While some model based claims say that CO2 residence times may be thousands of years, a global experiment in measurable CO2 residence time seems to have already been done for us.
By Christopher Monckton of Brenchley
Is the ~10-year airborne half-life of 14CO2 demonstrated by the bomb-test curve (Fig. 1, and see Professor Gösta Pettersson’s post) the same variable as the IPCC’s residence time of 50-200 years? If so, does its value make any difference over time to the atmospheric concentration of CO2 and hence to any consequent global warming?
Figure 1. The decay curve of atmospheric 14C following the ending of nuclear bomb tests in 1963, assembled from European records by Gösta Pettersson.
The program of nuclear bomb tests that ended in 1963 doubled the atmospheric concentration of 14CO2 compared with its cosmogenic baseline. However, when the tests stopped half the 14C left the atmosphere in ten years. Almost all had gone after 50 years. Why should not the other isotopes of CO2 disappear just as rapidly?
Mr. Born, in comments on my last posting, says the residence time of CO2 has no bearing on its atmospheric concentration: “It’s not an issue of which carbon isotopes we’re talking about. The issue is the difference between CO2 concentration and residence time in the atmosphere of a typical CO2 molecule, of whatever isotope. The bomb tests, which tagged some CO2 molecules, showed us the latter, and I have no reason to believe that the residence time of any other isotope would be much different.”
He goes on to assert that CO2 concentration is independent of the residence time, thus:
The total mass m of airborne CO2 equals the combined mass m12 of 12,13CO2 plus the mass m14 of 14CO2 (1):
(1) 
.
Let CO2 be emitted to the atmosphere from all sources at a rate e = e12 + e14 and removed by uptake at a rate u. Then the rate of change in CO2 mass over time is given by
(2) 
,
which says the total mass m of CO2, and thus its concentration, varies as the net emission, which is the difference between source e and sink u rates.
For example, if e = u, the total mass m remains unchanged even if few individual molecules remain airborne for long. Also, where e > u, m will rise unless and until u = e. Also, unless thereafter u > e, he thinks the mass m will remain elevated indefinitely. By contrast, he says, the rate of change in 14CO2 mass is given by
(3) 
,
which, he says, tells us that, even if e were to remain equal to u, so that total CO2 concentration remained constant, the excess 14CO2 concentration
(4) 
,
which is the difference between the (initially elevated) 14CO2 concentration and the prior cosmogenic baseline 14CO2 concentration, would still decay with a time constant m/u, which, therefore, tells us nothing about how long total CO2 concentration would remain at some higher level to which previously-elevated emissions might have raised it. In this scenario, for example, the concentration remains elevated forever even though x decays. Mr. Born concludes that the decay rate of x tells us the turnover rate of CO2 in the air but does not tell us how fast the uptake rate u will adjust to increased emissions.
On the other hand, summarizing Professor Pettersson, reversible reactions tend towards an equilibrium defined by a constant k. Emission into a reservoir perturbs the equilibrium, whereupon relaxation drains the excess x from the reservoir, re-establishing equilibrium over time. Where µ is the rate-constant of decay, which is the reciprocal of the relaxation time, (5) gives the fraction ft of x that remains in the reservoir at any time t, where e, here uniquely, is exp(1):
(5) 
.
The IPCC’s current estimates (fig. 2) of the pre-industrial baseline contents of the carbon reservoirs are 600 PgC in the atmosphere, 2000 PgC in the biosphere, and 38,000 PgC in the hydrosphere. Accordingly the equilibrium constant k, equivalent to the baseline pre-industrial ratio of atmospheric to biosphere and hydrosphere carbon reservoirs, is 600 / (2000 + 38,000), or 0.015, so that 1.5% of any excess x that Man or Nature adds to the atmosphere will remain airborne indefinitely.
Empirically, Petterson finds the value of the rate-constant of decay µ to be ~0.07, giving a relaxation time µ–1 of ~14 years and yielding the red curve fitted to the data in Fig. 1. Annual values of the remaining airborne fraction ft of the excess x, determined by me by way of (5), are at Table 1.
Figure 2. The global carbon cycle. Numbers represent reservoir sizes in PgC, and carbon exchange fluxes in PgC yr–1. Dark blue numbers and arrows indicate estimated pre-industrial reservoir sizes and natural fluxes. Red arrows and numbers indicate fluxes averaged over 2000–2009 arising from CO2 emissions from fossil fuel combustion, cement production and land-use change. Red numbers in the reservoirs denote cumulative industrial-era changes from 1750–2011. Source: IPCC (2013), Fig. 6.1.
| t = 1 | .932 | .869 | .810 | .755 | .704 | .657 | .612 | .571 | .533 | .497 |
| 11 | .464 | .433 | .404 | .377 | .362 | .329 | .307 | .287 | .268 | .251 |
| 21 | .235 | .219 | .205 | .192 | .180 | .169 | .158 | .148 | .139 | .130 |
| 31 | .122 | .115 | .108 | .102 | .096 | .090 | .085 | .080 | .076 | .071 |
| 41 | .067 | .064 | .060 | .057 | .054 | .052 | .049 | .047 | .045 | .042 |
| 51 | .041 | .039 | .037 | .036 | .034 | .033 | .032 | .030 | .029 | .028 |
| 61 | .027 | .027 | .026 | .026 | .024 | .024 | .023 | .022 | .022 | .021 |
| 71 | .021 | .021 | .020 | .020 | .019 | .019 | .019 | .019 | .018 | .018 |
| 81 | .018 | .018 | .017 | .017 | .017 | .017 | .017 | .017 | .016 | .016 |
| 91 | .016 | .016 | .016 | .016 | .016 | .016 | .016 | .016 | .016 | .016 |
| 101 | .016 | .015 | .015 | .015 | .015 | .015 | .015 | .015 | .015 | .015 |
| 111 | .015 | .015 | .015 | .015 | .015 | .015 | .015 | .015 | .015 | .015 |
Table 1. Annual fractions ft of the excess x of 14CO2 remaining airborne in a given year t following the bomb-test curve determined via (5), showing the residential half-life of airborne 14C to be ~10 years. As expected, the annual fractions decay after 100 years to a minimum 1.5% above the pre-existing cosmogenic baseline.
Now, it is at once evident that Professor Pettersson’s analysis differs from that of the IPCC, and from that of Mr. Born, in several respects. Who is right?
Mr. Born offers an elegantly-expressed analogy:
“Consider a source emitting 1 L min–1 of a fluid F1 into a reservoir that already contains 15.53 L of F1, while a sink is simultaneously taking up 1 L min–1 of the reservoir’s contents. The contents remain at a steady 15.53 L.
“Now change the source to a different fluid F2, still supplied at 1 L min–1 and miscible ideally with F1 as well as sharing its density and flow characteristics. After 50 minutes, 96% of F1 will have left the reservoir, but the reservoir will still contain 15.53 L.
“Next, instantaneously inject an additional 1 L bolus of F2, raising the reservoir’s contents to 16.53 L. What does that 96% drop in 50 minutes that was previously observed reveal about how rapidly the volume of fluid in the reservoir will change thereafter from 16.53 L? I don’t think it tells us anything. It is the difference between source and sink rates that tells us how fast the volume of fluid in the reservoir will change. The rate, observed above, at which the contents turn over does not tell us that.
“The conceptual problem may arise from the fact that the 14C injection sounds as though it parallels the second operation above: it was, I guess, adding a slug of CO2 over and above pre-existing sources. But – correct me if I’m wrong – that added amount was essentially infinitesimal: it made no detectable change in the CO2 concentration, so in essence it merely changed the isotopic composition of that concentration, not the concentration itself. Therefore, the 14C injection parallels the first step above, while Man’s recent CO2 emissions parallel the second step.”
However, like all analogies, by definition this one breaks down at some point.
Figure 3. Comparison between the decay curves of the remaining airborne fraction ft of the excess x of CO2 across the interval t on [1, 100] years.
As Fig. 3 shows, the equilibrium constant k, the fraction of total excess concentration x that remains airborne indefinitely, has – if it is large enough – a major influence on the rate of decay. At the k = 0.15 determined by Professor Pettersson as the baseline pre-industrial ratio of the contents of the atmospheric to the combined biosphere and hydrosphere carbon reservoirs, the decay curve is close to a standard exponential-decay curve, such that, in (5), k = 0. However, at the 0.217 that is assumed in the Bern climate model, on which all other models rely, the course of the decay curve is markedly altered by the unjustifiably elevated equilibrium constant.
On this ground alone, one would expect CO2 to linger more briefly in the atmosphere than the Bern model and the models dependent upon it assume. To use Mr. Born’s own analogy, if any given quantum of fluid poured into a container remains there for less time than it otherwise would have done (in short, if it finds its way more quickly out of the container than the fixed rate of exit that his analogy implausibly assumes), then, ceteris paribus, there will be less fluid in the container.
Unlike the behavior of the contents of the reservoir described in Mr. Born’s analogy, the fraction of the excess remaining airborne at the end of the decay curve will be independent of the emission rate e and the uptake rate u.
Since the analogy breaks down at the end of the process and, therefore, to some degree throughout it, does it also break down on the question whether the rate of change in the contents of the reservoir is, as Mr. Born maintains in opposition to what Pettersson shows in (5), absolutely described by e – u?
Let us cite Skeptical Science as what the sociologists call a “negative reference group” – an outfit that is trustworthy only in that it is usually wrong about just about everything. The schoolboys at the University of Queensland, which ought really to be ashamed of them, feared Professor Murry Salby’s assertion that temperature change, not Man, is the prime determinant of CO2 concentration change.
They sought to dismiss his idea in their customarily malevolent fashion by sneering that the change in CO2 concentration was equal to the sum of anthropogenic and natural emissions and uptakes. Since there is no anthropogenic uptake to speak of, they contrived the following rinky-dink equationette:
(6) 
.
The kiddiwinks say CO2 concentration change is equal to the sum of anthropogenic and natural emissions less the natural uptake. They add that we can measure CO2 concentration growth (equal to net emission) each year, and we can reliably deduce the anthropogenic emission from the global annual fossil-fuel consumption inventories. Rearranging (6):
(7) ![clip_image018[1]](http://wattsupwiththat.files.wordpress.com/2013/11/clip_image0181.png?quality=75 "clip_image018[1]"){kind=small}
.
They say that, since observed ea ≈ 2ΔCO2, the natural world on the left-hand side of (7) is perforce a net CO2 sink, not a net source as they thought Professor Salby had concluded. Yet his case, here as elsewhere, was subtler than they would comprehend.
Professor Salby, having shown by careful cross-correlations on all timescales, even short ones (Fig. 4, left), that CO2 concentration change lags temperature change, demonstrated that in the Mauna Loa record, if one examines it at a higher resolution than what is usually displayed (Fig. 4, right), there is a variation of up to 3 µatm from year to year in the annual CO2 concentration increment (which equals net emission).
Figure 4. Left: CO2 change lags and may be caused by temperature change. Right: The mean annual CO2 increment is 1.5 µatm, but the year-on-year variability is twice that.
The annual changes in anthropogenic CO2 emission are nothing like 3 µatm (Fig. 5, left). However, Professor Salby has detected – and, I think, may have been the first to observe – that the annual fluctuations in the CO2 concentration increment are very closely correlated with annual fluctuations in surface conditions (Fig. 5, right).
Figure 5. Left: global annual anthropogenic CO2 emissions rise near-monotonically and the annual differences are small. Right: an index of surface conditions (blue: 80% temperature change, 20% soil-moisture content) is closely correlated with fluctuations in CO2 concentration (green).
Annual fluctuations of anthropogenic CO2 emissions are small, but those of atmospheric CO2 concentration are very much larger, from which Professor Salby infers that their major cause is not Man but Nature, via changes in temperature. For instance, Henry’s Law holds that a cooler ocean can take up more CO2.
In that thought, perhaps, lies the reconciliation of the Born and Pettersson viewpoints. For the sources and sinks of CO2 are not static, as Mr. Born’s equations (1-4) and analogy assume, but dynamic. Increase the CO2 concentration and the biosphere responds with an observed global increase in net plant productivity. The planet gets greener as trees and plants gobble up the plant food we emit for them.
Similarly, if the weather gets a great deal warmer, as it briefly did during the Great el Niño of 1997/8, outgassing from the ocean will briefly double the annual net CO2 emission. But if it gets a great deal cooler, as it did in 1991/2 following the eruption of Pinatubo, net annual accumulation of CO2 in the atmosphere falls to little more than zero notwithstanding our emissions. It is possible, then, that as the world cools in response to the continuing decline in solar activity the ocean sink may take up more CO2 than we emit, even if we do not reduce our emissions.
Interestingly, several groups are working on demonstrating that, just as Professor Salby can explain recent fluctuations in Co2 concentration as a function of the time-integral of temperature change, in turn temperature change can be explained as a function of the time-integral of variations in solar activity. It’s the Sun, stupid!
It is trivially true that we are adding newly-liberated CO2 to the atmosphere every year, in contrast to the 14C pulse that ended in 1963 with the bomb tests. However, the bomb-test curve does show that just about all CO2 molecules conveniently marked with one or two extra neutrons in their nuclei will nearly all have come out of the atmosphere within 50 years.
To look at it another way, if we stopped adding CO2 to the atmosphere today, the excess remaining in the atmosphere after 100 years would be 1.5% of whatever we have added, and that is all. What is more, that value is not only theoretically derivable as the ratio of the contents of the atmospheric carbon reservoir to those of the combined active reservoirs of the hydrosphere and biosphere but also empirically consistent with the observed bomb-test curve (Fig. 1).
If the IPCC were right, though, the 50-200yr residence time of CO2 that it imagines would imply much-elevated concentrations for another century or two, for otherwise, it would not bother to make such an issue of the residence time. For the residence time of CO2 in the atmosphere does make a difference to future concentration levels.
To do a reductio ad absurdum in the opposite direction, suppose every molecule of CO2 we emitted persisted in the atmosphere only for a fraction of a second, then the influence of anthropogenic CO2 on global temperature would be negligible, and changes in CO2 concentration would be near-entirely dependent upon natural influences.
Atmospheric CO2 concentration is already accumulating in the atmosphere at less than half the rate at which we emit it. Half of all the CO2 we emit does indeed appear to vanish instantly from the atmosphere. This still-unexplained discrepancy, which the IPCC in its less dishonest days used to call the “missing sink”, is more or less exactly accounted for where, as Professor Pettersson suggests, CO2’s atmospheric residence time is indeed as short as the bomb-test curve suggests it is and not as long as the 50-200 years imagined by the IPCC.
And what does IPeCaC have to say about the bomb-test curve? Not a lot:
“Because fossil fuel CO2 is devoid of radiocarbon (14C), reconstructions of the 14C/C isotopic ratio of atmospheric CO2 from tree rings show a declining trend (Levin et al., 2010; Stuiver and Quay, 1981) prior to the massive addition of 14C in the atmosphere by nuclear weapon tests which has been offsetting that declining trend signal.”
And that is just about all They have to say about it.
Has Professor Pettersson provided the mechanism that explains why Professor Salby is right? If the work of these two seekers after truth proves meritorious, then that is the end of the global warming scare.
As Professor Lindzen commented when Professor Salby first told him of his results three years ago, since a given CO2 excess causes only a third of the warming the IPCC imagines, if not much more than half of that excess of CO2 is anthropogenic, and if it spends significantly less time in the atmosphere than the models imagine, there is nowhere for the climate extremists to go. Every component of their contrived theory will have been smashed.
It is because the consequences of this research are so potentially important that I have set out an account of the issue here at some length. It is not for a fumblesome layman such as me to say whether Professor Pettersson and Professor Salby (the latter supported by Professor Lindzen) are right. Or is Mr. Born right?
Quid vobis videtur?
Related articles
- Why and How the IPCC Demonized CO2 with Manufactured Information (wattsupwiththat.com)
Ferdinand: “- at 1 bar the CO2-only solution is completely in equilibrium and Henry’s law works. The Revelle factor isn’t relevant here as there is no buffer present and the solution is slightly acidic”
You’re waving Kip Hansen’s red scarf hard with ‘there is no buffer present.’ As now you’re not attempting to state that Henry’s Law was named one letter off and that it should be Henry’s Mistake. But that the DIC conjugates of CO2 simply don’t exist by diktat. To pull this prestidigitation[1] off you need to deny the entire chemistry of bicarbonate buffering before you get started. But if you acknowledge the bicarbonate buffering then you’ve snuck the Revelle’s factor into the discussion without mentioning it. You have begged the question: Assumed the very thing you need to prove.
[1] Mr. Monckton has, by the wonderful use of this term, forever earned the title Lord Monckton in my eyes.
There is also another way to determine CO2 residence time in the atmosphere that uses the Keeling curve directly. As is well known the Keeling curve contains a seasonal wiggle caused by the annual shedding of leaves by northern hemisphere forests. Freeman Dyson of the Institute for Advanced Study at Princeton pointed out that this gives us a clue to recycling of carbon dioxide in the natural world. His quick calculation using that wiggle gave an approximate lifetime of a carbon dioxide molecule in the air as seven years. This is is even shorter than the carbon-14 value from bomb fests, and both of them are definitely not even in the ball park with climate models.
I published an article about the bomb spike which should add some clarity. Fancy words or ideas are avoided.
A simple simulation of the spike was carried using the mirror (dual) between electrical and other physical fields where the same laws apply, units of measure are different.
This gives a close to perfect match.
The plot shown in the head article should be science style log-lin, a straight line results which is a basic science objective.
This image ought to be sufficient.
http://daedalearth.files.wordpress.com/2013/09/image-287-small.png?w=550&h=301
Note there are some additional details.
The spike is an almost perfect dual of a single pole electrical time constant, the simplest time constant there is.
This is the same as charging a reservoir to an exact starting point, and then allowing free discharge via a linear law resistance, with no further contribution from anything else.
The result is that curve. Plot traces overlay.
Given a time constant other parameters can if wanted be exactly calculated.
Now the codas
The data shown here is for the northern dataset with more recent data tacked on. I am fairly sure there is a defect in the northern data. Note the significant break in the data. This marks a cessation of data gathering. When it was resumed it was done to a more precise standard, all fairly crude back then, the old way of counting decay events over a period of time. The count time was increased considerably.
There were also changes in the sample collection method.
The data is relative to a reference, in fact there are two old northern datasets, one compensated. This means that isotope decay (the ~6ky) is compensated out, ignore that as a factor.
I am less clear on whether the changing underlying CO2 atmospheric proportion and 12C ratio have been handled, or at least properly.
The southern dataset, not shown above is very similar but has a slightly longer time constant. On careful review I reached the conclusion the late northern data matches the southern time constant.
The time constant value is about 16 to 17 years.
A second process which is not mentioned is the much faster spread from source around the globe and this fairly obviously affects the initial condition in addition atmospheric testing did not cease, there were further tests. Those slightly affect the data.
My interest was more about cosmogenic 14C. In that light I realised the effect of what is a simple low pass filter also has a phase characteristic. I followed up on that, a subject not mentioned further.
Arno Arrak: “As is well known the Keeling curve contains a seasonal wiggle caused by the annual shedding of leaves by northern hemisphere forests. ”
That’s a wonderful observation. Of interest and relation is that residential electricity usage — and so CO2 generated — peaks during both winter and summer. There is less variation in commercial usages, and it peaks in summer only. Industry is more or less flat with regard to season. But the implication from this is that plant biota is able to sink even against the excess CO2 production due peak summer electrical uses. No idea how that stacks up against nat gas and heating oil CO2 production. But it should be an fairly easy manner in which to put sanity checks on things.
Dikran,
” C14 is not replenished by the fluxes with the oceans”
There is definitely 14C outgassing from the oceans, albeit depreciated by the 1kyr residence (or is that efolding?) time. It is the very last choice of every biological process. The background from Nitrogen bombardment does not go away.
Ferdinand: I don’t have a habit of hanging out in threads after a day has passed, and I’m about to check out of this one. So rather than leave you hanging, let me argue your position for you. And this way you can see what the obvious and material problem is:
1. We have, via Henry’s law an empirically derived constant for the solubility of CO2 in water.
2. That constant is constructed from an equilibrium condition and after all buffering has occurred.
3. From the Bjerrum plot we can state plainly how much CO2 had to be dissolved in total to produce the dissolved free CO2. And if we treat the Revelle factor as nothing different, then it is just a statement of this.
4. Therefore the rate of uptake is determined on the basis of the remaining unbuffered CO2 in solution.
The issue of distinction here is whether 4. is valid or not. But without any question it is wholly invalid as stated. We cannot use the post-buffered free CO2 ratio or quantity to derive the pre-buffered CO2 uptake rate. It is absurd in the first order. But this is Climate Chemistry not Chemistry.
We all accept a great deal of special pleading and hand waving in the arguments from Historians, Cosmologists, Astronomers, and Climatologists. And we must. For without time machines, space ships, and star sized Star Trek replicators they cannot put their subjects on a bench. No interviews with Genghis Khan. No Solar System in flask. And no duplicate Earth to run experiments on. They must plead deference for their case and then simply hang out, wait, and hope for the evidence to roll in. Someday.
But this notion of uptake differences as wed to the Bjerrum curve is one of the remarkably rare cases when Climatology can go show its muster as a bonafide science. Science, not an ad-hoc mythology to support a large body of fiction, such as JRR Tolkien did in using the Silmarillion to give a life like depth to The Hobbit. Moreso than that it is a critical foundation underlying every discussion about carbon cycles that are so central to Climatology. But it makes absurd claims on the face of it.
But it needn’t. And it is so important that it should be Climate Warrior 101 work for anyone interested in the topic. This should be so ridiculously replicated that we have no interest or consideration in it. And more to the point, if it was or had been, then it wouldn’t be yet another instance of magical math that infests Climatology generally.
This is not ok. When even the most basic lab work possible, and some of the only lab work possible, in Climatology is completely without validation or any valid logical argument it remains that we are dealing with a Jonestown cult, and not serious science.
@ur momisugly Bart (re: 11/22/13, 4:09pm comment linking to your 1:16pm comment)
I realize that I am not one of those whom you want to hear from, but, I just have to tell you how pleased I was to read your 1:16pm comment! For the little my non-scientist opinion is worth to you, I think it is a GREAT analogy. Especially, since just this afternoon, I was trying to put into words (and could not) my analogy for: mixing ratio of different carbon isotopes vs. the total output rate of a given sink. I thought of how adding blue dye (and a much lesser amount of red) would end up still being visibly blue if the red were dilute enough and that this would have no effect on the removal rate of the imperceptively lavender water!
Okay, okay, laugh — out — loud, my thinking is way below yours on this (not even close, I know), but, at least SOMEONE commented. And it made my evening that I was thinking along the same lines as my highly admired Bart.
(and hopefully my posting this will get a high caliber scientist to read your 1:16pm post and comment!)
Great job, above, Bart!
You, too, J Quip and Doc Martyn!!
READ BART’S 1:16PM POST! (and comment, please)
Hurrah for the Science Giants of WUWT! #(:))
Dear Bart, you wrote:
“It is distressing to see an otherwise learned fellow essentially restate the “mass balance” bilge.”
The URL beneath the “bilge” says that the magnitude of sinks depends on the annual emissions, both natural and anthropogenic ones.
But this is physically impossible – it’s one of the memes that is sometimes “suggested” by the alarmists but it’s impossible.
The rate of absorption of CO2 by the oceans or by the biosphere only depends on the surrounding total CO2 concentration – the total CO2 that is already there. It cannot matter a tiny bit how much of this CO2 got there during the last year and it certainly cannot matter how much of this CO2 got there in the last year from human emissions separately, and from natural sources separately.
There is no way for the ocean or the biosphere to “distinguish” the CO2 molecules in this way.
The uptake is simply proportional, in the linear approximation, to (c-280 ppm) where “c” is the current overall concentration of CO2 in the air. Which of it was put there last week or in 1963 is irrelevant.
Bart:
I was going to respond to your analogy but either I don’t understand it or it’s too far from parallel to the real problem for us likely to join issue.
If the water in your analogy is the atmosphere and dye is carbon-14, the analogy doesn’t appeal to me, because if I understand it the carbon-14 measurements are not necessarily made near the blast sites (at the top of the bucket) but rather at random places in the world: it’s assumed that the carbon-14 got spread throughout the atmosphere pretty fast.
Maybe it would help if you made it more concrete by providing numbers. Say, the amount of water is initially 800 ml, including 0.016 ml of dye, the rate at which water enters is 219 ml/minute, including 0.00219 ml/min of dye and the rate at which water leaves is 213 ml/minute, including how much dye?
Bart says:
November 22, 2013 at 4:09 pm
Bart, argument by analogy is generally a waste of time for me. If you want to explain something, then just explain it. Otherwise we get lost in the differences between the analogy and the reality.
In reality, we have ~750 Gtonnes of carbon in the atmosphere, and humans are adding about 9 Gt per year through the burning of fossil fuels. In that situation, I say again that the turnover time of the average CO2 molecule in the atmosphere tells us nothing about the e-fording time for a pulse of added CO2. If it did, we wouldn’t be disputing whether the e-folding time is 40 years or over a hundred years …
Best regards,
w.
I owe Mr. Born an apology for mistranscribing his equation (3), which was barely legible on my computer. I am also not sure whether I transcribed his (4) correctly, for that too seems to have a problem with its units.
Dickranmarsupial, who continues to be obsessed with semantics rather than reality, interprets “residence time” to mean “turnover time” and then gives the IPCC’s definition of “turnover time”. However, as I had previously explained, the IPCC itself sometimes uses “residence time” as synonymous with “atmospheric lifetime”. In any event, in the head posting I had explained clearly and in mathematical terms what I had meant whenever I referred either to “turnover time” (a.k.a. “relaxation time) or to any other kind of time.
Willis Eschenbach also has a semantic hang-up and I am not the only one to find it unenlightening. So let me pose two questions that I hope are clear.
1. After how many years following the bomb-test pulse did the atmospheric concentration of 14CO2 fall by half? By 70% (close to e-folding)? By 90%?
2. After how many years following an immediate and total cessation of anthropogenic CO2 emissions would the atmospheric concentration of the excess of all isotopes of CO2 above 280 micro-atmospheres fall by half? By 70%? By 90%? Your calculations on this would be helpful.
I do not in any way suggest Willis’ calculations are wrong. They accord with the calculations of Lubos Motl, and with Professor Lindzen’s estimate, and with Jacobson’s, so he is in good company. As Housman’s Greek chorus used to put it, “I only ask because I want to know.” I wish he had said from the outset that his value for the adjustment time of CO2 differed both from that which the bomb-test curve indicates and from the IPCC’s value: then we could have avoided becoming bogged down in futile semantics.
Mr. Whitman continues to maintain that in the head posting I quoted private conversations with Professors Lindzen and Salby on 14 C. I did not do so, though I had mentioned a brief point by Professor Salby in a previous posting.
Mr. Erren errs, followed by Pippen Kool, when he says the 14CO2 bomb-test curve is explained by dilution. No, it is explained by uptake into sinks and non-replacement. To adopt and adapt the coin, very nearly all of the coins go out of circulation altogether. Pippen Kool, with troll-like impoliteness, calls my calculations “silly”: no, the values shown in Table 1 are in all respects correct: they show the exponential decay, moderated by the equilibrium constant, of 14CO2 from Professor Pettersson’s equation describing the bomb-test curve.
From this thread it is becoming apparent, whether Pippen Kool likes it or not, that the rate at which the anthropogenic excess of CO2 would decay from the atmosphere if we were to cease all CO2 emissions is likely to be below the IPCC’s estimate, though probably above the bomb-test curve’s description.
And, though Pippen Kool is not at ease with the use of mathematics, in the head posting I was presenting mathematical arguments from various sources and inviting comments on them. Where, for instance, does Pippen Kool get a 1000-year half-life for CO2 emitted to the atmosphere? Some Greenpeace handout? Even the exaggeration-prone IPCC is not that silly. The half-life is in decades, not millennia.
Pippen Kool says there are some questions that can be answered without math: such as “What is the velocity of the top of a bicycle wheel?” Here is my favorite question of that kind, which can be solved by logic rather than by math: “A cylindrical hole six inches long is drilled right through the center of a sphere. What is the volume remaining in the sphere?”
Jquip says:
November 22, 2013 at 8:31 pm
1. We have, via Henry’s law an empirically derived constant for the solubility of CO2 in water.
Agreed, but be aware that it is about CO2 as gas in water.
2. That constant is constructed from an equilibrium condition and after all buffering has occurred.
Henry’s constant is independent of buffering. The ratio between CO2 in the atmosphere and free CO2 in solution is fixed for a certain temperature, no matter if there is buffering or no buffering. With or without buffering the CO2 going into solution stops when pCO2 in air and solution are equal. In the case of fresh water that is at a very low level of total carbon. In the case of a buffer solution, that is at a high level of total carbon. In both cases one finds the same ratio between CO2 in the air and free CO2 in solution, thus the same Henry’s constant.
3. From the Bjerrum plot we can state plainly how much CO2 had to be dissolved in total to produce the dissolved free CO2. And if we treat the Revelle factor as nothing different, then it is just a statement of this.
It is the opposite: starting from the dissolved free CO2 according to Henry’s constant, we can calculate how much CO2 in total is dissolved at equilibrium. That is what the Revelle factor tells us.
4. Therefore the rate of uptake is determined on the basis of the remaining unbuffered CO2 in solution.
No, the rate of uptake is determined by the Revelle factor, which combines Henry’s factor and the buffer factor…
DocMartyn says:
November 22, 2013 at 4:43 pm
Ferdinand, Bermuda is well studied because of the hotels, beeches and off hours activity.
There the carbon cycle is highly constrained, as their is nowhere to go.
The land plant hypothesis I don’t buy, the positioning is wrong for matching to land chlorophyll.
I suspect marine over land, I am not wed to it, but I am skeptical.
I am sure that Bermuda is a nice destination for vacation (but I prefer the mountain area’s from Norway to Alaska…), but I don’t think that has much effect on the seawater pCO2/DIC from the Atlantic subtropical gyre.
The same CO2/DIC behavior can be seen in Hawaii (I admit, another nice subtropical paradise):
http://www.pnas.org/content/106/30/12235.full.pdf
Fig 1. shows that pCO2(aq) and pCO2(atm) vary in anti-phase at Hawaii.
But also at other parts of the (sub)tropic Pacific (see Fig. 5-2):
http://www.umeoce.maine.edu/docu/Fujii-JO-2009.pdf
pCO2 and SST are in phase, DIC in anti-phase. Thus temperature is far more important than biolife in the uptake and release of CO2 of seawater.
And here the average seasonal δ13C and δCO2 swings over a longer period (1990-2012) in the NH (Barrow and Mauna Loa), zeroed for the values of January:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_CO2_d13C_MLO_BRW.jpg
From the opposite change of δ13C it is clear that the seasonal CO2 swings are caused by vegetation. But as large parts of the oceans are net emitters of CO2 in summer, most of the CO2 swings in the atmosphere is from land vegetation in the NH.
How can residence time be calculated without any mention of the properties and processes of carbon dioxide in the atmosphere?
Because these have been written out of the “climate science” of AGW.
They, the real gas properties and processes, still exist in the main science disciplines and thus are very well known indeed, empirically known.
1. Carbon dioxide is being constantly washed out of the atmosphere as carbonic acid.
“The term “acid rain” is commonly used to mean the deposition of acidic components in rain, snow, fog, dew, or dry particles. The more accurate term is “acid precipitation.” Distilled water, which contains no carbon dioxide, has a neutral pH of 7. Liquids with a pH less than 7 are acid, and those with a pH greater than 7 are alkaline (or basic). “Clean” or unpolluted rain has a slightly acidic pH of 5.6, because carbon dioxide and water in the air react together to form carbonic acid, a weak acid.” (1)
All clean, unpolluted, precipitation is acidic because water in the atmosphere naturally absorbs all the carbon dioxide around – that is the main cause of weathering of rocks and the rusting of our garden furniture.
2. Carbon dioxide is a real gas, it is heavier than air and will always sink in the atmosphere if no other work is being done on it.
“CO2 is a gas that is heavier than air so it will therefore tend to sink to the bottom of the container, so there should be no need to make the container holding the sensor airtight.” (2)
As a real gas, and not ‘ideal’, carbon dioxide will expand when heated and becoming lighter than air will rise, when it cools and condenses it will again become heavier than air and sink.
(Ditto the majority real gases nitrogen and oxygen which comprise our fluid gas atmosphere and which every real weatherman knows is how we get our winds.)
(1)http://www.pharmachemicalireland.ie/Sectors/PCI/PCI.nsf/vPages/Education~Teachers~science-books-17-08-2011/$file/Extreme%20Environment%20Book.pdf
(2)
http://www.discoversensors.ie/sensors/sensor_equipment/carbon_dioxide_sensor/
From the perspective of real science disciplines these discussions on residence time appear, at best, naive.
“O would some god the giftie gie us
To see ourselves as ithers see us”.
Jquip says:
November 22, 2013 at 4:49 pm
But that the DIC conjugates of CO2 simply don’t exist by diktat. To pull this prestidigitation[1] off you need to deny the entire chemistry of bicarbonate buffering before you get started.
CO2 in fresh water has zero buffer capacity. When CO2 dissolves in fresh water, it forms bicarbonate and carbonate ions, but as that makes the solution acidic, the whole equilibrium reaction train is pushed to free CO2.
If you look at the Bjerrum plot for fresh water (pH 4), 99% is (free) CO2, 1% is bicarbonate and carbonate is quasy non-existing.
Thus in the case of fresh water, the solution as DIC is near entirely from free CO2 and Henry’s factor gives you how much total CO2 is dissolved in fresh water.
In the case of a buffer, exactly the same amount of free CO2 is dissolved in water (at a higher pH), but as free CO2 then is not 99%, but e.g. 50% (at pH 5.8), DIC doubles for the same amount of free CO2 at equilibrium per Henry’s constant.
Lord,
I beg to differ. Consider a collection of white balls (the co2 in the atmosphere) On a given moment a part of the balls is coloured blue (the bomb test c14). The collection has a rapid exchange mix with a far larger reservoir of white balls (the ocean co2). As a result of this exchange the balls in the smaller reservoir will all turn white, solely depending on the mixing speed.
A second process is the permanent diffusion of white balls from the small reservoir into the large reservoir which is a much slower process determined by the concentration gradient.
So we have a small co2 reservoir with a higher concentration (the atmosphere) an a larger reservoir with a lower concentration but with much more co2 (the ocean). Bomb test half life is a result of vigourous mixing, co2 half life is a result of gradient diffusion.
In the small reservoir the half life of the coloured balls is 14 years, the half life of all balls is 50 years.
Ferdinand Engelbeen,
You sir, continue to amaze me. You never tire of explaining CO2 equilibration with the ocean, nor tire of pointing out the errors made by many about the process (including in this instance, Lord Monckton). I admire your stamina…. and your patience. I also appreciate your consistent and reasoned critique of the Bern model, which has always struck me as clearly disconnected from the physical processes of mixing in the ocean, and which overstates the long term equilibration time for CO2 added to the atmosphere. I salute your effort.
stevefitzpatrick : “Ferdinand Engelbeen,You sir, continue to amaze me.”
What he said. Although I’ve had nothing to add to the discussion, I’ve learned a lot about carbon storage in the ocean from those comments.
Lord Monckton:
Since we’re posing questions, it may help us better understand your position if we could impose upon you to answer a few. Specifically, which of the following propositions do you believe Pettersson or your other authorities would dispute:
(1) The total mass of CO2 in the atmosphere equals the sum of the masses its three isotopic constituents. (My Equation (1).)
(2) The rate of change of the total mass of CO2 in the atmosphere equals the total rate of CO2 emissions minus the total rate of CO2 uptake. (My Equation (2).)
(3) The rate of change of the mass of 14CO2 in the atmosphere equals the total rate of CO2 emissions times the fraction of 14CO2 in those emissions minus the total rate of CO2 uptake times the ratio that the mass of 14CO2 in the atmosphere bears to the total mass of CO2 in the atmosphere. (Essentially my—original–Equation (3), although I mistakenly referred to the fraction of 14CO2 in the emissions as the cosmogenic fraction, whereas it is a little less than that because, I’m told, the fossil-fuel-source emissions are made of depleted carbon. )
I won’t ask you about my (original) Equation (4) since it merely defines a quantity. And, since doing so would involve solution of a differential equation, I’ll reluctantly refrain from asking whether under the hypothetical condition of equal emission and uptake rates you think your authorities would dispute that the quantity Equation (4) defines would decay with the indicated time constant. (After all this effort, though, I hope I can be forgiven for voicing disappointment that the math has proved so taxing and its implications so hard to appreciate.)
I ask those questions because they are the only assumptions from which the conclusion follows that little can be inferred from the bomb-test data about how long elevated CO2 concentration levels will last after the increased emissions rates that caused them have ceased. This could be verified, I’m sure, by doing numerical experiments based only on those assumptions and the bomb-test results (and, if you want, setting e-u in accordance with the Bern model). I used the e = u hypothetical only to finesse around resorting to numerical methods, i.e., to make the problem so simple that even this superannuated lawyer who hadn’t taken a math course since the Johnson administration could solve it by inspection. In the event, unfortunately, that hypothetical seems to have served only to make you think that my conclusions are based on its conditions. They’re not.
Looks like a consensus has yet to form and may never do so. Perhaps the participants could work out some method to arrive at consensus (nowadays a dirty word thanks to the IPCC).
What experiments and measurements would need to be performed in order to cast light on the areas of disagreement. ? Though perhaps this is likely to be next to impossible given the dynamic nature of the biosphere.
In my (okay, not-so-humble) opinion, no one has come near laying a glove on my reasoning above.
Ignominiously enough, however, I may have found a flaw myself. Although my hypothetical of a constant CO2 atmospheric concentration uses a condition obviously contrary to fact, I’m guessing that the time constant it yields for the carbon-14 decay (mentioned above after Equation (4) ) shouldn’t be too far from what was actually observed. If that’s true, though, the ratio of atmospheric carbon-dioxide mass to uptake rate should be around the 14 years Pettersson observed for the carbon-14-concentration decay rate. But most estimates of that ratio I’ve seen are considerably lower.
Obviously, I’ve missed something.
Monckton of Brenchley Please read the paper mentioned above:
Gavin C. Cawley, On the atmospheric residence time of anthropogenically sourced carbon dioxide, Energy & Fuels, volume 25, number 11, pages 5503–5513, September 2011.
http://pubs.acs.org/doi/abs/10.1021/ef200914u
Abstract:
A recent paper by Essenhigh (Essenhigh, R. H. Energy Fuels 2009, 23, 2773−2784) (hereafter ES09) concludes that the relatively short residence time of CO2 in the atmosphere (5–15 years) establishes that the long-term (≈100 year) rise in atmospheric concentration is not due to anthropogenic emissions but is instead caused by an environmental response to rising atmospheric temperature, which is attributed in ES09 to “other natural factors”. Clearly, if true, the economic and political significance of that conclusion would be self-evident and indeed most welcome. Unfortunately, however, the conclusion is false; it is straightforward to show, with considerable certainty, that the natural environment has acted as a net carbon sink throughout the industrial era, taking in significantly more carbon than it has emitted, and therefore, the observed rise in atmospheric CO2 cannot be a natural phenomenon. The carbon cycle includes exchange fluxes that constantly redistribute vast quantities of CO2 each year between the atmospheric, oceanic, and terrestrial reservoirs. As a result, the residence time, which depends upon the total volume of these fluxes, is short. However, the rate at which atmospheric concentrations rise or fall depends upon the net difference between fluxes into and out of the atmosphere, rather than their total volume, and therefore, the long-term rise is essentially independent of the residence time. The aim of this paper is to provide an accessible explanation of why the short residence time of CO2 in the atmosphere is completely consistent with the generally accepted anthropogenic origin of the observed post-industrial rise in atmospheric concentration. Furthermore, we demonstrate that the one-box model of the carbon cycle used in ES09 directly gives rise to (i) a short residence time of ≈4 years, (ii) a long adjustment time of ≈74 years, (iii) a constant airborne fraction, of ≈58%, in response to exponential growth in anthropogenic emissions, and (iv) a very low value for the expected proportion of anthropogenic CO2 in the atmosphere. This is achieved without environmental uptake ever falling below environmental emissions and, hence, is consistent with the generally accepted anthropogenic origin of the post-industrial increase in atmospheric carbon dioxide.
Janice Moore says:
November 22, 2013 at 9:10 pm
“I realize that I am not one of those whom you want to hear from…”
Don’t be silly. It is a delight to hear from you. Thank you for your kind comments.
Lubos Motl says:
November 22, 2013 at 11:15 pm
“There is no way for the ocean or the biosphere to “distinguish” the CO2 molecules in this way.”
Just so. You said “So it’s clear that the “excess uptake” (which is natural and depends on the elevated CO2 relatively to the equilibrium) is also 2 ppm pear year.” It is not clear at all, because this is a dynamic system.
Start with equation (7)
7) Un – En = Ea – deltaCO2
This is the stupid “mass balance” argument. It is said that, because the right side is positive, the left is also, and nature is a net sink. But, that ignores the fact that Un, the sinks, respond just as you say: WITHOUT DISTINGUISHING BETWEEN THE MOLECULES.”
This is a dynamic system, so Un expands or contracts in proportion to forcing whether natural or otherwise. That means there is a portion of Un which has expanded due to any increase in natural forcing, call it Unn, and there is a portion which has expanded due to anthropogenic forcing, call it Una, such that Un = Unn + Una. NOW, equation (7) reads
7) Unn – En = Ea – Una – deltaCO2
Now, the right side is no longer guaranteed to be positive, and we can say nothing about attribution from this equation alone.
Joe Born says:
November 22, 2013 at 11:59 pm
”…the carbon-14 measurements are not necessarily made near the blast sites (at the top of the bucket) but rather at random places in the world.”
Think of the top cm of the bucket as the atmosphere, and the bottom as the ocean and land reservoirs, and the drain as ocean and land sinks.
Willis Eschenbach says:
November 23, 2013 at 12:09 am
”In that situation, I say again that the turnover time of the average CO2 molecule in the atmosphere tells us nothing about the e-fording time for a pulse of added CO2.”
It does if you consider the case where sources and sinks are very active. In that case, the entire atmosphere is replaced very rapidly, and the C14 disappears long before it has had a chance to diffuse through the various reservoirs.
…the entire quantity of CO2 in the atmosphere is replaced very rapidly…
“Why should not the other isotopes of CO2 disappear just as rapidly?”
That’s an excellent question… perhaps there’s value in actually doing a proper research instead of philosophising? Just a thought.