:
http://www.woodfortrees.org/plot/hadcrut4gl/from:1850/to:2015
Have him or her print the page, cut off the time scale and temperature scale, cut the temperature series into vertical (overlapping) strips 20 years wide. Then you get to play. In this time interval there have been a number of large — VEI 5 or 6 — volcanic eruptions. No fair looking them up, or even counting them. I promise, though, that there are more than 10. So use a vertical ruler and mark 10 lines on this graph that you think are evidence of volcanic cooling from major eruptions. In order to “win”, your line has to occur no more than two years after the eruption, no fair counting misses that precede the cause!
Good luck!
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You need to play “hunt the volcano”. All it takes is a good friend who goes here:

That’s a pretty amusing way of doing it.
A more formal method would be to compare the signal to that of the appropriate feedback level of auto-correlated noise and see if you can find the signal using wavelets. The Null Hypothesis is that your signal is just due to random autocorrelated noise, and this is entirely testable using Monte Carlo simulations.
This is a pretty good paper that does this. In the paper when it comes to SST the ENSO signal is the only thing that crosses the 95% confidence interval. Nothing else does. No volcano signal in SST. Certainly not C02….
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.1738
Unfortunately they took down the cached copy in the last week and the links are broken. I saved off a copy It’s at:
https://www.dropbox.com/s/lw1kzdfjw0ifcdo/10.1.1.28.1738.pdf?dl=0
The general writeup of the method on the author’s website is here:
http://paos.colorado.edu/research/wavelets/
Peter
PS: If there’s interest I’m going to attempt to apply the same analysis to surface temperatures. Alas the wavelets tool in Octave are poor, I’ll have write my own.

BTW, what makes you think the trend is due to ln(C02) rather than noise? You have no evidence to support that. That also could be noise. Remember autocorrelated noise has energy proportional to 1/frequency. Also remember that you can’t see multi-hundred year period energy unless you actually collect the data…

My friend, I do not think “have no evidence to support that” means what you think it means, not when I present a picture with 165 years of temperature anomaly with a ln(cCO2) + T_0 drawn literally right down the middle of the data. Tht is substantial evidence to support it. No evidence would be historical data that did not scatter neatly around the log curve.
Is the data “sufficient” to prove the hypothesis? Of course not. For one thing, as you note, it is only a fairly short period of time, as these things go. For a second (which I didn’t show on this graph but do on others presenting the same fit) the acknowledged error bars of HadCRUT4 range from 0.1 C on the modern side to around 0.3 C in the 19th century (where I seriously doubt the honesty of the latter estimate). For a third, HadCRUT4 (and all of the other anomaly estimates) suffers from having been repeatedly “adjusted” in ways that almost always cool the past and/or warm the present, so that a substantial amount of the warming presented is due to data adjustment that may or may not be free from the biases that plague even the best-intentioned of data adjusters with a hypothesis to prove or an axe to grind. For a fourth HadCRUT4 doesn’t adjust for UHI at all (IIRC) and IMO UHI adjustments would obviously oppose and at least partly cancel the many “warming” adjustments made. For a fifth, there are many alternative hypotheses that might also explain the data, including the cumulation of many kinds of noise or the inclusion of neglected physics or features of nonlinear dynamics and deterministic chaos (as opposed to “noise”). For a sixth, the log CO2 model probably won’t work over the last 2000 years, maybe not even over the last 1000 years, although the global anomaly from before the invention of thermometers is known only by means of (contentious and inconsistent) proxies of various sorts and has even more uncertainty than the already substantial and probably underestimated uncertainty of thermometric estimates in the 19th century. At some point this uncertainty is so great that we literally don’t even know what we are supposed to be fitting.
None of which means that the graph above is not evidence in favor of the hypothesis that CO2 warms the climate according to the theoretically predicted and easily understood log concentration rule. Seeing this curve should — if you are unbiased and/or have managed to avoid making up your mind about it on non-objective grounds — take whatever degree of belief you had on the issue before you saw it and increase your degree of belief in the “CO2 has caused some or all of the warming over the last 165 years) and decrease your degree of belief in the alternative hypotheses including whatever you wish to assert is the null, not the other way around. Honestly, the hypothesis fits the data pretty damn well, and objections from my long list above and more besides notwithstanding, that fact alone makes the hypothesis more likely to be true, not neutral, not less likely. How much more likely is difficult to quantify, but given that the hypothesis I implement is the no-feedback no-lag pure mean field theory applied to the Earth as an open thermal system, I’d say that it is very substantial evidence that at least part of the warming observed (which is itself, note well, highly uncertain given the acknowledged error bars — it could literally be half of the median claim) is due to the increase in CO2 as a greenhouse gas.
Note well that I am far from alone in my personal belief that this is the case. Virtually all of the physicists including the most skeptical of them who speak or write on the issue agree on it, because one can walk through a derivation of the prediction and it makes sense. It also has considerable uncertainty because parts of the computation cannot be done precisely and the approximations used introduce uncertainty, as well as the fact that it is one component of a strongly coupled complex nonlinear chaotic double Navier-Stokes open system and so mean field results in general are certainly doubtable or could be overwhelmed or augmented by nonlinearities and feedbacks within the complex system.
The point is that the sensitivity implied by this damn good empirical fit is 1.8 C per doubling of CO2. This is a far cry from the median IPCC estimate, and is IMO more likely to be an overestimate rather than an underestimate because of the high probability of warming bias corrupting the anomalies (in a most non-scientific estimation process). But I don’t think that all of the warming in any of the major anomalies is due to adjustments or bias, and think that the case for anthropogenic CO2 contributing to the observed warming is a strong one, just as I think (at this point) that the argument for strong cooling due to anthropogenic or natural aerosols is a weak one. With this one correction — weak to neutral cooling due to aerosols — GCMs predict much more modest (and IMO more likely accurate) climate sensitivities, in the 1 to 2 C range. This is not overtly inconsistent with skeptic Lindzen and Choi’s estimate of around 1 C.
Don’t get me wrong. I am very much aware of the work of Koutsoyiannis on Hurst-Kolmogorov statistics in non-stationary climate processes, and yes, it is by no means certain that some, or all, of the observed 165 year warming is not due to the cumulation of either random or biased Hurst-Kolmogorov shifts. One can certainly run models to show that this hypothesis is capable of explaining the data, but alas those same models show that there is no more than a probability that the particular pattern observed would be produced, with alternatives with less robust cumulation of temperature rather more likely. The statistical models alone also are not easily made consistent with causal models or dynamical models (even simple ones) for the open system — the connection to the fluctuation-dissipation theorem, for example, is very difficult to imagine. The best one can say is that chaos is causing fluctuations that behave like colored noise or the like, which is descriptive but not very useful or testable.
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rgbatduke responded to my comment:

You have no evidence to support that.

I apologize, that was far too strongly worded. I should have said “you have insufficient evidence”. I’m usually more careful in my phrasing, sorry about that.
You presented all my skepticism in a very well written reply, which I mostly agree with. I learned a lot from your reply and really appreciate it. I have some more reading to do now…

Koutsoyiannis on Hurst-Kolmogorov statistics in non-stationary climate processes

I would love to get some references on that. Please post some, I’m still learning a lot in this area.
best regards,
Peter

Sorry, I should be more clear. I meant the part of the paper where they use the idea of deciding whether the hypothesis that there’s a signal, as opposed to the Null Hypothesis of “it’s noise”. As you point out you need at least 4 periods to ascertain anything about low frequency signals. A long term trend like C02 is as low frequency as it gets…

A monotonic trend has no (meaningful) frequency. Hence using Fourier analysis to extract its components is largely a waste of time on any timescale. Indeed, it contributes a whole frequency spectrum of components only because harmonic waves form a basis for the vector space of continuous functions (including monotonic ones) not because it has a “frequency”.
On the other hand, the fit to log CO2 above most assuredly is not noise on the timescale presented. Rather, there is clear evidence of noise around this physically motivated signal. Fourier analysis is numerical data in search of a cause and even with the FT or wavelet analysis in hand, one has to guess what MIGHT be producing what appears to be a signal at any given frequency unless one has a theory that can be used to reduce the dimensionality of the fit.
This is why wavelets and fourier analysis are relevant to the short period stuff — if nothing else, they characterize the short time/transient response rates of the climate, which is actually shockingly important because of the Fluctuation-Dissipation theorem, and which is shockingly neglected in climate science and modelling, although there is some very recent work by Majda, et. al. that IMO shows considerable promise with the sole complaint that it is focusing on low-frequency response. The primary dissipative modes are clearly high frequency stuff like the peaks observed in both wavelet and Fourier transforms, and should really be studied with Laplace transforms and autocorrelation methods, or with truly complex and somewhat ad hoc methods that attempt to identify and project out specific physics and observed physically motivated frequencies — arguably for example the 11 year cycle and the log CO2 response and possibly on the 6+ VEI volcanoes — and focus on the short period fluctuations that remain.
As I pointed out above, the fit I present is a no-lag, no-feedback fit to log CO2. It works more or less perfectly (perfectly within clearly visible, consistent short period noise). This is a serious problem for models that claim that there is a lot of “uncommitted warming” that is lagged by 30 to 100 years, or models that argue that there is or will be a twofold or better amplification of the warming due to water vapor feedback. Response could be lagged, no doubt, but this makes things more complicated and is thus not the default assumption as long as an unlagged model works. Similarly, there could be water vapor feedback (both ways!) but if so, it seems to have no impact on the overall log character of the response, which empirically must include all feedbacks. So 1.8 C/doubling could be interpreted as the climate sensitivity including all feedbacks — perhaps CO2 alone would have only produced 0.8C or 0.9 C — and if there is any uncommitted warming in some sort of invisible “pipeline”, it is cumulating and releasing in precisely the right way for it to be invisible, buried inside a nearly perfect log CO2 total response.
Wavelet analysis is relevant to ENSO, the SOI, perhaps (marginally!) to the PDO, to the NAO, AO, etc. Aside from ENSO, the multidecadal oscillations are at the edge of the fourier resolution from a 165 year sample, almost 2/3 of which predate truly global observation with reliable instrumentation. We are half a century to a century away from having enough, reliable enough, data to be able to resolve many of the theoretical hypothesis out of which the enormously complex model of climate must be built. In the meantime, we are stuck with unconfirmed guesses, beautiful theories, political arguments, and a whole lot of confirmation bias as people who want the world to wean itself from coal and oil use the specter of climate catastrophe to bolster their otherwise hard-to-sell arguments, and people who want to use coal and oil no matter what argue that increasing CO2 has no effect whatsoever and besides, we aren’t responsible for the increase.
The evidence strongly supports the assertion that we are largely responsible for the increase in CO2. The evidence strongly, but not conclusively, supports the assertion that the increase in CO2 has contributed to the general rise in global average temperature over the last 165 years. The evidence is absolutely clear that over this period, the net effect of increased CO2 both directly and as a side effect of producing cheap energy on human culture and society has been so overwhelmingly positive that it would not be far short of the mark to assert that the entire development of human civilization and its wealth and prosperity and contributions to the general weal has depended on it. Coal based energy lights the night and fuels our factories, and the CO2 released has only improved the Earth’s climate — so far — and has almost certainly been a tremendous blessing for the CO2-starved biosphere — so far. The evidence so far does not support the assertion of any sort of looming “climate catastrophe”, although neither does it rule such a thing out.
It is difficult to choose a prudent course, given the evidence. But it is absolutely impossible to choose a prudent course when all of the evidence and reason applied to the problem is horribly distorted before being presented to the public (by both sides) to lead to a foregone conclusion (in both) directions. One side ignores the tremendous benefits of coal based power, plus the inconvenient truth that we can live without it at the moment only at the expense of the greatest depression the world has ever known times ten. The other side ignores the fact that increasing CO2 could, at some level, create serious problems for the Earth’s biosphere and its human component. Prudence suggests — perhaps — that it would indeed be desirable to gradually shift global energy production into long term sustainable forms, simply because coal and oil are limited resources and we are in some sense squandering them if not because of the risks associated with altering ocean chemistry and/or introducing unpredictable shifts into the chaotic maelstrom of the climate. Prudence demands — for certain — that this transition should be slow and should proceed at a rate consistent with the economics of poverty and the inevitable advances of technology.
Should we be burning coal at an increasing rate to make electricity, especially for the world’s poorest people, as fast as we need to, ten to twenty years from now? Almost certainly. Should we still be doing so in 2050, or 2100? Almost certainly not. Should we continue to invest heavily in the development of alternative/sustainable energy resources? Of course, a no-brainer. Should we push the subsidized installation of those alternatives when they are clearly not economical, when the technology needed to support them is immature, when by doing so we divert money from the many other burning issues that confront us (like world peace, world education, world poverty, and the need to support research that might MAKE the alternatives the LESS expensive option in the long run?
I think not. Alternative energy sources are great, to the precise extent that they make economic sense. When something is economically optimal, one doesn’t have to force people to adopt it. The evidence of long term future costs is weak and at least partly trumped up, and analyses of cost-benefit of using coal in particular as an energy source that rely on failed computer models to predict expensive catastrophes and that ignore the obvious net present benefits are not convincing. On the other hand e.g. solar technologies are very close to maturing and will very likely become the least expensive alternative over the next decade or two at the most. Technological breakthroughs in energy storage would change everything. Development of thermonuclear fusion or LFTR would change everything. One cannot make enormously expensive decisions to implement immature technologies or the future will laugh at you even as the con artists who will line up to take your money thank you.
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What about the idea that trend can be due to auto-correlated noise? Or some other process such as whatever ended the LIA? I’m pretty sure I can create autocorrelated noise on some period in the time series replicates a ln() function. After all I’ve already done that for the GISS temperature record…

Of course this is possible. But is it probable? That’s a very, very, difficult question!
For one thing, to get the particular pattern observed at all, one has to make a small mountain of assumptions on the character of the autocorrelation time(s). Then one has to run many sequences (for an assumption pattern that works at all) because unbiased noise will drive temperatures down according to some smooth function (for a sufficiently short segment of the data) as likely as up, and most of the time will take three steps up and two down, pursue a drunkards walk deviation from any starting point, as likely up as down, across a long enough timescale.
Some fraction of the sequences will be close enough to your desired pattern that you can count them as “evidence” that the autocorrelated noise you’ve selected could be the cause of the warming observed. Yes, it requires the moral equivalent of flipping heads 25 out of 30 times or the like and hence is not “likely” but it is possible. If you choose just the right noise, you might get it down to within the p = 0.05 cutoff that “cannot be rejected” in a standard hypothesis test (although it is interpreted in many other ways, sadly).
Of course, this is precisely the argument used by the purveyors of the GCMs, which are de facto doing precisely this. They are running a strongly autocorrelated Markov process, one that does not conserve energy in the first place with constant forcing, let alone reflect actual energy imbalance in the open system, so it would drift in just this way if not renormalized to some sort of guess at energy conservation that also leaves the supposed forcing residual. The result is that any given GCM produces an enormous (shockingly so, if you’ve ever seen it) spread in possible futures for a tiny random perturbation of initial conditions and parameters for a fixed forcing schedule. Sometimes it warms a lot. Sometimes it doesn’t really warm at all. Sometimes it cools. Then they average all of these futures together and make some sort of claim for this being predictive, even though per model the observed trajectory of the planet is out there on the wrong side of the p = 0.05 cutoff for the ensemble of trajectories for a majority of the models in CMIP5. Then they (worse still) average all of the CMIP5 trajectories together and show the collective envelope of the perturbed parameter ensemble average trajectories to fool the eye into thinking that the observed trajectory is within their acceptable predictive range.
And here’s the real tragedy. They do this without the slightest shred of support from the combined theories of mathematics and statistics! There are no mathematical theorems I’m aware of that prove that the envelope of trajectories from a highly approximated, multivariate nonlinear chaotic model solved at an absurdly large integration stepsize that doesn’t even preserve detailed balance in a a stationary system has some necessary relation with the actual trajectory of a real system that is evolving consistently and with perfect balance all the way down to the subnuclear scale. And in any event, averaging multiple failed models does not produce a successful model in any theory of statistics with which I am aware. It certainly can, just as you can show that random chance can produce 25/30 heads and hence could be an explanation of why you are losing your shirt to a stranger who talked you into betting in a train station.
The question is — what are the (true, unbiased) odds? Which is globally more likely, 25/30 heads or meeting a stranger in a train station who likes to wager on coin flips who just happens to possess a coin or coins that produce a surplus of heads when flipped?
This is why one should stick with Ockham’s Razor. The model I present above (leaving out the volcanic bit) is effectively a one parameter model. Yes, it has to match scales with the arbitrary zero of the model lined up with the arbitrary zero of the anomaly, but this is a trivial shift up or down. The curvature is all . You expect this behavior on purely physical grounds, you look, and there it is. This isn’t betting with a stranger in a train station. This isn’t playing a much more elaborate game of chance with the GCM modelers. This is betting that our understanding of quantum mechanics, fluid dynamics, and radiation theory is not egregiously wrong as a simple mean field theory! Sure, there is noise, but the fit above is really, really good and it doesn’t require anything but the short-period variations associated with the reliable part of the wavelet or fourier transforms that characterize the short-period quasi-periodic variations of the climate to model the observation acceptably every time. It is literally a lot more likely to be correct than competing explanations, especially ones that rely heavily on random chance to obtain the observed (comparatively unlikely) pattern of warming in the first place.
With all that said, you should google up Koutsoyiannis’ papers (readily available on the web, for the most part). He works through the statistics of all of this a lot better, and shows that a lot of the climate’s variation can be explained — in the sense that it cannot be rejected — as a cumulation of delta-correlated punctuated equilibrium shifts, with or without an underlying bias. There is some evidence for this in the actual climate — the current “pause” being part of it. There was a “sudden” shift up from 1985 to 1997-1998, followed by a near plateau of temperatures. There was a simlar shift pattern in 1930 to 1945, followed again by a near plateau of temperatures. There are similar, but both smaller and longer shifts and plateaus visible in some of the VERY long time hydrological records Koutsoyiannis originally studied. One can see the same thing in Bob Tisdale’s SST curves, where it is very pronounced and where the shifts are often strongly correlated with ENSO activity either way. In other words, there is a possible causal basis underlying the statistical analysis — one isn’t just mixing up a particular recipe of autocorrelated noise that could explain the climate, one is proposing that e.g. multidecadal oscillations cause step shifts in a locally stable equilibrium set point, and that even if these shifts are random they can easily cumulate to produce a near-monotonic shift up or down over a century or two, however unlikely it is that this will persist indefinitely without help in the form of a (e.g. CO2 linked) bias. Where “easily” is understood to be strictly decreasing in probability the more times in a row heads are flipped without the bias.
Reality is, IMO, very likely to be a mix of these two things. The “local equilibria” being punctuated can be interpreted generically as a field of (locally stable) strange attractors of the complex highly multivariate nonlinear chaotic dynamics. In such a dynamical system, one expects the system to shift “randomly” (chaotically) between an orbit around any given attractor (an orbit producing, BTW, the short period spectra we started by discussing) to an orbit around a neighboring attractor after some number of cycles. However, climate is doubly non-stationary — the field of attractors itself is non-stationary. CO2 concentration variation (and, quite possibly, other things) may well shift the field of attractors, or “tip” the underlying contour of the stable points to make it somewhat more likely to shift to a warmer orbit than to a cooler one. The bitch is then to try to separate the inseparable — to infer the underlying dynamical structure of the inaccessible attractors from the chaotic progression of a single trajectory through an abstract space of almost inconceivable complexity, where there are almost cost certainly orbital fields of attractors distributed around superattractors that correspond, for example, to glacial/interglacial states, that are getting slowly pushed up or down by some truly long time scale dynamics.
Imagine shooting a pinball onto a vast smooth sheet. Underneath the sheet there is a grid of pins attached to the sheet that can more or less smoothly push it up here, pull it down there. The pins themselves are mounted on a second sheet with larger pins that can push up whole fields of smaller pins. Those pins are also mounted on a sheet with larger pins still, all the way down through an unknown number of steps to a sheet with only two very large pins that very, very, slowly move up or down relative to one another.
The trajectory of that pinball is, quite probably, our climate with only orbital, non-anthropogenic variation of our climate, or would be if the actual climate wasn’t strongly non-Markovian on top of everything else. Anthopogenic CO2 is slowly adjusting the legs of the pinball table itself, tipping it slowly over towards the warm-phase side of the table. But we have no good way to determine the rate of the tip, because we do not know how to predict the motion of one, single, layer of the underlying pins that are constantly shifting the topology of the top sheet on which the climate actually runs, swirling around a dimple a half dozen times before popping up over the lip and into a neighboring dimple, with curvature that moves it round super-dimples and super-duper-dimples ad nauseam.
To understand this, we have 50 years or so of halfway decent data — some would argue only 35, some might argue for even less, only 15 or 20 — plus another century plus of increasingly corrupt and incomplete instrumental data, followed by low resolution, high error proxy-based guesses about the trajectory of the pinball in the more remote past. Frankly, we don’t stand a chance. And we won’t stand a chance to make progress until somebody acknowledges the incredible difficulty of the task, difficulty that may require more patience than the three-year grant cycle, tenure-based-on-non-null-results dominated world of scientific research is capable of permitting.
Nobody wants to hear this, but I think it is very plausible that it will take fifty to a hundred more years of accurate measurements made with instrumentation we haven’t even thought of yet to get a handle on the data needed to understand the climate at a meaningful resolution. And even then it will be impossible as long as political and confirmation bias runs rampant in the field and distorts judgement with its religious save-the-world zeal.
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