Sudden Acceleration

For several years, there was an absolute spate of lawsuits charging sudden acceleration of a motor vehicle — you probably saw such a story:  Some person claims they hardly touched the accelerator and the car leaped ahead at enormous speed and crashed into the house or the dog or telephone pole or whatever.  Many folks have been skeptical that cars were really subject to such positive feedback effects where small taps on the accelerator led to enormous speeds, particularly when almost all the plaintiffs in these cases turned out to be over 70 years old.  It seemed that a rational society might consider other causes than unexplained positive feedback, but there was too much money on the line to do so.

Many of you know that I consider questions around positive feedback in the climate system to be the key issue in global warming, the one that separates a nuisance from a catastrophe.  Is the Earth’s climate similar to most other complex, long-term stable natural systems in that it is dominated by negative feedback effects that tend to damp perturbations?  Or is the Earth’s climate an exception to most other physical processes, is it in fact dominated by positive feedback effects that, like the sudden acceleration in grandma’s car, apparently rockets the car forward into the house with only the lightest tap of the accelerator?

I don’t really have any new data today on feedback, but I do have a new climate forecast from a leading alarmist that highlights the importance of the feedback question.

Dr. Joseph Romm of Climate Progress wrote the other day that he believes the mean temperature increase in the “consensus view” is around 15F from pre-industrial times to the year 2100.  Mr. Romm is mainly writing, if I read him right, to say that critics are misreading what the consensus forecast is.  Far be it for me to referee among the alarmists (though 15F is substantially higher than the IPCC report “consensus”).  So I will take him at his word that 15F increase with a CO2 concentration of 860ppm is a good mean alarmist forecast for 2100.

I want to deconstruct the implications of this forecast a bit.

For simplicity, we often talk about temperature changes that result from a doubling in Co2 concentrations.  The reason we do it this way is because the relationship between CO2 concentrations and temperature increases is not linear but logarithmic.  Put simply, the temperature change from a CO2 concentration increase from 200 to 300ppm is different (in fact, larger) than the temperature change we might expect from a concentration increase of 600 to 700 ppm.   But the temperature change from 200 to 400 ppm is about the same as the temperature change from 400 to 800 ppm, because each represents a doubling.   This is utterly uncontroversial.

If we take the pre-industrial Co2 level as about 270ppm, the current CO2 level as 385ppm, and the 2100 Co2 level as 860 ppm, this means that we are about 43% through a first doubling of Co2 since pre-industrial times, and by 2100 we will have seen a full doubling (to 540ppm) plus about 60% of the way to a second doubling.  For simplicity, then, we can say Romm expects 1.6 doublings of Co2 by 2100 as compared to pre-industrial times.

So, how much temperature increase should we see with a doubling of CO2?  One might think this to be an incredibly controversial figure at the heart of the whole matter.  But not totally.  We can break the problem of temperature sensitivity to Co2 levels into two pieces – the expected first order impact, ahead of feedbacks, and then the result after second order effects and feedbacks.

What do we mean by first and second order effects?  Well, imagine a golf ball in the bottom of a bowl.  If we tap the ball, the first order effect is that it will head off at a constant velocity in the direction we tapped it.  The second order effects are the gravity and friction and the shape of the bowl, which will cause the ball to reverse directions, roll back through the middle, etc., causing it to oscillate around until it eventually loses speed to friction and settles to rest approximately back in the middle of the bowl where it started.

It turns out the the first order effects of CO2 on world temperatures are relatively uncontroversial.  The IPCC estimated that, before feedbacks, a doubling of CO2 would increase global temperatures by about 1.2C  (2.2F).   Alarmists and skeptics alike generally (but not universally) accept this number or one relatively close to it.

Applied to our increase from 270ppm pre-industrial to 860 ppm in 2100, which we said was about 1.6 doublings, this would imply a first order temperature increase of 3.5F from pre-industrial times to 2100  (actually, it would be a tad more than this, as I am interpolating a logarithmic function linearly, but it has no significant impact on our conclusions, and might increase the 3.5F estimate by a few tenths.)  Again, recognize that this math and this outcome are fairly uncontroversial.

So the question is, how do we get from 3.5F to 15F?  The answer, of course, is the second order effects or feedbacks.  And this, just so we are all clear, IS controversial.

A quick primer on feedback.  We talk of it being a secondary effect, but in fact it is a recursive process, such that there is a secondary, and a tertiary, etc. effects.

Lets imagine that there is a positive feedback that in the secondary effect increases an initial disturbance by 50%.  This means that a force F now becomes F + 50%F.  But the feedback also operates on the additional 50%F, such that the force is F+50%F+50%*50%F…. Etc, etc.  in an infinite series.  Fortunately, this series can be reduced such that the toal Gain =1/(1-f), where f is the feedback percentage in the first iteration. Note that f can and often is negative, such that the gain is actually less than 1.  This means that the net feedbacks at work damp or reduce the initial input, like the bowl in our example that kept returning our ball to the center.

Well, we don’t actually know the feedback fraction Romm is assuming, but we can derive it.  We know his gain must be 4.3 — in other words, he is saying that an initial impact of CO2 of 3.5F is multiplied 4.3x to a final net impact of 15.  So if the gain is 4.3, the feedback fraction f must be about 77%.

Does this make any sense?  My contention is that it does not.  A 77% first order feedback for a complex system is extraordinarily high  — not unprecedented, because nuclear fission is higher — but high enough that it defies nearly every intuition I have about dynamic systems.  On this assumption rests literally the whole debate.  It is simply amazing to me how little good work has been done on this question.  The government is paying people millions of dollars to find out if global warming increases acne or hurts the sex life of toads, while this key question goes unanswered.  (Here is Roy Spencer discussing why he thinks feedbacks have been overestimated to date, and a bit on feedback from Richard Lindzen).

But for those of you looking to get some sense of whether a 15F forecast makes sense, here are a couple of reality checks.

First, we have already experienced about .43 if a doubling of CO2 from pre-industrial times to today.  The same relationships and feedbacks and sensitivities that are forecast forward have to exist backwards as well.  A 15F forecast implies that we should have seen at least 4F of this increase by today.  In fact, we have seen, at most, just 1F  (and to attribute all of that to CO2, rather than, say, partially to the strong late 20th century solar cycle, is dangerous indeed).  But even assuming all of the last century’s 1F temperature increase is due to CO2, we are way, way short of the 4F we might expect.  Sure, there are issues with time delays and the possibility of some aerosol cooling to offset some of the warming, but none of these can even come close to closing a gap between 1F and 4F.  So, for a 15F temperature increase to be a correct forecast, we have to believe that nature and climate will operate fundamentally different than they have over the last 100 years.

Second, alarmists have been peddling a second analysis, called the Mann hockey stick, which is so contradictory to these assumptions of strong positive feedback that it is amazing to me no one has called them on the carpet for it.  In brief, Mann, in an effort to show that 20th century temperature increases are unprecedented and therefore more likely to be due to mankind, created an analysis quoted all over the place (particularly by Al Gore) that says that from the year 1000 to about 1850, the Earth’s temperature was incredibly, unbelievably stable.  He shows that the Earth’s temperature trend in this 800 year period never moves more than a few tenths of a degree C.  Even during the Maunder minimum, where we know the sun was unusually quiet, global temperatures were dead stable.

This is simply IMPOSSIBLE in a high-feedback environment.  There is no way a system dominated by the very high levels of positive feedback assumed in Romm’s and other forecasts could possibly be so rock-stable in the face of large changes in external forcings (such as the output of the sun during the Maunder minimum).  Every time Mann and others try to sell the hockey stick, they are putting a dagger in teh heart of high-positive-feedback driven forecasts (which is a category of forecasts that includes probably every single forecast you have seen in the media).

For a more complete explanation of these feedback issues, see my video here.

  • hunter

    AGW has always depended on the suspension of analytical thinking skills to prevail in order to prevail in the public square.
    The application of even cursory critical thinking shows that that apocalyptic story that has been sold to the public and to policy makers is bogus.

  • AnonyMoose

    You’re right. The hockey stick and positive feedback are contradictory.

  • ERl Happ

    The atmosphere itself tests the greenhouse theorem on an annual basis. It does so at the tropical tropopause, where outgoing radiation meets ozone, producing a strong temperature maximum in August at that level. That maximum is in turn due to the seasonal heating of the northern land masses and a loss of global cloud cover. Global near surface air temperature peaks in August, even though the sun is furthest from the Earth at that time. That should tell us something about the importance of clouds in determining surface temperature.

    At the surface between the equator and 10°S the temperature peaks in March and at 200hPa it peaks in April. For those unfamiliar with this way of referring to altitude, the surface has an air pressure of about 1000hPa and the tropical tropopause 100hPa. At the tropopause which varies in height between the surface at the winter pole and 16km at the equator (average 10km) 75% of the atmosphere is beneath you. So the atmosphere is actually very thin.

    I guess the radiation that is absorbed by ozone at the tropopause is coming from the near surface air as it is moved by the trades towards the equator. The surface could not be responsible for the radiation that causes the temperature peak at the tropopause in August. The seasonal minimum temperature at the surface is actually in September. At that time the sea is 5°C cooler than in March.

    The potential for downward transfer of energy from the tropopause, where the maximum is in August, to the 200hPa pressure level where the maximum is in April, is of course there, and if greenhouse theory were valid, we would see it. The maximum at 200hPa would be shifted towards August. But it does not eventuate. I guess that testifies to the strength of the convectional force that cools the troposphere at all levels.

    Greenhouse theory is based on a misunderstanding of how the atmosphere works. The nature of the troposphere is apparent in the Greek derivation of the word ‘tropos’. Although I speak no Greek I believe it means ‘turning’.

    If one takes the trouble to actually look at the data from 1948 onwards the troposphere has not warmed at any level above the near surface layers that are in contact with a warmer ocean, layers that are warmed by surface contact, the release of latent heat of condensation and no doubt absorption of radiation by susceptible molecules. But, convection eliminates the possibility of downward transfer just as it does beneath the tropopause.

    The warming in the tropics, where more energy is received than emitted is slight. Most of the extra energy received has gone into evaporation rather than increased sea surface temperature. So, the increase in temperature at the equator, at cloud level, where the latent heat is released is about three times that at the surface. That energy has not propagated down to warm the surface either.

    On the other hand the surface warming at high latitudes in winter is strong, amounting to about five degrees in both hemispheres. There has been no warming in summer. In fact Antarctica has cooled in summer. That winter warming at high latitudes, when radiation is at a minimum, should indicate the importance of energy transfer by the ocean.

    There is another explanation as to why the Earth warmed strongly between 1976 and 1983, more slowly until 2005 and has cooled since, and you will find it at

    It is time to consign greenhouse theory to the scrap bin of speculative ideas based on too limited an appreciation of the way things actually work.

  • It is downright bizarre that you 1) quote this 15F figure as if I say that was what the Globe would warm, when I explicitly said that 10 to 15 F was what most of the continental United States would warm, and 2) would imply this is somehow my notion, conveniently omitting that it is in fact what both MIT and the UK’s Hadley Center — and even the IPCC — predicts based on stayin on our current emissions path!

  • It is downright bizarre that you 1) quote this 15F figure as if I say that was what the Globe would warm, when I explicitly said that 10 to 15 F was what most of the United States would warm, and 2) would imply this is somehow my notion, conveniently omitting that it is in fact what both MIT and the UK’s Hadley Center — and even the IPCC — predicts based on stayin on our current emissions path!

    And yes, pretty much every major climate model — and pretty much all of the paleoclimate data — suggests the climate is strongly nonlinear, which is why we have had periods of such rapid warming in the past.

  • Eric Anderson

    Dr. Romm:

    Thank you for taking time to comment on this blog and to correct a misperception regaring the warming figure that was quoted. I had a couple of follow up questions on your comments, if you might be so kind:

    – Does your estimate of 10-15F for the U.S. hold for the rest of the world, or is there an anticipated cooling elsewhere, such that the anticipated global average would actually be much smaller than 10-15F?

    – Given that the climate is strongly nonlinear and given, as you point out, that there have been periods of rapid warming in the past and that these periods have ultimately subsided, would it be fair to say that (at least on geological timescales) the climate is ultimately dominated by negative feedbacks?

  • hunter

    Dr. Romm,
    What is the global temperature increase you believe represents the consensus AGW position?

  • Hunter

    The ‘climate skeptic’ apparently will never be able to get his tiny, tiny mind to comprehend that the climate is not ‘long-term stable’. He uses this phrase time and time again, apparently utterly unaware that sharp switches between states are not just possible but are in fact the defining feature of the long term climate record. I pity him for his intellectual inadequacy.

    But we are running before we can crawl in trying to explain this. The ‘climate skeptic’ cannot even read. We see this because, as Joe Romm himself points out, “mean temperature increase in the “consensus view” is around 15F from pre-industrial times to the year 2100” bears little relation to what he wrote.

    Simpler things even than reading seem to be causing problems. While most pre-school children are able to look at something and describe in simple terms what they see, this skill has apparently been lost by the ‘climate skeptic’. Perhaps he could tell us what picture he’s looking at that he thinks can be described by the words ‘incredibly, unbelievably stable’, because it certainly isn’t this one.

    There is serious mental deficiency on display here. And I will bet plenty of money that the existence of ice ages will not trouble our ‘climate skeptic’. I would say in no more than a fortnight, we shall see the idiotic repetition of the same old ‘long-term stable’ nonsense.

  • Hunter

    Correct link… Perhaps he could tell us what picture he’s looking at that he thinks can be described by the words ‘incredibly, unbelievably stable’, because it certainly isn’t this one.

  • Andrew

    Hunter: perhaps you could explain why 1. You are linking to the TAR (hey, did you hear? There has been a report since then!) 2. You are just as confused about the “stability” of climate as Warren is. By which I mean you seem to think stable means “no change ever happens” and not “no “tipping points” or “run away greenhouses”. In electrical engineering terms, the climate is unconditionally “stable” because its feedback is negative ~even when you consider positive feedbacks~. This is a point which is not actually disputed. What you and Warren are both confused about is that climate science has dispensed with the electrical engineering definitions of feedback in favor of a completely different definition.

  • Ed Fargler

    Hunter probably believes that y=Sin(x) isn’t stable!

  • hunter- the real one

    Jennifer cannot deal with the fact that Dr. Romm is promoting some piece of garbage that actually pretendds temps are going to increase 15oF as serious science.
    Only a fool would promote or beleive this sort of alarmist science fiction could be confused as meaningful.

  • Eric Anderson

    Hunter wrote: “There is serious mental deficiency on display here.” Mirror, mirror, on the wall . . .

    I actually laughed out loud when I clicked on your link and saw you were pointing to the IPCC “reconstruction.” You need to spend some serious time at ClimateAudit, particularly in the archives.

    Second, Andrew is absolutely correct. The question is about long term stability, in the sense of being predominately subject to negative feedbacks. Long term stability, does not mean no fluctuations. Indeed, the fact that the very up’s and down’s you so triumphantly point to eventually give way to movement in the opposite direction (as opposed to spiraling out of control), is prima facie evidence of negative feedbacks and long-term stability.

  • Hunter

    Oh dear Eric and Andrew. Looks like you didn’t read the post. Why did I link to that graph? Perhaps because that is the graph we’re talking about!! Your illiteracy is remarkable and embarrassing.

    You clearly haven’t got a clue what feedbacks are. They do not mean than a change will eventually be replaced by the opposite change. They determine the magnitude of the change.

    But you’re not interested in science, are you? You’re just interested in spouting a lot of meaningless babble. You’re ignorant and unintelligent. The second one you can’t do much about, but you could at least work on the first one, if you want to avoid looking like a backward child in public.

  • hunter- the real one

    Our friend Jennifer/scientist/hunter is literally unable to imagine climate science outside the bounds of AGW. He/she is not alone, apparentyly.

  • Andrew

    Hunter-when on Earth did I say “a change will eventually be replaced by the opposite change”? I didn’t. Don’t put words in my mouth. And you might want to know that for a person who is “ignorant and unintelligent” to have and IQ of 180 is something quite strange indeed. Eric is to some extent misunderstanding my point, to, which isn’t helping your wanting to see enemies everywhere lurking in the corners to jump you…And I don’t really care whether Warren was discussing the TAR graph or not. Both of you should cite AR4, not an 8 year old document that was out of date when it was published.

  • Hunter

    Do my eyes deceive me, or are you claiming to have an IQ of 180? It is strange indeed, then, that you wrote ‘and’ when you meant ‘an’, and ‘to’ when you meant ‘too’, that you somehow failed to notice that my last post began “Oh dear Eric and Andrew…” and not “Oh dear Andrew…”, and that you can’t see the sense in posting a link to the very graph being mischaracterised by the ‘climate skeptic’. You really are spectacularly stupid.

  • Al’n

    Oh my. A typo. He can’t possibly be clever then, because all clever people are perfectly coordinated.

    I can only conclude, therefore, that you are also stupid, because you wrote “than” instead of “that”.

  • hunter

    Jennifer, you are the gift that keeps on giving.

  • Andrew

    Er, why yes I am a freaking genius you rude little brat. The only one who is being spectacularly stupid is you. For the last time-both you and Warren should be citing AR4 not the TAR. And anyone can make typos, it doesn’t prove they are smart or stupid. What’s more, you have no clue what I meant, and that you chose to not merely smear me in your post does not forbid me from defending myself. Eric must defend himself, because I am not him. I must defend myself, because I am myself. Do you mean to tell me that you intended no slight against me in your post? If so, then you are quite thick, unable to convey your meaning carefully enough to avoid coming across as insulting everyone you converse with. I mean really, read your posts carefully. If you intend your vitriol to be targeting an individual specifically, then use the damn targeting computer and lock on to that person. Because the force is not with you. But the farce is.

  • Eric Anderson

    Hunter, in fairness, I want to make sure I understand the wording of your comment: “[Negative feedbacks] do not mean than a change will eventually be replaced by the opposite change.” If you mean that the existence of a negative feedback in a system will not necessarily result in the system as a whole changing the sign of its vector over time, then I definitely agree with you on that point.

    Thus, in the particular example we are looking at, namely temperature (setting aside for a moment the significant issues of whether the concept of a global- or hemisphere-wide temperature makes sense, whether alleged proxies are in fact temperature proxies, etc.), we can say that if x drives increasing temperatures and if y is a negative feedback on x, it does not follow that temperatures will eventually vector negative, due to the mere existence of y. The same would hold true with a reversal the other direction. Fortunately, I did not say that the existence of a particular feedback will cause the sign of the vector to reverse, so I have nothing to be censured of in this regard.

    What I did say was that the up’s and down’s on the graph you pointed to “eventually give way to movement in the opposite direction (as opposed to spiraling out of control).” I also said that such an overall picture is “prima facie evidence of negative feedbacks and long-term stability.” I did not attempt to tie any particular movement to any particular feedback. This is entirely consistent with the last paragraph of the original post.

    In any oscillating system which, as far as anyone can tell, has never reached a “tipping point” in the past, there are only a finite number of possibilities (I’ll refer again just to our two variables for simplicity): (i) either feedback y becomes sufficiently strong to eventually cause the vector to reverse, (ii) x eventually loses some of its temperature-driving potential, which, in combination with y causes the vector to reverse, or (iii) some other factor outside of, or in combination with, x and/or y causes the reversal of the vector.

    Without making claims about any particular driver or any particular feedback, the observation of a dynamic oscillating system that changes the direction of its vector many times throughout history without once spiraling out of control, is, as I stated, prima facie evidence of negative feedbacks and long-term stability. The burden of proof is on anyone who posits that the system has somehow now become subject to mechanisms that would overpower the long-term stability of the system.

    I would be happy to discuss this further if you would be willing to do so sans the demeaning insults. Otherwise, I have no intention of responding further, as I trust I have adequately articulated my points.

  • Hunter

    “What I did say was that the up’s and down’s on the graph you pointed to “eventually give way to movement in the opposite direction (as opposed to spiraling out of control).””

    Lovely, so we agree on a very simplistic description of how temperatures have varied. Your comment in brackets is meaningless though, unless you literally mean by it that temperatures might go to zero or infinity. And the ups and downs in the temperature record are not in any way evidence of negative feedbacks or long term stability. No possible inference about those two things can be drawn. Your logic is faulty.

    “as far as anyone can tell, has never reached a “tipping point” in the past”

    You should not consider that everyone is as ignorant as you are. A ‘tipping point’ is a sudden jump in climate state in response to a smoothly varying forcing. We know all about these; look up “ice age”.

    In science, if someone is pontificating despite being unaware of basic and important results, it’s quite normal to tell them so. If you consider that a demeaning insult, then stop being so ignorant. The beliefs that you are expressing are a combination of factually wrong, logically meaningless and utterly irrelevant. For many years, people have been politely pointing out the flawed thinking shown by people like you, but you clearly haven’t listened. So if you can’t be bothered to educate yourself but prefer to speak from ignorance, then I am quite happy to tell you that in no uncertain terms.

  • Andrew

    Hunter, depending how you define “sudden” it is hard to see how any evidence about rates of change can be inferred from coarse data on such a time scale. So how do you define sudden? Please be specific, otherwise it is not clear what you define a “tipping point” is, or understand why you think ice ages are examples.

  • Eric Anderson

    Let’s try this one final time. Hunter wrote:

    “And the ups and downs in the temperature record are not in any way evidence of negative feedbacks or long term stability. No possible inference about those two things can be drawn. Your logic is faulty.”

    Nice try, but you are wide of the mark.

    On all three points.

    Let’s take them one at a time.

    “And the ups and downs in the temperature record are not in any way evidence of negative feedbacks or long term stability.” Wrong. In a dynamic system, oscillation around a norm over a long period of time is in fact precisely what we would expect to see if there are negative feedbacks and long-term stability. We can certainly debate how much weight should be assigned to any particular piece of evidence, but you are simply incorrect that the temperature record is “not in any way evidence.”

    “No possible inference about those two things can be drawn.” Wrong. An inference certainly can be drawn, and reasonably so. It would also be very reasonable to expect those who might challenge that reasonable inference to come forward with some evidence as to why the reasonable inference is incorrect. What you may have meant to say, but didn’t, is that it does not follow as a matter of logical deduction from the temperature record alone that the climate system is dominated by negative feedbacks or long term stability. Fortunately for me, I never stated that it did.

    “Your logic is faulty.” Wrong, as detailed above.


  • Jim

    I brought up earlier that NOX could fertilize trees and partially account for the supposed temperature spike recorded in some of the tree rings. Here is an article about how aerosols enhance light, and CO2, absorption by plants due to diffusion of the light. They claim this caused the trees to grow faster. Wouldn’t that cause the rings to indicate a greater temperature than actually occurred?

  • Eric Anderson

    Jim, this is one in a long line of reasons why tree rings are not a reliable proxy. There are so many unaccounted for variables, it is not clear to me how any reasonable confidence can be placed on tree rings as a proxy for temperature.

  • Paul Ralley

    thanks again for a clear and logically consistent post. Can I suggest a subtle amendment to your comment that positive feedback loops are very rare in nature (sorry if I misquote here). There are several examples (much more common than fission) such as population explosions and virus spreads which have clear positive feedback (e.g. a cold virus copies itself 10^6 in 24 hours). I consider that your point is entirely valid, I just thought it may close off tacky objections.

  • “in fact, we have seen, at most, just 1F (and to attribute all of that to CO2, rather than, say, partially to the strong late 20th century solar cycle, is dangerous indeed). ”

    Indeed, especially when you note all the siting problems (near heat islands, etc.) 😉

    On thing I might suggest generally, is that you require comments to be civil. I would think that this would encourage better, more in depth discussion and participation by knowledgeable folks on both sides of the debate.

    Eric’s patience is noted, but others will almost assuredly be drawn into a food fight, sooner or later.

    In any case, thank you for creating this site. I’ve learned a bit and will be back.