In the last post I showed that not only is CO2 increasing, its growth rate is also increasing. So, the growth rate of CO2 is faster now than it was just a few decades ago. Significantly so.

There’s a generic term for growth rate: it’s called “velocity,” and is the time derivative of the quantity in question. Since the quantity in question is CO2 concentration, the velocity is the CO2 growth rate.

But indeed the growth rate hasn’t been constant. It has increased, as shown in this graph:

Clearly the growth rate (the velocity) is increasing over time, and yes, the increase is statistically significant. There’s a generic term for the rate of change of velocity: it’s called “acceleration.” Over the past several decades, the acceleration of CO2 is not zero, it’s positive. So, the long-term growth rate (the long-term velocity) is higher now than it was just a few decades ago.

Much to my surprise, I got an email from Tim Curtain, objecting to my post. He says:

Your Blog “Open (sic) Mind” today claims (wrongly) that there is an increasing rate of change of the rate of growth of atmospheric CO2, which in your Gospel must mean acceleration of the rate of change of the anomaly:

He also included this graph:

No, Tim. I didn’t say there was an increasing rate of change in the rate of growth of atmospheric CO2. I said there was an increase in the rate of growth of atmospheric CO2. I think you need to improve your reading comprehension skills.

All the evidence indicates that the increase in the growth rate is, as far as the data show, roughly constant over the long term. In other words, the acceleration of CO2, which is the rate of increase of velocity, is constant. That’s why a straight line fits the velocity data well in the above graph. Linearly increasing velocity means constant acceleration.

It does not mean an increasing rate of change in the growth rate. It means a constant non-zero change in the growth rate. Likewise, it does not mean an increase in the acceleration, it means a constant (non-zero) acceleration.

It’s possible that the long-term acceleration is itself changing, but the evidence doesn’t suggest that (yet).

There’s a generic term for the rate of change in acceleration: it’s called “jerk.” There’s no evidence of any jerk in CO2 concentration over the long haul — the long-term jerk can’t be shown to be different from zero. But the long-term acceleration can be shown different from zero. That’s what “increase in the growth rate” means.

What I actually said (referring to the above graph) is this:

Clearly the annual change in CO2 concentration fluctuates. A lot. But it’s consistently positive, CO2 is growing. And there’s a trend there as well as fluctuation, an upward trend, because the rate of increase is itself increasing. I’ve superimposed a trend line on the above graph.

Note: “it’s consistently positive” refers to the growth rate (velocity). That’s why “CO2 is growing.” But growth rate (velocity) is not constant so “there’s a trend there as well as fluctuation.” In other words, velocity is changing, i.e., CO2 is accelerating. And it’s “an upward trend, because the rate of increase is itself increasing.” In other words, the acceleration is positive, not zero, and not negative.

I never claimed, or even implied, that the acceleration was changing. I showed that the velocity (the growth rate) is changing. It’s increasing — so the acceleration is positive. As I said at the end:

Yet one fact remains, inexorable. CO2 continues to grow, significantly faster now than just a few decades ago.

Is that clear enough for you, Tim?

Also to my surprise, another email on the same topic appeared in my inbox, also from Tim Curtin, offering these pearls of wisdom:


tamino (aka Grant Foster) like Schmidt and his co-authors including Mike Hockeystick Mann, and Kevin Trenberth and their Australian cheerleaders JQ and hc cannot actually do calculus:

My calculus is fine, Tim. It’s your reading comprehension that needs work.

Feel free to object to what I say. Please don’t object to what I didn’t say, at least, not to me. I never said there was any “jerk” — in the CO2 concentration.


113 responses to “Jerk

  1. To be fair, it isn’t the most intuitive thing to interpret graphs of velocity as a function of time. I presume he accidentally interpreted the y axis of your first chart as CO2 concentration rather than the 12-month difference that you actually plotted, and jumped to hysterical conclusions. This doesn’t make him less a jerk, but it probably could’ve been avoided with a more transparent/straightforward presentation of the data rather than arbitrarily plotting the annual change (somewhat arbitrary; I realize that doing that is a good way to deal with the annual oscillation).

    I’d find it easier to follow an analysis that was a simple polynomial fit to the data (either as-is or with a low-pass filter to get rid of the annual oscillation), but I see the difficulty in explaining that as well since many people aren’t at all familiar with calculus.

    [Response: Yet he himself graphed the annual change (not the CO2 concentration) as well as the acceleration, and labeled the lines with the correct units. Also, if someone is going to pontificate about climate change and CO2, shouldn’t that someone know what the CO2 graph looks like?

    And of course, if you excuse his mistake by suggesting he had difficulty interpreting a graph of velocity as a function of time, what does that say about his accusation that I can’t do calculus?]

    • Zach, there’s no need to be “fair” with respect to Tim Curtin. He’s a retired economist, although what proficiency as an economist he exhibited I cannot say except to note that he advised the Zimabwean and Papuan New Guinea governments at various times. But whatever his worth as an economist, he should have sufficient basic calculus skills that he can identify a velocity, and an acceleration.

      Of course having said that, Curtin shows such abysmal comprehension of so much in mathematics and in science that one is forced to wonder at his current capacity for rigorous thinking. This is hardly the forum to review examples of his howlers, but if you are curious wander over to Deltoid and look for Curtin’s contributions there, preserved for all posterity.

      Bring a packed lunch though, because it is a long record of his apparent determination to demonstrate to the world his deep state of non compos mentis.

  2. I got in the same bizarro argument with Mr. Curtain at Curry’s.

    Welcome to the Club!

    • “However the level 5 polynomial has a better fit:”
      Looks like he got you there!

      • It’s rather ridiculous. He did the same thing there as he did to Tamino in the email, except he made the mistake of actually saying “Thus there is no evidence for statistically significant accelerating growth in [CO2]”, instead of saying “increasing rate of change in the rate of growth of atmospheric CO2” like he did with Tamino . He’s now got his strawmen properly termed. Good for him and his polynomials!

      • Sadly, Grypo, Curtin’s 5th order polynomials nonsense (amongst so much other nonsense) is not new.

        I had essentially the same discussion with him a couple of years ago on Deltoid. As I mentioned to Zach above, for the morbidly fascinated I suggest going to Deltoid and doing some searching for relevant threads – better to leave the Stupid there than to repeat it here…

      • For those interested in a nice pwning of Curtin’s infatuation with 5th order polynomials and carbon dioxide in the atmosphere, read Lotharsson’s post here.

        It’s worth trawling the rest of the thread to see how Curtin didn’t get the problem with “overfitting”.

        [Response: Wow. Just … wow.]

  3. Hey, I don’t know calculus at all.

    But I don’t have any problem understanding the concepts of velocity and acceleration.

    Just sayin’. . .

    • Horatio Algeranon

      Galileo didn’t know calculus either…but somehow he managed (just barely).

      • Yes, but he was a skeptic, so he didn’t have actually to know anything. . .

        . . . according to some, anyway.

      • Horatio Algeranon

        Yes, Horatio learned somewhere on the internet (can’t remember where now) that Galileo actually built his first telescope to see if the Mann in the moon was really a hockey player, as some of his contemporaries had claimed.

        But alas, the magnification was not large enough to settle the matter. Galileo couldn’t make out whether it was a hockey stick or just a cane.

        That had to wait until just recently — when it was indeed confirmed with Hubble.

  4. Ages ago, as a senior in high school, I got very excited during a college visit when someone explained to me the concept of “jerk” and how it related to position and velocity and acceleration… I think it helped contribute to my decision to go to that college for my undergrad years.


  5. “What does that say about his accusation that I can’t do calculus?” … Hey, I said he’s still a jerk; it’s just not all that intuitive that you’re plotting the derivative of concentration approximated by the finite difference method. Maybe it’d help if you titled your plots and labeled the y axis “annual CO2 growth” or “CO2 growth rate” instead of letting the fact that you’re plotting a rate be implied by the units used. People are going to not read, look at the plots, and jump to conclusions. Of course, in this absurd debate, even if this particularly person doesn’t misinterpret your analysis accidentally, someone else is going to misrepresent it deliberately it so maybe there’s not all that much value in jerk-proofing these sorts of things.

    [Response: Look again at the y-axis of my plot. It’s labeled “CO2 growth (ppmv/yr)”.

    And look again at the original post, from which the graph is taken. Read the paragraph preceding the graph. How much clearer do I have to be?]

  6. Horatio Algeranon

    If you ever need a jerkmeter, this article describes one.

    Apparently, to measure jerks, you need “beryllium balls”.

    Who knew?

    • Yes, and not just any beryllium balls, either; I see that they must be “about ping-pong ball size”, enclosed in a hard vacuum, and brought to 30,000 RPM.

      “Who knew?” Not me, that’s for sure.

  7. I wouldn’t excuse Tim Curtain. He was careless in his reading, review, commenting … or he just doesn’t get it. Not an unusual appraisal for him.

  8. My calculus is fine, Tim. It’s your reading comprehension that needs work.

    I don’t think he’ll be reading this. He’s probably busy running around the deniosphere and shouting to everyone you called him a jerk because you ran out of arguments after he demonstrably proved you wrong.

    A bit like this.

  9. Timmy has had some “issues” with rates of change in the past, as readers of Deltoid will know all too well.

    • Aw, heck – dedicated Deltoid readers know that Timmy has issues with simpler concepts than rate of change…

  10. But Tim Curtin ought to be happy/delirious about the growth in CO2 levels ?

    Isn’t he the same guy that claims that CO2 is highly beneficial to agriculture, so halting CO2 emissions would have catastrophic effects on harvests, and lead to widespread famines ?

    • Yep, that’s him. He is incapable of or unwilling to understand any evidence that there are other ecosystem factors influenced by climate that may prevent his fantasies – many of which are derived from fitting curves to very limited selections of data – from being realised.

  11. Ian Forrester

    Tim Curtin also thinks that dissolving CO2 in sea water will make it suitable for drinking and irrigation:

    ……. a statement that itself shows none of the 255 has any scientific grasp whatsoever, as the oceans are not acidic now and never have been. Unlike [CO2], there is no data base for oceanic pH anywhere in the world, except at Townsville, where they tip hydrochloric acid into tanks to simulate what might happen if the oceans ever did become acidic. And even if they did, we could then use the sea for drinking and to irrigate the land.

  12. Thanks, Tamino; it’s curtains for Curtin.
    Actually, our Tim has a long and….um, distinguished (?) career of misrepresenting or misunderstanding facts. One can but hope that some day he will see the light, realise his mistakes, and repent, but I fear nothing of the kind will ever happen.
    An interesting discussion in this and the accompanying post of the increasing rate of change in CO2 in the atmosphere; thanks for the efforts.

  13. Tamino says “In the last post I showed that not only is CO2 increasing, its growth rate is also increasing. So, the growth rate of CO2 is faster now than it was just a few decades ago. Significantly so”.
    There are indeed problems with language. I know that in American as used by tamino and CDIAC (in its data on CO2) “growth rate” means absolute amounts. In English “growth RATE” means a rate of speed, eg miles PER hour, or fuel use, miles PER gallon, or interest PER “100”. Your graph shows a LINEAR upward trend in the absolute annual net addition to the atmospheric concentration, and the RATE of the increase in [CO2] p.a. revealed by OLS regression is given in my graph, but NEVER in any that you have ever displayed ASAIK, and certainly not here. It is:
    y = 0.0254x + 0.7656
    R² = 0.4105
    So the rate in your graph is a fixed amount of 0.0254 ppm per annum (as x is years). The linear trend is flat as it must be by definition of linear.
    Now it is possible that as you say “not only is CO2 increasing, its growth rate is also increasing”. So perhaps it is increasing exponentially? Well, I fit that exponential, which produces an upward curving line, NOT linear (=straight line), and here is the LS regression:
    y = 0.7736e0.0196x
    R² = 0.3879
    As the R2 shows the fit is less good than the linear, the exponential hypothesis needs to be dropped.
    So how about logarithmic, which of course shows a declining trend?
    Here’s the fit
    y = 0.4071ln(x) + 0.2133
    R² = 0.3665
    and it is worse than both the linear and the exponential.
    Now the constant linear annual increment in your graph and mine of 0.0254 ppm to the additional ppm is necessarily a falling percentage RATE of increase relative to the annually expanding base, which was 0.95 ppm in 1959 and 2 ppm in 2010. Extrapolating our graphs’ linear trend, we will reach by 2100 only an atmospheric concentration of 675 ppm, well below what Dutch greenhouse growers consider optimal, and also well below the BAU projections of the IPCC (AR4 WG1 Fig.10.20).

    [Response: This is an embarrassingly bad attempt to justify your mistaken objection to my post. The growth rate is the rate of change, the annual increment is an estimate of it, and your insistence that growth rate absolutely must be a reflection of percentage increase rather than amount increase is absurd. Hilariously enough, even if we *do* allow that ridiculous condition, you are *still* wrong.]

    2. Next, you said: “..there was an increase in the rate of growth of atmospheric CO2. I think you need to improve your reading comprehension skills”. I assume that you refer here to the absolute level of the atmospheric concentration, currently around 390 ppm. It is true that there was an increase in the LN decadal growth rates from 1959-68 (0.25% pa) to 1999-2008 (0.55% pa), with the average from 1959 to 2010 at 0.42% pa. That a priori seems to confirm your claim – but 1999 was a La Nina year, and 2008 was an El Nino, so the rate from 1999 to 2010 had already begun to drop back (but La Nina began only late in the year), while 1959, 1969 and 1979 were La Nina years, generating thereby lower % growth rates over the ensuing decade. But even 0.55% p.a. does not lead to the IPCC’s and your more apocalyptic predictions, as with BAU (=that rate) we again only get to 674 ppm in 2100.
    Plotting the total concentration from 1959-2010, the linear fit again cannot be beaten, at 1.4703 ppm pa, and R2=.99.

    [Response: Newsflash: the point is to get the trends — in CO2, its growth rate (velocity), even its acceleration — *apart* from the influence of el Nino. Your discussion is nothing but a diversion.

    As for a linear fit being unbeatable for total concentration– have you lost your mind? A quadratic is better, and the improvement is statistically significant. Interested readers are invited to confirm this for themselves.]

    Finally, I do not think you are right when you say “Linearly increasing velocity means constant acceleration”. What OLS linear trends show is a fixed annual increment, and therefore a declining percentage RATE of growth. Your “constant acceleration” implies and can occur only if there is an exponential trend, you have not shown that and you cannot, because there is not.

    [Response: I think you have lost your mind. Linearly increasing velocity does mean constant acceleration. And constant acceleration is not restricted to exponential trend. In fact, *truly constant* acceleration implies quadratic trend. Your insistence on percentage rates is indeed absurd.

    Even considering percentage increase rather than absolute increase, you’re *still* wrong. Interested readers are invited to log-transform the CO2 concentration, and note that there is no decline in its growth rate. In fact, even the growth rate of log-transformed CO2 (a.k.a. percentage growth rate of CO2) is increasing, i.e., log-transformed CO2 is also accelerating. So, CO2 growth is actually *faster* than exponential.

    The only valid reason for further discussion with you, would be its comedy value. But I’m afraid you’re not even funny any more.]

    • …a comment in which Tamino discovers that Timmy butchers even grade 7 physics concepts (such as linearly increasing velocity resulting from constant acceleration) whilst confidently asserting that he is correct.

      Welcome to the club. And a wise choice – two epic Deltoid threads are a testament to Timmy’s inability to perceive or admit even the most basic errors, let alone consider the impact of such errors on his hypotheses.

    • Told you!

  14. Correction – and apologies, 1959, I said “while 1959, 1969 and 1979 were La Nina years..”, actually they were El Ninos, hence the lower decadal growth, atmospheric CO2 and changes therein are always higher in El Ninos.

  15. Tony O'Brien

    Never came across the term in a scientific sense before. But so appropriate.
    You notice it driving passenger vehicles; people say they notice acceleration in determining jerkiness, but you can accelerate and brake quite hard without people noticing if you start and finish softly.

    Bit the same with the cold point they talk about in submarines (haven’t been in one just read books). The temperature does not change that much, but the rate of temperature change does.

    So the rate of CO2 concentration is increasing at a steadily increasing rate. No Jerk?

    • I have university course memories – IIRC jerk is a major consideration in elevator design & scheduling.

      • Kalman filters used employed in radar target tracking estimation sometimes model the process noise (i.e. maneuvering) as a white noise jerk. (see for example Estimation and Tracking Principles ,Techiques and Software, Bar Shalom and Li, YBS Publishing (or Artech House?), 1995. Also a number of papers in Aerospace and Electronics Transactions of the IEEE)

  16. The Mauna Loa atmospheric CO2 data is what I look to first, since CO2 is the limiting factor in this whole equation. Not surprising, not a lot of heavy Internet metal is lobbed at the Mauna Loa data recorder since it’s kind of hard to refute (accept all of it, or accept none of it). Atmospheric CO2 is a lot like total phosphorus in your local pond or lake. It’s the limiting factor to phytoplankton growth. If P goes off the scale, your clear lake becomes pea soup and you can’t ever clean it (we know from experience in Maine). In a way it would be great if sudden, unbridled atmospheric CO2 increases lead to sugar maple trees growing to 600 feet tall and white pines to 800 feet tall and corn plants to 18 feet tall but experience shows that’s not the case. ‘Fertilizers’ in the coarse sense don’t act that way. They tend to act more like zebra mussels, Dutch elm disease and American chestnut blight. Wish it weren’t the case.

    [Response: Mauna Loa isn’t the only observing location for atmospheric CO2. There are so many, and they’re in such good agreement, the increase in CO2 is indeed irrefutable.]

  17. I think if you don’t know the difference between a derivative and double derivative you really shouldn’t be saying anything about climate change or anything scientific at all for that matter… gee I wonder if there is some kind of way weeding out people that don’t have a base understanding of maths. Maybe some kind of test or exam at a learning institute or something… then you get a some kind of piece of paper stating you’ve passed such and such …oh well may be they’ll invent something like this one day …

    [Response: There are far too many people who have that piece of paper, but either lack basic analytical skills or let their ideology overrule judgement.]

  18. The only thing I can see that’s wrong with this post is that you’ve spelled Tim Curtin’s name wrong.

  19. Interesting that Tony O’Brien, Douglas Watts, Greg, and Stu N are not subject to moderation, while my posts previous to theirs will probably never see the light of day in Tamino’s open mindedness! Not cricket where I come from (India and South Africa).

    [Response: They will continue to be welcome here, you will not. You don’t get to decide who’s welcome in my house, I do, and your suggestion otherwise is not cricket where I come from (Earth).]

    • I would rather say that unlike the people Tim mentions, Tim himself tends to falsely accuse our host of inappropriate data analysis, while making one elementary mistake after the other. That should be a no-no in anyone’s book.

    • Rob Honeycutt

      Tim… Given the tone of the emails he received from you I would suggest you are lucky that Tamino is allowing you to comment at all.

  20. When I looked at the concentration graph in the previous post, I thought “gosh, that looks like it’s concave-upwards…so not only is CO2 increasing, but it’s doing so at an increasing rate–not a good thing!” Perhaps those who complained about this post did not bother to look at the previous post, and imagined you were plotting the same thing, and seeing a linear trend.

  21. Mr Curtin attempts to use the differences between English and American to bolster his lost position. I’m English. I understood Tamino’s position and language without difficulty (although I can’t judge all the statistical methods he uses).

  22. Here’s a simple graph at Wood for Trees. I’ve added a 12-month smooth and linear trend to the Mauna Loa data. You can clearly see that the trend is greater than linear, i.e., the annual increase is accelerating.

    If we look at the last 30 years, the acceleration is still there. If we reduce this to 20 years, it has almost disappeared, and the last 10 years shows no acceleration. Does this tell us anything or have I made the classic mistake of using noisy data over too short a timescale?

    [Response: I don’t think 10 years is long enough to conclude that the acceleration has stopped.]

    • Thanks. Thought so. :)

      • I hope, one day in the not too distant future, to see the rate of increase decelerating. And I hope it’s because we chose to take action, not because we were forced to.

      • It might be possible that increasing prices for fossil fuels will result in a deceleration.

    • One of the things you see in there is the fall of the Soviet Union and the satellite nations from 1990-2000. At the end you may see a bit of the industrialization of China.

  23. help me out here as I am apparently thinking about this incorrectly.

    Anthropogenic atmospheric CO2 started at ~0 ppm.

    It has grown to ~ 112 ppm. This growth started out very slowly. Assuming there is enough fossil fuel and our combustion behavior continues on its current pathway, it will be ~280 ppm by ~ 2050.

    Simple question, what is the growth rate from 0 ppm in 2011 to 168 ppm in 2050?

  24. TRC Curtain: “Finally, I do not think you are right when you say “Linearly increasing velocity means constant acceleration”. ”

    Absolutely hopeless. Utterly, abominably hopeless.

  25. Oh dear, it is curtains for poor old Tim ;) No surprises there, what is pathetic is how seriously these dissemblers take themselves.

  26. PeterD,
    “Thanks, Tamino; it’s curtains for Curtin”
    Sorry Peter, I just saw your earlier post, you beat me to it with the punch line.

  27. 168/39 = 4.31 ppm/year, over double of that for the last 10 years (2.01), which seems a lot. Where does the 280 come from?

    • TS, unfortunately I can only find CO2 scenarios from the TAR, here:

      Scenario A1F1 is the worst, with 567ppm at 2050. This means CO2 needs to increase another ~177ppm; for sure we’re not headed for scenario A1F1, but the increase to near 560ppm (i.e. increase on preindustrial of around 280ppm) is likely to happen sometime around or just after mid century. More optimistic scenarios have this occuring late in the 21st century.

      • That average increase of 4.3/year is, of course, a simple linear (!) increase from now. More realistically we’d start with the 2.0/year we’ve had over the last few years, so there would have to be a lot of acceleration to reach the same point over 4 decades. Does this extreme scenario require us to reach the point where the oceans become net CO2 contributors?

    • Steve Metzler

      Stu N:

      Scenario A1F1 is the worst, with 567ppm at 2050. This means CO2 needs to increase another ~177ppm; for sure we’re not headed for scenario A1F1, but the increase to near 560ppm (i.e. increase on preindustrial of around 280ppm) is likely to happen sometime around or just after mid century.

      Perhaps I misread you , but how exactly is 567ppm at 2050 significantly different from 560ppm just after mid century?

      I think JCH was asking, assuming that we started at ~280ppm CO2 in 1750 or so, and observing that we are at ~392ppm today, is it probable that we will add another 168ppm before mid century to take us to a pre-industrial doubling of 560ppm? I think it is very probable if we continue business as usual. And if we hit a tipping point with the methane clathrates, we could get there much sooner. That is one race mankind does surely not want to win.

      • “Perhaps I misread you , but how exactly is 567ppm at 2050 significantly different from 560ppm just after mid century?”

        I guess it’s not really. I was mainly trying to answer TrueSceptic’s question about where the 280ppm figure came from.

    • Yes, it’s commonly given as the pre-industrial level. To double it requires an additional 280 ppm. So far we’re at ~112 ppm.

      The internet is full of financial calculators for determining growth rates. All of them require a starting value greater than zero. So $1 will grow to $168 by 2050 if the holder can find an investment that yields 14%. I”m not a numbers person, so these calculators are the only thing I’ve got. They’e obviously inappropriate here because they are compounding interest. CO2 doesn’t grow additional CO2. The sky is a piggy bank, not Goldman Sachs.

      With anthropogenic atmospheric CO2 the start number for the additional 168 ppm is zero. The financial calculators hit the ditch. It takes a 28% growth rate to get a penny to $168 by 2050. To grow .ooo1 cents to $168, 44%. .0000001 cents to $168, 72%. In my deficient, non-numbers head, this the only thing I can think of to do to approximate starting at zero.

      Anthropogenic atmospheric CO2 has been doubling at ~40 years. Assuming human consistency and sufficient fossil fuel, that number is about to get smaller. Growing one penny in 1750 to $112 in 2010 is a 3.6% growth rate. This process started out at a very leisurely pace, but it is about become a 100-meter dash.

      • I see. Let’s take your figures as stated: 280 pre-industrial, 392 now, and 56o in 2050 (39 years from now).

        My simple calculation would be like simply adding money to an account, irrespective of how much money was already there; there is no compounding of interest. We could take 392 as our “capital” and derive a growth curve based on that but it would imply a constant %age increase. This figure would be 0.92%/year ((the 39th root of 560/392) – 1). This would like putting $392 in an account and earning compound interest at 0.92%/year (392 x 1.0092^39 = 560). In turn, this implies a growth of 3.6 (0.92% of 392) for the first year and 5.2 (0.92% of 560) for the last. This doesn’t look right as we are currently adding 2.0/year and there’s no way it will jump to 3.6 next year.

        Looking at these as distance (actually it’s called “displacement”), velocity, and acceleration, as Tamino did, makes more sense. We are currently increasing (velocity) at 2.0/year. We want the constant acceleration (the smoothest curve) that will add 168 in 39 years. Using the classic kinematic equation
        s = ut + 1/2(ft^2), where s = distance, u = initial velocity, t = time, and f = acceleration,
        168 = 2.0*39 + 1/2(f*39^2)
        gives us an acceleration (increase in the increase) of 0.118/year/year. This gives us 2.12 (2.0 + 0.118) for the first year and 6.62 (2.0 + 39*0.118) for the last and we can use the equation to get the figure for any year (not forgetting to add the initial 392, of course).

        This is all just curve-fitting though, and let’s hope we don’t reach 560!

  28. Philippe Chantreau

    Curtin, “Finally, I do not think you are right when you say “Linearly increasing velocity means constant acceleration”.
    WTH? Can’t you at least do a cursory read of your own post before spewing idiotic nonsense like this? You are demonstrating everything that needs to be known about climate denialism. People like you are the reason why it took me only one evening of reading about climate change to figure out what “side” the serious people were on. Even if all of climate science turns out wrong, it will not be because you or your like was right in any way.

    Then you go on whining about censorship. Do you realize that in this case, you would have been spared a lot of embarassment by having your posts deleted in moderation? No such luck though. Pity.

    • Vince Whirlwind

      “People like you are the reason why it took me only one evening of reading about climate change to figure out what “side” the serious people were on.”

      Exactly how I formed my opinion.

      I am suspicious by nature, and I have no automatic respect for academics or medicos, but the sheer nuttiness of nay-sayers like Curtain convinced me almost instantaneously of who to trust on this issue.

  29. Tim Curtin, Act I:

    tamino (aka Grant Foster) like Schmidt and his co-authors including Mike Hockeystick Mann, and Kevin Trenberth and their Australian cheerleaders JQ and hc cannot actually do calculus:

    Tim Curtin, Act II:

    Finally, I do not think you are right when you say “Linearly increasing velocity means constant acceleration”

    Ok, so I’m nursing some scalded nasal passages, and I may not be able to salvage my laptop….. but it was worth it!!!

    • It’s the New Calculus. All these old farts who learned the old fashioned calculus are sooooo out of date. Did you know that pi=4 and you can square the circle with just a straight edge and a rhubarb stalk?

    • Caerbannog.

      One day a history postgrad might do an analysis of the online history of Tim Curtin’s anti-science/anti-mathematics, and in the statistical breakdown of the commentary there will be multiple registerings of flooded keyboards, tea-soaked noses, and Curtains-for-Curtin.

      If only there could be multiple (or even single) registerings of dawning understanding for the same personage.

  30. I wouldn’t waste my (figurative) breath arguing with Tim Curtin. The guy is right up there with some of the more dense members of the climate-change blogoshpere. Those of us who skulk around the Deltoid blog know full well that no amount of evidence, logic and repeated whacks in the head with the clue stick will ever, ever eva!!!!! get him to acknowledge an error or change his mind.

    Your time is better spent elsewhere (regardless of how much I enjoyed your rather complete take down). Tim will learn nothing from the experience.

  31. I hope this question is on topic:
    Every time I look at the CO2-curve I am wondering why some of the upgoing seasonal swings seems to have a “knee”. 2008 is a recent example. My only idea is that ENSO could be part of an explanation. Does anybody know the reason?

    • The CO2 seasonal cycle (being truly linked to the seasons) has opposite phases in the north and south hemispheres. Because land area in the northern hemisphere is greater than the south, it has a bigger cycle and dominates in the global average and in measurements taken at Mauna Loa.

      I expect this latitudinal effect produces the “knee” you think you see (which is different in the Mauna Loa and global series) .

      Is this linked to ENSO? Partly. ENSO has different effects at different latitudes. I think it contributes to some of the irregular parts of the CO2 record (as Tamino demonstrated).

  32. Horatio Algeranon

    As Andre the Giant famously said in The Princess Bride: “I do not think it means what you think it means.”

    “Inconceivable” is right.

    • Horatio, that was Inigo Montoya, played by the inestimable Mandy Petinkin.

      And certainly one of the best movies ever made…

    • Or Humpty-Dumpty’s famous quote from Through the Looking Glass: “When I use a word it means eaxctly what I want it to mean. No more, no less.”

  33. An OT nitpick: in “The Princess Bride”, the remark about the meaning of “inconceivable” was made not by Andre the Giant but by Inigo Montoya (played by Mandy Patinkin).

    • Horatio Algeranon

      Man, this is one tough crowd (that knows it’s movies and takes them very seriously)

    • Careful. You don’t want to get statements from Goddard and Curtin too close to each other, the stupid might go critical.

    • Chris.

      Surely Goddard can’t be that Stupid that he is still pushing that canard?!

      I left a little homework for the Einsteins there, but I am not sure that Goddard will approve it:

      Bernard J. says:
      Your comment is awaiting moderation.
      April 14, 2011 at 3:23 am

      What happens when one fills a SCUBA tank with air?

      What happens when one leaves that tank in the corner of the garage for a week?

      Depending on the answers to these questions, I have a perpetual motion machine to sell…

      • Bernard,

        It is clear from his replies that Goddard is not only stupid but also arrogant in equal measure.

        The funny thing is that he realises that the “The temperate [sic] equilibrates with the surroundings.” Can he not see that this refutes his own claim? The pressure remains high yet has failed to maintain temperature above ambient, while on Planet Goddard high pressure somehow maintains high temperatures indefinitely despite heat constantly escaping to space.

      • I have written a sort-of more in depth discussion of Venus btw at SkepticalScience, not so much in response to Goddard, but perhaps instructive nonetheless. Somehow it got posted in the rebuttal archives but not as a ‘new post’ at SkS, so it probably won’t be widely seen

  34. Philippe Chantreau

    This is off topic but I couldn’t resist. Ya’ll better put the coffee aside, or you might add assault to injury on both nasal passages and keyboards.

    Check out on SkS Monckton’s new trick to hide the incline: if you don’t like what a graph shows, just angle it a little. I swear I’m not making this up:

    • As also noted (somewhat obscurely) in the comments, it actually is Mörner’s trick. He presented a similarly tilted graph at a EGU conference in 2006.

    • Philippe,

      You do know about Denial Depot, I hope?

      • Philippe Chantreau

        Oh gee; Morner, Denial Depot, Monckton, seems it is all a big contest for the funniest graph ever. They’re all so eager, it’s hard to stay current. Mr Beck would be proud…
        Must be hard for the folks at Denial Depot to keep up sometimes. They have to beat the odds every day; after all this is the kind of stuff of which it is said that you can’t make it up…

      • It does look straight out of Denial Depot, it’s true, but this is from the SPPI site. You can check it out there, go to page 33. (Warning 4Meg pdf download)

        Their intent is obviously rhetorical, but it’s all so bogus and desperate you have to laugh.

  35. David B. Benson

    In which we learn that some people are third derivatives.

  36. C’mon, Tim Curtin published the assertion that, because the biosphere consumes a given amount of carbon dioxide per year, reducing the amount of CO2 being added from burning fossil fuel will starve the biosphere. In E’n’E, of course. V20#7 2009, “Climate Change and Food Production”

  37. This is off topic.

    Some people in the blogosphere like to show temperature trends since January 2001. What would be interesting is if you showed the trends since January 2001, and rather than using actual temperatures, use synthetic temperature series based on a fixed trend, ENSO, volcanic, and solar influences. Basically, the same thing you’ve done in previous posts, except in reverse. I’m guessing that the trends you get will be very similar to the trends seen in the actual temperature data. It would be very difficult to argue that such trends are inconsistent with expectations since they are exactly the expectation.

  38. It certainly is fun to witness Curtin voluntarily strip himself of his credibility.

  39. It isn’t like Curtain had any math cred left. See for example

    Wherein he declared that $y^5$ was exponential.

  40. Thanks, MapleLeaf. I’m just warming up. :-)
    The Curtin In History, Part I [with apologies to historians and real Historical actors].
    Last century, many observers noted the appearance of an” Iron Curtin” between Russia and the West. A senior Politburo member was asked about the term, and responded, on condition of anonymity: “We decided to name it after Tim and to make it from iron, as it was important to ensure that it was sufficiently dense and impervious to resist penetration by ideas and thinking from the outside.”

  41. Bernard

    Returning to Goddard’s ‘hypothesis’ and to your engagement with it by way of ‘homework’ questions, can you clarify something for me please [as I am sadly a Soc Sci type person]?

    We are simply talking about the temp properties of fluids here aren’t we, so viscosity differences shouldn’t change the fundamentals. Therefore, if the pressure argument were to be valid, then ceteris paribus what should the water temperature be at the bottom of the Mariana Trench?

    If this is a spectacularly naive question I’d appreciate knowing why.

    • From what I’ve read of Goddard, he actually doesn’t have a physical hypothesis. It’s possible to read into his posts the idea that pressure per se engenders the heat, but then he states that the heat comes from the sun. What is missing (or so I believe) is any sensible physical mechanism linking the two.

      Goddard’s ideas are principally what Tamino has elsewhere referred to as “mathturbation,” which I define as “using math to muddy the waters.”

    • Hasis.

      My guess is that Goddard would wiggle out of the pressure issue by pointing out that water is essentially an incompressible fluid, which conveniently absolves him of having to worry about the ideal gas law in this context.

      Of course, in a roundabout way this has implications for the adiabatic thermodynamics of gas compression, and this is one of several matters upon which I’m waiting to see if Goddard eventually twigs. Far more relevantly-qualified scientists than I have already tried to set Goddard right, however, and in much more explicit fashion, so I’m not expecting that realisation will dawn for him any time soon.

    • I actually went back and read Goddard’s “Venus” post.

      What he and his follower’s don’t get is that asserting that atmospheric temperatures are determined by the ideal gas law is completely incompatible with the idea that atmospheric energy comes from the sun: there’s no term in the gas law for energy inputs. He uses the equation without connecting it to a physically reality; after all, we *know* that insolation is relevant–even Goddard acknowledges that both explicitly and implicitly.

      All of which is a long-winded way of exlaining why his idea is not internally coherent–bringing us back to the “mathturbation” concept once again.

  42. I find this discussion particularly interesting because I had almost the *identical* discussion about 4 years ago (via email) with a guy calling himself Bill Westmiller. I believe he was from California, so didn’t have Curtin’s language excuse.

    Specifically, Westmiller sent me a spreadsheet where he’d demonstrated that the rate of growth of CO2 was not accelerating, by:
    (1) using the percentage rate, rather than the absolute rate, just as Curtin argued above, and
    (2) looking at the *third* derivative, not the second, just as Curtin did.

    What is the likelihood that two people, separated by 4 years or so in time, would come up with such identical arguments? Or is there a hidden source for this stupidity that neither of them has revealed?

  43. Fielding Mellish

    I guess this is OT, but when I read some of Tamino’s posts I have to read the entire thing with comments twice to decide whether it’s real, or a gag post/inside joke where I missed the gag. Crikey, I don’t think Ken Kesey on mushrooms could dream up something approaching these deniosphere’s extremities. With apologies to Patti Smith and Al Bouchard, these deniodudes claim the role of a saint, with the consciousness of a snake–and that’s being unkind to snakes.

    • Never thought I’d see the Revenge of Vera Gemini quoted on the internet. Thanks Fielding – you made my evening.

  44. Ah, I see that Timmie goes all tone troll on us.

    Timmie, we’re talking about science here. It matters if you are correct in your reasoning or facts, not whether you express those facts and reasoning with perfect manners. You have made it quite clear that you don’t even know the proper definitions (e.g. velocity, acceleration, jerk…). Pray, why should we pay any attention to you other than to laugh at you?

    • Ray, laugh? Not exactly.

      I can’t forget the haste and horror on the epic Deltoid thread where we had to get in quick to deter Tim-of-superior-intellect from going ahead with his proposal to drink seawater (“suitably” acidified) for a day or two. Had ghastly visions of a silly man being carted off in an ambulance all because he’d talked himself into believing seawater could be rendered potable by adding lemon juice or some other such foolish thing.

      Never been able to read anything he’s written since without the combination laugh-gasp-facepalm reaction.

      • Adelady, ah, but had he gone ahead with the stunt (and survived), it might have made a sufficient impression that he might have learned something–if only that he is an idiot. And had he not survived, well, let’s just say, you deprived him of a Darwin award. As it stands, now we’ll never know if his learning curve has a positive slope, however shallow.

        Seawater, eh? I’m guessing he doesn’t live near the ocean.

    • IIRC Timmy has a bit of a penchant for going tone troll (check out the threads at Deltoid if you have a lot of time on your hands). From memory, which might be not entirely accurate, this seemed to occur more often than not after someone pointed out either:

      a) that his argument was complete bulldust, complete with references and logic, or
      b) that his offensive allegations about some other commenter were unsupported by any evidence

      It almost seemed like he relied on shifting the topic to tone (and other rhetorical distractions) when there was too much heat on his case ;-)

  45. ClimateForAll

    I hope you are as ‘open-minded’ as such that your blog suggests, because I would like to challenge that theory with a question.
    You stated:

    ‘I showed that not only is CO2 increasing, its growth rate is also increasing. So, the growth rate of CO2 is faster now than it was just a few decades ago. Significantly so.’

    Many of the CAGW predictions from noted scientists and panels around the world, have come under attack from many sectors.
    Co2 has been used in climate models to explain, rising temperatures, melting sea ice, more hurricanes, and my personal favorite, rising sea levels.
    Many environmental impact studies have predicted that as Co2 increases, many coastal areas will be inundated with erosion and flooding, due to rising sea levels.
    And MSM continues to quote scientists and environmental talking heads that suggest, ‘it’s worse than we thought,’ because we should expect anywhere from 2-6 feet of rise by centuries end.
    On 2-23-11, In the Journal of Coastal Research, Houston & Dean had this to say in their published paper::

    Without sea-level acceleration, the 20th-century sea-level trend of 1.7 mm/y would produce a rise of only approximately 0.15 m from 2010 to 2100; therefore, sea-level acceleration is a critical component of projected sea-level rise. To determine this acceleration, we analyze monthly-averaged records for 57 U.S. tide gauges in the Permanent Service for Mean Sea Level (PSMSL) data base that have lengths of 60–156 years. Least-squares quadratic analysis of each of the 57 records are performed to quantify accelerations, and 25 gauge records having data spanning from 1930 to 2010 are analyzed. In both cases we obtain small average sea-level decelerations.
    ———————————————————————————————- It is essential that investigations continue to address why this
    worldwide-temperature increase has not produced acceleration
    of global sea level over the past 100 years, and indeed why
    global sea level has possibly decelerated for at least the last
    80 years.

    My question to you is this:
    If Co2 rise is ‘faster’, ‘larger’, ‘increasing’ or whatever term you wish to use for the acceleration of CAGW, where is the evidence, in regards to sea level rise?

    [Response: CO2 rise is faster. That’s a fact.

    As for the utter nonsense from Houston & Dean, I dealt with that here.]

  46. After some 100 posts abusing me here, mostly in ad hominem vein, may I just say that this thread began with me querying Tamino’s claim that a linear upward trend implies acceleration of that trend. He kindly posted my own graph using his very same data showing that the trend line, whose formulae and R2s he NEVER posts on any of his contributions, showed no more than a constant 0.0254 ppm p.a. increase in the atmospheric concentration of CO2, rather than the accelerating increase he claimed his graph showed (which if true would be revealed by an exponential rather than a linear trend, with a better fit, i.e. better R2, but does not). Nothing posted here so far has contested these FACTS.


    [Response: How confused are you? Let me count the ways.

    Only the confused would think, or think I had claimed, that “a linear upward trend implies acceleration of that trend.” What I said is that a linear increase in *velocity* is equivalent to an acceleration of *value*. It’s a fact.

    That’s why the units of the rate of change of CO2 growth rate are NOT ppm per year, but ppm per year per year.

    The idea that growth rate has to refer to percentage growth rate is confused. It’s not uncommon among economists, who often think they can tell mathematicians and physicists how we should be doing our job, but in doing so they only further embarrass themselves.

    The entire idea that a trend has to be exponential in order to be accelerating is likewise confused.

    The notion that by insisting on percentage rates to characterize growth and/or exponential growth, you can then deny acceleration of CO2, is perhaps the most confused confusion you suffer from. Even the *percentage growth rate* is increasing because CO2 concentration is rising *faster than exponential*.

    Come to think of it, perhaps your most astounding confusion is believing that I’m gonna let you hijack any of my blog comment threads. B-bye.]

    [P.S.: I’m not interested in reviewing your paper pre-publication. Let us know when it’s published, then I’ll be glad to review it here on the blog.]

    • … showed no more than a constant 0.0254 ppm p.a. increase in the atmospheric concentration of CO2, rather than the accelerating increase he claimed his graph showed

      This tells us that someone can’t tell the difference between an increase and a change in that increase. The 0.0254 figure cannot possibly refer to the annual increase because that is easily seen to be around 2.0 at present, almost 80 times as great.

    • He kindly posted my own graph using his very same data showing that the trend line, whose formulae and R2s he NEVER posts on any of his contributions, showed no more than a constant 0.0254 ppm p.a. increase in the atmospheric concentration of CO2, rather than the accelerating increase he claimed his graph showed


      I hadn’t looked hard at the rusty line on Curtin’s graph before, but now that I have scrutinised it a bit more closely there seems to be something fishy about it. Do you know exactly how Curtin derived his “dppm” values, Tamino?

      And I note that Curtin is still, after having been repeated corrected over the last few years, seems to be rather clumsily using a calculus term for difference where he should more appropriately use a simple Δ.

      I’m not surprised that you’ve shown him the red card, although I was,/i> hoping that I might press him on whether he ever managed to figure out how I derived this particular extrapolation of the Keeling data. I’m sure that it’s eating him hollow that he was never answered on that matter…

  47. Tamino,

    Do you remember the guy who insisted heatedly that the global average top-of-atmosphere illumination was 1366 watts per square meter and not 1366 / 4, because “the whole thing was in sunlight,” or some such nonsense? Deja vu all over again…

  48. Dave Andrews


    For all your pretty graphs aren’t you missing something here?

    The Mauna Loa, et al, figures show a roughly steady increase in atmospheric CO2 but there has been a massive increase in the burning of fossil fuels since 1990, especially, but not restricted to, India and China.

    This huge increase is not being reflected by the Mauna Loa figures.

    [Response: You are mistaken.]

    • Dave Andrews,
      I’m not sure where you are getting your contention–atmospheric increase has held fairly constant at about 1/2 of emissions, with the rest acidifying the ocean.

      Are you perhaps mistaking velocity for the increase itself?