A Harde response

Earlier this year, I wrote a post about a paper by Hermann Harde that argued that most of the rise in atmospheric CO2 was natural. If you want more details of why this suggestion is nonsense, you can read my earlier post. What I was going to mention in this post is that a number of us have just published a response.

The history of this is essentially that Gavin Schmidt, as he suggested in this Realclimate post, set up an Overleaf document and contacted those who had shown interest. It was lead by Peter Köhler, and colleagues, from the Alfred-Wegener-Institut, but also included myself, Eli Rabett, and Richard Zeebe from the University of Hawaii at Manoa. Gavin Cawley also provided some very valuable comments and suggestions.

I don’t need to say too much about the details of our paper. It essentially highlights that the Harde paper confuses the residence time of an individual molecule (years) with the adjustment time for an enhancement of atmospheric CO2 (centuries). It also points out that you can’t model the evolution of atmospheric CO2 with a single equation. You need to consider at least two reservoirs (atmosphere and surface ocean) and this requires at least two equations that are solved simultaneously.

We also point out that it’s important to consider the Revelle factor, which limits how much of our emissions can be taken up by the oceans (we would expect – depending on how much we emit – that 20-30% of our emissions will remain in the atmosphere for thousands of years). Additionally, there were issues with Harde’s application of his model to paleoclimate, and there were a number of papers that he really should have cited (such as citing Essenhigh 2009 paper, while failing to cite Gavin Cawley’s response).

We end our paper by suggesting that Harde’s paper be withdrawn. I’m normally a little uncomfortable with suggesting that a paper that does not involve fraud, or plagiarism, be withdrawn. However, Harde’s paper is so obviously flawed that it is remarkable that it made it through the editorial, and review, process without being rejected. It might be better if it were withdrawn, but at least there is now a formal response that highlights the numerous issues.

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39 Responses to A Harde response

  1. Kevin ONeill says:


  2. Marco says:

    Quite a few papers have been retracted recently for making mistakes. In those cases, however, it supposedly(*) is the author that takes the initiative.

    (*) In reality, in some cases there very likely is pressure from the Editor(s) to retract.

    COPE actually states that “Journal editors should consider retracting a publication if they have clear evidence that the findings are unreliable, either as a result of misconduct (e.g. data fabrication) or honest error (e.g. miscalculation or experimental error)”

    Moreover: “Retraction should usually be reserved for publications that are so seriously flawed (for whatever reason) that their findings or conclusions should not be relied upon.”

    Harde’s paper definitely fits this category…

  3. Marco,
    Thanks, I hadn’t seen the suggestion that retraction should be considered if a paper’s findings are unreliable. It does make sense in cases where it’s obvious that the paper’s results are clearly flawed.

  4. dikranmarsupial says:

    Bravo indeed!

    I think the reason Prof. Harde’s paper made it through review can be found in the author information pack for the journal:

    Please submit, with the manuscript, the names, addresses and e-mail addresses of five potential
    referees. Note that the editor retains the sole right to decide whether or not the suggested reviewers
    are used.

    which seems to me a recipe for pal-review, I suspect I can guess some of those likely to have been on any such list. I suspect that is also how the earlier carbon cycle paper by Humlum et al. (which also was the subject of peer-reviewed comments) that was published in the same journal. IMHO journals should never do this. For any paper within the scope of the journal, there should be an action editor sufficiently familiar with the sub-field to identify suitable reviewers for themselves and if they can’t they shouldn’t handle it. However, they are only human and we all make mistakes…

    The problem with the paper is made very obvious by the fact that Prof. Harde doesn’t provide a plot of the output of his models against the observations, which is a very natural thing to do if you want to show that your model provides a good fit to the data. The closest we get in the paper is figure 3:

    I tried reproducing this myself, but plotting the actual ice core data, rather than giving error bars:

    Not so good. In particular it is clear that in the ice core data, the relationship between temperature and CO2 is linear, and the modern observations don’t fit the pattern of the ice core data (and neither does Prof. Harde’s model). It isn’t at all clear how the error bars for the observations for Harde’s figure 3 were calculated, I suspect they may be “subjective”.

    Note there are substantial problems with my diagram as well (I learned a lot from my discussions with the authors of the paper!), particularly the Vostok temperatures are regional Antarctic temperatures, rather than global temperatures. IIRC the Vostok core includes interglacial periods that were about as warm as it is now (if not warmer?), so if Prof. Harde’s model is correct, it is hard to see why CO2 concentrations were not approaching 400ppm then (I’d need to go and check the details on that, so caveat emptor).

    Anyway, it is a shame that the effort it takes to respond to ill-informed misleading papers, such as this one, is so much higher than it is apparently to produce them, but I’m glad someone took the trouble to do it in this case.

  5. dikranmarsupial says:

    Here is my attempt at implementing Prof. Harde’s model of post-industrial conditions, using an ODE solver to drive the model with observed temperatures:

    This shows why a temperature driven model for atmospheric CO2 with a short “residence” time can’t explain the observed rise in atmospheric CO2. The temperature data has lots of decadal+ scale variability, and a “residence” time of only 4 years isn’t enough to smooth it out, so it will predict that CO2 will rise with similar decadal+ scale variability. The trouble is that it doesn’t, the observed rise in atmospheric CO2 is pretty smooth, and a simple (and conventional) one-box carbon cycle model (based on the one in my paper) with an approx. 50-70 year adjustment time (don’t worry, it also has a residence time of 4-5 years ;o) does a much better job.

  6. dikranmarsupial says:

    Cheers, I’m glad there was a suitable venue to share the diagrams at last! I like your new avatar/icon BTW, if I had an avatar representing my work it would have to be an animated GIF of (apparently meaningless) numbers changing very slowly ;o)

  7. “It also points out that you can’t model the evolution of atmospheric CO2 with a single equation. “

    I can. It’s variously referred to as dispersive diffusion — a classical diffusion equation solved with a MaxEntropy distribution of diffusivity values. This maps to the heuristically determined set of factors known as the Berne formulation.

  8. Geo,
    Well, okay, but that is presumably determining net flux and your diffusion coefficient is presumably implicitly incorporating information about the two reservoirs.

  9. The numerical solution to diffusion in that geometry is a slab model, which is an infinite set of differential equations representing the flow between an infinite number of reservoirs. The analytical solution to that geometry is an erf. As an analogous application, the ocean/atmosphere interface is equivalent to the solid/vapor interface used for diffusional doping of a semiconductor. The industry has this process characterized very well and the erf works effectively.

    But with a range of diffusivities representing the different pathways to CO2 sequestration, the erf can be replaced with another formulation that takes into account the variability. So the Berne formulation is a heuristic for the description of the actual diffusional physics. They use the heuristic because that’s all they need apparently. There’s nothing wrong with it but they will never be able to approximate the diffusional fat-tail at infinite time because they are using a set of exponentials instead of an erf. The slowest exp decay is what they use for the fat tail.

  10. Everett F Sargent says:

    So, who will reply to Harde’s latest missive missile that misses massively? …
    Radiation Transfer Calculations and Assessment of Global Warming by CO2

    “Including solar and cloud effects as well as all relevant feedback processes our simulations give an equilibrium climate sensitivity of Cs = 0.7°C (temperature increase at doubled CO2) and a solar sensitivity of Ss = 0.17°C (at 0.1% increase of the total solar irradiance). Then CO2 contributes 40% and the Sun 60% to global warming over the last century.”

    Rust Never Sleeps

  11. Everett,

    So, who will reply to Harde’s latest missive missile that misses massively? …
    Radiation Transfer Calculations and Assessment of Global Warming by CO2

    I don’t know if anyone is going to bother with that one.

  12. cce says:

    Is there a link to this paper?

  13. cce,
    Good point. I managed to forget to provide a link in the post (fixed now). It’s here, in case you don’t want to read the post again 🙂

  14. angech says:


  15. KHome1990,
    Below is a figure that might help. It shows the cumulative emissions for the 4 different Representative Pathways (RCPs) and shows how the warming depends more on how much we emit, rather than on how fast. It also shows atmospheric concentrations (bubbles) and each dot on each line is a decade. The range is represented by the width band.

  16. Marco says:

    Wrong thread, ATTP!

  17. Everett F Sargent says:

    Figure 2.3 | Global mean surface temperature increase as a function of cumulative total global carbon dioxide (CO2) emissions from various lines of evidence. Multi-model results from a hierarchy of climate carbon-cycle models for each Representative Concentration Pathway (RCP) until 2100 are shown (coloured lines). Model results over the historical period (1860 to 2010) are indicated in black. The coloured plume illustrates the multi-model spread over the four RCP scenarios and fades with the decreasing number of available modelsin RCP8.5. Dots indicate decadal averages, with selected decades labelled. Ellipses show total anthropogenic warming in 2100 versus cumulative CO2 emissions from 1870 to 2100 from a simple climate model (median climate response) under the scenario categories used in WGIII. Temperature values are always given relative to the 1861–1880 period, and emissions are cumulative since 1870. Black filled ellipse shows observed emissions to 2005 and observed temperatures in the decade 2000–2009 with associated uncertainties.(WGI SPM E.8, TS TFE.8, Figure 1, TS.SM.10, 12.5.4, Figure 12.45, WGIII Table SPM.1, Table 6.3)

    (page 63)

  18. Comment on “Scrutinizing the carbon cycle and CO2 residence time in the atmosphere” by H. Harde, needed proof-reading.

  19. Pingback: 2017: A year in review | …and Then There's Physics

  20. Good news, the journal has published a commentary on the failure of the review process, see RealClimate for details. For once writing a comment paper has actually had an effect (from the journal response bit):

    In order to lessen the possibility of introducing bias into the peer review process, authors are no longer able to suggest the names of possible reviewers for their manuscript. To give more credit to the Editors for their work and increase a sense of accountability, published manuscripts will additionally provide the name of the editor who made the final decision.

    This is real progress. Journals really should never ask authors to suggest reviewers, it is a recipe for pal-review. If the editor is unable to identify suitable reviewers for themselves, then they are likely to be too inexperienced (not sufficiently aware of the broader research field, rather than their own specialism, which takes time), or the paper is outside the scope of the journal. If nothing else, an editor that wasn’t able to select reviewers ought to pass the paper on to another editor where the paper is closer to their expertise (I’m not sure that journals should allow authors to select the editor either – that also has resulted in problems in the past).

    I was rather less impressed by:

    “After much consideration by the editors at the time of publication, it was felt that the paper should not be retracted, but rather let it remain to stimulate further discussion about such a highly charged and contentious topic.”

    This is just ridiculous. The cause of the rise in atmospheric CO2 is not remotely a highly charged or contentious topic, and stimulating further debate on this issue (unless some startling new evidence comes along) is just an egregious waste of everybody’s time.


    All five suggested potential reviewers were invited by the Editor to provide formal reviews on the submitted manuscript. Two of them accepted the invitation and suggested ‘major revisions’ and ‘minor revisions’, respectively. Both reviewers asked the author for more clarity and better presentation, style and language; none of them raised any concern about the scientific content of the manuscript. We believe that this may have been because the reviewers lacked the impartiality and scientific expertise to provide an adequate science-based review.

    This implies, but doesn’t explicitly state, that the only reviewers invited to review were those suggested by the author, which is, shall we say, “sub-optimal”.


    During the initial manuscript submission, H. Harde suggested five potential reviewers. Most if not all of them are prominent individuals advocating that currently raising CO2 concentrations would be natural and not related to human influence.

    I think they have just identified the reviewers. It isn’t that easy to think of more than five scientists that would advocate rising CO2 concentrations being natural.

  21. I should add, I fully agree with

    It was also felt that although the implementation of the peer review of this paper had failed, no unethical action has been found in its publication.

    as a reason not to withdraw the paper. Much better than the reason that immediately preceded it! ;o)

  22. Pingback: An editorial response | …and Then There's Physics

  23. Story about this at RetractionWatch, which gives a link to Prof. Harde’s rejected response paper (with help from Murray Salby).

  24. Apparently there is another paper in review (?) on this topic by Ed Berry. So I suspect Harde’s paper might not be the last that time will be wasted on, by the reviewers if not the rest of the research community.

    Yet again it is a failure to understand the difference between residence time and adjustment time:

    3.3 IPCC confuses residence time

    IPCC (1990) properly concludes that the residence time of carbon dioxide molecules in the atmosphere is about 4 years. But the IPCC defines residence time incorrectly. The IPCC says residence time is “turnover time.” Here is a quote:

    The turnover time of CO2 in the atmosphere, measured as the ratio of the content to the fluxes through it, is about 4 years. This means that on average it takes only a few years before a CO2 molecule in the atmosphere is taken up by plants or dissolved in the ocean.

    This short time scale must not be confused with the time it takes for the atmospheric CO2 level to adjust to a new equilibrium if sources or sinks change.

    What IPCC calls “turnover time” is the 1/e residence time.

    IPCC defines two kinds of residence times: one residence time equals the average lifetime of molecule, and the other residence time equals the time for the “level to adjust to a new equilibrium” level.

    But both residence times are the same thing. All definitions of residence time are the same because all definitions measure residence time according to the change in the level of carbon dioxide. No one measures how long an individual carbon dioxide molecule stays in the air.

    [emphasis mine]

    The hubris of this is staggering. The IPCC carefully explain the difference between the two, but Berry insists that they must be the same thing. The highlighted bit is so obvious an error it is hard to see how even Berry has missed it. The residence time is not measured by changes in the level of carbon dioxide; if sources and sinks were constant the adjustment time would be infinite (as the carbon cycle would not adjust to an exogenous pulse of CO2 and atmospheric level would remain raised indefinitely), but there would still be a finite residence time because of the exchange flux.

  25. I had lengthy discussion with Ed Berry on this post. He’s completely unreachable with, as you say, a staggering amount of hubris.

  26. Apparently the article was submitted to an Elsevier journal, I wonder if it was “Global and Planetary Change” (as it has already published two papers on this topic). Hopefully the reviewers will spot the obvious errors (and hopefully not selected by Berry) and/or the editors will be more cautious this time.

    It is bizarre how people can refuse to accept they are wrong on this one, when the evidence is so strong (common sense ought to be sufficient to strongly doubt it being a natural phenomenon!).

  27. Marco says:

    “It is bizarre how people can refuse to accept they are wrong on this one”

    If your ideology depends on you understanding something the wrong way…

  28. True, but it would be more sensible to attack a later, weaker link in the chain, rather than whatis probably the strongest! It is quite some ideology if it means you can’t accept any part of it.

  29. Marco says:

    No need to attack those later links if you can cast doubt on an earlier one!

    Note also that some are deadly afraid that accepting A brings them one step closer to also accepting B. The infamous “slippery slope”.

  30. I glanced through Ed Berry’s text and I got the impression that he is not giving a correct description of previous scientific understanding of the carbon cycle. His three analogies at the beginning of his paper are all missing the point.

    A better analogy would be that there are two water pools, A and B, equal in size. Water is pumped from A to B through one tube. Then there is a recycling tube in which there is an equal flow of water from B to A. If undisturbed the water will circulate between the two pools and the water level will remain the same. This is a simple analogy of the undisturbed circulation of carbon dioxide between the atmosphere, corresponding to pool A, and the mixed layer of the ocean, corresponding to pool B. The water level corresponds to the carbon dioxide concentration level. The flow from B to A corresponds to the natural carbon dioxide emissions from the ocean to the atmosphere, the flow from A to B is the absorption of carbon dioxide from the atmosphere¨to the ocean.

    Now, assume that there is a drain connected to the wall of pool B in order that the water should not overflow the pool brims of the two communicating pools. If water from a hose flows into pool A the water level in the pools will increase. At first, all the water from the hose will increase the water level but then gradually the drain will begin to receive more and more water and finally, the water level will stabilize on a higher level. The flow from the hose corresponds to human carbon dioxide emissions, say 10 % of the natural emissions from the ocean to the atmosphere, and the flow through the drain corresponds to the flow of carbon dioxide from the mixed layer of the ocean to the main part of the ocean.

    Unfortunately, the carbon dioxide flow from the mixed layer to the main part of the ocean corresponds to a very narrow drain. The carbon dioxide level has to increase very much before the drain will stabilize the level at a much higher carbon dioxide concentration than we have today. We are still in the part of the process where most of the human carbon dioxide remains in the two pools and only a small fraction leaves through the drain pipe.

    I have based my analogy on the fundamental principles that were developed many years ago by Revelle and Suess (1957) and Bolin and Eriksson (1959). Those fundamental principles are a well-established and a widely accepted scientific basis for models of the carbon cycle, for example, the Bern model.

    Bolin, B., and Eriksson, E., 1959: “Changes in the carbon dioxide content of the atmosphere and sea due to fossil fuel combustion,” Rossby Memorial Volume (New York: Rockefeller Institute Press), pp. 130-142.

    Roger Revelle & Hans E. Suess (1957) Carbon Dioxide Exchange Between Atmosphere and Ocean and the Question of an Increase of Atmospheric CO2 during the Past Decades, Tellus, 9:1, 18-27, DOI: 10.3402/tellusa.v9i1.9075

  31. Marco says:

    There also is a case to be made against the increase being primarily natural because of a lack of credible sources and sinks for that increase.

    If we take, for example, Harde’s claim that only 10% of the increase is anthropogenic, this means 90% of the increase must be natural. Since the annual increase in atmospheric CO2 has been relatively constant at about half the annual anthropogenic addition, this means the natural net flux to the atmosphere must be about ten times bigger (and weirdly scaling with the anthropogenic contribution over the last few centuries, but let’s ignore that happy coincidence). This is an enormous amount of carbon. We’re talking about 80 Gt C per year at the moment, and while that gets progressively lower as we get back in time, we’d still talk about several thousand Gt C (around 3-3.5) since the industrial revolution.

    And then the accounting problems start: The net source isn’t the oceans, because we’ve measured an increase in dissolved inorganic carbon (and there is too little dissolved organic carbon in there for that to be the source). It isn’t vegetation, or there’d be no more vegetation. It isn’t soil, because there’d be no more carbon in the soil. So, where’s that source that Harde and Salby and Berry etc conclude must exist? A little bit from everything still doesn’t cut it. Volcanoes? Gee, another problem in getting that to go up to the required amount (it really is a lot of CO2 – we’re talking 10% of Deccan trap-like levels of emissions, but in a much shorter time period). And besides, what made volcanoes suddenly spew so much more CO2 in the air, and so happily in tune with anthropogenic emissions?

    If they would argue that the oceans are the source, but it’s from the deep oceans somewhere, where good DIC measurements are lacking, we still lack a credible sink. Sure, vegetation may have increased, but we’d have to talk about an increase of many factors to get to the required thousands of Gt carbon that needs to be taken up. We would have noticed that. Soil could potentially be easier to ‘sell’ as the sink, as it is more difficult to measure an increase in carbon content in the soil by about a factor 2-3 or so. That lacks a mechanism, though.

  32. Neither Hermann Harde nor Ed Berry seems to have read and understood the two seminal papers by Revelle and Suess (1957) and Bolin and Eriksson (1959). Harde has not cited any of those papers. Although Berry cites Revelle and Suess he is not aware of why this paper is so important. Perhaps someone should recommend Harde and Berry to study more climate science. A good beginning could be Spencer Weart’s“The Discovery of Global Warming”

    Spencer Weart, in that work, has written about the importance of the two papers Revelle and Suess (1957) and Bolin and Eriksson (1959) in the following essay with the title “Roger Revelle’s Discovery”:

    The introduction of this fairly detailed essay is :

    Before scientists would take greenhouse effect warming seriously, they had to get past a counter-argument of long standing. It seemed certain that the immense mass of the oceans would quickly absorb whatever excess carbon dioxide might come from human activities. Roger Revelle discovered that the peculiar chemistry of sea water prevents that from happening. His 1957 paper with Hans Suess is now widely regarded as the opening shot in the global warming debates. This essay not only describes Revelle’s discovery in detail, but serves as an extended example of how research found essential material support and intellectual stimulus in the context of the Cold War.(1)

    At the end of Weart’s text the importance of Bolin and Eriksson (1959) is described:

    Another two years passed before Bert Bolin and Erik Eriksson explained the sea water buffering mechanism in clear terms and emphasized what it meant. Unlike Revelle, they figured industrial production would indeed climb exponentially, and they calculated that atmospheric CO2 would probably rise 25% by the end of the century. Now the small community of geophysicists began to grasp that they could not rely upon the oceans to absorb all the emissions of fossil fuels.(31)

    It is rather impressing that Bolin and Eriksson in 1959 predicted that the rise of carbon dioxide content in the atmosphere could be 25 % in the year 2000 compared to 1880. Carbon dioxide had risen to 369 ppm in 2000. Assuming that it was 300 ppm in 1880 that is a 23 % rise:

  33. Marco says:

    “Perhaps someone should recommend Harde and Berry to study more climate science.”

    Yeah…people have. They just dig in more. Remember that both seem to come from a position that mainstream climate science is wrong, hence no need to understand the scientific papers by mainstream scientists.

  34. FWIW at Retraction watch, Prof Harde writes:

    I agree with Dr. Cawley [i.e. me – DM] that nature is a net sink, as long as anthropogenic activities are not zero. I had never doubts on this assertion. But I can’t follow the conclusion that in addition to human emissions increasing natural emissions cannot be the reason for an observed growing CO2 concentration.

    At least Prof. Harde agrees that the natural carbon cycle is a net carbon sink. However it seems to me to require some cognitive dissonance to accept that the natural carbon cycle takes more CO2 out of the atmosphere than it puts in, but at the same time to believe that the rise in atmospheric CO2 is a natural phenomenon.

  35. …and Then There’s Physics, you said in one of your previous comments here that:

    “I don’t know if anyone is going to bother with that one.”

    You were referring to whether anyone would bother with this trite “paper” from Harde and published in a predatory journal:
    “Radiation transfer calculations and assessment of global warming by CO2”

    Well, I think someone should write a formal comment or rebuttal to that paper, since Knutti et al. cited that “paper” in their recent review of climate sensitivity estimates:

    “Beyond equilibrium climate sensitivity”, figure 2 on page 4

  36. dikranmarsupial says:

    FWIW Murry Salby responds to Köhler here:

    Pretty much packs all of the climate skeptic carbon cycle myths into one “convenient” 90min talk. The above link is about where the stuff about Harde’s paper starts.

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