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Climate Hustle

Residence Time and Prof Essenhigh

Posted on 3 October 2013 by Glenton Jelbert

Residence Time is something that crops up now and then in the denialist literature.  A classic example is a 2009 paper titled “Potential Dependence of Global Warming on the Residence Time (RT) in the Atmosphere of Anthropogenically Sourced Carbon Dioxide” (Energy & Fuels 2009, 23, 2773) by Essenhigh.  Thankfully Gavin Cawley has now managed to publish a response, which should settle the matter (  However, I thought it might be helpful to explain the science with a simple analogy that is easily accessible.

In the original Essenhigh [1] paper a Sankey diagram is presented (reproduced below [2]).  It includes the following data:

Flows into the atmosphere:

  • 60Gt/y from vegetation
  • 90Gt/y from surface oceans
  • 5.5Gt/y from fossil fuels
  • 155.5Gt/y Total

Flows out of the atmosphere:

  • 61.3Gt/y into vegetation
  • 92Gt/y into surface oceans
  • 153.3Gt/y Total

Atmospheric content: 750Gt

Essenhigh's argument is that residence time (which is the content divided by the outflow) is 750Gt divided 153.3Gt/y, which equates to ~5 years.  Therefore human contributions are irrelevant because the molecules of carbon dioxide that we put into the atmosphere are removed within 5 years.

What he ignores (though it’s equally clear in his own diagram) is that there is a net flow into the atmosphere of 2.2Gt/year.  It is this flow that would be absent without fossil fuels (and other activities like deforestation) and therefore is rightly attributed to man’s behaviour.

Allow me to make a simple analogy with a queue (this idea comes from Prof David MacKay’s [3] highly readable Sustainable Energy: Without The Hot Air, which is available for free on-line):

Consider a queueing system which can handle 150 people per hour (cf 150Gt/y).  Suppose 150 people are arriving per hour, and there are 750 people in the queue (cf 750Gt carbon content in the atmosphere).  Then it is clear that a person will be in the queue for 5 hours (cf 5 year residence time).  

However, if the number of people arriving goes up to 155 people per hour, clearly the queue will grow (cf an increase in the atmospheric carbon content), even though the queueing system will initially continue to have a ‘residence time’ of 5 hours (though it slowly grows from there).

From this it is apparent that the residence time is not the pertinent factor.  In our analogy, the important factor is the number of people in the queue (cf the amount of carbon in the atmosphere).  It is this that changes over the order of hundreds of years, even though any given molecule is only in the atmosphere for 5 years.  The studies that calculate this time scale are not making the elementary error of forgetting about natural flows as is suggested in the Essenhigh paper.

For a more detailed discussion, including evidence from the shift in isotope concentration, see the more recent IPCC reports (also available for free). Section 2.3 (Chemically and Radiatively Important Gases), and Section 7.3 (The Carbon Cycle and the Climate System) are particularly relevant in this context.

The Essenhigh paper also makes the assumption that the exit flow is proportional to the atmospheric concentration (that is, that the exit from the atmosphere will increase as the CO₂ concentration in the atmosphere increases).  This quibble is not as central as the queue analogy discussed above, but nonetheless is an interesting demonstration of how simple assumptions can give wrong results.  The reality is that there are positive feedback loops in many cases, so that increased CO₂ causes heating which causes an increase in CO₂ (and other greenhouse gases) through the melting of permafrost, the heating of the oceans (which releases CO₂ as it heats), and the reduction of vegetation (for example the Amazon is projected to become drier as the climate changes).  This could cause abrupt and irreversible climate change.  Completely the opposite of Essenhigh's a priori assumption that higher concentrations cause higher uptake.

[1] Robert Essenhigh is an Emeritus Professor of Mechanical & Aerospace Engineering at Ohio State University.

[2] For the sake of readers who may not have access to Energy & Fuels, below is the diagram from Energy & Fuels 2009, 23, 2774

Essenhigh Energy & Fuels, 23, 2774, 2009, Figure 1

[3] David MacKey is the Regius Professor of Engineering at the University of Cambridge, and chief scientific advisor to the UK Department of Energy and Climate Change.

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Comments 1 to 21:

  1. XRAY1961 @1, there have, in the past, been increases in CO2 concentration as large, and even larger than that (though probably not as rapidly).  Therefore the mere fact of the increase does not prove that the increase was anthropogenic.  Further, it is logically possible that the timing was mere coincidence - so while that timing is highly suggestive of the cause, it does not establish it to the standard scientists would normally accept.  Fortunately, there are at least nine other lines of evidence that, together, establish beyond any reasonable doubt that the rise in CO2 concentration is anthropogenic.

    Of these, one of the most important, and the one that Gavin Cawley most favours, is the mass balance argument.  We know that the CO2 increase was anthropogenic, because each year, the total increase in CO2 is less than we put into the atmosphere.  Therefore nature is taking CO2 out of the atmosphere each year, and consequently cannot have caused the rise in CO2 concentration.


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  2. Therefore the mere fact of the increase does not prove that the increase was anthropogenic.

    I think that's not what XRAY1961 had in mind. I think he meant that since Essenhigh implies (or openly states?) that anthropogenic contribution is negligible, then the source of rising CO2 concentrations should be huge and therefore not difficult to isolate. So I wouldn't go with 'completely disproves', but it gives it a lot of problems.

    It's astonishing that such faulty papers could get published. Beyond belief, really. I guess a college student could make such a mistake, but this ...

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  3. BojanD/XRAY1061 The fact that CO2 levels have been increasing at a time anthropogenic emissions have been rising doesn't disprove Essenhigh's hypothesis, but the fact that they have been rising more slowly than anthropogenic emissions does (as Tom points out).

    The error usually made by these types of argument is to compare the gross volume of anthropogenic and natural fluxes into the atmosphere without considering the fluxes out of the atmosphere as well.  The rise in atmospheric CO2 levels is caused by the difference between total emissions and total uptake.  Anthropogenic emissions are small compared to natural emissions, but natural uptake is bigger still, and it is the difference between natural emissions and natural uptake that determines the natural comtribution of CO2 to the atmosphere (and it is negative!).

    FWIW Essenhigh's paper says very little about what is causing the rise in atmospheric CO2, just that it can't be anthropogenic because the residence time is short.  My paper explains why this is incorrect, residence time is short (4-5 years), but the conclusion does not follow.

    Anyone can make a mistake, however the NIPCC report cites Essenhigh's paper and uses similar arguments, that is a far more egregious error as the problems with Essenhigh's paper had already been widely discussed in climate blogs and in the journal itself.  It would ony take a google scholar search of the papers that cite Essenhigh's to have discovered that, which is basic scholarship.

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  4. The link in "Thankfully Gavin Cawley has now managed to publish a response, which should settle the matter (" doesn't work.

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  5. BillEverett The link works for me.  Hopefully the link in the article will be fixed shortly.

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  6. "Prof David MacKay’s [3] highly readable Sustainable Energy: Without The Hot Air"  This link is not working.  I think it wants to go to:

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  7. I do not think that Essenhigh's calculation of the residence time is accurate. Majority of CO2 molecules absorbed by the ocean and vegetation are not removed permanently but returned back to the atmosphere. So the more appropriate analogy would be: 150 people are processed an hour form the 750 in queue. 140 of them are returned back to queue, thus only 10 are removed from queue. Consequently the real residence time is 75 years, not 5.

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  8. vmin Residence time is defined as the mean length of time a molecule of CO2 remains in the atmosphere before being taken up by the terrestrial or oceanic reservoirs, so Essenhigh is correct in using the term residence time.  His error lies in not understanding the difference between residence time and adjustment time, which is the characteristic timescale with which the atmospheric concentration responds to a change in sources and sinks (which corresponds to your 75 year figure).  The IPCC define these differing definitions of lifetime in the glossary of the WG1 report, but unfortunately do not clearly distinguish between them in the report itself (although the 1990 report that Essenhigh cites makes the distinction very clearly).

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  9. Essenhigh's 5y residence time number is bogus not only because it fails to consider the natural inflow (emissions from ocean/biosphere back to atmosphere) but also because, due to limited capacities of the natural sink such as ocean, the flow rates (determined by Henry's law) change over time.

    Only a part of CO2 molecules has a residence time of rougly 100y (a bit more than 75y calculated by vmin@8 but the same ballpark). In case of 1000GtC emissions, that part is some 50% - i.e. 500GtC of the original emissions being absorbed by the ocean surface results in OA reaching new equilibrium, therefore no more CO2 can be absorbed by Henry's law.

    The rest (500GtC) must wait for the deep water mixing and the reaction with sediments which takes 1-10Ky. Only 300-400GtC is taken that way, again due to limited sediment capacity.

    The rest (100-200GtC) must wait for the rock weathering processes which take sometime from 100Ky to 500ky (depending on current geological conditions).

    So, the residence time is not a simple constant number when we are dealing with such big amounts comparable to the natural sink capacity. In case of the emission scenarios considered in Anthropocene, it means 10 to 20% of emissions will stay in A for up to half a million years.

    Obviously, such science is well beyond Essenhigh, who makes very basic mistakes (i.e. ignores the inflow & Henry's law) that preclude any understanding of carbon cycle in geological sense.

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  10. chriskoz Essenhigh's 5 year figure for residence time is correct, and indeed agrees with the figure given in the IPCC WG1 report.  His error lies in not understanding the distinction between residence time and adjustment time.

    We should not be too hard on Prof. Essenhigh, his research record in his own field (combustion) appears to be very good, and it is all too easy to make this kind of error in moving into a tangentially related field.  The email correspondence I had with Prof. Essenhigh while writing my response published in Energy & Fuels was generally very cordial.

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  11. A useful analogy (and a bit closer to the actual situation than the queue) especially here in Caifornia where lots of people have spas and swimming pools:

    My pump circulates water into and out of my spa at an input rate of **** (fill in your
     favorite number) and removes it at the same rate. But I have taken my garden whose
     and added water at a much smaller rate (&&&&). The residence time for any molecule of water in the spa is short compared to the time the hose fills an empty spa, but does anyone think that it is not the hose that is causing the water level in the spa to increase?

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  12. There is a grain of hope, losely related to Prof. Essenhigh's contentions.  Carbon dioxide varies about 7ppm annually or more accurately, 8 up and 6 down.  Natural processes remove far more CO2 than any silly system we could devise to sequester Carbon dioxide.  Of course we must first stop pouring Carbon dioxide into the atmosphere but then we could give Gaia a chance and restore her systems for removing CO2 to their full potential.

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  13. HELP!!! Could someone please help a poor confused bloke like me who comes here to help them do battle at the street level on the climate change front (think Daily Mail readers and the like)?

    For instance, when 'debating' with a typical denier on the "global warming has stopped" meme, I have tended to use the argument that it takes ages (plus or minus an age or two) for CO2 to fall out of the atmosphere (and sod what Newton might have to say on the topic because apples are a lot heavier than CO2 molecules and thus fall more readily).

    It follows that global warming cannot have stopped because the excess CO2 we have pumped into the atmosphere over that last half century or so is still airborne and will be there for a long time yet warming the planet as it does so. Five years is not even near half an age, so what number of years should I use in presenting my case, 5, 50, 75 or what?

    I imagine the answer lies in the article somewhere, but it is well hidden from a simpleton like me.

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  14. funglestrumpet @14.

    Archer 2005 concludes with the following line that may be what you are looking for. (I have edited a little it to make its meaning clearer.)

    A better approximation of the lifetime of fossil fuel CO2 for public discussion might be ‘‘300 years, except for 25% of the CO2 that lasts forever."


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  15. MA Rodger @ 15

    Thanks, that is exactly what I was looking for!

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  16. funglestrumpet @14:

    Man is adding CO2 and some of that is leaking back out. This we all seem to agree on. But..

    The argument described at the top is a simplified model. Too simplified. It assumes that the atmosphere is a pipeline. It obviously is not. While an engine might have most of the air coming in at one location then move to exit elsewhere, perhaps crudely approximated as a single file queue, the atmosphere has lots of CO2 rise high to areas where there are few sinks. There is no physics that I know that suggests a model of a queue applies. The CO2 is *not* following a path single file that takes it way up high and then spins and comes down to leave at the ground level. That 5 year figure is the result of a simplified queue model. You can forget about it unless perhaps you want to believe the man-made CO2 entering and leaving the atmosphere is doing so in as a queue.

    Another analogy is the difference between fast moving draft air in a narrow cooridoor that is open at each end. This is like a queue. The atmosphere instead is like a huge balloon with two openings near each other, where one opening slowly adds air and the other slowly removes it. In this balloon example, we have nothing resembling a queue.

    Besides that the flow is not like a queue IMO, you are asking a different question than what is presented above. The five year is supposed to be the average time for CO2 to move into the atmosphere and back out, but the question you are asking is how long before we return to the same quantity of CO2 we had if we stop adding CO2. You care about how long before the air in the balloon gets back to the same quantity if we remove one of the several drivers adding air into the balloon.

    If we stop adding, there will be a net loss of CO2 that will slowly work its way back towards a more natural condition. It will take many years to make it most of the way there, but like an exponetial decay curve (if that model were to resemble the effect) we would never really get back all the way. Of course, the earth is more complex. If we plant and manually sustain more trees (or add other CO2 sinks.. eg, consume CO2 via microorganisms that sequester the result in some chemical form), then we could not only get back to "normal" as defined by today's system but even go beyond it. And then there are planetary effects and basically a bunch of effects (feedbacks) that don't follow the exponential decay model either.

    Sorry to not give you a precise answer. You asked in the right place and some studies address that concern. I just wanted to give an idea that what you are asking has nothing to do with this abstract 5 year calculation.

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  17. funglestrumpet @14, here is take two (using two different analogies than the earlier air in balloon analogy, water in tank and food in body).

    The argument in this article (even if using a too crude model) is about how long it takes for a molecule of "man-made" CO2 to come into the atmosphere and leave.

    Is that what you care about? If I have a large tank to which I am adding water but from which some water is leaving, do you want to know how long before the water molecule I add leaves at the bottom? Do you care if the addition is slow and the escape is slow so that the transit time is 1000000 years? Would it make a difference to you if instead the addition and escape were super fast and took 1 second?

    I think the primary question (the question as goes global warming) is how fast that tank is being filled *after* we take into account the result of both the additions and the subtractions.

    Do you want to know how fast it takes for the food you eat to exit OR do you want to know how much weight you are putting on after taking into account how much you eat and what leaves the body?

    The latter is what is important. The argument above tries to make a claim about the latter based on (a crude) analysis of the former without taking into account net gains or losses.

    If you care about the latter, then the answer you want is how long it would take for the CO2 to return to "normal" (ie, to some base reference level after factoring out natural factors that may change that reference level over time) after we remove the "man-made" components. Ie, you want to know how long before I return to my "normal" weight after I stop eating that extra dessert after every meal. How long it takes for the food to pass through your body (very fast or very slow) is irrelevant.

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  18. funglestrumpet @14, here is the summary:

    We can roughly liken CO2 going into and out of the atmosphere using 3 analogies.

    1 -- We don't care about how long it takes for extra man-made air put into a ballon, or water put into a tank, or food put into a body, to exit.

    2 -- We care instead about how long it will take to return to normal volume once we stop adding the man-made air, water, or food.

    The argument described in this article crudely measures how long it takes a man-made molecule of air, water, or food, to exit, but that doesn't address what we care about: how long it takes for these systems to return to the normal levels after we stop adding the man-made air, water, or food. I don't care about the speed of travel in my body of my daily cheesecake (from entry to exit). I care about how long before I lose the weight I put on because of that cheesecake.

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  19. Jose_X @ 17, 18 & 19 Thanks for taking so much trouble and effort to answer the question I didn't ask, but should have. Now I understand it better, thanks to you, I rather think I might have won a few discussions in the past rather unfairly! Still, all's fair in love and war, isn't it?!

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  20. Could someone please explain what is known about the dependence of the fluxes upon the amount of CO2 in each compartment of the system? That is, which fluxes are proportional to the concentration of CO2, which fluxes have a rate-limiting bottle-neck that is indifferent to the concentration, which have a combination of these (saturable kinetics), and so on? How would the magnitudes of the fluxes change, for instance, if atmospheric CO2 was 200 ppm (or 600 ppm) instead of 400 ppm?

    The mass-balance argument suggests that nature has obligingly absorbed some of our excess CO2, with natural processes acting as a net sink, but is this something that could have been predicted from first principles, or is it simply an observation after the fact? To me, it suggests that sink fluxes are more active when there is more CO2 around, which is what I would have expected intuitively, but what does the evidence suggest?

    Note that I'm not talking about potential positive feedbacks from permafrost melting, and so on, just the main fluxes at work now.

    Thanks in advance for any clarification.

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  21. Leto @21.

    That's a lot of question you present in 21 ranging from the basic to the quite technical. I will not address most of it.

    CO2 is being absorbed by the oceans and the biosphere. For a long time that was but an inference based on ocean & atmosphere measurement & data for fossil fuel use. The biosphere absorption was not measured and assumed to be the sole missing CO2 sink. However, I hear the biosphere can now be assessed (estimated) as a sink.

    These two sinks were always predicted although it took some time to fully understand why oceans didn't absorb much more CO2 than they actually did. The oceans can now be modeled with some confidence as a CO2 sink (See the Archer link @15 or AR4 for instance.) The net effect of the biosphere is not something that can be predicted so easily. Plants will absorb more CO2 at higher levels up to a point but such absorption depends on the type of plant involved and relies on climate providing the environment to maintain such growth. This reliance on climate extends to carbon within soils which can also become a significant source/sink with changes in rainfall or temperature (eg the permafrost melting). Thus predicting future biosphere absorption is only for the brave.

    The amount of our emission that are presently absorbed is about 43% if changing land use is accounted for. This value waggles about with ENSO but has remained reasonably constant over the last half century. The value is simply the result of the rate of increase of our emissions. So far there is no obvious indication of changes in absorption in oceans or  biosphere. Although saying that, the last 18 months has seen inceases in atmospheric CO2 higher than I would have expected during ENSO-neutral periods. Is it a marker of things to come? We will have to wait and see.

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