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Settled Science - Humans are Raising CO2 Levels

Posted on 20 August 2011 by dana1981, MarkR

As a result of Murry Salby's fundamentally flawed arguments that the increase in atmospheric CO2 is a consequence of the increase in temperature, rather than vice-versa, a number of prominent climate "skeptics" have been taking up this argument (i.e. Watts, Curry, Bolt, Jo Nova).  In his post on the subject, Watts wrote

"I’m pretty sure Australian bloggers John Cook at Skeptical Science and Tim Lambert at Deltoid are having conniption fits right about now."

Indeed, we here at Skeptical Science have found the entire hubub over Salby's claims by those who claim to be serious climate skeptics rather frustrating.  This is because Salby's argument is akin to claiming the Sun revolves around the Earth.  We know it's wrong, we know why it's wrong, and we've known this for ages.  If somebody tells you the Sun revolves around the Earth, your reaction should not be "wow, this could revolutionize the entire field of astrophysics!", your reaction should be "no, unless you produce some absolutely extraordinary evidence, that's obviously wrong."  Of course, that will only be your reaction if you're a real skeptic.

Although we've addressed Salby's arguments in a few recent posts already (see here and here and here), we previously had not created a comprehensive rebuttal to the myth that the atmospheric CO2 increase is natural (though RealClimate has a good one, from which we borrowed some of the discussion on carbon isotopic signatures).  Thus we have now taken the opportunity to create this rebuttal.

Simple Accounting

The easiest way to prove that the atmospheric CO2 increase is man-made is through a simple accounting approach.  The equation for the change in atmospheric CO2 (ΔCatm) is

This says that if we ‘emit’ a ton of carbon by, say, triggering a volcano then the atmosphere will gain a ton. If we ‘absorb’ a ton of carbon by growing a tree, then the atmosphere loses a ton.  We can expand the equation by counting human emissions (HE) and absorption (HA) and natural emissions (NE) and absorption (NA) separately.

This works because carbon is additive. If a volcano emits a ton of carbon and a factory emits a ton then the atmosphere has gained two tons. This is a very simple balance sheet for the carbon cycle and fortunately there are ‘accountants’ who have measured some of these values for us.

Recently the amount of CO2 in the atmosphere has been rising at ~2 parts per million per year, or around 15 billion tons/year. Meanwhile  human emissions excluding land use change (like clearing or planting forests) are 30 billion tons per year. In billions of tons per year we have:

We can rearrange this:

Humans are also clearing rainforests and changing land use, but here we'll assume that human effects on absorption (HA) are not much different from zero, i.e.

So Natural Absorption (NA) must be bigger than Natural Emissions (NE). Nature is absorbing more CO2 than it is emitting. It is not causing atmospheric CO2 to rise at all - in fact it is acting to try and reduce atmospheric CO2, and thus the long term rise is entirely because of humans.

Ocean Acidification

The oceans are the Earth's largest carbon storage medium, so if the atmospheric CO2 increase were "natural", it would likely be coming from the oceans.  But we know the CO2 increase is not coming from the oceans, because the pH of the oceans is dropping (a.k.a. ocean acidification).

When CO2 is absorbed into a solution, it binds with a water molecule to form a molecule of carbonic acid:

CO2 + H2O = H2CO3

H2CO3 has a rather strong acidifying effect in that 95% of it turns into HCO3-.  This loss of an H+ ion causes the ocean pH to decrease (for more details on ocean acidification, see the OA no OK series).

In short, the fact that the pH of the oceans is decreasing tell us that they are absorbing more carbon than they are releasing, not vice-versa.

Oceanic CO2 Rising Fastest at the Surface

If CO2 were being driven into the ocean from the air, the oceanic concentration would rise fastest at the surface.  If CO2 were being expelled from the oceans, we would expect to see the opposite - decreasing concentrations at the surface.

The World Ocean Circulation Experiment (WOCE) and the Joint Global Ocean Flux Study (JGOFS) has observed that as we expect for CO2 being driven into the oceans, concentrations of CO2 in the oceans are rising fastest at the surface.

Atmospheric O2 is Decreasing

Burning carbon requires oxygen (O2), and when we burn an atom of carbon, the required oxygen becomes part of the CO2 molecule.  So if the CO2 increase is caused by burning carbon (fossil fuels), we would expect atmospheric O2 levels to decrease at the same rate.  And that's indeed what we observe (Figure 1).

Cape Grim O2

Figure 1: Atmospheric Oxygen Concentration observed from Cape Grim, Tasmania

There's no reason to expect that a natural release of CO2 would have any effect on atmospheric O2 levels.  On the other hand, the O2 concentration is changing exactly as we would expect from a fossil-fuel driven CO2 increase.

CO2 Rise is Smoother than Temperature

Some, most recently Murry Salby, have argued that the CO2 rise is in reponse to the temperature rise.  However, the temperature rise has been quite erratic (because there are many factors which impact the average global temperature, especially in the short-term).  If atmospheric CO2 changes were in response to temperature changes, then we would expect to see an erratic rise in CO2 as well.  Instead, the atmospheric CO2 increase is very smooth, similar to the increase in human CO2 emissions.

CO2 emission vs concentration

Figure 2: Human CO2 emissions (blue, left y-axis, Source: IEA) vs. atmospheric CO2 concentration (red, right y-axis, Source: Mauna Loa record)

Isotopic Signature

Carbon is composed of three different isotopes: carbon-12, 13, and 14.  Carbon-12 is by far the most common, while carbon-13 is about 1% of the total, and carbon-14 accounts for only about 1 in 1 trillion carbon atoms in the atmosphere.

CO2 produced from burning fossil fuels or burning forests has a different isotopic composition from CO2 in the atmosphere, because plants have a preference for the lighter isotopes (carbon-12 and 13); thus they have lower carbon-13  and 14 to 12 ratios. Since fossil fuels are ultimately derived from ancient plants, plants and fossil fuels all have roughly the same carbon-13 to 12 ratio – about 2% lower than that of the atmosphere. As CO2 from these materials is released into, and mixes with, the atmosphere, the average carbon-13 to 12 ratio of the atmosphere decreases.

Reconstructions of atmospheric carbon isotope ratios from various proxy sources have determined that at no time in the last 10,000 years are the carbon-13 to 12 ratios in the atmosphere as low as they are today. Furthermore, the carbon-13 to 12 ratios begin to decline dramatically just as the CO2 starts to increase — around 1850 AD. This is exactly what we expect if the increased CO2 is in fact due to fossil fuel burning beginning in the Industrial Revolution.

carbon 13 ratio

Figure 3: Atmospheric carbon-13 ratio observations from Cape Grim, Tasmania

These isotopic observations confirm that the increase in atmospheric CO2 comes from biogenic carbon, not from the oceans or volcanoes.  Some "skeptics" like Murry Salby argue that the carbon-13 ratio isn't unique to fossil fuels.  However, because the carbon-14 ratio has also decreased significantly (Figure 4), we know it's from old (fossil fuel) sources, not modern sources.  This is not new science either, it's something we've known for over half a century (Revelle and Suess 1957), and there  have been many studies confirming these results.  For example, Levin & Hesshaimer (2000):

"It has been erroneously argued that the observed atmospheric CO2 increase since the middle of the 19th century may be due to an ongoing natural perturbation of gross fluxes between the atmosphere, biosphere, and oceans. That the increase is in fact a predominantly anthropogenic disturbance, caused by accelerated release of CO2 from burning of fossil fuels, has been elegantly demonstrated through 14C analyses of tree rings from the last two centuries (Stuiver and Quay 1981; Suess 1955; Tans et al. 1979)."

14C ratio

Figure 4: Temporal change of carbon-14 ratio in tree rings grown at the Pacific coast (Levin & Hesshaimer 2000)

Settled Science

As you can see, there are many lines of evidence showing that the increase in atmospheric CO2 is due to human fossil fuel combustion.  Each one of these lines of evidence is very conclusive on its own, and when all put together, it's abundantly clear that the science is settled on this issue.

As you can see from the snazzy new button created by John Cook at the top of this post, we've created a new series entitled 'Settled Science'.  All too frequently we hear comments from "skeptics", like this one from Salby:

He said he had an “involuntary gag reflex” whenever someone said the “science was settled”.

“Anyone who thinks the science of this complex thing is settled is in Fantasia.”

There are some scientific issues for which the supporting evidence is so overwhelming and clear, that it's accurate to say the science is settled.  The anthropogenic nature of the atmospheric CO2 increase is one of those settled issues, whether it makes Salby gag or not.  In future posts in this series, we will investigate other issues for which the science is clearly settled.

This is the rebuttal to the myth CO2 increase is natural, not human-caused

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Comments 51 to 72 out of 72:

  1. ETR: Degassing? Didn't you read post 10? For one thing the oceans have not warmed enough to have been the source of CO2
    3. Not enough warming You may remember from post 8, that warm water can hold less CO2 than cold water. Our knowledge of Henry's Law and the CO2 equilibria allow us to calculate the increase in seawater temperature that would be needed to cause the observed increase in pCO2 in the atmosphere (i.e. the partial pressure (or 'concentration') of CO2). The results show that to explain the 100 ppm of additional CO2 added to the atmosphere since preindustrial times by ocean warming, the average temperature rise of the surface ocean needs to be about 10o C, much larger than has occurred. As we noted in post 8, the Henry's Law coefficient, KH, is dependent on temperature (and salinity to a lesser extent). However, there is no exact expression as seawater is sufficiently complex that the values for KH for seawater have been experimentally determined. For constant salinity, the pCO2 in the atmosphere doubles (i.e. =200% the initial concentration) for every 16oC increase in seawater temperature*. Atmospheric CO2 is now 140% of the preindustrial value (it increased by about 110 ppm from 280 to 390 ppm). Thus the temperature change required to sufficiently change the Henry's Law coefficient is 140/200 × 16 = 11oC.** This calculation shows that the surface ocean would on average have to have warmed by about 10oC since about 1750 if the oceans had been the source of the CO2. Plainly the ocean does not have a uniform temperature, so the changes would actually need to be even more extreme in some places. Of course, no such warming has occurred. *for the interested this is explained in detail in the appendix to: Takahashi et al. "Seasonal variation of CO2 and nutrients in the high-latitude surface oceans: A comparative study" Global Biogeochemical Cycles, 7(4), 843-878.
    ** actually a simplification of a partial dertivative
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  2. Doug, It is not my contention that the addition CO2 is coming from the oceans. That was my response to the hypothetic question posed by muon. If you have another potential answer, please share.
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  3. What next? Will we see some brave soul attempt to disprove the greenhouse properties of CO2, methane, and NO2?
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  4. Reinforcing the central thesis of the above article ... "Despite Rick Perry, consensus on climate change keeps strengthening" by Brad Pulmer, Washington Post, Aug 23, 2011 To access this article, click here
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  5. The question I would ask Salby is what he means by saying that anthropogenic emissions only account or 5% of the increase in CO2. Presumably he means that if the Industrial Revolution had not occurred then CO2 levels would still have gone up by 95% of the amount by which they did increase. That leaves the question of where the CO2 we emitted has gone and where the increase in CO2 we observe came from. If we assume that 97.5% of the CO2 we emitted has been soaked up by negative feed back we must assume that the same would be true of the CO2 from the natural source that is responsible for the observed increase. In other words there is an as yet undiscovered source which is emitting 19 times as much as we are emitting and an undiscovered sink which increases proportionately to increases in CO2 in the atmosphere and is currently absorbing a 19.5 times the amount we are emitting. That looks like a very big source and a very big sink - should be easy to find.
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  6. Skeptical Wombat If Salby's answer to your question were to be "if the Industrial Revolution had not occurred then CO2 levels would still have gone up by 95% of the amount by which they did increase" he would be very wrong. I suspect what Salby meant was that if you look at the additional CO2 that has been added since the industrial revolution, then only 5% of those molecules will be of directly anthropogenic origin. This is basically true and completely consistent with the cause of the rise being 100% anthropogenic. I know that sounds rather counterintuituve, but it is true. The reason that only about 5% of the molecules are of directly anthropogenic origin is that there is a vast exchange flux that each year exchanges about 20% of atmospheric CO2 with CO2 from the surface oceans or from terestrial biosphere. However this is a straight exchange and hence doesn't alter the atmospheric CO2 levels, but it does mean that anthropogenic CO2 is replaced by "natural" CO2. The action of the exchange flux has confused many, especially leading to the "residence time" argument discussed on another thread. This is well known to those who study the carbon cycle. I am currently writing an advanced version of the "residence time" rebuttal, and it will include a simple model that explains the 5% figure (and I'll include an analogy for those that don't like differential equations). BTW, the sinks and sources are not undiscovered; the figures given in the IPCC WG1 report are consistent with an anthropogenic cause of the rise and there being only a small fraction of anthropogenic CO2 comprising the excess.
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  7. Dikran I am not for a moment saying that Salby is right but I do believe that my interpretation is the only one consistent with the content of his talk and the way it is being interpreted by his followers. The known sources and sinks cannot account for the simultaneous and independent injection and removal of additional CO2 that Salby appears to require so IF he is right there must be some very big ones still to be found. Maybe some enthusiastic "skeptic" could pick up a Nobel Prize or something. I look forward to your rebuttal. I think I can manage differential equations.
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  8. 57, Skeptical Wombat,
    The known sources and sinks cannot account for the simultaneous and independent injection and removal of additional CO2
    This is wrong. Until you correct this misconception, you cannot properly evaluate the problem, or Salby's mistakes.
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    Moderator Response: [Sph] See correction/apology in comment below.
  9. 55, Skeptical Wombat,
    If we assume that 97.5% of the CO2 we emitted has been soaked up by negative feed back...
    This is wrong. You need to understand this better so that you know why.
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    Moderator Response: [Sph] See correction/apology in comment below.
  10. Am I right in assuming Sceptical Wombat was merely trying to find a way in which Salby's interpretation of a 5% increase could be fitted to the CO2 data? I don't think SW believes Salby for a moment, assuming the final statement in #55 was heavy on the irony?
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  11. i think you're right skywatcher. Sphaerica, you are misinterpreting swombats intention. He/she is correct. The only way for Salby's interpretation to be right is if we have missed a net flux term to the atmosphere that is temperature dependent and is very large (20x?) relative to anthro inputs. That also implies a much faster return time than we have assumed (otherwise the net change would have been larger), and that has operated in the past. Could we have missed such a thing? does it makes sense that it operates only during the post industrial era and not previously? Highly unlikely. But that's not all. This flux must have a delC13 like plants, no C-14 (old) and it must preferentially increase CO2 in ocean surface layers (must be terrestrial). Swombat is making the case that Salby's interpretation predicts the existence of a previously unknown flux with a particular location, behavior, composition and size. Finding that flux is the obvious next step Salby should have taken before going public, if he were a real scientist. It would be interesting seeing him try to pose some viable possibilities that meet these criteria. I thnk he would find it hard.
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  12. Sceptical Wombat wrote: "The known sources and sinks cannot account for the simultaneous and independent injection and removal of additional CO2 that Salby appears to require so IF he is right there must be some very big ones still to be found. This is not correct, as I said the known fluxes are sufficient to explain the 5% figure, it is well known by carbon cycle modellers, but it is in no way an indication that the rise is non-anthropogenic. See figure 7.3 from the most recent IPCC WG1 report: This shows a natural flux into the atmosphere of 210.2 GtC per year and a net natural efflux from the atmosphere of 212.4 GtC per year. These are very large compared to fossil fuel emissions of 6.4 GtC per year, and it is this large natural exchange flux of approx 20% of the atmospheric reservoir each year that confuses many into thinking our emissions don't matter. However the rise is governed by the difference between total emissions and total uptake, which is small compared with anthropogenic emissions. The only interpretation of Salbys talk that is correct is completely uncontraversial. I am hoping that Salby is conducting a hoax to see how many "skeptics" will swallow it hook, line and sinker. If he isn't then it will be hugely embarassing for him to have published something either wrong, or making a big fuss about something entirely uncontraversial, when he has a new book about atmospheric physics about to appear. He won't be the first person to have tarnished a good academic career in this way, so I hope that is not the case.
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  13. Stephen Baines wrote: "The only way for Salby's interpretation to be right is if we have missed a net flux term to the atmosphere that is temperature dependent and is very large (20x?) relative to anthro inputs. That also implies a much faster return time than we have assumed (otherwise the net change would have been larger), and that has operated in the past. ... Could we have missed such a thing?" No, we know the net environmental flux with good accuracy via the mass balance argument, so there is no way in which we could have missed such a thing (unless the carbon cycle is not a closed system and conservation of mass does not apply, but that is somewhat unlikely). The fluxes in Fig 7.3 of the recent IPCC WG1 do a good job in explaining the observed behaviour of the carbon cycle. Salby is either wrong or conducting a hoax.
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  14. Skeptical Wombat, Apologies. Re-reading your words, I realized that I misinterpreted them, and you were stating that an additional source (beyond anthropogenic) was not possible. I was, I think, confused by your later use of the term "negative feedback" "soaking up" vast amounts of anthropogenic CO2. Again, apologies. I must have been in cranky-old-man mode.
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  15. DM...A skeptic could always argue that we simply don't know all the terms well enough to do a proper mass balance. It's a variant of the common "Nature is incrutable and beyond the ken of mortal men - you are arrogant for trying" kind of argument. You see it in climate change and evolution debates all the time. My solution would be to make explicit what Salby's interpretation implies, given the other things we know to be true, so as to lay bare (in yet another way) the absurdity of his argument. It's an interesting and very challenging game. Beyond that, it is also powerful because it changes his argument from a simple negation to a concrete testable alternative proposition, something that the self-professed skeptics should be happy about! Basically he implies the existence of a massive, previously unidentified terrestrial flux of CO2 into the atmosphere (not to mention a nearly matching flux out of the atmosphere) with isotopic characteristics so specific that you'd think it would be impossible not to find it were you to look for it. You may even be able to suggest it's location more precisely geographically based on latitudinal and longitudinal patterns in the seasonality of CO2. Even more weirdly and coincidentally, Salby's implicit fluxes would have to be operating now, but not prior to the recent build up of CO2. Otherwise we would have seen wild fluctuations in CO2 over the last 10,000 years given the sensitivity implied instead of the relative stability. (Of course, given the magical thinking sometimes in evidence, this may not pose such a barrier.) It would be fun to see people at Curry's or WUWT scrambling about while trying to solve this puzzle. They should be motivated -- a hero's reputation is at stake. Plus find something like that and you'd have yourself a whole suite of Nature/Science papers, immediate admittance to the National Academy and grant money up the wazoo. Makes you wonder why someone don't try to find it, no? As you note, failure of mass balance assumptions is the other way around the mass balance argument. But how could mass balance fail? Either you'd be talking about loss of CO2 to space, in which case we wouldn't have CO2 or any atmosphere at all, or nuclear fission/fusion at ambient temp and pressure, which I think we would have noticed occuring!
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  16. Stephen Baines wroe "DM...A skeptic could always argue that we simply don't know all the terms well enough to do a proper mass balance." Yes, they could say that, but they would be wrong, the mass balance argument only requires estimates of anthropogenic emissions (which are taxed, so our estimates are pretty reliable and if anything an under-estimate) and observations of atmospheric CO2 (even WUWT accept that the Mauna Loa record is accurate). If the skeptics can't accept that, they will have no problem not accepting isotopic arguments either.
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  17. Humans are responsible for some of the rise in CO2 levels, but not all. Basic high school science- if water rises in temperature, gases are less soluble and thus released. (---snipped---)
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    Moderator Response: (Rob P) Please familiarise yourself with the comments policy. This site does not exist for the purpose of hosting contrarian graffiti a.k.a sloganeering. Stick to one aspect of the science at a time so that others may respond, and also find an appropriate thread in which to paste that comment.

    If you use the search function, you'll find thousands of posts which cover most aspect of climate science.

    As for your un-snipped comment see the OA not OK series - ocean warming is too small to affect the seawater CO2 uptake in any significant way.
  18. Greetings, I'm new here. I was directed to Murry Salbys 'C-14 proof', apparently 'Control of atmospheric CO2 Part 1&2' in the obscure 'Journal' 'Science of Climate Change'.

    Does anybody has any informations about where exactly he goes wrong in his proof?

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  19. EnderWiggin:

    First, you've posted the same question in three locations. That is bad form. In the main menu under the masthead, the "Comments" link will show any new comments on any thread, so posting your question once will allow it to be found easily.

    As for Salby, without a link to the papers I can't tell what that particular version of Salby's wanderings are wrong, but his name has been a frequent occurence here. You can use the search function at this site to find more, but in roughly chronoogical order here are several posts that discuss errors in Salby's work. I don't think he's come up with anything new in many years, so even old posts will probably cover any "recent"  errors.


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    Moderator Response:

    [BL] Edited 2023/01/12/ to delete a link that pointed to an unpublished web page.

  20. A follow-up to my comment @ 69, which was a response to EnderWiggin @ 68.

    On Tuesday, I did a search for the title and author (Salby) that EnderWiggin provided. I was able to find parts 1 and 2 on a site hosted at - but by Wednesday, that domain name had disappeared and could no longer be reached. does still exist, but has no signs of the papers. A bit of searching on their web page found a link to Eventually, the two papers were found on this page (Volume 1.2 December 2021).

    A bit of background. Klimarealistene is a well-known Norwegian climate "science" contrarian group. The "journal" Science of Climate Change is their creation. I suspect the change in web location has to do with reorganization of the journal's online pages. The old "scc" portion of the klimarealistene link was undoubtedly short for Science of Climate Change.

    On the main SCC page, they say:

    4 November, 2022

    The journal Science of Climate Change was funded by Klimarealistene in Norway in September 2020, and the first issue appeared in August 2021. Several additional articles have been published in 2021 and 2022, but due to a heavy work load on the Editor they have not been collected into Volumes before now. A few articles have also been delayed in being published. The Scientific Council of the Norwegian Climate Realists is at the moment working on a plan for the management of the journal from 2023. In the mean time I have stepped in as Editor to handle the backlog…

    The list of authors on their Volumes and Issues page reads like a who's-who of climate science contrarianism in Norway. Standard names such as Salby, Humlum, Harde, and Solheim dominate.
    So, the "obscure" journal, as EnderWiggin refers to it, looks like it is basically just a mouth-piece for Klimarealistene, so they can "publish" stuff and make it look like a journal. Credibility factor approaching zero.
    The two CO2 papers in question are co-authored between Salby and Hermann Harde. Interestingly, Salby is listed with an affiliation of "Ex Macquarie University" -a university he was fired from in 2013, after only 5 years. Not an inaccurate claim - he's clearly no longer there - but rather reeks of resume padding. (Of course, Salby is now "Ex Earth", having passed away in 2022.)
    Part 1 basically looks at C14 fluxes and argues that it can be used to estimate carbon uptake rates. Part 2 follows to look at recent (nothing older than 1956) variations in CO2 and temperature, to claim that anthropogenic contributions to the rise in CO2 are negligible.
    I didn't try to evaluate their math in detail, but basically it looks like yet another case of taking the short-term variation in CO2 concentrations and temperature, and making erroneous statistic correlations that mislead them about long-term trends. Same dog, same old tricks.
    In my comment above, the most applicable debunking is probably the one in this SkS post:
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  21. Thanks alot to Bob for his answers! I already knew the four articles on skepticalscience you linked to, but apparently the C-14-articles were not adressed therein.

    Sorry for posting several times, I just thought to increase my chance to get an answer. Next time, I'm going to post only once.

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  22. The C-14 article is just lipstick on an old pig - the same errors that permeate earlier papers are applied to C-14 concentrations instead of just CO2.

    The key  factor is that differentiation over the short term cannot tell you much about long-term processes.  There is a fundamental error, covered in the "correlation" link above, but not really expanded on or explicitly stated. Basically, when  you differentiate (look at the short-term rates of variation) you eliminate the constant terms. Many moons ago I expressed this in a private forum as follows:

    I am reminded of a math joke told to me years ago by a mathematician
    friend. (Yes, I know. "math joke" is an oxymoron. Don't ask me to tell you the one about Noah and the snakes.)

    Two mathematicians are in a bar, arguing about the general math knowledge of the masses. They end up deciding to settle the issue by seeing if the waitress can answer a math question. While mathematician A is in the bathroom, mathematician B corners the waitress and tells her that when his friend asks her a question, she should answer "one half X squared". A little later, when the waitress returns to the table, mathematician A asks her "what is the integral of X?". She answers as instructed, and mathematician A sheepishly pays off the bet and admits that mathematician B was right. As the waitress walks away, she is heard to mutter "pair of idiots. It's one-half X squared, plus a constant".

    Salby and Harde forget that integration is not complete without adding a constant - a moot point if you are just doing the integration symbolically, but absolutely critical if you want to put actual numbers on it. CO2 does track the integral of temperature - as long as you don't forget to add back in the constant that dominates the correlation. Without the constant, there is no correlation, which tells us that the short-term variations in temperature are not affecting the long term buildup of CO2. Because Salby sees a correlation between the noise in T and the noise in CO2, he mistakenly assumes that integration will entirely reverse the differentiation without reference to the constant.

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