On CO2 residence times: The chicken or the egg?

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?

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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) clip_image004.

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) clip_image006,

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) clip_image008,

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) clip_image010,

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) clip_image012.

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.

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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.

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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) clip_image018 clip_image020.

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] clip_image022.

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).

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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).

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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?

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292 thoughts on “On CO2 residence times: The chicken or the egg?

  1. Shorter version?

    If the residence time of CO2 is really (for example) 100 years, then we should have a lot more than 400 ppm in the atmosphere right now.

    Anthropogenic CO2 supposedly counts for about +6 ppm per year (when counting fuel burned). Over the last fifty years, that’s a good solid +300 ppm – in an atmosphere that’s only seen an 80 ppm increase.

  2. Seems like a nice catch there Christopher.

    I quickly scanned the paper to see if there was a mention of the natural radioactive decay of 14C, but didn’t see it. But, as I recall, the half life is 5700 years, so that is a small loss rate compared to the “loss of residence” loss rate.

    Fancy that; someone was out there doing a real experiment, and without a taxpayer funded grant !

    Thanks for putting it out here.

  3. “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?”

    Because you are looking at dilution of the 14C into the fixed carbon; the other isotopes are in equilibrium and won’t diminish.

  4. Pippen Kool says:
    November 21, 2013 at 2:08 pm

    You’re kidding, right?

    Dilution would mean that most of the CO2 with 14C molecules was still in the air, but constituted a smaller portion due to increase of total CO2 concentration since the end of the tests. But that’s not what has been observed. Not just the fraction but the absolute amount of CO2 with the 14C isotope has declined.

    Please try again more plausibly & less embarrassingly. Thanks.

  5. Chris, you are almost right, however the 14CO2 is calculated as a fraction of the total CO2, and so their is a dilution effect. You have to sum up the man-made CO2 going into the atmosphere, to work out how much the 14CO2:12C ratio is being diluted by the influx of ‘cold 12CO2.
    From the end-point of the decay gives one the ratio of the sizes of the two carbon reservoirs; atmospheric and everything else. The atmospheric carbon is talking to a carbon reservoir at least 30 times bigger, with a half-life of about a decade.
    I cannot make the number quite match a first order exchange rate unless I include a much higher influx of carbon, from volcanoes, into the atmosphere, annually.
    Catch you later

  6. You know, I bet most people knew what I meant. I am doing this on a cell phone….

    “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?”

    Because you are looking at dilution of the 14C BECAUSE IT IS INCORPORATED into the fixed carbon; the other isotopes are in equilibrium and won’t diminish.

    (and if you want to be picky, the ocean would also accumulate the carbon at a slow rate)

    The main pt is that once the carbon is out of the ground, it ain’t going away quickly e.g. with a 10 year half life.

  7. “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.”

    “Why should not the other isotopes of CO2 disappear just as rapidly?”

    This is an ABSOLUTE GEM of an interpretation, Lord Monckton. Absolutely beautiful. Not only for asking the right question, but by catching them at their own game.

    How so?

    This is their OWN methodology, stuff the greens use on tagging animals to check out populations. The tree huggers do that all the time.

    And now, when someone points out TAGGED molecules, they throw up their hands and say, “Wait! Wait! Wait! Wait! Wait! Wait! You can’t use our own methods against us! That’s not fair!”

    This is 100% the right approach on this. 12CO2 molecules out of industry don’t act any different – INDIVIDUALLY – than 14CO2 does.

    I also applaud you going through all that math and such, and giving them full voice of their take on it. VERY commendable! But it DOES all come down to:

    “Why should not the other isotopes of CO2 disappear just as rapidly?”

    BUSTED! ! ! ! !

  8. Et tu, Bomb test?

    Observation trumps theory every time. So it’s not a question as to whether the decay curve for C14 as measured is in error. But neither is it strictly necessary that it’s invariant; though I hardly expect it to vary much.

    But the Bern model is a bit of a problem. Admittedly I don’t know much about it, but a quick double check seems to reconfirm that Bern is not for decay as such, but a full carbon cycle. eg. It is using the ocean as part of a buffer to its impulse. So the impulse isn’t really an impulse, but half an impulse with the rest as introduced over time as the impulse decays. Which would, with some assumptions, match the Bern curve. Though as it seems to be widely considered to be a ‘pure’ sink model rather than a source/sink model this may just be a common misunderstading. Or it may just be a misunderstanding on my behalf.

  9. I sleep easy every single night. I never worry about co2 in the atmosphere reaching 600ppm, in fact I am in a hurry! I have stated that we need to increase our co2 output not decrease or steady it. By geological standards this is the 3rd or 2nd time it has been so low. The norm is far, far higher.

  10. Here is part of an analysis U did back in 2009:
    2) http://cdiac.esd.ornl.gov/trends/co2/contents.htm
    CO2 delta in the atmosphere from 1970 through 2004 averaged 1.5 ppm/yr. From 1958 to 1974 it averaged 0.9 ppm/yr. From 1994 through 2004 it has averaged 1.8 ppm/yr. Snip “On the basis of flask samples collected at La Jolla Pier, and analyzed by SIO, the annual-fitted average concentration of CO2 rose from 326.86 ppmv in 1970 to 377.83 ppmv in 2004. This represents an average annual growth rate of 1.5 ppmv per year in the fitted values at La Jolla. ” snip.
    That’s the one site that can be seriously affected by nearby emissions. All eight regularly measured sites track precisely. The major measuring sites are widely spread from north to south, and the uniform measurement results indicate that CO2 emissions are quickly and well mixed in the atmosphere.

    3) http://cdiac.esd.ornl.gov/ftp/ndp030/global.1751_2004.ems
    From tables accessible at 2) and 3) we can do some decadal average annual analysis as:
    Decade 1 2 3 4 5
    Years ’54-63 ’64-’73 ’74-’83 ’84-’93 ’94-`03
    Ave. annual fuel emissions (Gt/yr) 2.4 3.4 5.0 6.0 6.7
    Percent change decade to decade 42 47 20 12
    Ave. annual atmos. conc’n delta (ppm/yr) 0.8 1.1 1.4 1.5 1.8
    Atmos. conc’n delta per Gt emission (ppB) 333 324 280 250 270
    Implied atmospheric retention (Gt) 1.7 2.3 2.9 3.1 3.7
    Airborne fraction (%) 71 68 58 52 55
    Ocean uptake from fuel (Gt) 0.7 1.1 2.1 2.9 3.0
    Deforestation factor (%) guesstimate* 1.03 1.06 1.09 1.12 1.15
    Total emissions (Gt) 2.5 3.6 5.5 6.7 7.7
    Airborne fraction of total (%) 68 64 53 46 48
    Ocean uptake total (Gt) 0.8 1.3 2.6 3.6 4.0
    *The above fuel emissions from 3) do not include any factor for deforestation/land use. Recent total emissions have been estimated by AGW advocates as slightly less than 8 Gt/yr total, giving about an additional 15% for deforestation/land use. As deforestation is to a degree linked to third world population, we can assume that factor was sequentially lower going back to prior decades. Using a higher factor for prior decades won’t change anything much. Column 3 fuel emissions data corresponds almost exactly with IPCC SAR figures.

    While total average annual emissions have gone up by a factor of 3, ocean uptake has gone up by a factor of 5. That is hardly consistent with slow mixing or near saturation of surface waters. What seems to be happening is that increasing atmospheric partial pressure is increasing the rate of ocean uptake with the rate of increase slowed by surface warming/acidification. We can expect a large emissions
    increase for the next decade, with corresponding relatively large increase in partial pressure. It remains to be seen how much of that will be offset. The decade to decade rate of increase in fuel emissions has declined very rapidly, from mid 40s% to about 12%. Based on the last couple
    of years, one could expect the decade ’04-’13 to have total average annual emissions in the order of 9.0 Gt, with total fuel emissions near 7.6 Gt, (a decadal increase of 13%) and with an airborne
    fraction near 45%. After that, with declining petroleum, CO2 sequestration for tertiary petroleum recovery, and rising fuel prices driving major accelerations of efficiency, nuclear and renewables, the annual emissions to the atmosphere are likely to begin declining, and to reach a very low level by 2060 or so. The IPCC 50% probability estimate (Wigley et al) is very close to 7.5 Gt near 2010, but goes to 15 Gt by 2060, requiring a compound growth rate of 15% per decade, which isn’t going to happen.

    4) http://cdiac.esd.ornl.gov/pns/faq.html
    snip Q. How long does it take for the oceans and terrestrial biosphere to take up carbon
    after it is burned?
    A. For a single molecule of CO2 released from the burning of a pound of carbon, say from burning coal, the time required is 3-4 years. This estimate is based on the carbon mass in the atmosphere and up take rates for the oceans and terrestrial biosphere. Model estimates
    for the atmospheric lifetime of a large pulse of CO2 has been estimated to be 50-200 years (i.e., the time required for a large injection to be completely dampened from the atmosphere). Snip
    This range seems to be an actual range depending on time frame, rather than the uncertainty among models. [See (5) below].

    5) http://www.accesstoenergy.com/view/atearchive/s76a2398.htm
    For the above decades 1 through 5, we have now had 4, 3, 2, 1, and 0 half lives respectively. From 3) and 5) and using an average half life of 11 years, (based on real 14C measurement) we get a total remaining injection in 2004 from the prior 5 decades of 139 Gt, which equates to an increase in atmospheric concentration of 66 ppm. The actual increase from 1954 to 2004 was very near 63 ppm. This result lends some credibility to the 50 year atmospheric residence time estimate. [See (9) below]. A 200 year residence time gives an 81 ppm delta since 1954, which is much too high.
    Surprisingly, if we go all the way back to 1750 and compute the residence time using fuel emissions only we get a value very close to 200 years. (A 40 year ½ life gives a ppm delta of 99 vs an actual of 96 using 280 ppm as the correct value in 1750). If we assume that terrestrial uptake closely matches land use emissions, (this is essentially the IPCC assumption), and we know that the airborne fraction from 1964 through 2003 had a weighted average of 58%, to
    shift to a long term 40 year ½ life from a near term 11 year ½ life, we would have to have prior 40 year period weighted average airborne fractions like 80% for ’24-’63, and 90%-100% before that. Since emissions in the last 40 years have been 3 times higher than in the period from 1924 to 1963 and 30 times higher than 1844 to 1883 it is not too hard to believe that the rapid growth in atmospheric partial pressure has forced such a change in airborne fraction. With rising SSTs we can expect the partial pressure forced rate of ocean uptake to be offset to a growing degree. (Of course we now know that since 2003 we have not had rising SSTs, rather a slight cooling.)As emission rates decline in the future, and with the delayed impact of ocean warming the half life can be expected to begin growing again but it seems very unlikely that the residence time for a pulse of CO2 would get back to 200 years.

  11. Dear Lord,

    While indeed there is a quite fundamental difference between residence time and “excess decay” time (e-fold time either half life time for an excess amount above equilibrium), the 14 years e-fold time found by Petterson, based on the decay rate of the 14CO2 bomb test spike is too short, but the IPCC’s hundreds of years is way too long. Let me explain that.

    In theory, the behavior of any isotope of any molecule is the same (there are some small physical and stronger biological differences, but that is not the point here). That means that a 14CO2 spike and a 12CO2 spike in the atmosphere will behave in about the same way and simply spread over the other reservoirs with about the same speed.
    For the ocean surface and the fast growing and starving parts of vegetation, the exchanges are rapid and within a few years a new equilibrium is established. The more permanent parts of vegetation also take more 14CO2 in when there is a spike in the atmosphere. Not much difference as for 12CO2 (besides a small change in isotope ratio).

    The problem is in the deep oceans: what goes into the deep oceans is the 14C/12C ratio of the moment. What comes out of the deep oceans is the composition of ~1000 years ago. Thus the pre-bomb test ratio, minus the decay rate of 14C over that period. That makes that the amount of 14CO2 returning from the deep oceans is much lower than the amount of 12CO2, whatever the spike in 14CO2 and 12CO2 is today. That makes that the decay rate of a 14CO2 spike is a lot faster, compared tot the decay rate of a 12CO2 spike.

    Here the relative fluxes of 12CO2 and 14CO2 at the full height of the bomb spike in 1960:

    and here the situation in 2000:

    In 1960, some 99% of the 12CO2 going into the deep oceans returned from the deep oceans in the same year (of course not the same molecules, but a similar mass of the same isotopic composition), while only 45% of the 14CO2 in mass returned.
    In 2000, some 97% of the 12CO2 returned, while still only 75% of 14CO2 returned from the deep oceans…

    That makes that the decay of an excess amount of 12CO2 is a lot longer than of 14CO2. How much longer can be calculated from the increase in the atmosphere above equilibrium (which is anyway 99% 12CO2) and the amount which is absorbed by nature:
    We are currently around 230 GtC (110 ppmv) above equilibrium and the net absorption rate in multiple sinks is around 4.5 GtC/yr (2.2 ppmv/yr). That gives a decay rate of ~51 years or a half life time of ~40 years, near 3 times slower than for the 14CO2 bomb spike.

    A similar problem can be seen for 13CO2. Humans emit a lot of low-13CO2 (and zero-14CO2) into the atmosphere. But only 1/3rd of the theoretical decrease in the 13C/12C ratio can be found in the atmosphere. For the same reason as for 14CO2: what returns from the deep oceans is the isotopic composition of ~1000 years ago, long before the huge emissions of today. That can be used to estimate the deep ocean – atmosphere exchanges:

    which gives an exchange of ~40 GtC/year. The discrepancy in earlier years probably from unbalances in vegetation uptake/decay (not included in the calculation).

    Some look at the Bern model will be in a next message…

  12. Christopher M – you ask “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?“.

    The answer is that the uptake into the oceans from the atmosphere is not one-way and is not uniform. CO2 of the mostly non-14C variety is being emitted at the tropics and some other places, while CO2 as present in the atmosphere (ie, including the bombs’ 14C) is being absorbed in the higher latitudes. Together with the movement of atmospheric CO2 from the tropics towards the poles, that means that the 14C will disappear faster than the other isotopes.

    IMHO, the IPCC is indeed incorrect when it claims that CO2 remains in the atmosphere for centuries (in other than trivial amounts). According to my calculations, the ocean-atmosphere imbalance has a half-life of about 13 years, but that is not the whole story. I am working on it …..

  13. IF we conclude that higher temperatures cause CO2 outgassing

    ANF IF the CO2 that is outgassed acts to further increase the temperature…

    THEN the Earth’s climate woold be MASSIVELY unstable in the absence of an even MORE powerful negative feedbacks system

    SO either CO2 doesn’t cause (much) global warming,. or such a powerful feedback mechanism exists.

    Ergo we can all sleep peacefully in our beds while ‘unknown feedback factors (TM)’ keep the planet more or less within viable temperature limits.

  14. Wow. I never thought I’d see the day but…
    If you stick around long enough then Pippen Kool wins the day.

    Pippen, you are quite right. I understood what you meant.
    Although I wouldn’t be quite so confident as Mr Kool in so far as the understood rate of CO2 absorption by sinks is known – as the sinks are not constant. Even so, the total capability of the sinks is not the reason that a rare (unreplenished) component of the atmospheric CO2 is absorbed at a different rate to the total CO2.

    The rarer components are absorbed into every sink more quickly than commoner components as the rarer components are outsourced less quickly than the commoner components. That’s dilution at work.

    Pippen Kool is right today.

  15. Ferdinand: “In 2000, some 97% of the 12CO2 returned, while still only 75% of 14CO2 returned from the deep oceans…”

    This doesn’t work unless there is preferential outgassing on the basis of the isotope. If there is, then you haven’t mentioned it. If there is not, then this line of argument needs some serious support.

  16. I always enjoy the way the Warmists and closet Warmists find ways to spin away from the real science.

    If only we had a period when CO2 was increasing yet temps were staying flat, maybe they would see they got it wrong.

    Oh, wait….

  17. Oh dear!

    This piece is quite muddled and to me there appears to be a lot of obtuse language use to hide basic facts.

    Humanity digs up fossil fuels and releases CO2 in the atmosphere when burning it. This increases the concentration in the atmosphere and by hydrosphere-atmosphere interaction about half of the anthropogenic emissions is absorbed by the oceans (causing acidification or, if you insist, diminishes the alkaline number). For this increased amount of CO2 in the hydro- and atmosphere to decline it has to be taken out of it. One way is by increasing the total biomass on the planet. Another is by rock weathering. There may be more mechanisms still

    Anyway, this has absolutely nothing to do with the 14CO2 curve, since the bombs mostly increased the concentration of this isotope in the atmosphere, but hardly in the hydrosphere or biosphere. Still CO2 exchanges all the time between hydrosphere, atmosphere and biosphere. No wonder the anthropogenically increased 14CO2 isotope decreases faster in the atmosphere than the total anthropogenically increased concentration of CO2. Simples.

    If Lord Monckton is so sure of his story, why does it end with a question mark?

  18. About the Bern model…

    The Bern model used by the IPCC was originally based on an enormous use of fossil fuels: 3000-5000 GtC emitted in the atmosphere. That is from using near all available oil and gas and lots of coal. That makes that most of the relative fast exchanging reservoirs like oceans and vegetation are getting saturated and can’t cope with more CO2 in the atmosphere. Thus much slower processes (like rock weathering and chalk deposits in the oceans) must take over and even some part resides in the atmosphere forever.

    The error they made is using the partitioning for these enormous emissions also for the much smaller emissions up to today. The current total of CO2 emitted by humans since the start of the industrial revolution is ~400 GtC.
    The ocean surface reacts very fast (1-3 years) to changes in the atmosphere, but can not absorb more than ~10% of the change in the atmosphere (due to the buffer/Revelle factor) and thus that part indeed is readily saturated.

    The deep oceans and the more permanent storage in the biosphere are far from saturated, but are much slower (half life time ~40 years).
    The 400 GtC up to now, if fully mixed with the deep oceans and again in equilibrium with the atmosphere (after a few thousands of years…) will show an increase of 1% in CO2 in the atmosphere or 3 ppmv above equilibrium. That is all. If we stop all emissions today, the extra 110 ppmv of today will drop to 55 ppmv in 40 years, 27.5 ppmv in 80 years, ~14 ppmv after 120 years etc. Far from the hundreds of years decay time of the Bern model and with very little left for very long periods or near permanently.

    There is not the slightest indication that the deep oceans are saturating, neither does vegetation: the decay rate remained about the same over the past 160 years, as can be seen in “airborne fraction” of human emissions over time:

    neither in the years since Mauna Loa:

    Thus the Bern model may have merit for much higher emissions than today, but even then. While the deep oceans may saturate over time, there is no limit in capacity for carbon storage in vegetation, which can go on indefinitely until equilibrium, be it slower and slower over time when approaching equilibrium… After all, it is that ancient capacity from vegetation that we are burning today…

  19. Sisi says:
    November 21, 2013 at 3:21 pm

    If Lord Monckton is so sure of his story, why does it end with a question mark?
    >>>>>>
    Oh dear, Sisi, you ended with a question mark….

  20. We have reports from NASA of ‘greening the planet’, ‘greening deserts, reports of Amazon jungle being overrun by vines due to raised CO2, and large algal blooms in oceans. Yet, in light of this immense increase in the biosphere there are still people claiming that the ‘uptake rate’ U is a constant? That is absurd.

    The 14CO2 omb test curve plot starts before the planet greened so is not a good indication of current emissions or uptakes. It may well be that the current uptake rate is faster due to biosphere increases, masked by higher ocean temperatures that as Henry’s Law indicates will be outgassing more CO2. There are NO constants either e or u, the simplistic equations proposed are based on assumptions drawn from flawed understanding of the systems being modeled.

  21. Jquip says:
    November 21, 2013 at 3:10 pm

    This doesn’t work unless there is preferential outgassing on the basis of the isotope. If there is, then you haven’t mentioned it. If there is not, then this line of argument needs some serious support.

    There is a small difference by preferential outgassing of the lighter isotopes, but that is not the problem. The problem is that the main deep ocean sink places for all CO2 (all isotopes alike) are near the poles and the main source places are at the equator and that it takes ~1000 years for the deep ocean circulation (the THC – thermohaline circulation) to get from sink to source. Thus whatever composition/spike that gets in the oceans today doesn’t return today or not even in the next centuries. The composition (and concentration) which returns is that from ~1000 years ago, without bomb spike or fossil fuel “fingerprint”.

  22. @geran

    Isn’t it ironic? :D

    The difference is that the piece above the line is supposed to cast doubt on IPCC’s time frame that heightened concentrations of CO2 in the atmosphere (by burning fossil fuels) will recede. Apparently Lord Monckton does not have faith enough in his analysis to give a definite statement. I was making a comment on his piece and ended -after giving basic facts (quite simplistic, probably wrong when looked at in detail)- with a question that was supposed to convey my feeling that the Lord may not have been to certain of his piece and therefore did not come to a firm conclusion.

    Yes I ended with a question mark!

    ?

  23. Ferdinand: “The ocean surface reacts very fast (1-3 years) to changes in the atmosphere, but can not absorb more than ~10% of the change in the atmosphere (due to the buffer/Revelle factor) and thus that part indeed is readily saturated.”

    Wait just a second. To accept this claim I have to reject that Carbon Dioxide is soluable in water. Alternately, I have to accept that Henry’s Law is invalid and that Carbon bearing molecules exclude Carbon Dioxide from the water. Which is a bit like stating that water excludes Oxygen as water has Oxygen as part of it. When speaking of a ‘buffer’ or the ‘Revelle factor’ we are not speaking about solubility of Carbon Dioxide but the Ocean’s ph buffering.

  24. Ferdinand: “and that it takes ~1000 years for the deep ocean circulation (the THC – thermohaline circulation) to get from sink to source. ”

    Sure, just as you say. But that doesn’t answer to the immediate differences in isotope exchange in the short term. (Ignoring, as you mentioned, fractioning from weight.) To carry that idea you’d need to show that 14C ratios 1000 years before the 50 year bomb test window were significant. And to be sure, if we state that carbon can be sequestered now, and desequestered later; then there is no error. But it’s certainly not relevant to decay times in general.

  25. Lord Monckton,

    One also has to be suspicious of the total amount of CO2 said to be emitted by Man. It is in the political and financial interest of Greenpeace, the Sierra Club, David Suzuki and Al Gore, the UN/IPCC, various Green governments (including sort-of Obama’s), non-coal energy companies and all the Green energy companies/supporters/ideologues to maximize the amount of CO2 emitted. It will also be noted in the national interests of all industries and nations to maximize their apparent productive capability and activity: the US wants to show growth in the GDP to such an extent that they redefine what the GDP parameters are, for an example.

    All these anti-CO2 and pro-economic-health advocates will take the upside of CO2-production. This means that it is PROBABLE (high certainty) that the CO2 emissions we see are exaggerated and have been especially so since the early ’80s. And that means that the “missing sink” of CO2 is smaller than identified BUT the anthropogenic portion of the observed increase is less than attributed by the IPCC by their models: we just didn’t put that much into the air.

    There is no reason I can think of for underestimating the CO2 emissions of any category by any body that puts them out. All biases are to increased numbers, so the resultant error is to say we have emitted more than we have. Unless the IPCC agrees to say that their current models of CO2 removal from the atmosphere are wrong, this means that any errors in emission volume brings down the anthropogenic portion observed to date. Which brings us to looking at the oceans contribution as a greater cause, not an effect, of CO2 increases.

  26. Sisi says:
    November 21, 2013 at 3:46 pm
    @geran
    Isn’t it ironic? :D
    >>>>>
    Yes, it is. (But not to worry, irony only adds to the humor.) : )

  27. Well done, the fact that the concentration goes down while we are emitting a lot of CO2 into the atmosphere demonstrates that the bern model is either wrong or very incomplete. The reality is the sinks have a enough excess capacity to cope with everything we throw out plus some. If you read Dr. Salby’s discussion about this its pretty clear; the addition of Professor Pettersson’s work I am convinced. Lord Monckton’s write up on this is very good, thank you sir!
    v/r,
    David Riser

  28. @geran

    I am happy to see we agree on the irony stuff! 😋

    Now, do you have anything to contribute that substantially objects to the things I wrote in my first comment to Lord Monckton. I will be glad to hear it.

    Cheers!

  29. Jquip says:
    November 21, 2013 at 3:49 pm

    Wait just a second. To accept this claim I have to reject that Carbon Dioxide is soluable in water. Alternately, I have to accept that Henry’s Law is invalid and that Carbon bearing molecules exclude Carbon Dioxide from the water. Which is a bit like stating that water excludes Oxygen as water has Oxygen as part of it. When speaking of a ‘buffer’ or the ‘Revelle factor’ we are not speaking about solubility of Carbon Dioxide but the Ocean’s ph buffering.

    Henry’s law gives a constant ratio between dissolved CO2 in water and in air for a given temperature (and salt concentration). But that is for free CO2 (gas), not for bicarbonates and carbonates. In fresh water, CO2 is 99% of all inorganic carbon in the water, thus a 100% change in the atmosphere will give a near 100% change of CO2 in water.

    In seawater at pH 8.1 or so, CO2 is less than 1% of all carbon present, thus a 100% change in the atmosphere still gives a 100% change in free CO2, but at first instance only 1% extra on total carbon. But as that is an equilibrium reaction, also more bicarbonate and carbonate is formed, giving an about 10% change in total carbon. Thus seawater does absorb about 10 times more CO2 in total than fresh water, even if the change in total carbon is only 10% of the change in the atmosphere…

    Some theoretical background:

    http://www.eng.warwick.ac.uk/staff/gpk/Teaching-undergrad/es427/Exam%200405%20Revision/Ocean-chemistry.pdf

  30. Equation (7) is just stupid. u_sub_n may represent natural sinks, but those are dynamic, and expand in response to e_sub_a, as well as to e_sub_n. Without e_sub_a forcing it, u_sub_n would be smaller, and the left side of the equation would no longer necessarily be positive.

    People floating such utter bilge just show that they do not have the faintest familiarity with dynamic systems.

  31. There’s no reason to believe that atmospheric CO2 input or output is at a steady rate over time, but the post atomic test 14C isotopes do give you a way to measure the output rate of atmospheric CO2 during the period on your graph. Assuming (probably correctly) that the 14C was diffused homogeneously into the atmosphere by 1963 or 64 you can observe the rate the 14C was leaving the atmosphere at a given point in time, and since you know the concentration of 14C in relation to CO2, you can calculate how much overall CO2 was leaving. Depending on the frequency of the data collected, this could be useful to know. How much does the removal of CO2 from the atmosphere vary from month to month and year to year?

  32. Lord Monckton, you expressed yourself a little better here, but I still think this misses the point. The water bottle analogy relies on the fact that the flow rates are independent, as you alude to, the atmosphere is different to this, there is no flow regulator on the hole in the bottle and the exit of fluid is dependent on the height of the column of water in the container as the rate of exit of excess CO2 is dependent on the partial pressure of CO2 in the atmosphere. But, adding CO2 to the atmosphere also adds to the size of the hole, the biosphere reacts, not only by processing more CO2 but by expanding the density and reach of the sinks.
    With increase in CO2 the following happens.

    The dissolution of CO2 into the ocean increases
    The rate of photosynthesis increases
    The density of vegetation increases, further increasing the photosynthesis rate including the algae and microscopic organisms.
    and the distribution of vegetation increases, vegetation grows in more places.

    So the artificial fertilisation of the planet by mans emissions produces an artificial excess of CO2 which causes a resultant lingering expansion in the biosphere, this new sinking rate both grows slowly and diminishes slowly. If we were to stop emitting CO2 the artificially produced sinks, would likely take time to diminish, and in the process take up so much CO2 as to leave us with less CO2 than we started with, undershoot

    Using the bottle analogy we take a bottle of suficient height and put a hole in the bottom of a particular geometry, we fill the bottle at a certain rate exceeding the outflow, untill the resultant pressure gives an outflow equal the inflow, inject an infinitesimal amount of a marker fluid, the volume of fluid represents preindustrial equilibrium level of CO2, now we increase the flow rate into the bottle and some time later before the level has restabilised increase the size of the hole. Now lets, reassert the original preindustrial flow, take away mans emissions, – reduce the flow rate to the original rate – what happens to the level of the water, what happens to the marker volume. There will still be a volume of the marker in the fluid irrespective of the fact that there is less fluid in the container than when you started.

    This is the situation we have, between the time we emit, and the response of the biosphere there is an overshoot, the CO2 emission exceeds uptake and rises, over time the sink expands to balance the rise. Taking away the extra emission will likewise cause an undershoot. While we continually increase emission rates equilibrium will remain in overshoot territory, where we are now, take that away and the expanded sinks would undershoot CO2 starving themselves in the process.

    The critical element here is the response of the bioshphere to the extra CO2, the expansion in the size of the hole if you will, in particular the time constant and magnitude of the reaction. This should be able to be experimentally measured, just $1 million aught to do, I’m not greedy.

    Lord M, it seems to me that the static case is clearly wrong, but the decay rate of C14 only indirectly hints at the overall response of the biosphere to CO2 rise, the equilibrium time of the biosphere to a pertubation is likely to be shorter than either case. If the missing CO2 (50%) of anthropogenic emissions, is uptake within the first year, and is an artifact of biosphere response to increased CO2 then the half life of added CO2 is one year, and 97 % of equilibrium reached in less than 5 years.

    A final observation, all of these discussion describe a classic negative feedback response to CO2 rise with lags, the overshoot inherrent in such a system has to mean that in a rising CO2 scenario CO2 is above the equilibrium level, and therefore cooling is in the pipeline – no tipping point evident here

  33. @Ferdinand: “But that is for free CO2 (gas), not for bicarbonates and carbonates.”

    Yes precisely. But we’re not talking about the residence time of atmospheric bicarbonates. That’s where things go astray.

    @David Riser: “Well done, the fact that the concentration goes down while we are emitting a lot of CO2 into the atmosphere demonstrates that the Bern model is either wrong or very incomplete”

    The interesting thing about the Bern model is that it places half its pulse immediately elsewhere — literally, not in the atmosphere. The consideration about that is that it means that ‘actual’ pulse measured is 1/2 what is stated. And if you eyeball the two curves presented with the Bern centered on the 1/2 mark, they keep a good agreement with each other. Certainly the Bern model has some issues in insta-vaporizing large quantities of the pulse into a buffer as a discontinuity to the curve. But the flaws thereafter may be simply a usage problem rather than any significant errors with Bern itself.

  34. Jquip says:
    November 21, 2013 at 3:54 pm

    Sure, just as you say. But that doesn’t answer to the immediate differences in isotope exchange in the short term… …To carry that idea you’d need to show that 14C ratios 1000 years before the 50 year bomb test window were significant. And to be sure, if we state that carbon can be sequestered now, and desequestered later; then there is no error. But it’s certainly not relevant to decay times in general.

    The problem is with decay times when the differences in mass is enormous and when the mixing time also is enormous, as is the case here. Even so, the radiactive decay of 1000 year old 14CO2 from the deep oceans was more or less in equilibrium with the amounts of 14C newly made in the atmosphere.
    14C/12C ratio’s are established for some 50,000 years, as they are used for carbon dating. They are wiggle matched with real callendar dates, because 14C production by cosmic rays is not that fixed as you know. But they had to correct the tables after about 1870, as humans increased their output of 14CO2-free fossil CO2 (all 14C is below detection limit after ~56,000 years). And they had to make new tables after the bomb tests, as humans now doubled the background 14C/12C ratio…

  35. Oh! Derp. It just occurred to me that we’re speaking past each other. Bern isn’t about atmospheric residence but sequestration of the Carbon in Carbon Dioxide as some other Carbon molecule. The bomb test measurements are simply about Carbon Dioxide, and not what it gets converted into in some process elsewhere.

    It’s an apples and pigs problem.

  36. Lord Monckton:

    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).

    I don’t know who was first, but Pieter Tans from NOAA showed similar figures about the impact of temperature and precipitation on the sink rate of CO2 in nature, see his speech at the festivities of 50 years of Mauna Loa data (from sheet 11 on):

    http://esrl.noaa.gov/gmd/co2conference/pdfs/tans.pdf

  37. As Plants take up C12 faster than they take up C14, it would be expected that C12 would be removed from the atmosphere even more rapidly.

  38. Doug Proctor says:
    November 21, 2013 at 3:56 pm

    One also has to be suspicious of the total amount of CO2 said to be emitted by Man.

    All CO2 emissions are calculated from fossil fuel sales, in early days by the statistics people from the financial departments (taxes). As people have a quite healthy tendency to avoid taxes, I am pretty sure that the emission figures of most countries are underestimated…

  39. Jquip:
    The decaay time for 14C will be shorter as none is being returned from the deep ocean. A pulse of 12C does not have that advantage.

  40. 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).

    Nope…The relationship has been known for more than 20 years. See http://www.nature.com/nature/journal/v349/n6310/abs/349573b0.html . Unlike, Salby, however, those authors did not misinterpret these results to make outlandish claims.

  41. Bart says:
    November 21, 2013 at 4:18 pm

    Equation (7) is just stupid. u_sub_n may represent natural sinks, but those are dynamic, and expand in response to e_sub_a, as well as to e_sub_n. Without e_sub_a forcing it, u_sub_n would be smaller, and the left side of the equation would no longer necessarily be positive.

    Except that there is not the slightest indication in the 14CO2 decay or in the residence time or any other observation that u_sub_n expanded more than a few %, only in ratio with the increase of the atmosphere, thus with a near constant half life time of ~40 years over the past 50+ years.

  42. IPCC –> IPeCaC –> Ipecac

    Very funny! For those who missed the joke, check out wiki…

    Syrup of ipecac /ˈɪpɨkæk/, commonly referred to as ipecac, is derived from the dried rhizome and roots of the ipecacuanha. It is typically used to induce vomiting, which it accomplishes by irritating the lining of the stomach (gastric mucosa) and by stimulating part of the brain called the medullary chemoreceptor trigger zone.

  43. Sisi says:
    November 21, 2013 at 4:06 pm
    Now, do you have anything to contribute that substantially objects to the things I wrote in my first comment to Lord Monckton. I will be glad to hear it.
    >>>>>
    Okay…your “points” reflect your belief system, but cannot be substantiated, except in you belief system.

  44. bobl says:
    November 21, 2013 at 4:24 pm

    The critical element here is the response of the bioshphere to the extra CO2, the expansion in the size of the hole if you will, in particular the time constant and magnitude of the reaction.

    A pitty for your grant, but that is already investigated:

    http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf

    The whole biosphere might have been a small source of CO2 before 1990 (about 0.5 GtC/yr), increasing after 1990 to about 1 GtC/yr sink capacity…

    If the missing CO2 (50%) of anthropogenic emissions, is uptake within the first year, and is an artifact of biosphere response to increased CO2 then the half life of added CO2 is one year, and 97 % of equilibrium reached in less than 5 years.

    Nature doesn’t make a distinction between human and natural CO2, total CO2 is about 110 ppmv above equilibrium, sink rate about 2.2 ppmv/yr, or a half life time of ~40 years…

  45. Humans are emitting something around 33 billion tons CO2 per year (there are various estimates you know).

    Natural processes are absorbing about half of that or 16.5 tons CO2 per year (it might be a little less than half which is were the various estimates start to produce problems).

    The natural process absorption rate appears to be more related to how much Excess CO2 there is in the atmosphere rather than our emission rate. The half is just a fluke. Natural processes have been absorbing about 1.5% of the Excess CO2 above 280 ppm.

    Now the Excess CO2 is something some people might object to. But CO2 appears to reach an equilibrium level around 280 ppm in non-ice-age conditions because it has been right around this level for the past 24 million years ever since C4 plants/grasses evolved. That is where the Earth’s biosphere wants to be at.

    If we stopped emitting today, the natural processes would continue to absorb 16.5 tons per year of CO2 out of the atmosphere but the rate would decline over time as the excess CO2 in the atmosphere above the equilibrium level gets lower and lower.

    It would take about 130 years to go below 290 ppm and then several decades more to get to 280 ppm.

  46. Ed_b: “The decaay time for 14C will be shorter as none is being returned from the deep ocean. ”

    As someone else today mentioned tagging animals, I’ll use that analogy here. Canadian Geese are born, migrate here, there, and the other place, then end up as supper. Our interest is not the entire lifecycle of a Candadian Goose but only how long it camps out in one location. That is, how long it is a resident for the area we are interested in.

    As geese come in we tag some of them with radio collars and note the date. When those tagged geese leave, we note the date. But we don’t care where that geese goes to thereafter. Whether or not they return next year. When they were born, or when they ended up on the menu. And we most certainly don’t care about geese that we don’t tag, that enter our region of interest.

    That there is very little 14CO2 being returned from the ocean is the ideal condition. As unlike geese, it’s a real problem attaching radio collars to greenhouse gas. Given that this confounding factor is minimized, we have far less adjustements and other data magic to perform to get an answer in the realm of sensibility.

  47. Ferdinand Engelbeen explains that “what goes into the deep oceans is the 14C/12C ratio of the moment. What comes out of the deep oceans is the composition of ~1000 years ago “. The oceans are emitting CO2 mainly at low latitudes, and absorbing CO2 mainly at high latitudes. The CO2 absorbed at high latitudes is taken down quite quickly into the deep ocean via the Thermohaline Circulation (THC). The CO2 released at low latitudes has taken several hundred years to be transported from the high latitudes through the deep ocean by the THC, so has low 14C. Hence the observed decline rate in atmospheric 14C is faster than for the other isotopes – as per Sisi’s comment.

    The absorption of CO2 into the deep ocean is basically a 2-stage process. Ocean-atmosphere CO2 imbalance, such as is caused by man-made CO2 emissions, has a half-life of about 13 years, as any excess atmospheric CO2 is taken up by the ocean surface layer fairly quickly. In this first stage, the CO2 concentration in the surface layer increases, but not by as much as simple arithmetic would suggest because of chemical changes. The second stage is somewhat slower, as CO2 (or C) moves from the surface layer to the deeper ocean.

    Jquip – in reply to Ferdinand’s “The ocean surface [..] can not absorb more than ~10% of the change in the atmosphere (due to the buffer/Revelle factor) [..]”, you say “To accept this claim I have to reject that Carbon Dioxide is soluble in water. Alternately, I have to accept that Henry’s Law is invalid and that Carbon bearing molecules exclude Carbon Dioxide from the water.“. By my understanding of the Revelle Factor, it actually increases the amount of CO2 that the ocean can absorb, though Ferdinand has stated the opposite. My understanding is that Revelle found that as CO2 is absorbed into the ocean about 90% of it quite quickly undergoes chemical changes, and hence the increase in CO2 concentration in the ocean is only about a tenth of what might have been expected. Hence the ocean can in fact absorb about 10 times more CO2 than might otherwise have been expected. If Ferdinand is indeed correct, then you must also be correct in arguing that it implies that Carbon bearing molecules exclude Carbon Dioxide from the water. Since that appears to be impossible, I suggest that Ferdinand must be wrong.

    Doug Proctor – Much of the stats for man-made CO2 emissions come from reported oil and gas production and consumption. Since production is taxed, there is indeed an incentive to understate it (but no evidence that this happens). Also, OPEC impose production quotas on their members, based on stated reserves. This encourages their members to overstate reserves and understate production. I would expect estimates of man-made CO2 emissions to be roughly in the right ball park.

    Pippen Kool – Your comments make no sense to me. You talk about the 14C being “incorporated into the fixed carbon” while the “other isotopes are in equilibrium“. The simple fact is that once the 14C is in the atmosphere, it is just part of the atmospheric CO2 and behaves virtually identically to all CO2 in all respects.

  48. re the 2-stage process – I should clarify that the THC is not the only mechanism by which CO2 or C gets from the surface layer to the deep ocean.

  49. OK, to continue this analogy: but with one change. We DO care about the number of geese that are present (from any cause), but have only tagged a few of those that are present.

    If 5000 geese are in the county, one night 25 were sprayed with green paint. A few nights later, 15 were sprayed with orange paint. A week later, 35 were sprayed with yellow paint. The paint wears off at a known rate, but the geese fly in and fly out – also at unknown rates, but presumably at constant rates. The total number of geese appears to be rising over time. Natural deaths of all of the geese present, and death by embarrassment of being painted must also be considered. 8<)

    Do you see how the problem is both a little more complicated – and also somewhat simpler than as originally stated? How many painted geese remain at any given time after the first ones were painted?

    The bomb tests started in 1945 with only 3 small bombs. They stopped in the early 60's – underground tests since 1960's don't create measurable CO2 in the air.

  50. Ferdinand Engelbeen says:
    November 21, 2013 at 5:00 pm

    “Except that…”

    No exceptions. The CO2 sinks all respond dynamically to increase or decrease in partial pressure.

    joeldshore says:
    November 21, 2013 at 4:58 pm

    Salby observed that CO2 evolves as the time integral of temperature anomaly, not proportional to it. If you have any reference which suggests this was explicitly stated in any notable venue prior to him, please provide it from an un-paywalled source.

  51. Mike Jonas: it implies that Carbon bearing molecules exclude Carbon Dioxide from the water. Since that appears to be impossible”

    Rather, I suggest that Ferdinand is correct but that he and I are discussing different things. If we’re talking about the entire life span of a carbon atom bonded only and solely to two oxygen atoms, then I agree with what Ferdinand has put forward. More than that, I suggest that this is the proper sense of what the Bern curve is representing. The lifespan of carbon as carbon dioxide, and not the residency of carbon dioxide in the atmosphere. This not only rectifies the differences in argument, but in the curves, and with the 1/2 buried initial impulse permits that we can explain why the Bern curve still declines under 1/2 total. But then, of course, we don’t care about greenhouse gases not in the atmosphere, if we’re interested in atmospheric effects.

    ” You talk about the 14C being “incorporated into the fixed carbon” while the “other isotopes are in equilibrium“. ”

    What he was attempting to state is that the total CO2 in atmosphere has gone up. So by [dilution], if not corrected for, the Bomb test curve will decline too quickly. On merits that’s correct, and I can’t say whether that correction has been performed or if it is a fresh breath of raw data. But if it is not corrected then, by eyeball, 2000 is at 0.1. And the correction for [dilution] would produce that as [.116] if CO2 had not increased. So that’s fine, but it doesn’t come close to putting the two curves in the same neighborhood.

  52. “And the correction for dillution would produce that as 1.16 0.116 if CO2 had not increased.”

    Supposedly I will someday learn to proof read before posting and not after.

  53. Although I’ve read it over several times, I still have not found anything in this post that disproves the point I’ve been trying to make.

    My point, as Lord Monckton says, is that “the decay rate of [the atmosphere's carbon-14 content] 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.” My rationale is set forth in Lord M’s discussion of Equations (1)-(4) above.

    Now, according to Lord M., Professor Pettersson tells us that the fraction of injected CO2 remaining in the atmosphere at time t is given by:

    f_t = \frac{e^{-\mu t} + k}{1+k}.

    I don’t profess any expertise on which to base an opinion regarding that equation’s validity, but, if it’s correct, it seems only to give us the value of \frac{dm}{dt} in Equation (2) above. Specifically, if the mass of \mathrm{C0}_{2} injected into the atmosphere is m_0 at t=0, the rate of \mathrm{C0}_{2} mass change, which is necessarily the difference e-u between emissions and uptake rates, is given by

    \frac{dm}{dt}=-\mu\frac{e^{-\mu t}}{1+k}m_0.

    But this merely gives a value for the concentration-change quantity in Equation (2) above; it says nothing about Equation (3), which is the rate at which the ^{14}\mathrm{C0}_{2} mass changes.

    Stated another way, Fig. 3 above seems to me to be comparing apples with oranges; one trace is total \mathrm{C0}_{2} concentration, while the other is the concentration of ^{14}\mathrm{C0}_{2}. It’s true, as Lord M. says, that a Pettersson k value of 0.015 will yield a terminal value different from the Bern a_0 value of 0.217, but Fig. 3 shows only the trace of the Bern relationship; it doesn’t give the Petterson relationship, because we have no basis for inferring Pettersson’s \mu value. The other trace, which depicts the (measured) time constant of the rate of ^{14}\mathrm{C0}_{2}-concentration decay, is a different animal.

    In case it proves helpful, I’ll mention that Willis Eschenbach referred to this issue in his Appendix to this post:http://wattsupwiththat.com/2012/05/06/the-bern-model-puzzle/, and the post where I was converted from Lord M’s position to my current one can be found here: http://wattsupwiththat.com/2013/07/01/the-bombtest-curve-and-its-implications-for-atmospheric-carbon-dioxide-residency-time/#comment-1352996.

  54. Well, as much as I admire and esteem the inimitable Lord Moncton, I fear that there is a conflation of two very different things in the head post.

    One is the turnover time, and the other is the response or adjustment or e-folding time.

    The “turnover time” is how long an average molecule stays in the atmosphere. According to the IPCC:

    Turnover time (T) is the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M/S.

    From both estimations of sources and sinks, and from observational (bomb-test) evidence, the turnover time appears to be on the order of 5 to 8 years. This is not much disputed.

    Response or adjustment time, on the other hand, is how long it takes for an emitted pulse of CO2 into the atmosphere to decay to half (or 1/e) of the original value. From the same IPCC source:

    Adjustment time or response time (Ta) is the time-scale characterising the decay of an instantaneous pulse input into the reservoir. The term adjustment time is also used to characterise the adjustment of the mass of a reservoir following a step change in the source strength. Half-life or decay constant is used to quantify a first-order exponential decay process.

    These two (response and turnover times) are totally different measurements, which are measuring different things. The turnover time (from bomb tests) is the average time a molecule stays in the atmosphere before being absorbed—5-8 years.

    The residence time, on the other hand, is a half-life (or e-folding time). Rather than being an average of actual times like the turnover time, it is the time constant for an exponential decay process. That’s a very different beast than the average of actual lifetimes of molecules in the atmosphere.

    I hope that this will illuminate the confusion. There are two times, not one. Turnover is short (~5-8 yrs) Response or e-folding time is longer . Estimates range from about 40 to over 100 years.

    Now, as to determining from observations what the e-folding time is, the problem is that we don’t have enough data to determine yet whether there is a long tail or not. The Bern model partitions emissions into four parts of fixed sizes, with three of them having e-folding times of 2.57 years (14%), 18 years (68%), and 171 years (3%), and the fourth (about 15%) hanging around forever … me, I don’t see that as likely, but like I said, to date the difference between the Bern model and a simple single e-folding time of ~40 years is lost in the noise …

    Best regards, and Lord Moncton, my thanks to you for all you continue to do.

    w.

  55. Ferdinand Engelbeen, please note that CO2/DIC at the surface of the ocean is denuded, with respect to 5m down, due to biotic photosynthesis.
    Pretending that the surface is in ‘equilibrium’, with respect to CO2 and O2, is a dumb mistake. just LOOK at the data for the composition of biotic gasses and DIC in actual sea water.

  56. The 14C (as CO2) bomb test is pretty close to a single-turnover experiment, essentially measuring the off rate, that is the rate of exit from the atmosphere. There is a steady state level of production from cosmic rays, that sets the minimum level of 14C. So there is an on rate as expressed in the equations above.

    Lets do math.

    dC/dt = N – kC (1),
    where C is 14C as CO2, N is a fixed rate of 14C formation from cosmic rays, and k is the off rate, that is the rate 14C leaves the atmosphere, not to return. If you can’t get past this part, give up.

    This is a non-homogeneous differential equation. Let assume C can be expressed as the product of U and V where U is the solution to the homogeneous equation.

    C = U*V (2)
    dU/dt + kU = 0 (3).

    With solutions
    U = A*e^(-kt) (4)

    Because dC/dt = dU/dt*V + U*dV/dt, we can substitute (2,3) into (1).

    dU/dt*V + U*dV/dt + U*V = N (5)

    Rearranging

    V*(dU/dt + U) + U*dV/dt = N (6), and because of (3)

    U*dV/dt = N (7) and

    dV/dt = N / U (8).

    Substitute (4) into (8) and

    dV/dt = N*A*e^(kt) (9).

    Integrating from 0 to t

    V = N/Ak * (e^(kt) – 1) (10).

    Solutions of C are A1 * U*V + A2 * U, so after some multiplication

    C = A1*N/k *(1-e^(-kt) ) + A2 * e ^(-kt) (11)

    At t=0, C = A2, and at t = inf, C = A1*N/k. Let A1 = k and A2 = N + Xo, where Xo is the excess 14C we start with at t = 0, then

    C = N * (1-e^(-kt)) + (N + Xo)* e^(-kt) (12).

    Rearranging we get

    C = N*(1 – e^(-kt) + e^(-kt) ) + X * e^(-kt) (13), or finally

    C = N + Xo e^(-kt) (14), and since C = N + X, after rearranging

    X = Xo e^(-kt) (15).

    Clearly, we see the fixed amount N and the decay of the excess X with rate constant k. When I fit the data using this equation, I get a half-life of about 5 years for 14C using ORNL data. My previous attempt failed to subtract N from C first. I just fit the fall, which was a mistake.

  57. Willis, I believe you have missed something very important.
    Imagine that the pulse added 1,000 units of 14C to the atmosphere and 14C has a first order rate of disappearance from the atmosphere of a decade.
    If the atmospheric reservoir was exactly the same size as the reservoir it is rapidly interacting with then the atmosphere will end up near 500 units after 5 decades.
    If the atmospheric reservoir was one third the size as the other reservoir then the atmosphere will end up near 250 units after 5 decades.
    If the atmospheric reservoir was one ninth the size as the other reservoir then the atmosphere will end up near 100 units after 5 decades.
    If the atmospheric reservoir was one nineteenth the size as the other reservoir then the atmosphere will end up near 50 units after 5 decades.
    If the atmospheric reservoir was one thirty ninth the size as the other reservoir then the atmosphere will end up near 25 units after 5 decades.

    The END POINT tells you the ratio of the relative size of the interacting reservoirs. It matters not a tinkers cuss what the mechanism of exchange is, what is happening is that the 14C is leaving the atmosphere much more quickly than it is appearing.

    There is a quite easy way to model the process. Assume that one third of the 90 GtC that is fixed annually in the ocean falls 50 m before it is oxidized, then half of this falls a further 50 m before being oxidized, , then half of this falls a further 50 m before being oxidized and so on.
    What you have is the rapid transport of organic ‘marine snow’ into the depths from the surface, which is of course denuded of CO2/DIC.
    This process depends, of course, on the rapid movement of fecal matter and dead organisms. these have been timed as falling at 16–368 m per day.

    http://www.int-res.com/articles/ame/27/a027p057.pdf

    The moment you stop thinking like a chemist and think like a biochemist, it becomes understandable.

  58. Hoser, don’t forget that the 14C is expressed as 14C:12C ratio and that the total 12CO2 has increased since the bomb tests.
    You have to use Anders estimate of annual CO2 release to work out the amount of dilution of 14C, this increases the decay constant to about 7.5 years.

  59. “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.”

    The carbon cycle diagram displayed has information on this. They say the plant reservoir has diminished by 15 Gtons C. They aren’t sure that it’s down – the range is -45 to +15. But the key is that the reservoir size is only 350-550 Gt. We’ve burnt about 400 Gt. If the plants had gobbled it, we’d live in a very different world.

    “For instance, Henry’s Law holds that a cooler ocean can take up more CO2.”
    Yes, but not very much. The ice age transition records tell us, as Ferdinand has often explained, that it’s about 8ppm per °C. Again the diagram says 20 Gtons C gained by the surface ocean, and 135 by the deep. That’s due to the air ppm increase, not cooling.

    “Is the ~10-year airborne half-life of 14CO2 demonstrated by the bomb-test curve (Fig. 1, …”
    Fig 1 clearly says a 14 yr half-life.

    What I’d like to see from Salby and/or fans is their equivalent of that carbon cycle budget diagram. If the CO2 in the air came out of the sea, where did our 400 Gt go?

  60. Ferdinand Engelbeen says:
    The problem is in the deep oceans: what goes into the deep oceans is the 14C/12C ratio of the moment. What comes out of the deep oceans is the composition of ~1000 years ago.

    I’m not so sure the deep oceans play much of a role WRT to short term C14 decay.

    The CO2 exchange between the atmosphere and the hydrosphere all takes place at the interface, not in the deep oceans. Following the sudden increases in atmospheric C14, some of those molecules will quickly be absorbed by the ocean surface. And some of them will be given up again to the atmosphere.

    I agree there’s a serious deficit in C14 levels in the deep oceans. But that doesn’t matter. What matters is the C14 deficit in the ocean surface. And that deficit although finite, will be a lot smaller.

  61. I’m VASTLY suspicious of all the “authoritarian proclamations” made about the “influence of ocean acidification” by CO2, having some effect on the rates of absorption and off gassing.

    Evidently, these folks are oblivious to the fact that the pH of the ocean, with the Henry’s law, current…absorption of CO2 should be somewhere around 5.7 (well less than 7 and quite “acid” as it would be). Instead, when the oceans are measured, they are actually fairly alkaline, around 7.8, if I recall correctly, and some of the specious claims put the “acidification” in the realm of going from 7.8 to 7.7 (or basic to basic, to be technically correct). The primary reason for this discrepancy, versus PURE WATER, is the “buffer” effect of the vast amount of dissolved species in all ocean water.

    Since the exact distribution and pH chemistry is somewhat muddled, hard to track, and can VARY from region to region, we have a situation where:

    1. Claims of a truly observable pH shift from 7.8 to 7.7 are DUBIOUS at best.

    2. IN a parallel manner, claims that the CO2 absorption and desorption rates are “self influenced” by claimed pH shifts caused by CO2 absorption, also are DUBIOUS claims.

    I recall some famous Latin saying that translated loosely means: Ignorance is NOT cured by application of more ignorance to the original problem.

  62. Nick Stokes – The plants seem to be net absorbers – http://www.impactlab.net/2008/06/09/scientists-surprised-to-find-earths-biosphere-booming/ – but we’re looking at 15-16mmt/mth compared with man-made of about 1500mmt/mth. So your main point appears to be correct.

    Jquip – My interest is in the take-up rate of CO2 from the atmosphere by the ocean. As I understand it, that is mostly what ChristopherM was getting at with his figures for 14C. My understanding is that the Revelle effect adds greatly to the amount of CO2 that the ocean is able to take up in the short term, compared with a ‘no chemical change’ scenario.

  63. Pippen Kool says:
    November 21, 2013 at 2:08 pm
    Because you are looking at dilution of the 14C into the fixed carbon; the other isotopes are in equilibrium and won’t diminish.
    =================
    having got into the fixed carbon, it is no longer in the atmosphere.

  64. Bill Illis says:
    November 21, 2013 at 5:26 pm
    The half is just a fluke. Natural processes have been absorbing about 1.5% of the Excess CO2 above 280 ppm.
    ================
    it seems unlikely to be a fluke. the absorption has remained constant at 1/2 of human emissions for as long as they have been reporting, while the percentage absorption of CO2 above 280 ppm has not remained constant.

    this is one of the unexplained mysteries of CO2 and human emissions, because if the AGW theory is correct, absorption should not be 1/2 of human emissions. Rather it should be a percentage of total CO2. But it isn’t. Which tells us that the theory that the CO2 comes from fossil fuel burning is wrong.

  65. And here is:

    Dr. Murry Salby to speak for himself.

    Note: In all the many times (and some of you realize that it has been, indeed, many,) I have posted my hero, Dr. Salby’s, lecture on this site, NOT ONCE HAS A SCIENTIST OF WUWT given us his or her detailed comments on the complete content of that lecture. While I have taken notes from it and could post a detailed summary of the video, I have nothing to add.

    Has all my posting of Dr. Salby’s lecture been for nought? Has NO ONE watched his lecture? Why–in–the–world haven’t you?

    One of the WUWT Science Giants ought to:

    1. Watch Dr. Salby’s 2013 Hamburg lecture;
    2. Write* a post for WUWT
    A. summarizing (with completeness and accuracy) its contents; and
    B. Commenting on what Dr. Salby says in that lecture.

    *Written so that so non-scientists can understand you — Dr. Salby did it (yes, I understand what he says — just could not ever analyze it for accuracy); i.e., the above scientist-author needs to have: 1) mastered the topic; AND 2) be a good teacher.

    Why has NO ONE done this?

    I sure wish I could — I would have long ago.

    *********************************************

    Please forgive my tone above. I just have grown tired over the past 6 months of reading so many lukewarm, tentative, “Well, …. maybe he has a point….. hm…. I just don’t know……. why doesn’t he get it published in a peer reviewed periodical? …….. hm…. …. ,” comments re: Dr. Salby’s work. And then, Ferdinand Englebeen stomps over and bellows that Salby is mixed up …. and NO ONE (that I can recall) but Bart (God bless you, Bart, one of “David’s Mighty Men” of science) defends Salby to any significant degree.

    WUWT is about more than being a semi-exclusive club for banter between scientists, isn’t it? It’s about teaching, too, is it not? Teaching is, after all, how we will win the battle for truth.

    Thus, THANK YOU, CHRISTOPHER MONCKTON, for twice now getting the word out (at least to some degree) about the content of Dr. Salby’s magnificent work.

    And I’ll bet I come back here tomorrow and see that my post was, as usual, completely ignored. That’s okay, v. a v. me and my zany posts, but PAUSE AND CONSIDER THE DISSERVICE YOU ARE DOING TO A GREAT SCIENTIST WHO HAS PUT HIS CAREER ON THE LINE FOR US ALL. — In caps so as you auto-scroll past an “oh, great, a Janice Moore post” (eye roll) you might see this!
    #(:))

  66. Is the assumption of homogeneous dispersion accurate?
    Being denser, wouldn’t 14CO2 sink faster, and thus be removed faster than 12CO2?

  67. Mike Smith – you say “I’m not so sure the deep oceans play much of a role WRT to short term C14 decay. The CO2 exchange between the atmosphere and the hydrosphere all takes place at the interface, not in the deep oceans.“. I think you are basically correct, but it is important that the absorption by the ocean of CO2 takes place in the higher latitudes and can be followed quite quickly by it sinking to the deeper ocean. Ocean CO2 emissions, on the other hand, take place mainly in the lower latitudes, so do not contain any recently-absorbed 14C. Well, not much.

  68. “Pippen Kool says:” – ad nauseam – various nonsense about CO2 residence times.

    You write about “carbon” as though this is something alien to this planet and the life-forms which inhabit it. May I take this opportunity to inform You, that You ARE a Carbon Based Life-form, and ALL the food you ever ate during your life is made from, and based on Carbon. CO2 is the vector gas which make all this possible. The so called residence time, can be as little as ten minutes, or several years, depending on whether there is plant life nearby to absorb the gas, and animals nearby to consume that plant growth. Its all a bit more complex than you imagine, “Pippen Kool”.

    Fatuous buffoons who claim that we must reduce the amount of CO2 in the atmosphere are wholly ignorant of the life processes which depend upon this rare gas, and why its concentration varies over time irrespective of the actions of the planet’s inhabitants, and the effects of its concentration at the various levels in the atmosphere over time.

  69. “Janice Moore says:
    November 21, 2013 at 10:08 pm”

    And soon we hope, since Professor Salby has been on a lecture tour of Britain recently, and spoke to some “non-scientific” audiences, thus putting these matters into a possibly better frame of understanding for the layperson. Accordingly we may hope to see a recording of one of these recent lectures, soon to be released on video.

    “They also serve who only stand and wait.” – John Milton

  70. Jquip says:
    November 21, 2013 at 5:56 pm`

    That there is very little 14CO2 being returned from the ocean is the ideal condition.

    In this case it is a disturance, because you are looking at a ratio: the ratio is going much faster down than the total count, giving the false impression that the decay rate is much faster than it is in reality…

  71. Sorry, Lord Monckton, but the 10-year residence time of carbon-14 is clearly not the same quantity as the “residence time” of CO2 i.e. the timescale at which the excess concentration of CO2 decreases.

    The carbon-14 decreases this quickly because there are many “carbon-neutral” processes in which the carbon-14 is absorbed by the oceans or the biosphere and replaced by carbon-12. Even if the CO2 in the atmosphere were not decreasing at all (assuming we stop emissions), it would still circulate and the relative concentration of carbon-14 at all places would tend to converge to a uniform fraction. The timescale needed for the homogenization of the isotopes is clearly shorter than the timescale needed to reduce the overall CO2 which actually depends on excess uptake.

    It’s trivial to see that the residence time of CO2 is of order 30 years or longer. We emit 4 ppm worth of CO2 a year; the CO2 concentration increases by 2 ppm per year. 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. The excess CO2 above the equilibrium value for our temperature- which is still around 280 ppm – is about 120 ppm so one needs about 30 years to halve the excess CO2 and 50 years to divide it by e.

  72. Janice Moore: ” I just have grown tired over the past 6 months of reading so many lukewarm, tentative, ‘Well, …. maybe he has a point….. hm…. I just don’t know……. why doesn’t he get it published in a peer reviewed periodical? ‘”

    I’m no more informed than you, but, if my understanding is correct, the complete code and data aren’t out there. Absent that, serious students would not be able to resolve dispel the ambiguities in his talk. (I don’t recall what I found ambiguous, but, even if I hadn’t listened to the talk, my experience with doping out technical disclosures would make me pretty sure they exist.)

  73. Mike Jonas says:
    November 21, 2013 at 5:58 pm

    The absorption of CO2 into the deep ocean is basically a 2-stage process. Ocean-atmosphere CO2 imbalance, such as is caused by man-made CO2 emissions, has a half-life of about 13 years, as any excess atmospheric CO2 is taken up by the ocean surface layer fairly quickly.

    The deep ocean exchanges largely bypass the ocean surface as well as at the downwelling as at the upwelling sites. For a large part there is very little diffusion of CO2 (and other stuff and temperature) between the ocean surface and the deep oceans.

    If Ferdinand is indeed correct, then you must also be correct in arguing that it implies that Carbon bearing molecules exclude Carbon Dioxide from the water.

    Henry’s law simply says how much free CO2 is in water for a given pressure in the atmosphere, independent of other carbon species in solution.
    the Revelle factor shows the increase of total carbon, that is free CO2+ bicaronate + carbonate in solution for a change of CO2 in the atmosphere.
    In fresh water, there is practically no increase in carbonate and bicarbonate, while in seawater, a large part of the extra CO2 entering the solution is transformed into other carbon species. The Revelle factor shows how much more. See:

    http://www.eng.warwick.ac.uk/staff/gpk/Teaching-undergrad/es427/Exam%200405%20Revision/Ocean-chemistry.pdf

    While it is 10 times more than for fresh water, it is only 10% of the changes in the atmosphere…

  74. A side point about which I would welcome any enlightenment: On another thread, Dr. Brown raised the point that the Bern equation appeared nonsensical on its face if, as it is advertised, it’s supposed to be an impulse response to emissions only. We know that natural emissions are greater than those from burning fossil fuels but that they are largely canceled out by uptake. But, if you ignore uptake, the Bern impulse response, which has a constant, a0 term would imply that concentration grows to infinity in response to a more or less constant emissions rate.

    I’m sure there’s a simple answer that a reader here knows, and I’d be grateful to hear it.

  75. DocMartyn says:
    November 21, 2013 at 6:44 pm

    Ferdinand Engelbeen, please note that CO2/DIC at the surface of the ocean is denuded, with respect to 5m down, due to biotic photosynthesis.
    Pretending that the surface is in ‘equilibrium’, with respect to CO2 and O2, is a dumb mistake. just LOOK at the data for the composition of biotic gasses and DIC in actual sea water.

    Biological processes indeed play an important role in the CO2 exchanges and reduce pCO2 (and increase δ13C) of the surface waters. But that doesn’t play much role in the change of DIC and pCO2 over time: CO2/bi/carbonate levels are not the restricting factor for sea life, the lack of nutritients is. pCO2/DIC/pH of the surace waters simply follows the change in the atmosphere as can be seen in the near 30 year series of the North Atlantic gyre at Bermuda:

    http://www.biogeosciences.net/9/2509/2012/bg-9-2509-2012.pdf

  76. So C14, which is chemically and biologically indistinguishable to the biosphere and atmosphere decays with a ? half life of 50 years and is not seen to return.This decay being much faster than the predictions made in Australia that it could be a thousand years.
    So if through natural innovation our carbon intensive industries are replaced by other technology at an economical price, anthropogenic CO2 will be mostly gone in two lifetimes.
    So there is no problem.
    By the Lord’s maths
    Quod Erat Demonstrandem

  77. Lord Monckton writes “Since there is no anthropogenic uptake to speak of, they contrived the following rinky-dink equationette:” I should just point out that this is actually just the same “equationette” that Prof. Salby presented in his Sydney Institute talk (http://www.youtube.com/watch?feature=player_embedded&v=YrI03ts–9I) at 8:58. The only difference is that the sum of all sources has been broken up into two terms, representing anthropogenic sources and natural sources.

    Also as others have pointed out, the IPCC do not claim that residence time is 50-200 years and indeed if you actually read the report you will find they take care to explain the difference between residence (turnover) and adjustment times. This claim is widely made on climate blogs, but that doesn’t make it true, and one wonders how it persists, given that it is so easily shown to be wrong (e.g. look up “lifetime” in the glossary of the AR4 WG1 report).

    The residence time argument was put forward by Prof Robert Essenhigh in the journal Energy and Fuels, who also published my paper (http://pubs.acs.org/doi/abs/10.1021/ef200914u) explaining the flaws in Prof. Essenhigh’s conclusion (his estimate of residence time is essentially correct and uncontraversial but it is adjustment time that is relevant to the long term increase in CO2, not the residence time).

    The mathematical flaw in Salby’s correllation analysis is explained here http://www.skepticalscience.com/salby_correlation_conundrum.html . Salby is not by any means the first to notice or explain this correllation, it was first reported by Bacastow back in 1975.

    Lastly, I recommend people read this article by noted climate skeptic Fred Singer, who points out that the use of arguments on this topic only serves to bring the skeptic side of the climate debate into disrepute (although I wouldn’t use the particular term that he used). The article is called “Climate deniers are giving us skeptics a bad name” and can be found here:

    http://www.americanthinker.com/2012/02/climate_deniers_are_giving_us_skeptics_a_bad_name.html

    • *dikranmarsupial* commented on On CO2 residence times: The chicken or the egg? .

      Good comments.

      I was thinking of the residence time vs adjustment time: if we think of Carbon-14 as a poisonous substance we dump into a pool of water in a very small, closed system, from which we get our drinking water it is easier to understand. The pool is poisonous, but as time goes the water goes into the acquifer, comes out again elsewhere, precipitates and runs down the hill to the pool and replenishes what was lost. The “residence” time in this case is infinite, but the “adjustment” time to get to equilibrium reflects the movement of the whole system. Also, the final poison concentration (equilibrium) is determined not by the initial concentration in the pool but by the total amount of poison and the total amount of water in the system.

      So with Carbon-14, equilibrium is reached when what is going out is equal to what is coming back in. The size of all the carbon-12 and carbon-14 in the system determines the final concentration. If we can make the assumption that there is no chemical or electrical or biological system that prefers to hold (or release) Carbon-14, then the final equilibrium concentration allows us to calculate the entire carbon reservoir involved.

      (What we need to know is the total, original concentration of carbon-14 put into the atmosphere. We could make an estimate at peak measurement, and then simply use that as a fixed “known”, even if the number is actually off, if what we are looking for are numbers either in the 50 or 500 year size. The error won’t matter with accuracy of that level.)

      Since we have been significantly increasing the carbon content of the atmosphere since nuclear testing ended, the adjustment time will appear faster than actual, i.e. we have increased the atmospheric portion of the carbon reservoir. So both the adjustment time and the equilibrium concentrations need to be corrected for this.

      The noted winter-summer change in CO2 noted at Mauna Loa is very interesting in that it says the world “breathes” CO2, but is this biological or temperature? The change is obviously Northern Hemispheric dominated, but is it the lower temperatures of winter that cause absorption of CO2 into cold water, or the biological decomposition during the summer that increases the CO2 – because biological plant activity should decrease, not increase atmospheric content? Previous studies show planckton growth in the Antarctic Ocean and English Channel (the articles I have read) determine the CO2 content above those waters. Or is it “obvious”? Is the change actually reversed, and controlled by the biologic activity of the Southern hemisphere, which absorbs CO2 in their summer (our winter) and releases it in their winter (our summer) when decomposition exceeds “composition”?

      Bottom line: I think Monckton is wrong about residence time vs adjustment time, as you note. But perhaps we can use the Carbon-14 values to estimate the total carbon budget in the cycle (as a multiple of atmosphere only?) and then work our way towards residence time.

      On Fri, Nov 22, 2013 at 8:29 AM, Watts Up With That? wrote:

      > dikranmarsupial commented: “Lord Monckton writes “Since there is no > anthropogenic uptake to speak of, they contrived the following rinky-dink > equationette:” I should just point out that this is actually just the same > “equationette” that Prof. Salby presented in his Sydney Institute ” >

  78. Mike Smith says:
    November 21, 2013 at 8:20 pm

    The CO2 exchange between the atmosphere and the hydrosphere all takes place at the interface, not in the deep oceans. Following the sudden increases in atmospheric C14, some of those molecules will quickly be absorbed by the ocean surface. And some of them will be given up again to the atmosphere.

    Yes and no: the deep ocean-atmosphere exchange largely bypasses most of the ocean surface: the main sink place in the NE Atlantic gobbles a lot of CO2 out of the atmosphere: the pCO2 pressure of seawater there is pretty low at around 150 μatm, while the atmosphere is at 400 μatm, thus pushing a lot of CO2 directly in the oceans:

    http://www.pmel.noaa.gov/pubs/outstand/feel2331/exchange.shtml

    The polar waters there are directly sinking into the deep oceans. They return hundreds of years later at the West coast of South America, mostly directly upwelling, to the joy of the fishermen there…

    The ocean surface indeed is in quick equilibrium with the atmosphere, but that has a limited capacity: only 10% of the change in the atmosphere will show up in the ocean surface layer, due to the Revelle factor. That is as good the case for 14CO2 as for 12CO2. The 90% must go elsewhere:

  79. Correction, the half life of residency of C14 in the atmosphere is about 12 years.
    In a biological model of drug clearance in the mammal, in five half lives its gone.
    from the Gaia point of view that’s of no great consequence in the life of the biosphere.CO2 may neverthless be good for the biosphere and help it manage the next cooling.

  80. Bart says:
    November 21, 2013 at 6:05 pm

    No exceptions. The CO2 sinks all respond dynamically to increase or decrease in partial pressure.

    Taking the 150 GtC/yr exchange rate for granted for the dynamic equilibrium state, the current net input-output difference is ~4.5 GtC/yr for an extra 230 GtC (100 ppmv) above equilibrium. Or an increase of 3% hardly a change.

    If – as you prefer – the exchange rates increased a threefold over the period 1960-2010 (or a sevenfold if only caused by increased deep ocean exchanges) to explain the increase in the atmosphere without human emissions, then the decrease rate of 14CO2 in the atmosphere would have been increased a threefold (or sevenfold) over the same period too. Of which there is not the slightest sign…

  81. ferdberple says:
    November 21, 2013 at 10:02 pm

    it seems unlikely to be a fluke. the absorption has remained constant at 1/2 of human emissions for as long as they have been reporting, while the percentage absorption of CO2 above 280 ppm has not remained constant.

    It is just coincidence, caused by the fact that human emissions are increasing slightly quadratic over time, which makes the increase in the atmosphere also slightly quadratic and therefore the sinks also slightly quadratic increasing over time. That leads to a astonishing fixed ratio between human emissions and “airborne fraction”:

    If human emissions stay equal or are reduced, the ratio will change accordingly…

  82. Wrong model.
    The “single” residence time is applicable to the first order differential equation only.
    CO2 is described by higher order differential equations and has several “residence times” depending on the way it is emitted.

    The bomb explosion leads to a fast decay of emitted CO2.
    A slow emission excites a long living CO2-mode.

    Just take a simple second order equation (overdamped harmonic oscillator).
    It has two exponentially decaying solutions. One decays fast, another one decays slower. Which solution you hit, depends on the way you excite it.

    As far as I remember, IPCC counts 7 CO2 modes leading to 7 decay times.
    One of the decay times is indeed very fast, about 5 years.

    But there are other modes with much slower decay times.

  83. It is a remarkable indication of the intelligent interest that Anthony’s readers take in understanding the science of climate change that so many should have replied in such interesting detail to my posting on the lifetime of CO2 in the atmosphere and its implications for future global warming.

    George E. Smith rightly points out that I ought to have mentioned the isotopic decay rate of 14CO2, which is 5730 years. As he also rightly says, this is too long a decay rate to have any relevance to present calculations. In fact, the decay rate is approximately equal to the source ate from cosmic rays, which is why atmospheric 14C had been near-constant until the bomb tests.

    “Pippen Kool”, supported by DocMartyn and M. Courtney, says that 14C is being “diluted into the fixed carbon”, asserting, without evidence, that “the other isotopes are in equilibrium” (with what, it is not made clear), and that they “won’t diminish”. Well, they have diminished, in the active reservoirs with which we are concerned. In the Neoproterozoic, 750 million years ago, there was at least 30% CO2 in the atmosphere. Today it is 0.04%. It is not merely the 14C/12C ratio but the absolute quantity of 14C that has declined.

    Mr. Engelbeen, supported by Mr. Jonas, Edb and Lubos Motl, says 14C diminishes many times faster than 12C, on the ground that there are many carbon-neutal processes by which the hydrosphere and biosphere take up 14C and replace it with 12C. The oceans take up 14C at high latitudes, where it sinks to the ocean floor, not to emerge again for 1000 years, while the 12C that sank to the ocean floor 1000 years ago is emerging today in the tropics. However, since we are unable to measure these natural fluxes, the effect that this has on the residence time of 12C is guesswork, while the residence time of 14C, the only isotope whose decay we can reliably measure, is definitely short. Mr. Motl argues that because today’s CO2 concentration is 120 ppmv above the 280 ppmv pre-industrial baseline the airborne half-life of CO2 is about 30 years and the e-folding time is 50 years. If it were as simple as that, Professor Pettersson would not have written his book, and Professor Salby would not have endured dismissal from his university.

    Sisi says the bombs increased the concentration of 14C in the atmosphere but hardly in the hydrosphere or biosphere. Well, they must have increased it in the hydrosphere and biosphere, because that is where 96% of it must have gone once it left the atmosphere. Sisi also says, “If Lord Monckton is so sure of his story, why does it end with a question mark?” The reason, clearly stated in the head posting, is that contradictory schools of thought were evident and I was not sure which was true, so I gave an account of both and asked what people thought. Sisi complains that the language was “obtuse”. Perhaps a course in mathematics would be of benefit to Sisi in understanding mathematical posts.

    Ian W says the biosphere CO2 sink may be working still faster now, thanks to atmospheric CO2 enrichment and the consequent observed global increase in net plant productivity, than at the time of the bomb tests. However, as other commenters have pointed out, the oceans are a far larger CO2 sink.

    Doug Proctor makes the useful point that someone should check how much CO2 we are actually emitting worldwide, rather than accepting the official values. He suspects there may have been an exaggeration, since that would advantage the profiteers of doom. Given the history of exaggeration by so-called “scientists” in this field, he may be right.

    Bart rightly points out that equation (7), a rearrangement of Skeptical Science’s hooby-dooby equation (6), is defective because it assumes the climate object is static when it is in fact dynamic.

    Bobl says the half-life of CO2 in the atmosphere may be as little as a year. That seems too short, given the behaviour of the 14C decay curve.

    Joel Shore, who continues to have difficulty in being polite, accuses Professor Salby of making “outlandish claims”, but without saying what it is that the Professor had claimed and why he thought the Professor was wrong. Mere yah-boo, in fact. Yah-boo is not science – unless you are an etiquetically challenged climate extremist.

    Mr. Born remains unconvinced by my summary of Professor Pettersson’s conclusions from the bomb-test curve. However, as has been pointed out, his equations (3, 4) are dimensionally challenged, and his model of a dynamic object is unduly static. He does not like Professor Pettersson’s comparison of the bomb-test curve with the Bern decay curve on the ground that the curves model distinct isotopes of CO2; however, as many have pointed out, for all relevant purposes the isotopes behave identically. He fails to appreciate the error made by the Bern model in choosing an absurdly elevated equilibrium constant that is contrary not only to theory but also to the empirical evidence from the bomb-test curve. And he says there is no basis for Pettersson’s rate-constant of decay, when, as Pettersson himself explains, his value best fits the observed curve, for there is no theoretical method of determining the decay constant, so he determined it empirically.

    Willis Eschenbach presumes – incorrectly and on no evidence – that I do not understand the distinction between turnover time and response (or e-folding) time. In my opening sentence I had specifically mentioned the airborne half-life (i.e. response time) of 14CO2; I had wondered whether it was the same variable as the IPCC’s residence time; and I had explained in the post that the airborne or residential half-life of 14CO2 is self-evidently ten years: one has only to find the closest value to 0.5 in table 1 and see that it is the ten-year value. Willis had made the same inappropriate remarks about Professor Pettersson’s posting on this subject: but the Professor, too, had drawn his distinctions very carefully and correctly in the papers underlying the posting. It should no more be assumed that a layman knows no elementary mathematics than that an eminent professor knows none. Besides, in the bomb-test curve the turnover time and response time are not too different from one another because both are very short. The objective of the posting was to enquire why the response time of the usual isotopes of CO2 should be any different from that of radiocarbon as established by the bomb-test curve.

    Hoser goes around the houses, mathematically speaking, to derive the exponential decay function (his equation 15), but neglects to modify it with the necessary addition of the equilibrium constant k, whose value Hoser accordingly assumes to be zero. However, the approximate ratio of the contents of the atmospheric to the biosphere/hydrosphere reservoirs is known and can be derived from Fig. 2; therefore k > 0, and specifically k = 0.015.

    Mr. Stokes, in a characteristically confused comment, says that if the plants had gobbled some of the CO2 we had emitted we’d live in a very different world. Well, we do. NASA has measured the net primary productivity of plants during the satellite era (i.e., the rate at which the global mass of all trees and plants increases), and it has indeed increased substantially, through CO2 fertilization. Mr. Stokes then objects to my accurate citation of Henry’s Law, on the ground that it does not make very much difference. Well, in that event it would be most instructive to know what is causing the strong temperature-dependence of the annual fluctuations in net CO2 emission as determined by Professor Salby from measurements at Mauna Loa.

    Mr. Hugoson is rightly suspicious of the notion of “ocean acidification”. There is indeed remarkably little empirical evidence for the supposed decline of 0.1 pH units since 1750 in the oceans. Indeed, a prize is on offer for the first person to design an automated pH monitor that will, for the first time, allow a reasonably comprehensive sampling of the oceans for changes in pH.

    Janice Moore, supported by Alan Smersh, asks why Professor Salby’s work has not received more attention, here at WUWT as well as elsewhere. She asks why there is no summary of his work here (apart from a couple of mentions of it by me). I have prepared such a summary, recently revised with additional slides from his presentation kindly supplied by Mr. Mulholland, and I hope that Anthony will find space for it soon.

  84. Janice Moore says:
    November 21, 2013 at 10:08 pm

    Hey Janice, I have followed Salby’s presentation in Hamburg in detail and have commented in the WUWT thread:

    http://wattsupwiththat.com/2013/06/21/nzclimate-truth-newsletter-no-313/

    and I have travelled to London to see him in person and to give him my objections. Unfortunately there was little time for discussion, and I wasn’t properly dressed to follow the organizers in the catacombs of the Parliament (no tie…) and he was rather evasive in his answers. As far as I know, he never discussed things out at any blog either.

    - Salby is wrong about the impossibility to make a distinction between fossil fuels and plant decay:
    Fossil fuels are completely devoid of 14C, plants are not.
    The whole uptake – decay balance can be calculated from the oxygen balance. Which shows that the whole biosphere is a net absorber of CO2. The earth is greening. Thus the whole decrease of the 13C/12C ratio in the atmosphere is caused by human emissions, not by plant decay.

    - Salby calculates the theoretical migration of CO2 in ice cores to fit his hypothesis (if the data don’t fit the hypothesis, then the data must be wrong, where have I heard that before?). But there is not the slightest proof of such high migration over time (not even measurable in the coldest ice cores over 800 kyr). If he was right, one would have negative CO2 values during the long ice ages, effectively killing near all life on earth.

    That are two clear errors, both easily found in the scientific literature, which Salby hasn’t read or ignored. Neither has he defended his view on these points.

    Thus sorry, Janice, until further notice, I am far from convinced by Salby’s speech in Hamburg and London…

  85. It should of course be noted that the surface area of the oceans is actually dwarfed by the surface area of cloud water droplets which are both cold and when they form CO2 free. By Henry’s law these droplets will take up a lot of CO2. This is true from the equator to the poles. Rain is continually washing CO2 from the atmosphere to the surface where no doubt it either remains and is used by the biosphere, sinks in the oceans or outgasses back into the atmosphere. It is not the simple cycle of waiting in the atmosphere for its turn to be ‘uptaken’.

    And of course this is a totally meaningless argument. CO2 has does not drive atmospheric temperatures in the real world, it has not heated the atmosphere resulting in more water vapor which is a fundamental requirement for AGW. Indeed it would appear that not only is there no tropical tropospheric hot spot but also that tropospheric humidity is dropping. AGW is a falsified hypothesis.

  86. Ferdinand Engelbeen says:
    November 22, 2013 at 3:41 am
    ……….
    - Salby calculates the theoretical migration of CO2 in ice cores to fit his hypothesis (if the data don’t fit the hypothesis, then the data must be wrong, where have I heard that before?). But there is not the slightest proof of such high migration over time (not even measurable in the coldest ice cores over 800 kyr). If he was right, one would have negative CO2 values during the long ice ages, effectively killing near all life on earth…….

    You shoud read: “CO2 diffusion in polar ice: observations from naturally formed CO2 spikes in the Siple Dome (Antarctica) ice core” Ahn, Headly, et al – Journal of Glaciology, Vol. 54, No. 187, 2008

    ABSTRACT. One common assumption in interpreting ice-core CO2 records is that diffusion in the ice does not affect the concentration profile. However, this assumption remains untested because the extremely small CO2 diffusion coefficient in ice has not been accurately determined in the laboratory. In this study we take advantage of high levels of CO2 associated with refrozen layers in an ice core from Siple Dome, Antarctica, to study CO2 diffusion rates. We use noble gases (Xe/Ar and Kr/Ar), electrical conductivity and Ca2+ ion concentrations to show that substantial CO2 diffusion may occur in ice on timescales of thousands of years. We estimate the permeation coefficient for CO2 in ice is 4 10–21 molm–1 s–1 Pa–1 at –238C in the top 287m (corresponding to 2.74 kyr). Smoothing of the CO2 record by diffusion at this depth/age is one or two orders of magnitude smaller than the smoothing in the firn. However, simulations for depths of 930–950m (60–70 kyr) indicate that smoothing of the CO2 record by diffusion in deep ice is comparable to smoothing in the firn. Other types of diffusion (e.g. via liquid in ice grain boundaries or veins) may also be important but their influence has not been quantified.”

    Perhaps some ‘slightest proof’ ?
    It has even been peer reviewed.

  87. Ferdinand the fixation of carbon in the upper ocean denudes the SURFACE of carbon, both CO2 and DIC, where there is biological carbon fixation

    This generates a dis-equilibrium state, a steady state. The denuded upper 5 m are in dis-equilibrium and there is a net flux of carbon from the atmosphere and from below.
    Where the waters are shallow, carbon cycling is rapid between the surface and the bottom, and the net influx from the atmosphere will be modest.
    Where the waters are deep, carbon cycling is slow between the surface and the bottom, and the net influx from the atmosphere will be large.
    At the surface DIC is converted into dissolved organic matter, a major fraction of which sinks rapidly;

    On the way down the DOC is converted to CO2/CH4 depending on ecology.
    However, the falling of ‘marine snow’ is the fasted rate of carbon transport in the oceans and this rate and mass transfer, determines the rate at which carbon is mixed from the atmosphere into the depths.

  88. Joe Born says:

    A side point about which I would welcome any enlightenment: On another thread, Dr. Brown raised the point that the Bern equation appeared nonsensical on its face if, as it is advertised, it’s supposed to be an impulse response to emissions only. We know that natural emissions are greater than those from burning fossil fuels but that they are largely canceled out by uptake. But, if you ignore uptake, the Bern impulse response, which has a constant, a0 term would imply that concentration grows to infinity in response to a more or less constant emissions rate.

    No, the natural emissions that matter are not greater than the burning of fossil fuels. The point is that what you call “natural emissions” are just rapid exchanges between reservoirs. This is the picture that you should have in your head: There are three reservoirs of CO2 with rapid exchanges between them, the atmosphere, the biosphere, and the ocean mixed layer. Then, there are sources and sinks of CO2 that are locked away from these reservoirs with one being the carbon in fossil fuels (another being the deep ocean).

    When you say there are large natural emissions, what you are talking about is just exchanges into the atmosphere from the biosphere and ocean mixed layer. However, these are a very different beast than emissions of a new source of carbon into these three reservoirs.

    When we emit a slug of CO2 into the atmosphere from burning fossil fuels, some of it quickly leaves the atmosphere as it rapidly equilibrates between the three reservoirs. However, from there on, the process by which it leaves these three reservoirs is much slower.

  89. Ian W – Thanks for the ‘slightest proof’. Logically, it has to happen. Nice to see the logic confirmed.

  90. Lord Monckton:
    I appreciate the effort that went into the post. While I regret (but it would have been unrealistic to expect otherwise) that the readership response has not ended up providing a more all-encompassing synthesis of the theories it sets forth, I am at least permitting myself to imagine that I have accomplished my own, more-modest goal, which was to alert you to the level of unease engendered by Pettersson’s drawing the inferences he does from the bomb-test. Since I only bat about .300 in similar attempts these days, I’ll count myself fortunate.

    I hasten to reiterate that I have no opinion about the validity of Pettersson’s equation itself; I merely have strong reservations about his inferring a value of its \mu from the bomb-test data. And I am not satisfied by his defense of the post he wrote last summer.

  91. Ferdinand Engelbeen – You say “The deep ocean exchanges largely bypass the ocean surface as well as at the downwelling as at the upwelling sites.”. The first part must be saying that movements in the deep ocean aren’t in the surface, which is true by definition. Downwellings and upwellings obviously do move between the surface and the deep. Maybe you are saying that water resident in the surface layer, and water resident in the deep, do not mix. There may be a sense in which this is correct, but to my mind it is not meaningful, the point being that an upwelling for example brings new water to the surface – it becomes the surface – and the ocean-atmosphere CO2 exchange is driven by pCO2 difference at the surface. Downwelling similarly (in reverse).

    You also say “extra CO2 entering the solution [..] is 10 times more than for fresh water, it is only 10% of the changes in the atmosphere”. Here, your “10% of the changes in the atmosphere” is irrelevant. If ocean-atmosphere pCO2 imbalance causes a ton of CO2 to move from the atmosphere into the ocean, then the ocean’s CO2 content initially increases by a ton. But the Revelle effect then kicks in, and most of the CO2 changes chemically, allowing the ocean to take up a lot more CO2. Thus the Revelle effect greatly increases the ocean’s ability to absorb CO2. As you say, about 10 times.

    In a later comment, you say “Biological processes indeed play an important role in the CO2 exchanges and reduce pCO2 (and increase δ13C) of the surface waters. But that doesn’t play much role in the change of DIC and pCO2 over time “. Here you are presumably talking about the surface layer. Of course you aren’t going to see much change in DIC and pCO2 over time, because the surface layer is always trying to balance with atmospheric pCO2. But, as DocMartyn points out, “At the surface DIC is converted into dissolved organic matter, a major fraction of which sinks rapidly” and this “is the fasted rate of carbon transport in the oceans and this rate and mass transfer, determines the rate at which carbon is mixed from the atmosphere into the depths”. In other words, there is an ongoing transfer of C from the surface layer to the deep – the ‘second stage’ that I referred to earlier – and this does result in the surface layer absorbing even more CO2 from the atmosphere.

  92. I can see it both ways personally, with oceans being such an unknown for the most part. We really can not answer this question conclusively until you prove the other part wrong. We have two valid hypothesis, so in the interest of science what we need to find out is how CO2 concentration differs in the following scenarios on our planet:

    A warming world with no human emissions
    A cooling world with no human emissions
    A warming world with human emissions
    A cooling world with human emissions

    And from that we could figure out a fairly exact attribution. Of course, a cooling world coming into play might answer the question by itself, but its far from certain. I read most of what people posted here, and I can see two plausible situations that can not both be right. So design an experiment and prove your case correct through actual data and an actual experiment.

  93. @Bobl

    You really took the wind out of my sails with your exquisite explanations and improved analogy. I too felt the analogy needed upgrading. I would add that the drain hole be conceived rather as a number of pinholes at different heights with the flow through each sink responding to the addition of fluid according to its vertical height below the ‘waterline’. Adding a viscosity change with temperature is realistic too. There are additional holes above the waterline that will start leaking if the level rises. There are akin to the CO2-starved sinks that are presently almost inactive.

    I was happy to see the references to fresh water and Henry’s Law. The seas have only about 1/2 the CO2 of fresh water. Rain and rivers carry CO2 into the oceans where it is gobbled up by numerous processes, leaving around 620 ppm. The ocean water evaporates to make more fresh rain water which has double the CO2, and it falls again to feed those sinks, stripping the atmosphere.

    Many posts/articles concentrate on the ocean-atmosphere as if it were only about Henry’s Law and partial pressures. But the interaction involving fresh water and sea water and the water cycle is very important. Melt Antarctica and there will be nothing left for the plants to eat unless the oceans give back. This may be the missing sink. It is a stripping process similar to the one that dries the stratosphere. It is the same as the process used by Giant Sequoias which each emit about 500 gallons per day (in the morning) and harvest water vapour from the ‘Frisco fog. Rain, with over 1100 ppm CO2 falling into rivers and oceans, is the agent of a massive CO2 sinking process.

  94. You have to give it to him: he always forces us to consult our dictionaries (or is it dictionarionettes?).

  95. Lord Monckton writes “Willis Eschenbach presumes – incorrectly and on no evidence – that I do not understand the distinction between turnover time and response (or e-folding) time. ”

    Lord Monckton also wrote in his article “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.”, which unambiguously asserts that the IPCC think that the residence time of CO2 is 50-200yr. The IPCC do not think that the residence time is 50-200yrs, but instead about four years, and give a figure for the adjustment time of about 100 years. This seems to me to be good evidence supporting Willis’ criticism.

    See the glossary of the AR4 report for details under “lifetime”, which says:

    “In more complicated cases, where several reservoirs are involved or where the removal is not proportional to the total mass, the equality T = Ta no longer holds. Carbon dioxide (CO2) is an extreme example. Its turnover time is only about four years because of the rapid exchange between the atmosphere and the ocean and terrestrial biota. However, a large part of that CO2 is returned to the atmosphere within a few years. Thus, the adjustment time of CO2 in the atmosphere is actually determined by the rate of removal of carbon from the surface layer of the oceans into its deeper layers. Although an approximate value of 100 years may be given for the adjustment time of CO2 in the atmosphere, the actual adjustment is faster initially and slower later on. ”

    http://www.ipcc.ch/publications_and_data/ar4/wg1/en/annexessglossary-e-o.html

    The C14 measurements give an estimate of residence time because C14 is not replenished by the fluxes with the oceans and terrestrial biota. To estimate the adjustment time, it is necessary to consider the action of the sources as well as the sinks.

  96. dikranmarsupial, there is a major difference between a reservoir and a sink, and one should never use the two interchangeably. A reservoir has multi-dimensional fluxes, at minimum an influx and efflux, whereas a sink has uni-dimensional flux, an influx into the sink and efflux from the system. Systems also have an input, again this is a uni-dimensional flux, an efflux or influx into the system.
    With respect to the carbon cycle, the input is volcanic CO2 that goes into the atmosphere at about 0.28 GtC per year; enough to replace the whole of the carbon content of the Biosphere in 150,000 years.
    The atmosphere is a reservoir, with both CO2 influx and efflux.
    The oceans are a reservoir, with both CO2 influx and efflux.
    Mineraliztion of biotic carbon, either as carbonates or a organic carbon rich sediments, is a sink.
    (Over millions of years subduction of the Earths crust performs a shake and bake of the mineralized carbon, previously ‘sunk’, via volcanoes. However, as the timescales are more than two orders of magnitude slower that the total carbon turnover time of 150 Ky, we can treat these processes as inputs and sinks.)
    Never use the term ‘Sink’, when you mean efflux into a reservoir.

  97. dikranmarsupial says:
    November 22, 2013 at 8:08 am”The C14 measurements give an estimate of residence time because C14 is not replenished by the fluxes with the oceans and terrestrial biota.”

    Yes it is. Or at least it is as the delta between the bomb-spike atmospheric pulse and the pre-existing background value approaches zero. As this happens, the exchange between the two approaches (approaches) equilibrium. This is close now, yet the first order exponential decay curve (e.g. the Jungfaujoch data in Levin et al Tellus 2010, 62B, 26-46) appears not to be changing rapidly, and is still indicating a half-life decay time of ~10 years in the 1997-2007 window. (If you have a direct data file for the Levine data, I would love a copy).

    In fact, it may well be that changes in human emissions (power stations etc) may well be masking the atmospheric-scrubbing of CO2, and making this decay time look longer than it really is.

    The 14C experiment is still running, and it’s not looking good for the IPCC.

  98. Janice Moore,
    Thank you for posting the link to Dr Salby’s lecture. Although it was a bit technical and immersed in a lot of math, there is a very clear take away point.

    He showed how climate models show future temperatures tracking projected CO2 so closely the two lines appear indistinguishable. Salby is arguing that CO2 tracks not temperature but the integral of temperature. Look at the recent RSS satellite temperature dataset compared with CO2 over the same period. You all remember the divergence. He then added a third line – the integral of temperature, and hey presto – this tracked the CO2 line almost exactly.

    There is a prediction in all of this. If CO2 tracks the integral of temperature, then model predictions will continue to diverge from the temperature datasets, and the divergence will become greater and greater. At some point it will be obvious that the models are wrong.

  99. Ferdinand,
    The methods in Bates et al are not impressive. We can do much better than take samples “skewed to the spring” and ship them to Scripps “stored several months to several years”.

    As much as they should be congratulated for actually measuring, this harks of measurements of the “surface” interchange with instruments dragged by ships at several meters depth. What we should be doing is actually measuring the uptake in the polar regions and the outgassing in mid latitude and equatorial regions. We know where they are, or at least we think we do.

    The elephant in the room is biology. One only need look at the ridiculous isotopic swings in the early Triassic to see the impact biological activity can have on isotopic composition. See Jonathan Payne et al 2004 or reference in:

    http://geosciencebigpicture.com/2012/07/15/carbon-isotope…-the-biosphere/

    While your point is well taken that current ocean outgassing represents a Viking era isotope ratio, the plankton get the first shot at that Carbon on the way out, and they are clearly starved for it. See Wolf-Gladrow et al or above.

    CO2 is not the only limiting nutrient, but the Bermuda gyre (or any of the ocean dead zones) is precisely the place where one expects limitation from a variety of nutrients. It is not the place to gauge global ocean biological Carbon uptake.

  100. Thank you Joe Born. Your initial civil critique of Monckton on other threads and blogs led to this thread’s value.

    Your calm and civil response on one of those other threads to being called a troll is a classic.

    John

  101. gymnosperm says:
    November 22, 2013 at 9:14 am
    “The elephant in the room is biology.”

    A hole-in-one, I think.
    And the elephant in the biological room may well turn out to be carbonic-anhydrase. People do study it in the biosphere, but try finding it discussed in IPCC-related literature.

  102. Christopher Monckton said,

    “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?”

    - – - – - – - – -

    I have enthusiastically followed both Lindzen’s and Salby’s public talks and written words since 2008 and 2011 respectively, however, I do not recall either of them discussing the 14C from atmospheric atomic bomb tests.

    Monckton does not quote them but uses his own words to relate private conversations on 14C.

    I would like to have their own direct words publicly documented on the 14C topic.

    Does anyone know if Lindzen or Salby have publicly addressed formally and specifically the 14C topic?

    John

  103. Pettersson’s model has atmospheric carbon in dynamic equilibrium with terrestrial and marine carbon. If you insert a slug of extra atmospheric carbon, the trees and the plankton will start growing faster (experiments confirm that plants grow faster with more CO2) and eventually the atmosphere will return to its original CO2 levels. The Bomb Curve allows us to quantify the word “eventually”.
    If Pettersson is correct, it follows that: a) if CO2 is continually added at a constant rate, the atmospheric levels will rise and then stay constant (because the trees and plankton can never quite catch up to the atmosphere), and b) if CO2 is added at a constantly accelerating rate, the atmospheric levels will rise linearly without ceasing, at a rate proportional to that acceleration.
    If Mr. Born was right (and no-one thinks he is) then there would be no reason to expect a CO2 equilibrium to exist.

  104. The pseudonymous “Dickranmarsupial” complains that I have confused residence time with adjustment time. On each occasion where I was specifying the type of time that I was talking about I did so in explicit, mathematical terms, on most occasions quoting others.

    In climate science, like it or not, “residence time” is sometimes used as the equivalent of “atmospheric lifetime”, also known as “adjustment time” (as, for instance, IPCC 1995 does when discussing the atmospheric persistence of aerosols, using the term “residence time” in one sentence and, referring to exactly the same thing, “atmospheric lifetime” in the next sentence). IPCC (1990, 1995) both use “atmospheric lifetime” to describe their 50-200yr estimates of CO2′s residence time or adjustment time.

    On a single occasion in the head posting I used the term “residence half-life” (the only point at which I myself used the word “residence” at all), because the persistence of 14CO2 in the atmosphere follows an exponential decay curve, albeit moderated by an equilibrium constant: and I submit that it was entirely clear from the context what I was talking about.

    Where I was referring to the turnover time, and that, too, has a variety of names, such as “relaxation time”, and is shorter than the residence time, I made that quite explicit, and again defined it mathematically.

    Perhaps it would be helpful if people were to eschew futile semantics. If Dickranmarsupial thinks that I have defined or used any of the terms imprecisely, let him explain exactly where I have departed from the well-understood mathematics of exponential decay, which was – after all – the principal focus of the head posting.

  105. Monckton says in his response to Eschenbach’s critique: “The objective of the posting was to enquire why the response time of the usual isotopes of CO2 should be any different from that of radiocarbon as established by the bomb-test curve.”

    No one here has been able to show why it is otherwise. The half-life of atmospheric CO2 seems to be established at ten years, or several decades instead of the absurd claim of several centuries. Thanks is due to Lord Monckton for this very important posting.

  106. Mr. Whitman says I quoted Professors Lindzen and Salby on 14C. I did no such thing. I quoted Salby on the notion that the integral of surface temperature change is very closely correlated with CO2 concentration change, and Lindzen as supporting Salby’s conclusions. I only mentioned Salby (and hence Lindzen) at all because the head posting was speculating on whether Professor Pettersson’s theory might help to explain both Salby’s result and the embarrassingly large “missing sink” of CO2.

    I have no idea whether Professors Lindzen or Salby had considered the implications of the bomb-test 14C decay curve, which is why I did not cite them on the subject.

  107. Ian W says:
    November 22, 2013 at 4:22 am

    You shoud read: “CO2 diffusion in polar ice: observations from naturally formed CO2 spikes in the Siple Dome (Antarctica) ice core”

    I have read that: it confirms that the migration of CO2 in a “warm” ice core like Siple Dome (-23 °C) is very small. The migration after 2.7 kyr broadens the resolution of the ice core from ~20 years to ~22 years and at full dept (70 kyr), from ~20 years to ~40 years. That is all. No big deal. For the much colder Vostok (- 40 °C) and Dome C ice cores, the migration is even much smaller. That is also confirmed by the fact that the ice cores CO2 / temperature ratio remains the same (at about 8 ppmv/°C) for each glacial-interglacial transition back in time. If there was any substantial migration, the ratio would fade over time.

    Not according to Salby: after 100 kyr the measured CO2 peak of ~100 ppmv would have been 10 times higher, thus ~1000 ppmv. After 2×100 kyr 10,000 ppmv etc… But as migration decreases the peaks, it doesn’t change the average over the period of interest, or for each glacial period the measured level of 180 ppmv according to Salby would be about 70 ppmv, in the second period below zero,…
    Which of course is impossible as below 180 ppmv all C3 plants suffer from suffocation…

  108. If Monckton of Brenchley wrote “IPCC (1990, 1995) both use “atmospheric lifetime” to describe their 50-200yr estimates of CO2′s residence time or adjustment time.” Actually, the 1990 report clearly distinguished between turnover (residence) time and adjustment time, in section 1.2.1 on page 8:

    “The turnover [DM: i.e. residence] 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
    betorc 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 tor the atmospheric
    CO2 level to adjust to a new equilibrium if sources or sinks
    change This adjustment time, corresponding to the lifetime
    in Table 1 1, is of the order of 50 – 200 years, determined
    mainly by the slow exchange of carbon between surface
    waters and the deep ocean The adjustment time is
    important for the discussions on global warming potential,
    cf Section 2 2 7″

    C14 is not significantly replenished from the oceanic or terrestrial reservoirs, so its decay is a measurement of the turnover or residence time, and are not an estimate of the adjustment time. As a result the decay rate of 14CO2 is not an indication of the rate at which a pulse of CO2 is taken up by the other reservoirs.

    The glossary entry I mention explained that for most atmospheric constituents the residence time and adjustment time are the same but that is not the case for CO2 (which is constantly replenished from the oceanic and terrestrial reservoirs). As a result mentioning the use of adjustment time in connection with aerosols only adds to the evidence that you are not distinguishing between adjustment time and residence time.

    Further details are given in my paper on this subject, published in response to Prof. Essnhigh’s paper on residence time. http://pubs.acs.org/doi/abs/10.1021/ef200914u .

  109. Oh, hurrah! At least five of you read my post! #(:))

    Alan Smersh, thank you for the support. The Hamburg lecture video I linked, by the way, already does what you are looking for in a new video, I think, but, as Vince Causey (thank you, Mr. Causey for letting me know my post was worthwhile) pointed out, perhaps, an annotated version with more explanation of the physics and math would be helpful.

    @Christopher Monckton — that is great news! Looking forward to it. And, thank you, for letting me know that you gave my post your attention. That knowledge was, per se, encouraging.

    And thank you to all you scientists commenting above this has been a great thread for learning.

    *****************************************

    To underscore what to me was the most persuasive (out of the many excellent cites to evidence above) point:

    … 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.

    (emphasis mine)

    BAM! T.K.O. — “Aaand the winner is….. Christopher Monckton of….er……… {hastily consult cheat sheet in palm of hand}……. BRENCHLEY!” (loud cheers and enthusiastic applause from the crowd — while the IPCC and its sorry little bunch of supporters sadly slink away out the back door……. Oh, I just feel so bad for them — NOT!).

    Take a bow!

  110. Ian W says:
    November 22, 2013 at 4:08 am

    It should of course be noted that the surface area of the oceans is actually dwarfed by the surface area of cloud water droplets which are both cold and when they form CO2 free. By Henry’s law these droplets will take up a lot of CO2.

    Rain is fresh water, fresh water will contain very little CO2 at a pressure of 0.0004 bar, which mostly was released from the same warm oceans where water vapour was entering the atmosphere. When water vapour cools at some height, it will take some CO2 from that height and temperature. When it drops to the ground, water may evaporate and release its CO2 content again. For 1 mm water height (1 l/m2) of rainfall, the CO2 content of the lowest meter above ground level can be increased with maximum 1 ppmv CO2…

    You can calculate that yourself with the atmospheric CO2 pressure and temperature for CO2 solubiity in fresh water, here for 1 bar:

    http://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html

  111. Nick Stokes says:
    November 21, 2013 at 7:36 pm

    “They say the plant reservoir has diminished by 15 Gtons C. They aren’t sure that it’s down – the range is -45 to +15.”

    I used to have one of those humorous sheets that get passed around graduate departments entitled “A Guide To Reading the Literature”. Some of my favorites were:

    “Of great theoretical and practical importance” = It’s the only problem I could solve.
    “It is believed…” = I think
    “It is generally believed…” = A couple of other guys think so, too
    “Correct to within an order of magnitude” = wrong

    Basically, what you are saying here is, they haven’t really got a clue.

    Lubos Motl says:
    November 22, 2013 at 1:42 am

    “It’s trivial to see that the residence time of CO2 is of order 30 years or longer. We emit 4 ppm worth of CO2 a year; the CO2 concentration increases by 2 ppm per year.”

    It is distressing to see an otherwise learned fellow essentially restate the “mass balance” bilge.

    dikranmarsupial says:
    November 22, 2013 at 2:43 am

    “The mathematical flaw in Salby’s correllation analysis is explained here http://www.skepticalscience.com/salby_correlation_conundrum.html

    A shallow analysis which totally misses the integral dependence on temperatures, and the idiotic “mass balance” argument thrown in for good measure,

    Ferdinand Engelbeen says:
    November 22, 2013 at 3:05 am

    This is beside the point. I do not agree with your analysis, which is heavily influenced by the erroneous “mass balance” argument. But, it is beside the point. We can argue about whether the feedbacks are strong enough to take out the anthropogenic component without a shrug (they are, as is evidenced by the temperature dependency of atmospheric CO2), but either way, equation (7) from the article is hooey.

    Ferdinand Engelbeen says:
    November 22, 2013 at 3:41 am

    “But there is not the slightest proof of such high migration over time (not even measurable in the coldest ice cores over 800 kyr). “

    There is, and he reviews it. He is not just making an assertion. He is backing it up with analysis.

    joeldshore says:
    November 22, 2013 at 5:14 am

    “No, the natural emissions that matter are not greater than the burning of fossil fuels.”

    This is an assertion with no proof. It is quite evident from the temperature dependency of atmospheric CO2 that they are. This is not a recirculating fountain. It is a fountain with a large drain, a huge natural pipeline in, and a tiny little human input in.

    DocMartyn says:
    November 22, 2013 at 8:22 am

    Important distinctions. The fountain analogy, which Joel et al. prefer to employ, is all reservoir, no sink.

    Vince Causey says:
    November 22, 2013 at 9:09 am

    “There is a prediction in all of this. If CO2 tracks the integral of temperature, then model predictions will continue to diverge from the temperature datasets, and the divergence will become greater and greater. At some point it will be obvious that the models are wrong.”

    Yes. And, judging by the temperature dependent slope of atmospheric CO2, which has flatlined in rate, and the ever increasing emissions, that day should not be too long in coming.

    Forget the cant and narrative for a while, everyone, and focus on this. Suppose the atmospheric CO2 is described by the differential equation

    1) dCO2/dt = (CO2eq – CO2)/tau + a*H

    CO2eq = equilibrium CO2 level, which is essentially dictated by global temperatures
    tau = a time constant
    a = fraction of anthropogenic CO2 which is not rapidly absorbed
    H = anthropogenic inputs

    This is a toy equation, but it is representative of everything we are discussing. The term -C02/tau is the natural sink rate. The warmist argument is that the effective tau is very large, so that the equation essentially becomes

    2) dCO2/dt := a*H

    and a is approximately 1/2. This agrees, on a very superficial and erroneous level, with observations.

    Salby’s argument is essentially* that tau is short, so that the equation is approximately

    3a) dCO2/dt := (CO2eq – CO2)/tau

    and further, that

    3b) dCO2eq/dt = k*(T – Teq)

    where k is a coupling factor, T is global temperature anomaly, and Teq is an equilibrium temperature.

    In all cases, H is greater than zero, so it is always trivially true that dCO2/dt – (CO2eq – CO2)/tau is positive, which is the “mass balance” argument, and is totally useless.

    So, the argument is all about whether tau is short or long, i.e., whether the sinks are powerful or weak. The evidence indicates that it is short, and equation (3b) is matched to a very high degree of fidelity in the collected data.

    *I do not want it to be misunderstood that I am restating Salby’s argument – I am not. This is my own argument, using Salby’s work as backup. I am not putting words into Salby’s mouth, and he may or may not disagree with my extension of his argument.

  112. Mike Jonas — “Thus the Revelle effect greatly increases the ocean’s ability to absorb CO2. As you say, about 10 times.”

    Ferdinand had the grace not to call me out on making the same mistake in speaking to him about Henry’s Law that is required to state that the Revelle factor alters Carbon Dioxide uptake in any fashion. Consider: We have CO2, Bicarbonate and Carbonate. If you consider these to be different: Henry’s Law and the Revelle factor contradict one another. But the issue is that CO2, Bicarbonate and Carbonate are freely transposable to one another. More to the point, they don’t simply ‘exist’ within the water but are constantly converting from one to another on the basis of the conditions local to each molecule. If the average of all local conditions gives a ph of X, then we can speak about the average fraction of CO2 that will exist at any given time as one of the three conditions. But because any given molecule of interest is varying its state, there are no issues with Henry’s Law at all.

    If, however, you have a known equilibrium condition and a known PH, then you will measure CO2 directly and only as being in violation of Henry’s Law. And this can lead you to all sorts of strange conclusions: Such that the Revelle factor — ph buffering — changes the rate at which CO2 is dissolved in solution. Which is simply not the case. You are measuring just one component of a volatile equilibrium of CO2, Bicarbonate, and Carbonate. Such that if we are interested in dealing with the ocean as a CO2 sink, it is not the partial pressure of CO2, but the partial pressure of dissolved inorganic carbon, or the DIC, that Ferdinand referred to.

    So if someone states that Revelle’s law is material to conditions, or to the impulse response rate, then you know it’s one of Kip Hansen’s scarves. Or, like me, they forgot to consider that DIC’s freely convert one to another constantly and below the time scale of interest.

  113. DocMartyn says:
    November 22, 2013 at 4:35 am

    Ferdinand the fixation of carbon in the upper ocean denudes the SURFACE of carbon, both CO2 and DIC, where there is biological carbon fixation

    Agreed, but that is only important if the CO2 fixation changes with increased CO2 pressure in the atmosphere, which is hardly the case as there is more than sufficient CO2 and derivates in seawater to serve far more biolife. CO2 is not the limiting factor…
    See Feely e.a. for the effect of temperature, pCO2 and biolife from poles to equator:

    http://www.pmel.noaa.gov/pubs/outstand/feel2331/exchange.shtml

    On the way down the DOC is converted to CO2/CH4 depending on ecology.
    However, the falling of ‘marine snow’ is the fasted rate of carbon transport in the oceans and this rate and mass transfer

    The figures I have seen are between 2 and 6 GtC/yr for the “raining out” of organic carbon from the upper ocean layer into the deep oceans. The inorganic carbon flux via the THC is estimated (by me) at about 40 GtC/yr, based on the “thinning” of the 13C/12C ratio caused by fossil fuel burning in the atmosphere:

  114. Bart says:
    November 22, 2013 at 10:31 am

    I had meant to segment off the part starting at “Forget the cant and narrative…”, but it is there, so I will leave it. If the tau of the bomb test is about 14 years, then the total contribution of H to CO2 is approximately

    CO2(H) = a*tau*H

    It is said that the integral of a*H is on the order of the change observed so, if that is roughly 100 ppmv in roughly 100 years, we can upper bound this as a*H is less than 1 ppmv/year equivalent. So, the net contribution of H to CO2 is on the order of less than 14 ppmv. Pretty negligible.

    “In all cases, H is greater than zero, so it is always trivially true that dCO2/dt – (CO2eq – CO2)/tau is positive, which is the “mass balance” argument, and is totally useless.”

    That is not quite right. The “mass balance” argument is that dCO2/dt – H is less than zero, which means that CO2eq – CO2 + (a-1)*tau*H is less that zero. If tau is short, then

    CO2 := CO2eq + a*tau*H

    so, CO2eq – CO2 + (a-1)*tau*H := -tau*H is always less than zero. It is still meaningless. In a dynamic system, the “mass balance” argument is a statement of a triviality.

  115. “…there are no issues with Henry’s Law at all.”
    Yes there are. Henry’s Law is statement of equilibrium. Knowing the equilibrium constant does not tell you the rate constants without further information.

    Why might that matter?
    Because CO2 and bicarbonate are indeed transposable to one another, but the reaction is quite slow compared to diffusion-limited reactions. The can of cola losing its fizz after reaching room temperature is more complex than it first appears. Which is why nature ubiquitously makes use of carbonic-anhydrase to speed up the exchange reaction by a factor of more than a million.

    Where might that matter?
    At locations which are not at equilibrium: Carbon sources and carbon sinks where there is life. Which is most places. And not necessarily photosynthesizing life. A cold ocean that is absorbing CO2 (driven by pH/Revelle factor) can do so faster with non-photosynthesizing microscopic life-forms floating at or near the surface (and vice versa). The question is how much?

  116. Rob: “Equation 3 is not dimensionally correct. e14e has units of ([m]/[t])^2. LHS is in units of [m]/[t]”

    In changing variables from my original equation here: http://joannenova.com.au/2013/11/monckton-bada/#comment-1343249, Lord M. made it (in his words) “dimensionally challenged.” Rather than “e14e” on the RHS, it should have been “ce,” where c is the (dimensionless) cosmogenic carbon-14 fraction.

    Good catch; I missed that in reading the post. I guess I saw what I expected to see.

  117. Pippen Kool says:
    November 21, 2013 at 2:24 pm

    You know, I bet most people knew what I meant. I am doing this on a cell phone….

    “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?”

    Because you are looking at dilution of the 14C BECAUSE IT IS INCORPORATED into the fixed carbon; the other isotopes are in equilibrium and won’t diminish.

    (and if you want to be picky, the ocean would also accumulate the carbon at a slow rate)

    The main pt is that once the carbon is out of the ground, it ain’t going away quickly e.g. with a 10 year half life.

    Which is precisely why the bomb tests are important measures that show that carbon residence time is much shorter than IPCC models employ. It does go away quickly. The rate at which it disappears from the atmosphere and becomes fixed (in organic matter) can be measured by comparing the initial, pre-bomb test conditions to the period immediately after the bomb test, and then monitoring the return, after the tests, to initial conditions. C-14 is produced by the reaction of high-energy radiation (mostly cosmic) and nitrogen isotopes. When it decays it decays to different nitrogen isotopes. So its presence is completely independent of other sources of carbon isotopes. Since baseline C-14 concentrations are independent of any stable carbon isotope releases natural or anthropogenic, the pulse of the bomb-generated isotope provides an independent measure of carbon isotope atmospheric residence time.

    That bomb generated material DID go away with a 10 year half life. That data is at present the only important, empirical measure of atmospheric residence time for carbon isotopes. Because it is a slightly heavier isotope than C-12 or C-13, it will a have a very slightly different residence time based upon temperature fractionation effects that also effect oxygen isotopes. That will be more than offset by the reaction of stable carbon with heavier oxygen isotopes, so it is irrelevant.

  118. I just checked the coins in my purse. I’m dutch so they are euro coins. Eleven years ago all my coins were dutch euros with our queen. Now all my coins are not dutch because of the dilution of the dutch coin pool with the european coin pool. Atmospheric c14 is similar, because of the huge dilution pool that is available in the ocean. The bomb test curve measures cash flow. Not profit and loss.

  119. Lord Monckton, thank you for your response. You say that you are not mixing up the residence time and the response/adjustment/e-folding time, which I call the “e-folding time” to avoid misunderstanding..

    However, your article starts by saying:

    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?

    The first of these measures the average residence time of an individual CO2 molecule in the atmosphere, using the half-life of 14CO2.

    The second of these is an estimate of the time constant for the decay towards equilibrium of an injected pulse of CO2.

    So clearly, the answer is no, they are not “the same variable”.

    It appears to me that the thrust of your argument is that the answer to your opening question is an emphatic “yes” … if I’m wrong, please explain.

    I got into this question in my normal fashion … by using the historical emissions and atmospheric concentration data to actually do the calculations for the e-folding time for an injected pulse of CO2. My calculations put it at about 38 years.

    And in fact, one reason that I think that humans are responsible for the majority of the increase in CO2 is the quality of the fit between a very simple exponential decay model, and the observed reality. Here are the results of that analysis.

    That analysis was done using single-time-variable exponential decay of the estimated emissions (including emissions from biomass). My calculations for that graph used an e-folding time of 38 years …

    This is quite similar to the e-folding time calculated by Jacobsen, who found a figure of 43 years (including emissions from biomass).

    So in answer to your question,

    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?

    I would say the answer is, emphatically no. They are two different variables. One is the molecular atmospheric residence time, call it 5-10 years. The other is the e-folding time for the decay of a pulse of injected CO2. Jacobsen and I put that at about 40 years.

    The IPCC, on the other hand, uses the “Bern Model“, which I understand and have done the calculations for, but which I find unphysical and unbelievable. In any case, the Bern model divides the atmospheric CO2 into parts with different e-folding times. These are on the order of 3, 18, and 171 years for the various atmospheric fractions. So the IPCC says there is no one single fixed e-folding time for CO2.

    Best regards,

    w.

  120. Ferdinand Engelbeen says:
    November 22, 2013 at 3:41 am

    - Salby is wrong about the impossibility to make a distinction between fossil fuels and plant decay:
    Fossil fuels are completely devoid of 14C, plants are not.

    ===================================================================
    A question. Is the line in bold based on assumption or actual analysis?

  121. Mike Jonas says:
    November 22, 2013 at 6:05 am

    Downwellings and upwellings obviously do move between the surface and the deep.

    One need to make a differentiation between the ocean suraface layer (the mixed layer) and the deep oceans. The former is where most sunlight enters, most biolife is present and wind stirrs the waters and makes a rapid exchange between water and atmosphere possible. The latter is for 90% of the area isolated from the surface, as there is very little migration between the deep oceans and the surface. The only relative important carbon flux is by dead bio material dropping out of the surface layer.
    The main sink places are of course part of the surface, but they are sinking directly into the deep (or intemediate waters from the Southern Ocean). That are the places where the largest CO2 uptake happens without mixing with the rest of the ocean surface. The same for the upwelling: of course that gets to the surface, but again without much mixing with the rest of the surface layer before upwelling. Only afterwards, the upwelling spreads to a larger area where the extra CO2 content is released thanks to increased temperature.
    The exchange of CO2 between the deep oceans and the atmosphere thus is mostly independent of what happens in the mixed layer. And a lot slower because of the limited exchange rate (directly or indirectly) between the atmosphere and the deep oceans…

    But the Revelle effect then kicks in, and most of the CO2 changes chemically, allowing the ocean to take up a lot more CO2. Thus the Revelle effect greatly increases the ocean’s ability to absorb CO2. As you say, about 10 times.

    Sorry, but that is a misinterpretation of the Revelle factor, which says that a change in CO2 of the atmosphere induces a change of CO2 in (sea)water which is a lot smaller: an increase of 30% CO2 in the atmosphere gives an increase of 3% in total carbon (DIC) in the ocean surface layer. That indeed is about 10 times more than what is dissolvable in fresh water, but only 10% of the change in the atmosphere.

    That is an important point, as of the 9 GtC human emissios, 4.5 GtC/yr is the increase in the atmosphere, only ~0.5 GtC/yr is absorbed by the ocean’s mixed layer, ~1 GtC/yr is absorbed by vegetation and ~3 GtC by the deep oceans…

  122. Gunga Din, yes, the radioactive half life of C14 is about 5,000 years, but fossil fuels have been underground for hundreds of millions of years, so virtually all of the C14 will have decayed long ago.

  123. Monckton of Brenchley on November 22, 2013 at 10:01 am

    [bold emphasis by me-JW]

    Mr. Whitman says I quoted Professors Lindzen and Salby on 14C. I did no such thing. I quoted Salby on the notion that the integral of surface temperature change is very closely correlated with CO2 concentration change, and Lindzen as supporting Salby’s conclusions. I only mentioned Salby (and hence Lindzen) at all because the head posting was speculating on whether Professor Pettersson’s theory might help to explain both Salby’s result and the embarrassingly large “missing sink” of CO2.”

    . . . ”

    - – - – - – - –

    Christopher Monckton,

    I appreciate your response. Thank you.

    Please re-review my comment to you; here it is for your convenience. Please see bold emphasized text.

    John Whitman on November 22, 2013 at 9:40 am said

    [@Christopher Monckton]

    I have enthusiastically followed both Lindzen’s and Salby’s public talks and written words since 2008 and 2011 respectively, however, I do not recall either of them discussing the 14C from atmospheric atomic bomb tests.

    <b<Monckton does not quote them but uses his own words to relate private conversations on 14C.

    I would like to have their own direct words publicly documented on the 14C topic.

    Does anyone know if Lindzen or Salby have publicly addressed formally and specifically the 14C topic?

    John

    So, in bold you see that I did not say as you stated “Mr. Whitman says I quoted Professors Lindzen and Salby on 14C”, instead I clearly stated you did not quote Lindzen or Salby on 14C.

    Instead of you quoting Salby, I said that you did relate, in your own words, a conversation you said you had with Salby. Here are your words,

    WUWT Guest Post ‘Towards a theory of climate’ by Christopher Monckton of Brenchley

    “. . .

    First, I [Christopher Monckton] asked [Murry Salby] whether the rapid, exponential decay in carbon-14 over the six decades following the atmospheric nuclear bomb tests had any bearing on his research. He said that the decay curve for carbon-14 indicated a mean CO2 atmospheric residence time far below the several hundred years assumed in certain quarters. It supports Dick Lindzen’s estimate of a 40-year residence time, not the IPCC’s imagined 50-200 years.

    . . .”

    And that quote of yours is also a part of the basis of me inferring that you were referring to something Richard Lindzen related to you in conversation which was directly or indirectly related to 14C.

    Again, I would like to see Salby and Lindzen directly address the excellent dialog we are having wrt Joe Born’s 14C position which you (CM) have teed up so well for WUWT.

    John

  124. Ferdinand Engelbeen says:
    November 22, 2013 at 11:42 am

    … One need to make a differentiation between the ocean surface layer (the mixed layer) and the deep oceans. The former is where most sunlight enters, most biolife is present and wind stirrs the waters and makes a rapid exchange between water and atmosphere possible. The latter is for 90% of the area isolated from the surface, as there is very little migration between the deep oceans and the surface. The only relative important carbon flux is by dead bio material dropping out of the surface layer.

    Thanks, Ferdinand. Curiously, in many parts of the ocean this is not true. The largest migration on earth (in tonnes of living creatures) is the nightly migration of billions of sea creatures from their daytime depths of around 200-400 metres up to near the surface where they feed, and then back down to the deep ocean again. Since they are eating at or near the surface, and then returning to the depths each night, the nightly migration is one of the generally overlooked transport pathways in the full carbon cycle, although there is some research in that area.

    Regards,

    w.

  125. Bart says:
    November 22, 2013 at 10:31 am

    There is, and he reviews it. He is not just making an assertion. He is backing it up with analysis.

    The theoretical migration in the Siple Dome ice core which was referenced by Ian W, was calculated from a measured increase of CO2 in the neighbourhood of remelt layers, not exactly a measured migration in “normal” layers of ice cores. But even if we accept this theoretical migration, then there is a 10% broadening of the resolution of that particular ice core over 2.7 kyr and a doubling of the resolution at full depth (70 kyr).

    Thus all what this migration did is decreasing the resolution, which still should be sufficient to show an increase of 2 ppmv sustained over 40 years some 70,000 years later. Let it be that that similar increases as the 70 ppmv over the past 50 years would anyway be noticed.

    That is very far from the 10-fold decrease in the peak-CO2 of 280-300 ppmv sustained over a period of 10,000 years that Salby claims…

  126. michael hart: “Because CO2 and bicarbonate are indeed transposable to one another, but the reaction is quite slow compared to diffusion-limited reactions.”

    No, this is irrelevant and related to the error I just mentioned. It is correct to state that Henry’s is equilbrium. And it is correct to state that the partial pressures give us a response time for a reservoir model; it satisfies all the constraints necessary for its proper use. It is wholly incorrect to state that the statistical instantaneous snapshot of CO2 states as ‘which DIC is which’ is relevant to that at all. If our disequilbrium is strong enough then it is correct to state that we will violate Revelle’s factor for a period of time when diffusing from the atmosphere to the sea. But then, Revelle’s factor isn’t a constant, nor a law, but a suggestion. And you can find that different oceans have different opinions on what the precise value should be. But what Revelle’s cannot do is modify the reservoir model in terms of sinking from the atmosphere to the sea. And your soda analogy does not address this at all; specifically it’s going in the other direction.

  127. Ferdiand: “Sorry, but that is a misinterpretation of the Revelle factor, which says that a change in CO2 of the atmosphere induces a change of CO2 in (sea)water which is a lot smaller: an increase of 30% CO2 in the atmosphere gives an increase of 3% in total carbon (DIC) in the ocean surface layer.”

    No, this is incorrect. Revelle’s doesn’t refer to DIC for that DIC which is still just CO2. What instantaneous statistical snapshot of what carbon is in which state is wholly irrelevant. As on time scales much shorter than our interest, each DIC is transposing into any other DIC constantly and as the molecule local conditions dictate.

  128. Gunga Din says:
    November 22, 2013 at 11:41 am

    Ferdinand Engelbeen says:
    November 22, 2013 at 3:41 am

    – Salby is wrong about the impossibility to make a distinction between fossil fuels and plant decay:
    Fossil fuels are completely devoid of 14C, plants are not.

    ===================================================================
    A question. Is the line in bold based on assumption or actual analysis?

    dikranmarsupial says:
    November 22, 2013 at 11:47 am

    Gunga Din, yes, the radioactive half life of C14 is about 5,000 years, but fossil fuels have been underground for hundreds of millions of years, so virtually all of the C14 will have decayed long ago.

    ======================================================================
    So the “yes” is that it’s assumed there is no carbon14 in fossil fuels?
    Fossil fuels haven’t been tested for it?

  129. Willis: “The IPCC, on the other hand, uses the “Bern Model“, which I understand and have done the calculations for, but which I find unphysical and unbelievable.”

    The only good information I can dig up on the Bern model is that it is used as a reservoir model where detritus (decomposition) and plants are used as reservoirs. However, this is impermissible. CO2 uptake by plant life is not a factor of differences in pressure between CO2 external to the plant, and the carbon already sequestered by the plant. Decomposition is just an edge case of aerobic life. Which certainly does consume plant carbon and emit CO2 by respiration. But, once again, this does not occur on pressure differences between the plant carbon sequestered in the animal and the partial pressure of CO2. So it is absolutely correct to state that it is unphysical in this regard. Strictly, it is violating the considerations necessary for a reservoir model. As a secondary consideration it is utilizing estimations of aerobic life, but ignoring the rest wholly and arbitrarily without justification.

    How significant that is to results is a wholly different question. But if the sum total of plant and animal life is significant to our interests, then quite strictly Bern is out of bounds for use. And if it is significant, then certainly the notion that there is a constant e-folding time is out of bounds as well. And that makes a distinct problem if we are estimating emitted CO2 versus sunk CO2 on the idea that the e-folding time is constant and that we have a valid reservoir model. As to whether or not that is the case, I could hardly say at this point.

  130. Lord Monckton, John Whitman above references your comments in your most interesting previous post:

    WUWT Guest Post ‘Towards a theory of climate’ by Christopher Monckton of Brenchley

    “. . .

    First, I [Christopher Monckton] asked [Murry Salby] whether the rapid, exponential decay in carbon-14 over the six decades following the atmospheric nuclear bomb tests had any bearing on his research. He said that the decay curve for carbon-14 indicated a mean CO2 atmospheric residence time far below the several hundred years assumed in certain quarters.

    . . .”

    This is a clear indication of the conflation I am referring to. The problem is that the term “residence time” is being used for both turnover time and for e-folding time.

    The bomb-test 14C data applies only and solely to the turnover time, which is how long an individual CO2 molecule hangs out in the atmosphere before being absorbed somewhere at the surface. Since the bomb tests “tagged” individual molecules, we could see how long those molecules stayed airborne before being absorbed somewhere at the surface.

    Unfortunately, the bomb-test data can tell us absolutely nothing about the e-folding time, which is the time constant of the natural exponential decay in atmospheric concentration of a pulse of CO2 emitted into the atmosphere. This is the “several hundred years” you refer to. The e-folding time has nothing to do with the airborne lifetime of your average CO2 molecule. That’s turnover time, a separate question.

    Instead, the e-folding time is how long it takes the CO2 concentration to decay after the emission of a concentration-changing pulse … and that is not related to how long an individual CO2 molecule stays aloft. How long a CO2 molecule stays airborne is turnover time, as measured by bomb-test 14C. The “several hundred years” you reference is e-folding time, not turnover time.

    All the best to you,

    w.

  131. Bart says:
    November 22, 2013 at 10:31 am

    This is beside the point. I do not agree with your analysis, which is heavily influenced by the erroneous “mass balance” argument.

    No, it is quite essential and has nothing to do with the mass balance argument. Your reasoning starts with:

    1) dCO2/dt = (CO2eq – CO2)/tau + a*H

    But that is already a wrong start: the sinks don’t make any differentiation between CO2 from humans and from nature, thus there is no “fixed” amount of human emissions that resides somewhat longer in the atmosphere. The real uptake is:

    1) dCO2/dt = (CO2eq – (CO2+H))/tau

    And the decay rate depends of the difference between total CO2 and CO2eq at one side and tau.

    WIth a fast decay rate, total CO2 will decay fast to CO2eq and vv.

    But we see that CO2 is increasing over time at a rate about halve of the increase of H

    Thus either H is the cause of the increase of CO2 or as Bart and Salby says, tau is huge and a natural increase in circulation causes the increase in total CO2, thereby dwarfing H.

    But then, the increase in the natural circulation must follow the increase in H at exactly the same ratio over the past 50 years of accurate measurements. Which implies that the threefold increase of H over time is mimicked by a threefold increase in all natural emissions (and therefore natural absorbances) over the same period.
    For which there is no proof, to the contrary:
    - there is no such change in decay rate of 14C, which should be diluted much faster over time
    - the same for the 13C/12C ratio: no change in dilution.
    - there is no threefold decrease in the estimated residence time, even a slight increase over the most recent ones.

  132. Ferdinand, take off you chemistry hat for a moment and put a biology hat on.
    You state, “The only relative important carbon flux is by dead bio material dropping out of the surface layer”.
    Now let us do some numbers.
    The total marine biotic carbon mass is about 2 GtC.
    The flux of carbon through this 2 GtC is 55 GtC per year.
    The 55 GtC is converted to CO2 in the upper 5 m, or into dead matter or into fecal matter.
    Dead matter and fecal matter fall, on average, at something like 200 m per day.
    A fraction dead matter and fecal matter is intercepted on the way down, along all the depths, and is converted to CO2/CH4. Some fraction of dead organic carbon is mineralized, and joins the 15,000,000 GtC of Kerogens down there already.
    If CO2 was non-atmospheric and only existed as an aquatic species, as CO2/DIC, we know what the profile would look like, it would be much the same as phosphate;

    So phosphate is denuded at the surface, where photosynthesis is active. Organism take it up and it goes down in excreta and dead creature.
    Phosphate diffuses upward and sideways into areas where biotic productivity is high. With carbon the atmosphere provides an extra dimension of transport, CO2/DIC at the surface in areas of low biotic productivity and can be transferred to areas where CO2/DIC is low.
    The swings in the Keeling Curve show that atmospheric CO2 is a buffer for the marine surface, so when it is summer over the productive ares, CO2 goes down, and when it is winter, the atmospheric CO2 goes up.
    Nothing to do with Henry’s Law at all.

  133. Bart says: November 22, 2013 at 10:31 am
    “Nick Stokes says: November 21, 2013 at 7:36 pm

    ‘They say the plant reservoir has diminished by 15 Gtons C. They aren’t sure that it’s down – the range is -45 to +15.’

    Basically, what you are saying here is, they haven’t really got a clue.”

    Not at all. They are saying that the amount of vegetation has changed very little. They think there is a little less, but it could be a little more.

    What they are saying, with great confidence, is that vegetation has not absorbed any significant part of the 400 Gt C that we have burnt. So where has it gone?

  134. ” Willis Eschenbach
    The largest migration on earth (in tonnes of living creatures) is the nightly migration of billions of sea creatures from their daytime depths of around 200-400 metres up to near the surface where they feed, and then back down to the deep ocean again.”

    Willis, after they, they descend, digest and defecate.
    Note also that averaging over days the concentrations of biological’s, with respect to depth, ignores daily movements of predator and pray.

  135. John Whitman: “Your calm and civil response on one of those other threads to being called a troll is a classic.”

    Thank you for the kind words. In Lord M’s defense, though, I have to confess that as an uncredentialed dilettante I had resorted to being (only slightly) provocative in order to make sure the issue got his full attention. He is a valuable asset, and it’s worth a little effort to prevent his persistence in that error from compromising his effectiveness.

  136. Willis Eschenbach says:
    November 22, 2013 at 12:45 pm

    “Unfortunately, the bomb-test data can tell us absolutely nothing about the e-folding time, which is the time constant of the natural exponential decay in atmospheric concentration of a pulse of CO2 emitted into the atmosphere. This is the “several hundred years” you refer to. The e-folding time has nothing to do with the airborne lifetime of your average CO2 molecule. That’s turnover time, a separate question. “

    Not necessarily so. Consider this analogy.

    We have a bucket of water. It has an inflow from a hose, and an outflow from a hole or drain in the bottom. The rates of the two are balanced so that a particular level of water has been established in the steady state.

    Now, we add a little blue dye at the surface. This blue dye will diffuse throughout the bucket over time. We measure the blueness of the top cm or so (assume the bucket is several cm deep). The blueness of the water will decrease over a timeline associated with the rate of diffusion, which bears little relation to the rate at which water is flowing out of the drain.

    So far, so good, and in perfect accord with what you have stated. BUT, there is a hidden assumption here. That assumption is that the drain is weak, and the rate of outflow is slow relative to the diffusion.

    If the drain is powerful, and the rate of inflow proportionately also powerful in order to establish the steady state level, then the draining of fluid in general will dominate the diffusion process, and the rate at which the blueness of the upper cm decreases will be reflective of the rate at which all the water drains away.

    So, the question before us is, as always, is our “drain” weak, or powerful? If Salby is correct, and I am convinced that he is, then the “drain” is powerful, and it is quite likely that your turnover time and e-folding time are approximately the same.

  137. Rob: “Equation 3 is not dimensionally correct. e14e has units of ([m]/[t])^2. LHS is in units of [m]/[t]”

    My original equation corresponding to Equation (4), too, was rendered “dimensionally challenged” in hte way I described above in connection with Equation (3): the cosmogenic carbon-14 fraction c should replace the carbon-14 mass e14.

  138. Ferdinand Engelbeen says:
    November 22, 2013 at 12:58 pm

    “But that is already a wrong start: the sinks don’t make any differentiation between CO2 from humans and from nature…”

    You really could have stopped right there and said “I do not understand your equations.” It would have been a lot shorter.

    “Thus either H is the cause of the increase of CO2 or as Bart and Salby says, tau is huge…”

    For fast response, tau is small. But, you have already conceded that the “mass balance” argument depends on the response time. And, arguing that the response time is slow because the mass balance says it must be is a circular argument.

    “But then, the increase in the natural circulation must follow the increase in H at exactly the same ratio over the past 50 years of accurate measurements. “

    No, it must simply overwhelm it. This is typical feedback system behavior.

    Nick Stokes says:
    November 22, 2013 at 1:03 pm

    “…the range is -45 to +15…”

    So, it could have increased by a factor of 3, according to their calculations? Am I reading this wrong?

    “What they are saying, with great confidence…”

    95%? Do you have any idea what my level of confidence is in their levels of confidence?

  139. Willis Eschenbach says:
    November 22, 2013 at 12:05 pm

    Since they are eating at or near the surface, and then returning to the depths each night, the nightly migration is one of the generally overlooked transport pathways in the full carbon cycle, although there is some research in that area.

    Thanks for that interesting info! Should make it as “dead and alive” material dropping out of the surface layer… Seems that BATS is involved, should have given a follow-up with more information by now…

  140. Ferdinand Engelbeen – I suspected that we were at cross purposes but couldn’t put my finger on it. Now I have it (I think!). When I said that the Revelle Effect meant that the ocean could take up 10 times as much CO2, I was talking about quantity, and I used the unit “ton” in my example. You are talking about percentage: “an increase of 30% CO2 in the atmosphere gives an increase of 3% in total carbon (DIC) in the ocean surface layer“. Also, where I am talking about the surface layer, meaning the physical layer next to the atmosphere, you are talking about the ‘mixed layer’ which excludes things like upwellings and downwellings. You say “only ~0.5 GtC/yr is absorbed by the ocean’s mixed layer,[..] and ~3 GtC by the deep oceans“. Using those numbers, my argument is that 3.5 GtC is absorbed from the atmosphere by the physical surface layer, and 3.5 GtC of that then goes on to the deep. The reason I use the physical surface layer, not the ‘mixed layer’ is that the processes which cause CO2 to transfer between atmosphere and ocean cannot distinguish between the ‘mixed layer’ and the other bits – all it sees is the physical surface layer. CO2 cannot jump from the atmosphere into the deep without going through the physical ocean surface layer.

    So my argument stands. To make sure we are now clear on this, I’ll restate the mechanism:
    – Ocean uptake (say) of CO2 is driven primarily by pCO2 difference between physical ocean surface and atmosphere (Henry’s Law).
    – When CO2 is absorbed, pCO2 in the physical ocean surface layer goes up and in the atmosphere goes down, as they ‘aim’ for balance.
    – Once in the physical ocean surface, most of the CO2 then undergoes chemical change.
    – This reduces pCO2 in the physical ocean surface, thus allowing more CO2 to be absorbed.

    Jquip – As I trust the above makes clear, there is no deviation from Henry’s Law, in fact it is crucial to the equation. It also agrees entirely with your statement that “CO2, Bicarbonate and Carbonate are freely transposable to one another“. But AFAIK Bicarbonate and Carbonate do not affect pCO2, only CO2 does. I have been quite careful to distinguish between CO2 and C in my comments, and hopefully I haven’t mixed them up anywhere, eg,: “there is an ongoing transfer of C from the surface layer to the deep” and “THC is not the only mechanism by which CO2 or C gets from the surface layer to the deep ocean“. Note also that (a) the rate of uptake by the ocean may be quite different to ‘pure’ Henry’s Law because of the Revelle Effect, and (b) when the ocean emits CO2, the Revelle Effect acts as a multiplier there too.

  141. Bart says:
    November 22, 2013 at 1:23 pm

    You really could have stopped right there and said “I do not understand your equations.” It would have been a lot shorter.

    Sorry, it’s late here… Agreed that it boils down to a short or long(er) tau. But an estimated e-fold decay rate of ~50 years is somewhere between the two extremes you showed. Slow enough to allow the accumulation of a part of the human emissions and fast enough to give the thight following of CO2 levels after temperature during ice ages…

    No, it must simply overwhelm it. This is typical feedback system behavior.

    Sorry, but that can’t be true: the human input is not zero, it is about 3% of the natural throughput. If the human input increases a threefold and the increase in the atmosphere follows that at the exact same ratio over a period of 50 years, then the natural throughput must have increased a threefold over the same period to give the same effect.

  142. Lord Monckton:

    Since with Mr. Eschenbach’s help we may still have your attention, I’ll respond to a few of your comments.

    Monckton of Brenchley: “[Joe Born’s] equations (3, 4) are dimensionally challenged.”
    I believe you’ll find that the originals weren’t.

    Monckton of Brenchley: “however, as many have pointed out, for all relevant purposes the isotopes behave identically”
    If you study my work carefully, you’ll find that I have not assumed otherwise.

    Monckton of Brenchley: “his model of a dynamic object is unduly static”
    Although it’s true that I highly simplified things to set forth the principle, that principle does not depend on e and u’s being either constant or equal, and the fact that I did not intend such a limitation should have been evident from my following comment at JoNova’s, from which you abstracted my equations: “Also, if the emission rate p exceeds the sink rate, the total mass of atmospheric CO2 will rise until such time, if any, as the sink rate catches up, and, unless the sink rate thereafter exceeds the emission rate, the mass M will remain elevated forever.”

    It’s true that I additionally set forth a thought experiment in which e and u were kept equal in order to make m a constant and therefore make Equation (3) into a linear equation whose solution could be obtained by inspection. But nothing else depended on that relationship.

  143. Mike Jonas: ” But AFAIK Bicarbonate and Carbonate do not affect pCO2, only CO2 does.”

    That’s the problem in sum. The pCO2 you’re after for Henry’s is pDIC. Remember, at one instant in time one molecule is CO2, at another it is one of the other DIC’s. Statistically, in aggregate, for any given instant in time we can expect x% of the CO2 to be bonded up as Bicarbonate and y% as Carbonate. Between instants the same ratios will hold, but it won’t be the same molecules in the same state.

    With regards to partial pressure, we derive that from the moles of CO2 alone. But that doesn’t work here precisely as CO2 is getting itself merry at any given instant as one of the three DICs. And so partial pressure must be considered as the moles of DIC and not as the moles of dissolved CO2 that is — in this one and very instant CO2 — rather than one of the other conjugates. This confusion is where the claims of rate differences arise from.

    If this is not understood, or is held to be wholly wrong: I shall not refute it thus ::kicks rock:: But I’ll offer you and anyone else the opportunity to construct a lab table experiment that doesn’t put a tiny adjustment on Henry’s but entirely refutes it as the most wrong-headed thing to come across the pike. It’s an opportunity for any takes to claim a Nobel Prize for showing that Henry’s isn’t just wrong, but so wrong that it’s off on the order of 1:10 in the worst possible direction — despite that we’ve been using it, experimentally with success, for ages.

  144. Wow! I cant believe I’ve read the whole thing. (so far)
    Although I only understand about 10% of it, seeing my favorite Boffins thrashing out a chicken or egg question is fascinating.

  145. Lord M.

    Shall we agree that the halflife of added CO2 lies somewhere between 1 and 10 years depending on the magnitude of the negative feedback response of the biosphere to a change in CO2 and how much of the annual CO2 gap (missing CO2) is caused by additional uptake.

    Remember my analysis only considers delta CO2, positing that the biosphere removes 50% of any excess per annum based on the emission gap that exits the system over the year, since the excess removed is small, 50 % of emissions or about 3ppm – of the order of 0.75 percent of the total sinking capacity I think its consistent with a whole of atmosphere turnover of the order of 100 years. That the biosphere can respond to change in CO2 quickly and deeply doesn’t in my mind preclude a longer halflife for whole of atmosphere turnover. What it does suggest in my mind is that the turnover rate is being limited by the relative starvation of the biosphere for CO2, that is the sinking rate is saturated and turnover rate is not constant and should increase with CO2 level. This seems logical to me.

    By the way, the estimate of a 6 percent greening 2000 – 2012 (0.5 % PA) does seem to be broadly consistent with a 0.75% increase in CO2 sinking PA providing some evidentiary support that the missing CO2 is very possibly due to increased biological uptake.

  146. DocMartyn says:
    November 22, 2013 at 12:58 pm

    Okay, both hats were a little worn out, but I do follow your reasoning. Except for the last sentences:

    The swings in the Keeling Curve show that atmospheric CO2 is a buffer for the marine surface, so when it is summer over the productive ares, CO2 goes down, and when it is winter, the atmospheric CO2 goes up.
    Nothing to do with Henry’s Law at all.

    The swings of nDIC in seawater at the Bermuda’s between summer and winter (8 K difference) are around 30 μmol/kg, between 2030 and 2060 μmol/kg. Thus really, carbon availability is not an issue for biological life in seawater. See Fig. 4 in:

    http://www.biogeosciences.net/9/2509/2012/bg-9-2509-2012.pdf

    But the combination of temperature and biolife certainly influences the pCO2 in seawater in opposite ways. What we see at Bermuda is that pCO2 in summer is slightly above the pCO2 of the atmosphere during 2-3 months, while nDIC is at minimum. Thus temperature is the winning factor in seawater, despite the increased biological activity in summer, that a part of nDIC removed. Another part is emitted from the oceans into the atmosphere durign that period. The rest of the year the oceans near Bermuda are net absorbers for CO2 from the atmosphere.

    The seasonal swings in the atmosphere are caused by land plants, which are far more abundant in the NH than in the SH where the seasonal swings are much smaller…

    And if you look at the trends in Fig. 5, nDIC increases with about 10% of the increase in the atmosphere, the combination of Henry’s law and the Revelle factor still at work, despite all biological activity…

  147. Jquip – As you say, “With regards to partial pressure, we derive that from the moles of CO2 alone. But that doesn’t work here precisely“. and you refer to “a tiny adjustment on Henry’s“. In other words, the process is as I describe it, but there is a tiny variation from what could be expected from Henry’s Law and the actual CO2 concentration. A tiny variation doesn’t affect the argument.

  148. Jquip says:
    November 22, 2013 at 2:13 pm

    That’s the problem in sum. The pCO2 you’re after for Henry’s is pDIC.

    Wait a minute, something like pDIC doesn’t exist. It is pCO2, as Henry’s law is only for the solubility of gases. As bicarbonate and carbonate are not gases, they don’t play any direct role in pCO2 or Henry’s law. But they do play a very important indirect role.

    Remember, at one instant in time one molecule is CO2, at another it is one of the other DIC’s. Statistically, in aggregate, for any given instant in time we can expect x% of the CO2 to be bonded up as Bicarbonate and y% as Carbonate. Between instants the same ratios will hold, but it won’t be the same molecules in the same state.

    All transformations between free CO2, bicarbonate ions and carbonate ions are equilibrium reactions dependent of pCO2 in the atmosphere at on side and H+ ions (pH) at the other side.

    If pCO2(atm) is higher than pCO2(aq), then CO2 is pushed into the oceans, if it is reverse, then CO2 is pushed out of the oceans. In all cases, an 100% increase of CO2 in the atmosphere will give you a 100% increase of free CO2 in the ocean surface.
    But free CO2 is less than 1% of total DIC in seawater, thus in first instance a 100% increase of CO2 in the atmosphere will increase total DIC only with 1% (that happens if the buffer was saturated).
    But as we have equilibrium reactions, more CO2 in solution pushes the reactions to more bicarbonate and more carbonate ions. But that also gives more H+ ions, thus the pH lowers, pushing the equilibrium reactions back towards bicarbonate and free CO2.
    The net effect is that the original 1% increase in DIC gets up further to 10% when everything is again in equilibrium. That is the Revelle factor…

  149. Ferdinand Engelbeen says:
    November 22, 2013 at 2:01 pm

    “If the human input increases a threefold and the increase in the atmosphere follows that at the exact same ratio over a period of 50 years, then the natural throughput must have increased a threefold over the same period to give the same effect.”

    The difference between sources and sinks has to have increased threefold. But, that is only a constraint on the difference, and that difference is dynamic, as the sinks respond to source activity.

  150. Ferdinand: “All transformations between free CO2, bicarbonate ions and carbonate ions are equilibrium reactions dependent of pCO2 in the atmosphere at on side and H+ ions (pH) at the other side.”

    Ah, no. This is a complete misunderstanding. And I’ll say the same thing to you as I said to Mike Jonas: Grab the Nobel Prize and produce an experiment that demonstrates it. This is not some queerly confounding construction such as the whole of the climate — it is something as simple as what can be trivially constructed on a lab table.

    And if there’s any validity — proper empiricism — behind what you’re stating then you don’t get the Nobel Prize, but you do know how to link every reader of this thread to the lab-table experiment they can do themselves. If it has not been properly validated by experiment then: Shut up. Go design it and win the Nobel Prize. But if you’re not interested in international fame and glory then you need to get your head around the semantics of Henry’s that reduce the problem to partial pressure and why that is invalid when we’re speaking of the volatile equlibrium of CO2 as one of its various conjugates at any given instsant in time.

  151. Gunga Din says:
    November 22, 2013 at 12:36 pm

    So the “yes” is that it’s assumed there is no carbon14 in fossil fuels?
    Fossil fuels haven’t been tested for it?

    radiocarbon dating needed corrections for the years from 1870 on and later, due to the “thinning” of the normal production rate of 14C in the atmosphere by the use of fossil fuels.

    The difference anyway is used today to calculate the biogenic fraction of fuels:

    http://www.rug.nl/research/isotope-research/projects/biogenic-carbon-determination

    and

    http://www.rug.nl/research/isotope-research/projects/sannemeasurements.pdf

  152. Bart says:
    November 22, 2013 at 3:08 pm

    The difference between sources and sinks has to have increased threefold. But, that is only a constraint on the difference, and that difference is dynamic, as the sinks respond to source activity

    As there is no difference in sink rate for “human” CO2 and “natural” CO2, only an increase of the natural emissions at the same rate as the human emissions will give the same result…

  153. Ferdinand Engelbeen says:
    November 22, 2013 at 3:37 pm

    “As there is no difference in sink rate for “human” CO2 and “natural” CO2, only an increase of the natural emissions at the same rate as the human emissions will give the same result…”

    Incorrect. Total sinks expand in response to increased forcing from either source. If natural forcing is dominant, then dominant sink expansion will be in response to natural forcing.

  154. I am disappointed that nobody, especially Willis, has commented on my post here. I think it clears up a lot of confusion regarding the 14C results using a simple analogy.

  155. If you follow the long line of links from the link at the top of Monckton’s post you get to an article by Solomon et al in PNAS in 2008. They do many things in the paper, but they have estimates of the the amount of future conc’s of CO2 in the atmosphere. Needless to say, the decreases do not match Monckton’s. The reason is that Monckton is looking at an isotope that is not in equilibrium with the CO2 in the fixed carbon; his isotope goes into a very large pool of carbon, much much larger than the CO2 in the atmosphere (afterall, which is measured in ppm). So of course it’s quickly diluted, never to be seen again at measureable amounts.

    The IPCC is not interested in the residence time of individual molecules of CO2, they are interested in the resisdence time of the high CO2 levels….These will someday in the long future go down as they are absorbed into the oceans (not good, actually). And this is measured in 1000 year half lives. Not 12 or what ever Monckton’s half life is. (hmmm, should I reword that…nah)

    The point is that Monckton’s calculations has nothing to do with the IPCCs worries and they are completely silly. Apples and oranges.

    And BYW, I really like Hans Erren’s analogy, it is perfect. I was going to use one with blue dye in tide pools, but his is better.

  156. Jquip says:
    November 22, 2013 at 3:27 pm

    The solubility of CO2 at 1 bar in fresh water at 20°C is 1.7 g/l or a DIC of 0.46 g/l
    The solubility of sodium bicarbonate in fresh water at 20°C is 90 g/l or a DIC of 12.8 g/l
    or an 28-fold.

    The difference between the two solutions:
    - 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.
    - the bicarbonate solution still is not saturated with CO2 and no CO2 escapes from the solution. If one applies 1 bar CO2 pressure, more CO2 will get into solution. Until the pCO2 of the solution also gets 1 bar. That is at about 0.46 g/l free CO2 DIC to satisfy Henry’s law. As free CO2 is less than 1% of DIC, total DIC then may reach 46 g/l. The Revelle factor in this case is very low and a 100% change in CO2 above the solution will give about a 100% increase in DIC. The solution is slightly alkaline.

    In both cases DIC exists in all three forms: free CO2, bicarbonate and carbonate. But the ratio between them is completely different.
    In CO2-only 99% is free CO2, the rest is bicarbonate and hardly any carbonate
    In the bicarbonate solution, 1% is free CO2, most is bicarbonate and some is carbonate

    Thus Henry’s law shows how much CO2 resides in solution as free CO2 for a given temperature and CO2 pressure in the atmosphere with or without buffer capacity, regardless of pH.
    In the case of fresh water that is all CO2 that gets in the water
    In the case of the bicarbonate solution, far more CO2 gets in the water but then is transformed to bicarbonate and carbonate. That is the Revelle factor.

    Now slowly add acetic acid to the bicarbonate solution. In first instance, nothing happens. Then at a certain moment CO2 bubbles start to form and continu to bubble up until very little CO2 is left in solution. During the whole time DIC decreases, the Revelle factor increases, but Henry’s law remains intact at all times as until the last moment the same amount of free CO2 is present in solution for the same CO2 pressure in the atmosphere above it.

  157. Bart says:
    November 22, 2013 at 4:07 pm

    Incorrect. Total sinks expand in response to increased forcing from either source. If natural forcing is dominant, then dominant sink expansion will be in response to natural forcing.

    Let us formulate it different: Natural forcings are dominant, thus human emissions follow the same fate as the natural emissions. As we see that both human emissions and the net sink rate increased about threefold over 50 years time, that means that the natural emissions also increased a threefold over time.

  158. The other thing about this discussion is that reminds of an argument I had with three engineers from Dow Chemical many years ago on a long bike ride. My question was what was the speed of the top of a bicycle wheel relative to the speed of the bike. They were going into calculations and pi R square and sin tan and diameter and on and on and they could not really answer the question. And they didn’t believe it when I finally told them the answer but what’s new…

    But you don’t need math to answer that question anymore that you need it for Monckton’s question. The math seems like it’s used just to obfuscate.

  159. Pippen Kool says:
    November 22, 2013 at 4:19 pm

    And this is measured in 1000 year half lives.

    And that is nonsense for the foreseeable long future. The current decay rate is ~50 years e-fold time. There is no saturation of the deep oceans in sight, neither of vegetation (which is an unlimited sink).

  160. 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.

  161. Ferdinand Engelbeen says:
    November 22, 2013 at 4:35 pm

    You are mixing models. You are comparing one essentially without dynamic feedback, that with direct accumulation of human inputs, to one with strong dynamic feedback, that in which human inputs are quickly sequestered and natural forcing dominates.

  162. 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.

  163. 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.

  164. 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.

  165. 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.

  166. 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.

  167. 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.

  168. @ 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! #(:))

  169. 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.

  170. 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?

  171. Bart says:
    November 22, 2013 at 4:09 pm

    I am disappointed that nobody, especially Willis, has commented on my post here. I think it clears up a lot of confusion regarding the 14C results using a simple analogy.

    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.

  172. 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?”

  173. 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…

  174. 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:

    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.

  175. 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”.

  176. 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.

  177. 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.

  178. 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.

  179. 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.

  180. 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.

  181. 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.

  182. 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.

  183. 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.

  184. 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.

  185. “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.

  186. Lubos Motl says:
    November 22, 2013 at 11:15 pm

    ”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.

    …Which of it was put there last week or in 1963 is irrelevant.”

    To tell the truth, I am not sure exactly where you are coming from. It definitely matters which of it was put in when, and from what source. What came in last week, or in 1963, added to the current pool which drove the sinks to their current level of activity. Maybe there is a clue in your initial statement:

    ”The URL beneath the “bilge” says that the magnitude of sinks depends on the annual emissions, both natural and anthropogenic ones.”

    It depends on the time weighted accumulation of emissions, which is the current concentration. The toy equation I have given previously is

    dCO2/dt = (CO2eq – CO2)/tau + a*H

    CO2 = atmospheric concentration
    CO2eq = equilibrium concentration
    tau = time constant
    a = fraction of integrated H which stays in the atmosphere after fast equilibration with other reservoirs
    H = human input rate

    The sink activity is -CO2/tau. But, CO2 is partially dependent on H, the anthropogenic input. For this particular system, dCO2/dt – H < 0 with H greater than 0 is not even an observation when tau is “short”, it is a tautology:

    dCO2/dt – H = (CO2eq – CO2)/tau + (a-1)*H

    But, tau short implies CO2 := CO2eq + tau*a*H is the approximate solution, hence

    (CO2eq – CO2)/tau + (a-1)*H := -H < 0

    yet clearly, as tau approaches zero, H approaches zero effect on CO2.

  187. Wu, the answer is that molecules of CO2 in the atmosphere are constantly being exchanged with CO2 from the oceans and terrestrial biosphere, which predominantly contain the lighter isotopes 12C and 13C. 14C on the other hand is produced (in tiny quantities) naturally by the action of cosmic rays and it undergoes radioactive decay fairly rapidly (on a geological time scale). This means that the oceans and terrestrial biosphere contains very little 14C.

    Now when the bomb 14C02 is exchanged with C02 from the oceans and terrestrial bioshpere, it is almost certainly going to be with 13CO2 because that is what those reservoirs predominantly contain. This means that 14C rapidly decays out of the atmosphere as it is REPLACED with 13C.

    A molecule of 13CO2 when it is exchanged with CO2 from the oceans and terrestrial biosphere is also almost certainly going to be with 13CO2 because that is what those reservoirs predominantly contain. This means that the level of 13CO2 stays broadly the same (unless the carbon cycle is perturbed, for instance by fossil fuel emissions).

    The key point to bear in mind is that the very large fluxes into and out of the atmosphere means that individual molecules only stay in the atmosphere for about four or five years (the residence to turnover time) before being exchanged with CO2 from the other reservoirs. However this exhgange doesn’t affect the total amount of CO2 in the atmosphere as it is a straight swap. The residence time depends on the total VOLUME of the flux out of the atmosphere. The rate at which atmospheric CO2 changes on the other hand depends on the difference between total emissions and total uptake (as Prof. Salby says), and that governs the adjustment time, which is an enturely different thing.

  188. Everything comes down to the efficacy of the sinks.

    If they are very powerful, then the bomb test indicates the removal rate for all CO2 being sunk.

    If they are very weak, then the bomb test indicates the time for dilution due to diffusion into the various reservoirs.

    The fact that CO2 is dominated by temperature dependent forcing and not by human inputs argues forcefully that the sinks are, in fact, quite powerful.

    This being the case, the bomb test is more likely representative of the rate of removal of all CO2.

  189. Monckton of Brenchley says:
    November 23, 2013 at 12:52 am

    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%?

    My thanks, Lord Moncton, I do like a man who asks interesting questions.

    Per your Figure 1 above, the formula for the remaining fraction f of 14C after a number of years T is

    f = e( T/14 + 0.015 ) / 1.015

    However, that formula contains both an error and an oddity.

    The error is that they’ve left out a minus sign, and the formula should be:

    f = e( -T/14 + 0.015 ) / 1.015

    The oddity is that this is only microscopically different from the usual formula for exponential decay, which is

    f = e( -T/tau ) (Equation 1)

    where “tau” is the time constant, in this case 14.

    The difference at one year is 0.0001, and decreases with increasing time T.

    So I will compute this using the normal formula, and not their odd formula. Solving Equation 1 for T, we get:

    T = -tau Ln(f) (Equation 2)

    where “Ln” is the natural log to the base “e”.

    This allows us to answer all of your questions. IF the remaining fraction is 0.5, 0.7, and 0.9, then

    T (years) = -tau * Ln(f) = -14 * Ln(.5) = 9.7 years
    T (years) = -tau * Ln(f) = -14 * Ln(.7) = 16.9 years
    T (years) = -tau * Ln(f) = -14 * Ln(.9) = 32.2 years

    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 have calculated tau as 38 years for the e-folding time for the exponential decay of an injected pulse of CO2. I calculated tau as an optimized value to match actual emissions and atmospheric concentrations. Given that tau is 38 years, in parallel with the earlier example we find:

    T (years) = -tau * Ln(f) = -38 * Ln(.5) = 26.3 years
    T (years) = -tau * Ln(f) = -38 * Ln(.7) = 45.8 years
    T (years) = -tau * Ln(f) = -38 * Ln(.9) = 87.3 years

    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.

    I do not find any “futile semantics”. I find the conflation that bedevils this issue all over the web. People think there is one “residence time”, and they conflate the turnover time and the e-folding time. They either think they are the same, or they think one means something about the other. They are totally different, independent measures, and one means nothing about the other.

    You asked Prof. Salby what the bomb test results showed about the e-folding time of an injected pulse. He claimed, and you seemed to agree, that they supported some particular value or another.

    I disagree with both you and Prof. Salby. I still hold that the bomb-test results (turnover time) tell us nothing about the e-folding time of an injected pulse. Nor does the e-folding time of a pulse tell us anything about the turnover time (bomb-test results). The turnover time is not in dispute, and never has been. The e-folding time of a pulse, however, is the subject of much debate.

    My best to you,

    w.

  190. ‘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.’ Lord Monkton.
    With some credit to PK this was in a TV interview,from memory,of Professor Flannery,on an ABC Australia news bulletin.
    If my memory serves me correctly, he said that the CO2 we emit now could change the climate for up to one thousand years, presumably by the multiplier effects written into the GCM’s, but not a half life, but not stated, and using the word ‘could’, so open to any interpretation.
    This is a far cry from an instantaneous half life of twelve years as shown by the C14 decay curve after the Monte Bello nuclear tests.
    I still struggle to understand why, if the half life of CO2 in the atmosphere, which affects the climate,is 50 years,why has not some of the marker C14, in proportion to the dilutions caused by uptakes and inputs,made it back into the atmosphere?
    Since the tests occurred in the 50′s there has been more than a single half life.

  191. Mr. Eschenbach:
    “T (years) = -tau * Ln(f) = -14 * Ln(.5) = 9.7 years
    T (years) = -tau * Ln(f) = -14 * Ln(.7) = 16.9 years
    T (years) = -tau * Ln(f) = -14 * Ln(.9) = 32.2 years”

    Did you instead intend 9.7, 5.0, and 1.5?

  192. Myrrh says:
    November 23, 2013 at 3:20 am

    1. Carbon dioxide is being constantly washed out of the atmosphere as carbonic acid.

    Myrrh, fresh water may absorb some CO2, but with 0.0004 bar in the atmosphere the quantities are very low. I calculated it some time ago: if the rain absorbs CO2 to saturation at the (cold) place of formation, drops to the ground and evaporates again, 1 mm of rain (1 l/m2) will give an increase of 1 ppmv in the first meter (1 m3) of air. That is all. Simply negligible…
    The term “acid rain” was used for precipitation containing SO2 and NOx giving a much lower pH to rainwater than from CO2 (and effectively reducing the CO2 content, due to the lower pH!).

    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.

    That is right of emitted pure and in huge quantitities. Without wind it will not readily disperse in the rest of the atmosphere. But most of the (human and natural) sources of CO2 are relative small and/or already diluted when emitted. These quantities are reasily dispersed in the rest of the atmosphere, where similar levels ae found from sealevel to the lower stratosphere over the oceans and from a few hundred meters to the lower stratosphere over land.

  193. stevefitzpatrick says:
    November 23, 2013 at 4:47 am
    Supported by Joe Born…

    Ferdinand Engelbeen,
    You sir, continue to amaze me.

    Thanks for your kind words…

    I was once one of the early users of the Internet (begin 1990′s) and saw that it was used by a lot of activist groups while the industry was completely absent on that new medium.
    Because I was working in the chlorine/VCM/PVC industry at that time (oh horror, chlorine = dioxins!), I defended my job based on my own knowledge of what happened in the factory I was working for in a few discussion groups (like Dioxin-l).
    You may try to imagine the kind of reactions I received there. But they were worse than you ever can imagine. Despite that, I simply confronted them again and again with facts and could convince a lot of the more moderate people, never mind the fanatics, who never will be convinced.

    Anyway I learned a lot of these discussions by simply ignoring any personal insults and keep myself on the facts where I have some knowledge of. That seems the best way to convince people, except some people who never will be convinced anyway…

  194. Bart says:
    November 23, 2013 at 10:39 am

    Everything comes down to the efficacy of the sinks.
    If they are very powerful, then the bomb test indicates the removal rate for all CO2 being sunk.
    If they are very weak, then the bomb test indicates the time for dilution due to diffusion into the various reservoirs.

    Besides that the 14CO2 decay rate of ~14 years is in fact a mix of a decay rate and the residence time (as diluted by 14C poor deep ocean water), the 14 years is not particularly fast.

    As Gösta Petterson calculated, with a decay rate of 14 years, about halve the atmospheric increase is from humans, the other halve by nature. To decrease the human emissions to near zero, you need to increase the natural emissions/sinks a lot over time, but that should be visible in the 14C/12C ratio too. But there is no change in the sink rate of 14CO2 over the past 50 years…

  195. Ferdinand Engelbeen says:
    November 23, 2013 at 2:25 pm

    14 years is plenty fast enough to keep the human contribution to less than 10% of the overall rise. Less than 10% is insignificant.

  196. Willis Eschenbach says:
    November 23, 2013 at 12:28 pm

    “I still hold that the bomb-test results (turnover time) tell us nothing about the e-folding time of an injected pulse. “

    You really should read through my analogy above. It’s all a question of how powerful the sinks are.

  197. Monckton of Brenchley says:
    November 22, 2013 at 3:33 am

    I did not set the rate constant k to zero. It is used in the final equation. The point was to deal with a fixed value of 14CO2 derived from cosmic rays. You did point out a flaw that I have since dealt with. See http://wattsupwiththat.com/2013/11/22/excerpts-from-salbys-slide-show/#comment-1482818. The steady state of 14C should be kept as N/k, but understand N was somewhat arbitrary, so effectively I let N stand for N/k (an implicit substitution). Using N/k instead, C would have been N/k + X. The meaning of N then was what I said, a steady rate of 14CO2 input, leading to a stable amount equal to N/k. So equation 15 is still correct.

    That said, DocMartyn is right, I did not consider the “steady-state” being a ratio of 14C to 12C where 12C is increasing. I’ll have to do solve the equation for that model and refit the data.

  198. Bart says:
    November 23, 2013 at 6:19 pm

    Does it matter whether he gets it or not? Or, is he the canary in the coal mine to determine whether arguments are clear enough for a well educated person? Or do you want to determine is whether an argument is strong enough to crack through not just regular stubborn, but dadgum stubborn?

  199. Mr. Born sneers that “the math has proved so taxing” for me and suggests I am not capable of solving a differential equation. Yet my head posting simply reproduced his argument and that of Professor Pettersson, discussed possible implications for Professor Salby’s research, and asked whether readers thought Mr. Born or Professor Pettersson or the Bern model or the IPCC or “Skeptical Science” was correct. Since Mr. Born has reverted to the troll-like rudeness with which he began, I shall not comment further, except to note that Mr. Born now accepts that the relaxation time derived by Professor Pettersson from the bomb-test curve appears, after all, to be correct.

    Willis Eschenbach continues to fail to concede that Professor Pettersson had clearly defined his terms mathematically. He was wrong to accuse the Professor of not understanding the distinction between the relaxation time and the e-folding time, both in his response to the Professor’s original posting and then in his response to mine. He now says there is a confusion between these terms “all over the Web”: however, there was no such confusion either in the Professor’s posting or in mine. We can perhaps agree that it is unfortunate that the IPCC itself uses “residence time” to apply both to relaxation time and to adjustment time; but the mathematical definitions of the Professor were precise.

    Mr. Eschenbach then takes issue with a missing minus sign on one of my diagrams. My apoloies. However, the text of equation (5) shows the minus sign clearly.

    He grumbles that he does not understand the Professor’s equilibrium constant: but it is clearly described, and its derivation and importance outlined, in the head posting.
    He expresses surprise that the Professor’s value for the equilibrium constant yields results remarkably close to using an unmodified exponential decay function. Yet that is inevitable, since the unmodified exponential decay function is the degenerate case of the decay function with an equilibrium constant where that constant is zero, and Professor Pettersson’s value is very close to zero at only 0.015, which is the ratio of the IPCC’s estimates of the contents of the atmospheric to its estimates of the contents of the combined biosphere and hydrosphere sinks.

    The importance of allowing for the equilibrium constant was explained in the head posting: it is that the Bern Model’s value for that constant is 0.217, which would imply that about a fifth of any CO2 emitted to the atmosphere over and above the presumed equilibrium value 280 ppmv would remain in the atmosphere indefinitely. That does make quite a difference to the decay curve, compared with Professor Pettersson’s real-world equilibrium constant of only 0.015.

    The difference between the Professor’s calculations based on the bomb-test curve and those of Mr. Eschenbach turns out to be smaller than the difference between those of the IPCC and those of Mr. Eschenbach.

    Based on the bomb-test curve half of the excess 14CO2 would be gone in 10 years, 70% in 17 years and 90% in 32 years. Mr. Eschenbach’s values for all anthropogenic CO2 are 26, 46 and 88 years respectively from the point at which all our emissions cease (which they will, but probably not until the fossil fuels have run out). We can perhaps end by agreeing that the hundreds or even thousands of years mentioned by the IPCC and others are more than somewhat on the high side. I should really have asked him what he reckons the IPCC’s corresponding values would be.

    Finally, it would be mightily discourteous of me not to thank Bart for his persistence in answering numerous erroneous points made by other commenters. He concludes, by his own method, that there is a statable case that a significant fraction of the excess of Co2 over the presumed pre-industrial equilibrium arises not from anthropogenic emission but from temperature change, and considers it possible that the bomb-test curve may after all be as applicable to 12C and 13C as it is to 14C.

    Who is correct? As I said in the head posting, it is not for a mere layman like me to say. But it does seem that the IPCC – as so often – appears to have exaggerated.

  200. Monckton of Brenchley: “Mr. Born now accepts that the relaxation time derived by Professor Pettersson from the bomb-test curve appears, after all, to be correct.”

    What I accept-and have never disputed–is that the bomb-test evidence should indicate the “turn-over time,” defined by the IPCC according to Mr. Eschenbach, as “the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M/S.” Indeed, you reported in the head post that I positively asserted this by paraphrasing me thus: “[T]he excess 14CO2 concentration . . . would . . . decay with a time constant m/u.” And I have no reason to doubt Professor Petterson’s 14C02 curve from which ought to be able to infer that quantity. You also accurately represented my position that this “tells us nothing about how long total CO2 concentration would remain at some higher level to which previously-elevated emissions might have raised it,” and I have yet to find a reason for abandoning that position.

    I have found the discussions of “relaxation time” too confusing to take a position on that.

    Finally, I am the last person to sneer at another’s difficulty with mathematics; to paraphrase Gene Fowler, I have to stare at equations until drops of blood form on my forehead. I was merely disappointed that it had prevented us from making more progress.

  201. Bart says:
    November 23, 2013 at 9:55 am

    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.

    Bart, good to hear from you. Perhaps what you say is true, perhaps not … but since here in the real world the turnover (molecular atmospheric residence time constant) is 14 years, and the e-folding time of an injected pulse is three times that at ~ 40 years or more, I don’t see why that matters.

    w.

  202. Lord Monckton, thank you for your response. Since I’ve answered your questions, perhaps you could answer one of mine. I refer to your comment cited above:

    First, I [Christopher Monckton] asked [Murry Salby] whether the rapid, exponential decay in carbon-14 over the six decades following the atmospheric nuclear bomb tests had any bearing on his research. He said that the decay curve for carbon-14 indicated a mean CO2 atmospheric residence time far below the several hundred years assumed in certain quarters.

    I don’t understand the math involved in drawing any conclusion about the e-folding time of an injected pulse (the “several hundred years” you mention above) from the turnover time.

    We know the turnover time from the analysis of the bomb-test data. It has an e-folding time of 14 years.

    How does knowing that tell us anything about the response of the system to a pulse? What is the math connecting a 14 year time constant for the turnover of airborne molecules to the e-folding time of the decay of an injected pulse?

    So that’s my question. I showed you the math I used … now I’m asking for the math connecting the turnover time on the one hand, to the e-folding time of the decay of an injected pulse on the other hand.

    My best to you,

    w.

  203. Approximately 1/3 of all fossil fuel derived CO2 emissions are from transport. Another 1/3 or more from coal fired power stations

    During the period from 1980 to 1990 all vehicles around the world switched from emitting CO1 to CO2 with the introduction of the catalytic converter. Prior to this point, all petrol powered vehicle emissions consisted primarily of the deadly Carbon Monoxide, not the highly beneficial Carbon Dioxide.

    During this same period of time we also saw the rapid industrialisation of India and China. Accounting for more than 1/3 of the entire global population.

    That is more than a third of the words 6.5 billion population industrialising and a third of the words CO2 emissions (transport) coming on line in the same short 10-20 year period.

    An “emission pulse” like nothing we’ve seen before or are ever likely to see again. Yet, there was no discernible signal, for these two massive simultaneous events, over and above the CO2 trend of 2ppm annual increase, already in place since at least the 1950′s.

    This unprecidented human derived CO2 “emission pulse” is simply missing from the CO2 record. There is no signal for human CO2 emissions in the data. None.

    That is a major problem the entire MMGW narrative.

  204. Willis Eschenbach: “We know the turnover time from the analysis of the bomb-test data. It has an e-folding time of 14 years.”

    Do you have an opinion on how solid that number is?

    I ask because, unless I got some nomenclature fouled up, that value seems around twice what the IPCC says (and I opined above) it would be. As you said above, the IPCC defines turnover time as M/S, where M is total atmospheric-CO2 mass and S is its sink, or, in this post’s parlance, uptake, rate. And, ignorant of their definition, I had come to the same value (“m/u” after Equation (4) above) for the time constant of excess-carbon-14 removal.

    But this source http://en.wikipedia.org/wiki/Carbon_dioxide says M is 3160 gigatonnes, and this one http://en.wikipedia.org/wiki/Carbon_dioxide_in_Earth's_atmosphere says S is 450 gigatonnes per year. That would make the turnover time M/S equal 7 years, not 14.

    That’s what caused me to say above that “I may have found a flaw myself” in my own reasoning: the observed decay in excess 14CO2 seems to have taken twice as long as my reasoning would suggest.

  205. Willis,
    I think you do a great job of reminding people about the difference between turnover time and e-folding. It’s important and too little appreciated.

    But I don’t think it is the distinction here. The difference between them is really this. Turnover time is the rate CO2 would disappear if the return pathways were blocked. It’s the oneway rate. e-folding is the two-way rate, taking into account the rate at which it returns from the sinks. In this case C14 can return. So it is a version of e-folding.

    I think the clear mistake in the interpretation of Fig 1 is that it is a C14 fraction, ie ratio to C12. But to be an analogue for response to elevated CO2, it should be an absolute concentration, as if the C14 were diffusing independently, as it is. Now during the period of Fig 1, we’ve been pumping fossil C into the air that has no C14. So to get absolute C14 concentrations, the numnbers in Fig 1 should be converted.

    What is plotted is Δ = [(C14/C)_now-(C14/C)_1950]/(C14/C)_1950
    =1000*[(c14_now/C14_1950)/u-1]
    where u=(C_now/C_1950)

    u is the ratio by which total C in the air has increased

    What should be plotted is

    c14_now/C14_1950-1 = Δ*u+u-1

    Adding u-1, which cound be up to about 0.2 in this period, means the correct Δ will never return to 1. We knew that, because Δ would have changed even if there had been no bomb tests (dilution). That makes a very different story.

  206. Ferdinand Engelbeen says:
    November 23, 2013 at 1:28 pm
    Myrrh says:
    November 23, 2013 at 3:20 am

    1. Carbon dioxide is being constantly washed out of the atmosphere as carbonic acid.

    Myrrh, fresh water may absorb some CO2, but with 0.0004 bar in the atmosphere the quantities are very low. I calculated it some time ago: if the rain absorbs CO2 to saturation at the (cold) place of formation, drops to the ground and evaporates again, 1 mm of rain (1 l/m2) will give an increase of 1 ppmv in the first meter (1 m3) of air. That is all. Simply negligible…
    The term “acid rain” was used for precipitation containing SO2 and NOx giving a much lower pH to rainwater than from CO2 (and effectively reducing the CO2 content, due to the lower pH!).

    Ferdinand, I prefer calculations from the empirically established science on the subject which is as I have quoted example and which your post serves only to deflect from the point I am making.

    Water is the universal solvent, this is ignored in AGW’s claims about residence time of carbon dioxide in the atmosphere to the extent that rain, precipitation, has been written out of the AGW carbon cycle – this is absurd..

    All, pure, clean, natural unpolluted rain is acidic, because the water in the atmosphere has formed carbonic acid with any and all the carbon dioxide it meets.

    No matter how much carbon dioxide is introduced into the atmosphere, it will all be precipitated out in this – and – the residence time of water in the atmosphere is around 8-10 days.

    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.

    That is right of emitted pure and in huge quantitities. Without wind it will not readily disperse in the rest of the atmosphere. But most of the (human and natural) sources of CO2 are relative small and/or already diluted when emitted. These quantities are reasily dispersed in the rest of the atmosphere, where similar levels ae found from sealevel to the lower stratosphere over the oceans and from a few hundred meters to the lower stratosphere over land.

    Whether one molecule or thousands, carbon dioxide is heavier than air. It will not readily rise in air. It will always sink in air unless work is being done on it. That is its nature.

    These are the two basic reasons why the gazillion tons of carbon dioxide released into the atmosphere from countless fires and volcanic eruptions over millenniums are no longer in the atmosphere!

    Carbon dioxide cannot accumulate in the atmosphere because of its nature.

    It is immediately apparent that any claiming carbon dioxide ‘accululates in the atmosphere’ are not scientists, showing as they do an abyssmal absence of knowledge about the real physical properties and processes of real gases.

    This is all very well known in real science where such knowledge is crucial –

    “CO2 is invisible and odourless, so it is difficult to detect a growing concentration caused by leaks.
    Being heavier than air, CO2 does not dissipate easily.” (1)

    So, when ‘climate scientists’ claim ‘carbon dioxide is well mixed in the atmosphere’ then real scientists in countless disciplines involving gases, including such as traditionally trained meteorologists, know they are listening to physical nonsense.

    (1) http://www.boconline.ie/en/sheq/gas-safety/dispense-gas-safety/dispense-gas-leaks/dispense-gas-leaks.html

    That is my point, until these two immense natural processes are brought back into discussions on AGW there is no science of the natural world being discussed.

  207. Bart:
    I apologize for failing earlier to acknowledge your response to my comment about the dye analogy you presented. That response did indeed make what you intended clearer.

    To my way of thinking, though, ambiguities remain that frustrated my reducing it to mathematics. I thought of a way, but to me that way doesn’t seem very well to parallel what we know about the world, so it’s not likely what you had in mind. Additionally, the way I thought of involves some partial differential equations, which laymen like me don’t undertake lightly. (I remember finding the math challenging when I tried using them here http://wattsupwiththat.com/2012/07/13/of-simple-models-seasonal-lags-and-tautochrones/.)

    I won’t presume to ask you for a mathematical rendition of what you mean. Still, you may want to think about reducing your analogy to mathematics if you intend to use it further.
    In any event, I thank you for your response.

  208. Joe Born says:
    November 23, 2013 at 12:53 pm

    Mr. Eschenbach:

    “T (years) = -tau * Ln(f) = -14 * Ln(.5) = 9.7 years
    T (years) = -tau * Ln(f) = -14 * Ln(.7) = 16.9 years
    T (years) = -tau * Ln(f) = -14 * Ln(.9) = 32.2 years”

    Did you instead intend 9.7, 5.0, and 1.5?

    Actually, what I intended was:

    “T (years) = -tau * Ln(f) = -14 * Ln(.5) = 9.7 years
    T (years) = -tau * Ln(f) = -14 * Ln(.3) = 16.9 years
    T (years) = -tau * Ln(f) = -14 * Ln(.1) = 32.2 years”

    The log should have been of the remaining fraction, not the fraction absorbed.

    Many thanks,

    w.

  209. Bart says:
    November 23, 2013 at 6:19 pm

    Willis Eschenbach says:
    November 23, 2013 at 12:28 pm

    “I still hold that the bomb-test results (turnover time) tell us nothing about the e-folding time of an injected pulse. “

    You really should read through my analogy above. It’s all a question of how powerful the sinks are.

    Thanks, Bart. I tried that, and couldn’t see either what you were driving at, or what the outcome would be. Perhaps if you could explain it in real-world terms, rather than using an analogy of bowls and pipes, it might be easier to grasp.

    In addition, you keep saying if the sinks are “powerful” something different happens than if they are weak … if you could produce the math for that, and indicate where and how the transition happens, it would help.

    Finally, an exponential decay with a time constant of 38 years is hardly “powerful”, at least in my book. So I’m not clear what your claim has to do with the real world.

    I offer you the same invitation I offered Lord Monckton—produce the mathematics that links the turnover rate of an airborne molecule, with the decay rate of an injected pulse.

    I don’t think such a relationship exists. For example, we know that the sinks increase with the increasing atmospheric concentration … but for the turnover time, there’s no change in atmospheric concentration. So where is the relationship?

    If either you or Lord Monckton bring on the math, a connection between turnover time and e-folding time might be believable.

    Until then, I’m gonna stick with exponential decay for both, with no connection between the two …

    Many thanks,

    w.

  210. Joe Born says:
    November 24, 2013 at 4:17 am

    Willis Eschenbach: “We know the turnover time from the analysis of the bomb-test data. It has an e-folding time of 14 years.”

    Do you have an opinion on how solid that number is?

    I ask because, unless I got some nomenclature fouled up, that value seems around twice what the IPCC says (and I opined above) it would be. As you said above, the IPCC defines turnover time as M/S, where M is total atmospheric-CO2 mass and S is its sink, or, in this post’s parlance, uptake, rate. And, ignorant of their definition, I had come to the same value (“m/u” after Equation (4) above) for the time constant of excess-carbon-14 removal.

    But this source http://en.wikipedia.org/wiki/Carbon_dioxide says M is 3160 gigatonnes, and this one http://en.wikipedia.org/wiki/Carbon_dioxide_in_Earth's_atmosphere says S is 450 gigatonnes per year. That would make the turnover time M/S equal 7 years, not 14.

    That’s what caused me to say above that “I may have found a flaw myself” in my own reasoning: the observed decay in excess 14CO2 seems to have taken twice as long as my reasoning would suggest.

    If you use the calculation M/S, you’ll get the half-life rather than the e-folding time. Per Figure 1, this is 9.7 years. Since the values for the exchanges between the atmosphere and the ocean/biosphere/lithosphere are not well constrained, that is little different from the 7 years that you calculate.

    In terms of the solidity of the numbers, it is quite likely that the bomb-test results are more accurate that our estimates of e.g. the annual global flux from the atmosphere to the surface …

    w.

  211. Pippen Kool on November 21, 2013 at 2:08 pm
    “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?”Because you are looking at dilution of the 14C into the fixed carbon; the other isotopes are in equilibrium and won’t diminish.

    So you are refuting the whole basis of radiotracer measurement, a core methodology of biokinetics, nuclear medicine, industrial processes and countless other scientific disciplines? Why do people have such a hard time with the concept of a representative tracer? The only real question here is the representativeness of the bomb-generated 14CO2.

    Some of the bomb 14C may have been particle associated so would fall out quickly. But such is the nature of a thermonuclear detonation that both the combustion-gasification to CO2 and the vertical mixing into the atmosphere would have been highly effective.

    Put it this way, if an H bomb cant uniformly and representatively mix (labeled) CO2 into the atmosphere, then no human activity can.

    Half life = 0.693 x residence time
    Residence time = half life / 0.693

    I dont see the need for the pages and pages of discussion of this simple relationship.

  212. Willis Eschenbach:“[I]t is quite likely that the bomb-test results are more accurate that our estimates of e.g. the annual global flux from the atmosphere to the surface. ”
    Thanks a lot for that response. Your opinion accords with my gut feeling, but of course it’s reassuring that someone more conversant with the literature shares that feelimg.

    Willis Eschenbach: “If you use the calculation M/S, you’ll get the half-life rather than the e-folding time.”
    Thanks for that, too, although for me it’s bad news. To me it made sense for M/S to be the e-folding time. For it to be the half-life, not so much. Well, you win some, you lose some.

  213. Willis Eschenbach says:
    November 24, 2013 at 1:49 am

    <.I"…and the e-folding time of an injected pulse is three times that at ~ 40 years or more…"

    Says who? What measurement do we have that tells us this with assurance, comparable in SNR to the bomb test curve?

    Joe Born says:
    November 24, 2013 at 6:03 am

    Still, you may want to think about reducing your analogy to mathematics if you intend to use it further.”

    Consider the case where C14 is such a small portion of the total gase that it diffuses so that its relative concentration approximately obeys

    dC14/dt = -C14/tau_d

    But, C14 is also subject to the sinks, in proportion to how much there is, so that we have to add an additional term

    dC14/dt = -C14/tau_d – C14/tau_s = -C14/tau

    where tau = tau_d*tau_s/(tau_d+tau_s).

    The total time constant tau, which is what we observe in the bomb test, is composed of the diffusion time constant tau_d and the sink time constant tau_s by the same formula which tells us the resistance of two electrical resistors in parallel. You can think of it as the C14 always taking the path of least resistance.

    As in electrical circuits, the time constant which dominates is that which is smallest. If tau_s is much smaller than tau_d, then tau := tau_s, where the colon before the equals sign means “approximately equal”. Conversely, if tau_d is much smaller than tau_s, then tau_d dominates, and tau := tau_d.

    The size of tau_s quantifies the dynamic power of the sinks, i.e., how quickly they expand or contract in response to greater or lesser forcing. If tau_s is very long, then tau_d dominates, and the bomb test curve gives us no insight into tau_s. BUT, if tau_s is very short, then the bomb test curve is dominated by it, by the sink activity, which affects all CO2 molecules more or less equally.

  214. Half life = 0.693 x residence time
    Residence time = half life / 0.693

    CO2 half-life = 10 years
    Resdence time = 14.4 years

  215. Bart:

    I appreciate the valiant effort, but I’m afraid I’m unable to reconcile your math with your model.

    I hasten to add that I’m no scientist, so the comments below merely flow from my having dealt with a lot of technical experts over the years; you’ll probably want to trot your math by the smart guys. But here are my thoughts for what they’re worth.

    In the first place, the dye diffuses from the top of the bucket to the bottom, where the sink is, so the diffusion and outflow processes operate in series, not parallel.

    Second, while diffusion between two well-mixed reservoirs across a discrete boundary is exponential, what you have is diffusion through the height of bucket, which is more complicated; you can think of it as an infinite number of infinitesimal reservoirs disposed in series. For an example of calculating the result of an analytic solution (for simpler boundary conditions), see the math in the R code for that previous post of mine I mentioned, or, much better, consult a heat-transfer or other diffusion-relevant text.

    At the end of the distributed diffusion operation, i.e., at the bottom of the bucket, the sink operates to set one of the diffusion operation’s (time-varying) boundary conditions. For me that math would be too tricky to do analytically; I’d have to resort to a numerical solution–if I were inclined to attempt a solution at all. No doubt the scientists who frequent this site would be better able to point you in the right direction.

    Even so, I’m not convinced that analogy describes the carbon cycle well, although I can’t completely rule out being persuaded.

    As I said, though, you may want to shop that idea around to the experts.

  216. phlogiston says:
    November 24, 2013 at 9:52 am

    So you are refuting the whole basis of radiotracer measurement, a core methodology of biokinetics, nuclear medicine, industrial processes and countless other scientific disciplines?

    They use 14C of the nuclear tests to follow the fate of human induced CO2 in the (deep) oceans and in Antarctic firn and ice cores, together with CFC’s and some other human induced stuff. Much easier to follow than a slight difference in 13C/12C ratio…

    But that doesn’t say much about the value of 14C for the decay time of an excess amount of CO2 in the atmosphere, as there is a problem with the return rate of 14C from the deep oceans:

    For 12CO2, the current return rate is ~97% of what goes into the oceans.
    For 14CO2, the current return rate is ~60% of what goes into the oceans.
    That is because the long return time (~1000 years) between deep ocean sinks and sources.

    Which makes that the decay rate for a 14CO2 spike is a lot faster than for a 12CO2 spike (or total CO2, as 12CO2 is near 99% of all CO2).

  217. Willis.
    “If either you or Lord Monckton bring on the math, a connection between turnover time and e-folding time might be believable.

    Until then, I’m gonna stick with exponential decay for both, with no connection between the two …”

    I’ll take up that; the math is interesting. It’s basically dynamic equilibrium. You have a forward and back reaction; these settle into a sort of equilibrium which may be stable, or may shift. e-folding time is the half-life (actually, 1/e) style constant of the shift of the quasi-equilibrium (with forward and back) to zero. A complication – it may not go to zero.

    Turnover time is in wiki as residence time. It isn’t a half-life; it’s just the ratio of the forward reaction rate to what is there. It’s the time in which the stuff would vanish if the initial loss rate kept up with no back reaction of flow. Nothing exponential implied.

    e-folding is the time constant of the actual decay of a pulse, with forward and back reaction, assuming that it decays exponentially. People quote a similar number even if decay isn’t exponential. But if it doesn’t decay to zero at all, that is a problem. That is why the Bern model, say, doesn’t have just one such number.

    Pettersson’s curve is describing decay of a C14 pulse, and claiming it to be exponential. In that sense, he is talking about an e-folding time. If it were actually C14 concentration, he could argue that C would behave similarly, and so he would have the decay time.

    But he’s wrong. His Δ is derived from the C14/C ratio, and since that won’t return to its previous value, Δ won’t return to zero. It will become negative. The reason is that from fossil fuel, we have released a whole lot more C without C14. If there had been no bomb test, Δ would gave gone negative; probably to about -0.2. So his fit of an exponential doesn’t work.

  218. Lubos Motl on November 22, 2013 at 1:42 am

    Sorry, Lord Monckton, but the 10-year residence time of carbon-14 is clearly not the same quantity as the “residence time” of CO2 i.e. the timescale at which the excess concentration of CO2 decreases.

    The carbon-14 decreases this quickly because there are many “carbon-neutral” processes in which the carbon-14 is absorbed by the oceans or the biosphere and replaced by carbon-12. Even if the CO2 in the atmosphere were not decreasing at all (assuming we stop emissions), it would still circulate and the relative concentration of carbon-14 at all places would tend to converge to a uniform fraction. The timescale needed for the homogenization of the isotopes is clearly shorter than the timescale needed to reduce the overall CO2 which actually depends on excess uptake.

    It’s trivial to see that the residence time of CO2 is of order 30 years or longer. We emit 4 ppm worth of CO2 a year; the CO2 concentration increases by 2 ppm per year. 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. The excess CO2 above the equilibrium value for our temperature- which is still around 280 ppm – is about 120 ppm so one needs about 30 years to halve the excess CO2 and 50 years to divide it by e.

    - – - – - – - -

    Lubos Motl,

    I agree with your qualitative logic that the change over time of atmosphere composition of 14C from bomb testing is a different situation than the change over time of atmosphere composition of CO2 from a increase in CO2 from fossil fuels.

    That said, the 14C related atmosphere composition study gives valuable and precise flux information (as Willis suggests in November 24, 2013 at 9:12 am) from atmosphere to surface. Information that indicates the sinks are more powerful than is generally estimated from studies (supporting the Bern model) that were done without using a 14C study.

    John

  219. Joe Born says:
    November 24, 2013 at 1:03 pm

    “In the first place, the dye diffuses from the top of the bucket to the bottom, where the sink is, so the diffusion and outflow processes operate in series, not parallel.”

    That would be claiming that, if there were no diffusion, and the dye held together in drops, it would never exit the drain. But, assuming the drops are, at best, neutrally bouyant, it is eventually going out the drain.

    Think of the problem this way. The limiting case would be where the bucket had no bottom at all, and the flow rate is such that an entire bucket’s worth of water exits in one second. Then, in one second, the dye is gone – it never even got a chance to diffuse.

    It always helps to envision the reductio to extreme conditions to make things clear (no pun intended).

  220. Bart, Willis, and Lord M

    I agree with Bart here that there is a dynamic equilibrium and a static equilibrium at work. The Decay of C14 in the atmosphere does give us a clue about the rate of processing through sinks, but I think there are different effects at play with differing time constants, that probably act to increase the sinking rate transitorially. I think however Tau, (The decay time constant) is likely to be a function of the CO2 level and time rather than a simple constant. A Series of exponential decay functions acting together.

    In this (I might add – extremely interesting discussion) a number of quantities were examined, that each models in their own way. But I think we’ve been holding at least three different discussions.

    I and maybe Bart have been interested in how the sinks expand to consume added CO2. That is the second derivative of CO2 through sinks, what is the acceleration of CO2 sinking rate with respect to CO2 level.

    Willis and Lord M have been addressing what happens when one adds a pulse of CO2 to a static system where that pulse essentially doesn’t affect concentration, like adding a tracer dye to water. In this case the tracer both gets diluted by the extra CO2 entering the system and will appear to have a shorter time constant than expected by virtue of the fact that sinks may be expanding.

    I have to conceded that the Bomb test curve may well account most of the dynamic equilibrium (expansion of sinks) by virtue that it measures all effects, that is – being experimental the time constant of this curve likely incorporates the long term effect of sink expansions.

    I think we should however recognise that there are more than one decay curves at play here and the final level of CO2 is heavily dependent on the sinking rate and the change in the sinking rate with CO2 level, The analysis so far presumes that there will be a retained fraction for example, a hysteresis effect, but that depends on whether one approaches equilibrium from above or below.

    Consider the thought experiment, Assume a preindustrial level of forestation. (Possibly denuded due to burning, particularly in the northern hemisphere after the LIA) CO2 is in equilibrium at 280PPM. CO2 is brought up 50% to modern levels, Bioproductivity is up 30% of that, almost 15% , so biological sinks are more expansive and sinking 15% more CO2 than preindustrial, perhaps more from regrowth.

    Now in our thought experiment, suddenly take away the extra CO2 that’s maintaining the sinking capacity above preindustrial. What happens? The System is now out of balance, sinks exceed sources and CO2 falls precipitously until the sinks die off at a low CO2 level, since the CO2 is very low now the die off is great, and falls below the equilibrium state, (mankind dies out from lack of food), CO2 slowly rises equilibrium is restored at a level lower than but approaching preindustrial. This is a classic oscillatory response to a perturbation of a system containing a lagged negative feedback.

    I would really love for us to get together and work out math that better describes this process. I don’t intuitively think that either Willis or Lord M have the whole picture unless dynamic responses of feedback to the level of CO2 are properly taken into account.

    One more point, this is a dynamic system we are dealing with, simple scalar models are not very useful in describing the behaviour of systems with large numbers of time dependent responses. This is a warmist problem too, you can’t just add, feedback responses that differ in time/magnitude characteristic. The IPCCs net 3 gain in the climate suffers this problem, – it’s scalar, but what of the physical mechanisms, multiple effects involving water vapour, cloud, ice melting occurring over multiple time-frames with different lags. These are competing, and according to the IPCC, overwhelming negative feedbacks also operating at different again magnitudes and lags, and yet the IPCC concludes these will all add up to a simple scalar number, tada – 3 – with the positive feedbacks outweighing negative ones by 3:1.

    I might as well say “42″ I’d be just as close to the truth.

  221. Bart says:
    November 24, 2013 at 11:35 am

    Willis Eschenbach says:
    November 24, 2013 at 1:49 am

    <.I"…and the e-folding time of an injected pulse is three times that at ~ 40 years or more…"

    Says who? What measurement do we have that tells us this with assurance, comparable in SNR to the bomb test curve?

    Thanks for the question, Bart. I personally think it is on the order of 40 years because that is what I calculated. It was one of the first climate calculations I ever did, actually. It is a fit between the know (or estimated) emissions and the known (or estimated) change in CO2. I used data back to 1850, with ice core data for CO2 prior to 1959 and Mauna Loa data since, and CDIAC emissions for fossil fuel plus estimates of CO2 emissions from land use / land cover changes.

    I later found out that using similar data and methods, Jacobson came to about the same answer.

    Lord Moncton says Lindzen also says around forty years, although I don’t know how he’s gotten that answer.

    The problem is that to date, the datasets are not long enough to distinguish between two hypotheses. One hypothesis is the Bern model, the other is a simple single exponential decay model. But they give very, very similar answers. We need about another quarter century of data to be able to distinguish between the two hypotheses.

    w.

  222. This analysis is just plainly wrong. You’re comparing the response of a system to a pulse, to the response of that system to a constant input. No scientific ground at all. Period.

  223. Ferdinand Engelbeen says:
    November 24, 2013 at 1:15 pm
    phlogiston says:
    November 24, 2013 at 9:52 am


    For 12CO2, the current return rate is ~97% of what goes into the oceans.
    For 14CO2, the current return rate is ~60% of what goes into the oceans.
    That is because the long return time (~1000 years) between deep ocean sinks and sources.

    Which makes that the decay rate for a 14CO2 spike is a lot faster than for a 12CO2 spike (or total CO2, as 12CO2 is near 99% of all CO2).

    Thanks for the clarification. But this difference in return rates makes the 14CO2 data from the atmosphere more, not less, useful and precise. It means that we are measuring just removal only, not removal mixed up with recycling. That’s the whole point of a radiotracer kinetic measurement. This whole thread discussion seems to be predicated on profound confusion about what we really mean by a kinetic measurements. We want to know from the 14C bomb data just what the decay term of CO2 from the atmosphere is. Period. You cant reply to that and say “ah but we cant measure loss because there is always contribution happening at the same time”. You could just as well say – following your logic (and that of many others) to its conclusion, that “CO2 in the atmosphere is not getting any less, therefore there is NO loss of CO2 from the atmosphere at all – it really is an immortal Sky God”.

    It is precisely because H bomb 14CO2 is not recycled (or less recycled) that the measured 14C loss rate is an accurate measurement of CO2 loss from the atmosphere, and thus valuable scientific data. This is the basis of radiotracer measurement – to single out just one kinetic term of a complex recycling system with many kinetic terms. Because we are measuring loss does not mean that we do not believe that CO2 recycles to the atmosphere. In fact because there is some 14CO2 recycling from the ocean means only one thing – that the real loss of CO2 from the atmosphere is faster, not slower, than the measured 10 year half life / 14 year residence time.

    So the CO2 input to the atmosphere from the ocean is a significant factor. I guess that IF (a big if) the real rate of CO2 loss from the atmosphere was precisely known, then the difference between the 14CO2 removal rate and the total CO2 loss rate would allow us to pin down defintively the supply rate of CO2 from the ocean and – by inference – the supply rate from land and anthropogenic sources.

    There is of course an obvious and strong reason why the climate community is very uncomfortable with research and measurement into CO2 loss from the atmosphere. If CO2 is lost from the atmosphere with a half life of only one or two decades, it means that if/when industrial output of CO2 plateaus and stops rising, due to population stabilization for instance, folks driving newer cars etc. then within a decade or two atmospheric CO2 will also equilibrate, stop rising and stabilize. But a fictitious very long / infinite life of CO2 in the atmosphere allows the doom-mongers to black-mail politicians with scenarios of indefinitely increasing atmospheric CO2 and AGW.

  224. Half life = 0.693 x residence time
    Residence time = half life / 0.693

    What is the need to invoke the completely redundant parameter “e folding time”?
    I think its for a socio-biological and not a scientific reason – it happens to be a certain poster’s favourite pet parameter.

  225. bobl: “I would really love for us to get together and work out math that better describes this process.”

    Okay, here’s a first stab. As I will show, it assumes the simplified model that Professor Pettersson’s Equation (5) above tacitly assumes. That is, it departs from my simpler model (referred to in some circles as the “bathtub model”), but it ignores the further complications imposed by the various heterogeneities in the non-atmosphere processes.

    Consider a first reservoir (the atmosphere) containing a mass m_1 of carbon and a second reservoir (trees, soil, oceans, etc.) containing a second mass m_2 of carbon. For the sake of Professor Pettersson, though, we’ll model those reservoirs as being respective volumes V_1 and V_2 containing their respective masses of a (for the moment, homogeneous) ideal gas, which represents the carbon.

    Let’s further assume a simple slightly permeable membrane (representing transpiraton, outgassing, photosynthesis, etc.) through which the gas can pass at a net rate of mass flow (rate of natural emissions minus rate of uptake) proportional to the concentration difference between the two reservoirs:

    \frac{dm_2}{dt}=-\frac{dm_1}{dt} = (\frac{m_1}{V_1} - \frac{m_2}{V_2})\mu,

    so that, if \frac{V_1}{V_2} equals some fraction k, the system is a equilibrium if m_1=km_2: the net mass flow will equal zero (although exchange between the reservoirs may actually be proceeding furiously).

    Now let’s say that that this equilibrium condition prevails at time t=t_{0^-} and therefore that m_1= \frac{k}{1+k}M_0. But at t=0 we add \Delta M to the system, in particular, to the first reservoir, so that m_1 becomes \Delta M+\frac{k}{1+k}M_0 .

    Equilibrium having thus been upset, m_1 will decay from that value to the new equilibrium value \frac{k}{1+k}(M_0+\Delta M). More concretely:

    m_1= \frac{k}{1+k} (M_0 + \Delta M)+ \frac{1}{1+k} \Delta M e^{-\mu t}.
    This is equivalent to Professor Pettersson’s Equation(5) above, as we can see by defining the fraction f(t) as the difference \frac{m_1(t)-m_1(0^-)}{\Delta M}. Substitution and rearranging transforms that definition into f(t)= \frac{e^{\mu t}+k}{1+k}, i.e., into Equation (5) above.

    Note that the tacit assumptions of Professor Pettersson’s Equation (5) dictate the difference e_n-u between emissions and uptake but are silent about what e_n or u is individually, and we’ve argued above that the excess-carbon-14 decay rate depends more on the actual value of u than on the difference.

    Before I address that, though, I’ll change the external stimulus to a step rather than an impulse. That is, rather than adding \Delta M instantaneously at t=0, we’ll add mass to the first reservoir at a rate e_a. I hate to do that, because it makes the math a little more complicated than I can ordinarily do without error in the haste with which I’m doing this, but I think people consider the increase important. So I’ll put this out there as a solution and hope some of the scientists out there will vet it:

    m_1(t)= m_1(0) + \lambda\tau e_a (t - \tau e^{-t/\tau})

    where \tau = \frac{k}{1+k}\frac{V_2}{\sigma} and \lambda = \frac{k}{1+k}.

    Or something like that.

    Now let’s tag a fraction c_0 of the first-reservoir contents m_1 at instantaneously t=0 and call the tagged part (corresponding to the excess carbon-14) m_{114} so that m_{114}(0)=c_0m_1(0). Passage through the membrane will cause some of the tagged contents to be exchanged with the other reservoir, giving it a tagged portion m_{214}. (We’re ignoring the pre-bomb-test carbon-4.)

    Ignoring any difference in kinetics between tagged and untagged contents, we’ll say those quantities vary as follows:

    \frac{dm{114}}{dt}=\frac{m_{214}}{m2}e_n- \frac{m{114}}{m1}u,

    where m_{214}=\frac{m{114}}{m1}u. Note that we get the right-hand side’s m_1 and m_2 from the previous equations, but e_n and u are not, although their difference is dictated by e_a, m_1 and m_2

    Without solving that equation, we can tell by inspection that taking Professor Petterson’s model into account reduces the tagged-contents decay rate, although my guess is that the difference isn’t great when realistic numbers are plugged in. Also note solving that last equation would give the total first-reservoir tagged mass $m_{114}$, which have to be divided by m_1 to give the excess-concentration value ordinarily used in bomb-test-result discussions.

    I’d have to think about how to solve that last equation, so I’ll stop here and see whether anyone wants to take this further.

    [On the capitalistic theory that "That which is rewarded, is encouraged; and that which is taxed, is discouraged" the mods would like to thank Joe Born for properly and systematically using the "Test" pages for his formatting and hyertext markups of the math equations in this reply. Very effective, very useful in maintaining the clarity of his equations. Whether those equations are completely accurate or completely correct or not is a different matter worthy of further discussion, but their clarity has seldom been more evident. Mod]

  226. Unfortunately, the equations are wrong. So if anyone’s still here, don’t puzzle over them; I’ll fix them after lunch.

  227. bobl says:
    November 24, 2013 at 5:36 pm

    “I think we should however recognise that there are more than one decay curves at play here…”

    Quite likely. However, it may be the case that one is dominant. The bomb test curve certainly seems to be so.

    Willis Eschenbach says:
    November 24, 2013 at 10:30 pm

    So, your conclusion is based on your assumption that the atmospheric concentration is driven overwhelmingly by human inputs. Something I and others are certain is untrue.

  228. Bart says:
    November 25, 2013 at 9:17 am

    Willis Eschenbach says:
    November 24, 2013 at 10:30 pm

    So, your conclusion is based on your assumption that the atmospheric concentration is driven overwhelmingly by human inputs. Something I and others are certain is untrue.

    Look, Bart, you’re free to conclude what you want from my calculations. You can even ignore my calculations and adopt the belief that I, and Mark Jacobson who I cited above, and Richard Lindzen, are basing our conclusions on assumptions.

    But that doesn’t change the facts that I did the calculations, and you didn’t. When you’ve done so, you can tell us where my conclusions based on actual calculations are wrong …

    Or you can just continue with your fantasies about what I base my conclusions on. Me, I’m clear that I base them on my calculations, as I’m sure Jacobson and Lindzen do as well, but you’re free to believe what you wish.

    w.

  229. Willis Eschenbach says:
    November 25, 2013 at 10:07 am

    “When you’ve done so, you can tell us where my conclusions based on actual calculations are wrong …”

    They are wrong because they are based on the assumption that the atmospheric concentration is driven overwhelmingly by human inputs.

    Concluding that atmospheric concentration is driven overwhelmingly by human inputs because of your long time constant is therefore circular reasoning.

  230. Bart, a few more comments. You think I base my conclusion by assuming that humans drive the CO2. In fact, that’s exactly backwards.

    See, back more than a decade ago, I went into this thinking like you, that the CO2 rise wasn’t from humans. So I thought, well, I can falsify the claim that the CO2 is anthropogenic by showing that the emissions don’t actually match the measurements of atmospheric CO2.

    But I found the exact opposite. I found that the emissions and the measurements of airborne CO2 match almost perfectly using the simplest form of the exponential decay of an injected pulse. Here again are the results of my calculations:

    As you can see, the human emissions are both necessary and sufficient to explain the buildup of CO2 in the atmosphere.

    So if you wish to claim that the CO2 is entirely or mostly due to something other than human emissions … then you get other questions, among them being, what has happened to the human emissions?

    Another question, of course, is if it’s not humans, then what is causing the rise in CO2 …

    Now, from the Vostok ice core data, as well as from theoretical calculations, we know that there is an increase in CO2 on the order of 15 ppmv per degree of warming … might be a bit more or less, but that’s the neighborhood. It’s from the fact that when the ocean warms, it releases CO2.

    The problem, of course, is that the globe has only warmed less than a degree in the last hundred years, and that’s far too little to explain the ~ 100 ppmv increase in CO2 in the last hundred years.

    All the best,

    w.

  231. Willis Eschenbach says:
    November 25, 2013 at 10:31 am

    “But I found the exact opposite. I found that the emissions and the measurements of airborne CO2 match almost perfectly using the simplest form of the exponential decay of an injected pulse.”

    You do not seem to realize that this is a very superficial match to low order polynomials. This are not at all difficult series to match via an affine mapping.

    What is difficult to match is the kind of detail here.

    “As you can see, the human emissions are both necessary and sufficient to explain the buildup of CO2 in the atmosphere.”

    Sufficient, yes. Necessary, no.

    “…what has happened to the human emissions?”

    They have been absorbed into land and ocean sinks, which are obviously far more active than conventionally assumed.

    “Another question, of course, is if it’s not humans, then what is causing the rise in CO2 … “

    I have presented my model many times in these message boards. This blog post provides an overview. This model matches the dCO2/dt – temperature relationship linked above. The emissions data do not, and there is very little room left in this model for emissions to have significant impact.

    “The problem, of course, is that the globe has only warmed less than a degree in the last hundred years, and that’s far too little to explain the ~ 100 ppmv increase in CO2 in the last hundred years.”

    It is possible if there is a temperature dependent pumping action of CO2 into the atmosphere. Such activity is precisely what I outline in the model linked above.

    The bottom line: The rate of change of atmospheric CO2 is clearly affinely related to temperatures. Human generated emissions are not temperature dependent. Hence, human emissions are not what is driving atmospheric CO2.

  232. Okay, once more, with feeling.

    As I will show, the following treatment assumes the simplified model that Professor Pettersson’s Equation (5) above tacitly assumes. That is, it departs from my simpler model (referred to in some circles as the “bathtub model,” in which the emissions’ constituents are completely independent of the uptake’s), but it ignores the further complications that considering various non-atmosphere processes’ heterogeneities would entail.

    Consider a first reservoir (the atmosphere) containing a mass m_1 and a second reservoir (trees, soil, oceans, etc.) containing a second mass m_2. For the sake of Professor Pettersson’s model, we’ll assign those reservoirs respective volumes V_1 and V_2, which contain their respective masses m_1 and m_2 in the form of a (carbon-representing and, for the moment, homogeneous) ideal gas.

    Let’s further assume that the reservoirs communicate with each other through a simple, slightly permeable membrane representing transpiration, out-gassing, photosynthesis, etc. Specifically, the gas passes through the membrane at a net rate of mass flow proportional to the concentration difference between the two reservoirs so that when no mass is being added to the system:

    \frac{dm_2}{dt}=-\frac{dm_1}{dt} = (\frac{m_1}{V_1} - \frac{m_2}{V_2})\sigma.

    If \frac{V_1}{V_2} equals some fraction k, therefore, the system is at equilibrium when m_1=km_2: the net mass flow will equal zero (although exchange between the reservoirs may actually be proceeding furiously). In the real world, of course, we expect the flow rate to exhibit a more-complex relationship with the concentrations, but this model adopts that simple relationship.

    Now let’s say that the just-described equilibrium condition prevails at time t=0^- and therefore that m_1= \frac{k}{1+k}M_0 at that instant. But let’s also say that at t=0 we add \Delta M to the system. In particular, we add it to the first reservoir, so that m_1 becomes \Delta M+\frac{k}{1+k}M_0 .

    Equilibrium having thus been upset, m_1 will decay from that value to the new equilibrium value \frac{k}{1+k}(M_0+\Delta M). More concretely:

    m_1= \frac{k}{1+k} (M_0 + \Delta M)+ \frac{1}{1+k} \Delta M e^{-\mu t},

    where \mu=\frac{\sigma}{V_2}\frac{k+1}{k}. This is equivalent to Professor Pettersson’s Equation(5) above, as we can see by defining the fraction f(t) as the ratio \frac{m_1(t)-m_1(0^-)}{\Delta M} that the remaining added first-reservoir mass m_1(t)-m_1(0^-) bears to the added mass \Delta M. Substitution and rearranging transform that definition into f(t)= \frac{e^{\mu t}+k}{1+k}, i.e., into Professor Pettersson’s Equation (5) above. Note that we’ve specified the decay constant \mu‘s value only in terms of fictional quantities k, V_2, and \sigma; we have not constrained what numerical value we could assign it.

    Note also that the tacit assumptions of Professor Pettersson’s Equation (5) dictate the difference e_n-u between emissions and uptake but are silent about what e_n or u is individually. We’ve argued elsewhere that the excess-carbon-14 decay rate depends more on the actual value of u than on the difference.

    Before considering carbon-14, though, I’ll change the external stimulus to a step rather than an impulse. That is, instead of adding \Delta M instantaneously at t=0, we’ll begin at that time to add mass to the first reservoir at a rate e_a. We consider this modification because the effect of continually increasing CO2 became an issue in the comments. With that stimulus, the solution becomes:

    m_1(t)= m_1(0) + \frac{k e_a}{k+1} \left[  t - \frac{1}{\mu}(1-e^{-\mu t})\right].

    Now let’s simulate the bomb tests by tagging a fraction c_1(0) of the first-reservoir contents m_1 instantaneously at t=0 and call the tagged portion (corresponding to the excess carbon-14) m_{114} so that m_{114}(0)=c_1(0)m_1(0). Note that m_{114} is the total tagged-portion mass in that reservoir; to obtain the quantity ordinarily considered in bomb-test discussions would require dividing that quantity by m_1. The other reservoir, too, may get an initial dose m_{214}(0)=c_2(0)m_2(0), giving it a tagged portion m_{214}(t) = m_{214}(0) + m_{114}(0)-m_{114}(t). (We’re ignoring the pre-bomb-test carbon-14.)

    Also ignoring any difference in kinetics between tagged and untagged contents, we’ll say that the respective reservoirs’ tagged contents leave those reservoirs in proportion to the ratios they bear to the respective reservoirs’ total contents:

    \frac{dm_{114}}{dt}=\frac{m_{214}}{m_2}e_n- \frac{m_{114}}{m_1}u.

    Note that we get the right-hand side’s m_1 and m_2 from the previous equations, but e_n and u are both arbitrary, although e_a, m_1, and m_2 dictate their difference. Conversely, knowing \frac{dm_{114}}{dt} doesn’t tell us much about the time constant 1/\mu with which \Delta M (added CO2) would leave the first reservoir.

    At this point I’m inclined to think we’d have to resort to a numerical solution to the equation for m_{114}, so I’ll stop here and see whether anyone wants to take this further. But I hope some will consider this a useful synthesis of Professor Pettersson’s model and what we’ve said about the bomb test’s limitations as an indication of how long a concentration increase lingers after a temporary emissions bubble.

  233. Joe Born says:
    November 25, 2013 at 12:19 pm

    “If \frac{V_1}{V_2} equals some fraction k…”

    Why should k be constant? Plants grow, sediments accumulate. There is no theoretical constraint on this variable.

  234. Bart: “Why should k be constant? Plants grow, sediments accumulate. There is no theoretical constraint on this variable.”

    Because it is in Professor Pettersson’s model. I can’t speak for him, but I assume he’d say he hasn’t tried to model every possible aspect of the universe, only enough to get some sense of what would happen if things were this simple. I’m no scientist, but my experience is they do that kind of thing all the time.

    Also, k doesn’t keep the rate of uptake and natural emissions constant; it only helps determine whether their difference should be increasing or decreasing.

  235. Is half-life really a valid concept to use in regard to atmospheric CO2? An increase in a trace gas like CO2 in the atmosphere should increase the rate of photosynthesis given sufficient sunlight and water, and appropriate temperatures. So the more CO2, the faster it should be changed to plant material. This effect is significant enough for professional greenhouses to raise CO2 levels and pay for it with increased plant growth. We are not expecting less atmospheric CO2, we are expecting more.

    BTW, there is a great carbon cycle graph at the top of:

    http://en.wikipedia.org/wiki/Carbon_cycle

    And where is talk of putting excess carbon in the soil? The world is short on topsoil.

  236. Willis Eschenbach on November 25, 2013 at 10:31 am

    As you can see, the human emissions are both necessary and sufficient to explain the buildup of CO2 in the atmosphere.

    - – - – - – - -

    Willis Eschenbach,

    Wouldn’t Feynman expect you to “bend over backwards” to provide a few caveats, like all other things being equal? Wouldn’t he urge you to have a special kind of integrity to point out all possibility that there are a few exceptions, a few provisos, and a couple of quid pro quos?

    Note: the above italicized line is from Genie in the movie ‘Aladdin’. : ) I always wanted to use it in a comment.

    Willis, I think your statement is not sufficient without qualification. I think it is not necessary unless there is an exhaustive and comprehensively balanced increase in the knowledge of the carbon cycle undertaken first***.

    Another thought => Do you suggest the existing Bern model is necessary and / or sufficient? Can any model categorically be necessary and / or sufficient; as a model per se?

    *** mega funds available for carbon cycle research from hopefully curtailing failed CGM modeler’s activities.

    John

  237. John Whitman says:
    November 25, 2013 at 2:08 pm

    Willis Eschenbach on November 25, 2013 at 10:31 am

    As you can see, the human emissions are both necessary and sufficient to explain the buildup of CO2 in the atmosphere.

    - – – – – – – -

    Willis Eschenbach,

    Wouldn’t Feynman expect you to “bend over backwards” to provide a few caveats, like all other things being equal? Wouldn’t he urge you to have a special kind of integrity to point out all possibility that there are a few exceptions, a few provisos, and a couple of quid pro quos?

    Note: the above italicized line is from Genie in the movie ‘Aladdin’. : ) I always wanted to use it in a comment.

    Despite your nasty and untrue implication about my integrity, and your attempt to hide your insult behind Richard Feynman, I stand by what I said. Mathematically, the straight simple exponential decay of the amount of CO2 injected into the atmosphere fits the historical atmospheric CO2 concentration record extremely well.

    The “necessary” part of what I said refers to the fact that an explanation for the increase in CO2 is necesssary.

    The “sufficient” part means that human emissions alone do an excellent job of explaining the historical record to date.

    So yes, it is both necessary and sufficient.

    Now, are there other things that might fill that need? Sure. So what?

    Are there “provisos”? No, not other than we’re talking about the real world, with all that that means. I used the data from the historical emissions to estimate the historical atmospheric CO2 concentration … what provisos would you like me to add to that?

    Did I bring up other evidence? Yes, I discussed the Vostok and theoretical change in CO2 as the ocean warms, and showed that it is not sufficient to explain the rise in CO2.

    Willis, I think your statement is not sufficient without qualification. I think it is not necessary unless there is an exhaustive and comprehensively balanced increase in the knowledge of the carbon cycle undertaken first***.

    Sorry, that’s not clear. You think what is not necessary?

    Another thought => Do you suggest the existing Bern model is necessary and / or sufficient?

    Sure. It fits the data at present as well as the simple model … although that nay not be true in the future, as one of the two will win out for accuracy. But at present, both are sufficient.

    Can any model categorically be necessary and / or sufficient; as a model per se?

    A “model” is just another name for an “explanation”. The difference is that the model generally includes the math.

    So it’s not obvious what you are asking. It is the explanation which is necessary. Whether or not that explanation is sufficient depends on whether you need to make other assumptions or advance supporting ideas, or whether it fully explains the observations by itself.

    What I’m putting forward is the explanation that an injected pulse of CO2 decays over time in an exponential manner. This idea of exponential decay not a novel idea, and it is certainly not my own idea. It is a common occurrence in the real world.

    In addition, given the historical record of CO2 emissions, exponential decay fully explains the observations.

    Now, as I said above, if you think the increase in CO2 has some other cause, or that it decays in some other fashion, then perhaps you can support your explanation by doing the math, as I have done for my explanation.

    w.

    PS—John, you opened by attacking my scientific integrity. As a result, your stock, and the weight I give your ideas and opinions, just fell precipitously, I had thought better of you than to make such a slimy accusation.

  238. Willis Eschenbach says:
    November 25, 2013 at 4:07 pm

    “Mathematically, the straight simple exponential decay of the amount of CO2 injected into the atmosphere fits the historical atmospheric CO2 concentration record extremely well. “

    Are you now talking about the bomb test curve? Or your superficial fit of accumulated emissions with atmospheric measurements?

    “The “necessary” part of what I said refers to the fact that an explanation for the increase in CO2 is necesssary.

    The “sufficient” part means that human emissions alone do an excellent job of explaining the historical record to date.

    So yes, it is both necessary and sufficient.”

    That is some just awful mutilation of terms with precise technical meaning, Willis. In a mathematical proof of an equation, we do not say something is “necessary” because it is necessary for someone to solve the equation. We say it is “necessary” if there is no other way it can be solved.

    Your fit of some slightly quadratic time series by an affine mapping does not at all establish uniqueness of the solution.

    “Yes, I discussed the Vostok and theoretical change in CO2 as the ocean warms, and showed that it is not sufficient to explain the rise in CO2.”

    You haven’t even bothered to read up on my model, have you?

  239. I’m now quite unconvinced by the exponential plot Fig 1. The first issue is that it is a hybrid of a number of results. But I’ve been trying to track its provenance.

    Prof P refers to a paper by Svetlik. I couldn’t find the paper, but I did find this well presented poster. I looked at the corresponding figure, and it didn’t look very exponential. Then I tracked down this page by someone who seems to be a co-author. They did a closer study of the later section and said:
    “As seen from FIG. 1, 1963, the activity of radiocarbon begins to decrease approximately exponentially. In the 80s of the last century decline is slowing and around the early 90s is now stable with approximately linear relationship (see Fig. 2). “
    and they show regressions.

    But the poster also noted other concerns. As I mentioned above, what Prof P has plotted is actually from a C14/C ratio. If it goes to zero, that means the ratio is back to where it was in 1950. But there are several reasons to not expect it to return:
    1. the amount of C14 added was a lot. It doubled atmospheric. The sinks are finite. C14 will be permamently raised.
    2. However, we’ve also been adding C free of C14. This increases the denominator in the ratio, by a larger amount. So the ratio will actually go to a lower value than 1950, except…
    3. there’s a third effect that they call the Seuss effect. Like Beck, they are sampling in places where there is an excess of CO2 from nearby human activity, and also a daily fluctuation with photosynthesis. This again affects the ratio, and may be the biggest issue. And there’s no reason to expect that has remained stable since 1950. They plot short-term fluctuations at some of the sites. It’s large and you can see diurnal patterns etc.

    I’m very dubious. If it isn’t exponential, there isn’t a single decay time. It depends on where you look. And if it doesn’t decay at all…

  240. Bart says:
    November 25, 2013 at 5:34 pm

    Willis Eschenbach says:
    November 25, 2013 at 4:07 pm

    “Mathematically, the straight simple exponential decay of the amount of CO2 injected into the atmosphere fits the historical atmospheric CO2 concentration record extremely well. “

    Are you now talking about the bomb test curve?

    Well, since I didn’t say “bomb test” anywhere, I’ll let you figure that out.

    Or your superficial fit of accumulated emissions with atmospheric measurements?

    So in your world of snar, a successful fit is “superficial”?

    You’re all mouth and no math, Bart. You’ve not shown any other fit to the historical data over the last hundred years. My fit is to a well established model, that of exponential decay. How on earth is exponential decay “superficial”? Many natural processes are well modeled using exponential decay … does your sneering apply to all of those other processes as well?

    Put up the math for your more successful fit to the last hundred years of CO2 increase, Bart, before you start getting all snarky about my math …

    w.

  241. Willis Eschenbach says:
    November 25, 2013 at 10:34 pm

    “So in your world of snar, a successful fit is “superficial”? “

    I’ve explained why it is superficial. Either you didn’t understand it, or you didn’t read it. Given the pronounced and often bizarre disconnect typical between what I write and you respond, I suspect the latter.

    “My fit is to a well established model, that of exponential decay.”

    The plot here is of exponential decay?

    I think you mean it is a single lag smoothed accumulation of emissions. Big deal. You have two slightly quadratic time series. The odds of fitting them reasonably well with an affine mapping are essentially the odds of them having the same curvature – 50/50. A coiin toss.

    But, the model of emissions driving atmospheric CO2 is diverging from its superficial similarity. In the last decade, the rate of change of atmospheric concentration has become effectively constant, while the rate of change of emissions has continued increasing. You can even see the incipient divergence in your plot, and you don’t even carry it out to the present day.

    “So in your world of snar, a successful fit is “superficial”?

    It’s a lousy fit. Bring it up to date, and try a numerical differention, and show me how well it fits then.

    “You’ve not shown any other fit to the historical data over the last hundred years.”

    Yes, I have. You’ve just studiously ignored it.

    Look at what I have written and study it, and you will learn.

    Or, plow your head back into the sand, and ignore anything you don’t find convivial. I don’t really give a rodent’s derriere. But, don’t expect me, at least, to take you seriously when you get up on your pompous soapbox and ignore anything anyone else tries to show you.

  242. Willis Eschenbach says:
    November 25, 2013 at 10:34 pm

    Willis, I have had several rounds of discussion with Bart, still going strong each time again.

    According to Bart (and Salby), the increase in the atmosphere is caused by a sustained increase in temperature above an arbitrary baseline. That is because the short term variability of T perfectly matches the short term variability of dCO2/dt. From that point, Bart and Salby integrates T with some offset and factor, which matches the increase of CO2 in the atmosphere.

    But that gives a lot of problems:
    - that means that for a small sustained increase in temperature, CO2 (from the oceans) continuous to be released at a near constant rate with a continuous increase in the atmosphere as result. Without any effect from the increase of CO2 levels in the atmosphere on the input and output fluxes.
    - the continuous increase has no measurable effect on turnover time, isotopic composition (13C/12C and 14C/12C ratio’s).
    - to dwarf the human emissions, the increased turnover (total sinks still ~4.5 GtC/yr larger than total sources) must mimic human emissions at exact the same timing and increase rate, thus increasing the turnover a threefold in the period 1960-2012, and thus reducing the residence time a threefold.
    - that means an increase of ~150 GtC in/out over a year for natural releases/uptake in 1960 to ~450 GtC now, or if it comes from the deep oceans only a sevenfold increase in turnover for that reservoir, again without affecting isotopic composition of the atmosphere or residence time estimates.
    - for each different period in time, you need a different offset and factor to match the T-dCO2/dt trend. The latter gets very low over glacial-interglacial transitions and virtuall zero over the glacial periods.
    Salby therefore calculates a theoretical migration of CO2 in ice cores that isn’t measured at all to fit his theory…

    Further, Bart’s graph of the current increase in uptake is a little misleading. If you plot the variables with the same units then you get this:

    where a fixed percentage of human emissions (the “airborne fraction”) is plotted and human emissions minus the decay function of CO2 based on the pressure difference observed – temperature controlled setpoint.

    And if you look at the trends of Bart’s plot then you see that the trends don’t match, thus the integral of T gives a too high CO2 level. If you try to match the trends, then the amplitude of the variability is too low.

    The problem is in the scale factor: the amplitude is not changed by integrating T or dT/dt, but it changes with the difference in slopes between T and dCO2/dt. Thus there is a fundamental error by combining the variability and the trend of T.

    Regards,

    Ferdinand

  243. Bart, you’ve commented above on your model. I’d read it before, but this time at your urging I took a closer look. Here’s the problem that I see. You say:

    If we look at the relationship between CO2 and temperatures, it is apparent that to a very high degree of fidelity that

    dCO2/dt = k*(T – Teq)

    CO2 = atmospheric concentration
    k = sensitivity factor
    T = global temperature anomaly
    Teq = equilibrium temperature

    k and Teq are parameters for a 1st order fit. They may change over time, but are well represented by constants for the modern era since 1958 when precise measurements of CO2 became available.
    This is a positive gain system – an increase in temperatures produces an increase in CO2 concentration.

    Actually, you’ve postulated a curious system. Not only does an increase in temperatures produce an increase in CO2, as you say. The problem is that a constant temperature also produces an increase in CO2 …

    In your formula above, let us assume that the temperature T is a constant, and that T > Teq. In that case, since both K and Teq are also constants, then dCO2/dt will also be constant, and will be greater than zero. In other words,

    dCO2/dt = C

    The problem is that if we integrate your equation for the situation of a constant temperature > Teq, we get

    CO2 = C t

    And that means that with a constant temperature, as time goes on and on the amount of CO2 in the atmosphere will increase without limit … which seems very doubtful.

    What am I missing here?

    w.

  244. Bart says:
    November 26, 2013 at 4:12 am

    Willis Eschenbach says:
    November 25, 2013 at 10:34 pm

    “My fit is to a well established model, that of exponential decay.”

    The plot here is of exponential decay?

    I think you mean it is a single lag smoothed accumulation of emissions. Big deal.

    Here’s the plot again …

    Indeed the plot shows exponential decay. There is no smoothing, nor is there any lag. The total amount present in the atmosphere at any instant is subject to simple exponential decay, as the CO2 is sequestered at the surface in a whole variety of ways. To that each year is added the new emissions. The result is the curve shown in black above. In other words, yes, the plot shows the very simplest, single-time-constant exponential decay.

    w.

  245. Mr. Eschenbach:

    I’m not adept at accessing data sets, and I was wondering whether the the data you based that graph on are handy. (I did try a link in a previous post of yours, but it was broken.)

  246. Willis Eschenbach on November 25, 2013 at 4:07 pm said,

    John Whitman says:
    November 25, 2013 at 2:08 pm

    PS—John, you opened by attacking my scientific integrity. As a result, your stock, and the weight I give your ideas and opinions, just fell precipitously, I had thought better of you than to make such a slimy accusation.

    - – - – - – - -

    Willis Eschenbach,

    I intended an ironic paradox by contrasting the Feynman ideas with your necessary and sufficient categorization of attribution of modern CO2 increase. Your certainty seemed too much without any caveat, quid pro quo, proviso, or exception.

    I see that I have seriously miscalculated my ‘ironic paradox’. I was insufficiently civil and unnecessarily insensitive. I apologize for that.

    My intention was not to say you lacked integrity in any way in your comment (November 25, 2013 at 10:31 am). I was trying in a witty way to draw out your skeptical ‘caveats, quid pro quos, provisos, or exceptions’ of your necessary and sufficient. It was my misjudgment to try to do it the way I did.

    {Note: To me ‘necessary and sufficient’ is the strongest epistemological evaluation a human can make with his capacity of reason.}

    John

  247. @Ferdinand Engelbeen and Ian W

    Ian sez, “It should of course be noted that the surface area of the oceans is actually dwarfed by the surface area of cloud water droplets which are both cold and when they form CO2 free. By Henry’s law these droplets will take up a lot of CO2.”

    Ian is correct.

    Ferdinand sez, “Rain is fresh water, fresh water will contain very little CO2 at a pressure of 0.0004 bar, which mostly was released from the same warm oceans where water vapour was entering the atmosphere. ”

    Ferdinand is correct in that fresh water would contain very little CO2 at a pressure of 0.0004 bar but the pressure is 1.0 bar. The chart presented at http://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html again referenced.

    So when water droplets form they remove CO2 (rapidly) from of the atmosphere. Rain that falls into the ocean or sinks into the ground maintains this concentration until it is either heated or frozen.

    Ice particle clouds of course contain no CO2. In winter water freezes and expels all the CO2 into the atmosphere. I have not been able to find a figure for the mass of all the fresh water that freezes in the NH winter: however for each cubic metre of water frozen, 3 kg of CO2 is emitted. For sea ice it is the same because sea ice is frozen fresh water, not frozen salt water.

    If the NH sea ice is 1 m thick on average and everything else north of 50 degrees freezes to the conservative average depth equivalent to 0.1 m of water (Siberia is 20x that), there would be:

    (15m km^2 x1/1000 + 76m km^2 x 0.1/1000 x 3/1000 mass fraction that is CO2) = 68 gigatons of CO2 released from water into the atmosphere during NH winter.

    It only takes 38 gigatons to change the atmospheric concentration of CO2 by 5 ppm (the seasonal variation) so the cooling oceans must be absorbing some of it. In summer the snow and ice melts, absorbing all 68 gigatons of CO2 again and the oceans give it back.

    If CO2 has a strong net forcing, the only possible conclusion would be that Winter is a major cause of global warming and summer is a major cause of cooling.

    To reduce the atmospheric concentration of CO2 to 350 ppm will require the melting of 130,000 cu km of ice – a small fraction of the ice on Greenland.

  248. Crispin in Waterloo but really in Ulaanbaatar says:
    November 26, 2013 at 4:31 pm

    Ferdinand is correct in that fresh water would contain very little CO2 at a pressure of 0.0004 bar but the pressure is 1.0 bar

    Crispin, the atmospheric pressure is 1 bar (or less at height), but the solubility of CO2 in water only applies to the partial pressure caused by CO2 itself (per Henry’s law), not to the other constituents of the atmosphere… Thus you have to multiply all your figures with 0.0004 bar for CO2, which makes that the total circulation still is huge (because of the huge mass of water circulating through the atmosphere), but the change in local levels is negligible.

  249. @Ferdinand

    Read Henry’s Law again. I see the slip you made and I was impressed at how clever it was but I for one and not fooled as this is my bread and butter.

    I think your are quite intelligent enough to do this, meaning that I don’t think you are unaware that CO2 absorption in water is other than 3 g /litre as per the link you provided yourself! You are introducing a figure from the micro-atmosphere side (being the volumetric fraction of the atmosphere) and trying to pass that off as the ‘pressure’ to apply to the amount of CO2 that will be absorbed but water. The pressure at sea level is 1 bar, and yes, about 0.0004 of that is provided by the CO2 component of the atmosphere. The other 0.9996 is provided by other components and all of it acts on the CO2.

    You will probably get traction on other channels with that sleight of hand but not WUWT. The mass of CO2 that is absorbed in a litre of fresh water at 5 Degrees C at a pressure of 1 bar is 3 g, or if you prefer, 1127 ppm(v). Deal with it.

    There are two grand themes missing from the CAGW science: there is not nearly enough carbon based fuels to take the atmospheric concentration above about 540 ppm, and if Antarctica were to melt completely it would strip the entire atmosphere of CO2 and we would be begging the oceans to yield its treasure.

  250. John Whitman says:
    November 26, 2013 at 4:19 pm

    Willis Eschenbach on November 25, 2013 at 4:07 pm said,

    John Whitman says:
    November 25, 2013 at 2:08 pm

    PS—John, you opened by attacking my scientific integrity. As a result, your stock, and the weight I give your ideas and opinions, just fell precipitously, I had thought better of you than to make such a slimy accusation.

    - – – – – – – -

    Willis Eschenbach,

    I intended an ironic paradox by contrasting the Feynman ideas with your necessary and sufficient categorization of attribution of modern CO2 increase. Your certainty seemed too much without any caveat, quid pro quo, proviso, or exception.

    I see that I have seriously miscalculated my ‘ironic paradox’. I was insufficiently civil and unnecessarily insensitive. I apologize for that.

    As precipitously as your stock fell, it has risen again. You are indeed a gentleman, sir.

    w.

  251. Crispin in Waterloo but really in Ulaanbaatar says:
    November 27, 2013 at 6:40 am

    Read Henry’s Law again.

    Well, here it is:

    http://dictionary.sensagent.com/Henry's%20law/en-en/

    At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

    The total pressure of the atmosphere is 1 bar.
    The partial pressure of nitrogen is 0.79 bar
    The partial pressure of oxygen is 0.21 bar
    the partial pressure of CO2 is 0.0004 bar

    The solubility of O2, N2 and CO2 each is for their own partial pressure in the atmosphere per Henry’s law…

  252. Ferdinand Engelbeen says:
    November 27, 2013 at 10:29 a
    from my little physics, each gas behaves as if it alone occupies the space.So CO2 acts at its own partial pressure in our atmosphere as if it alone occupied the atmosphere, so therefore acts at its own partial pressure at the gas liquid interface.

  253. It appears that this page has not yet been abandoned, so I guess I should admit another error I made above. It doesn’t affect anything else, but I noticed last night that I had misstated the way in which the Pettersson system responds to a step increase in added emissions. (I think) I’ll correct that here, and I’ll show my sums so that no one will be tempted to take my word for the replacement relationship.

    To calculate the behavior that the atmospheric-carbon-mass-representing variable m_1 exhibits in response to a step in emissions, we restate the relative-“concentration” relationship in terms of M-m_1 instead of m_2, and we drop the assumption that no change is occurring in the variable M, i.e., in the mass representing all the carbon-cycle carbon (but not the carbon held hors de combat in, e.g., petroleum or coal). That is, we state that the rate at which the first-reservoir-content’s mass m_1 changes equals the sum of (1) a quantity proportional to the difference \frac{M-m_1}{V_2}-\frac{m_1}{V_1} between the reservoirs’ concentrations and (2) the rate \frac{dM}{dt} at which mass is added to the system (representing the rate at which carbon previously imprisoned in coal or petroleum is added to the cycle of life):

    \frac{dm_1}{dt}= (\frac{M-m_1}{V_2}-\frac{m_1}{V_1})\sigma+\frac{dM}{dt}.

    Rearranging that equation gives us the following:
    \frac{dm_1}{dt}+\frac{V_1+V_2}{V_1V_2}\sigma m_1=\frac{dM}{dt}+\frac{\sigma}{V_2}M.
    Into this equation we substitute a time-constant value \tau=\frac{V_1V_2}{V_1+V_2}\frac{1}{\sigma} and a constant-stimulus-gain value \lambda=\frac{V_1}{V_1+V_2}:
    \frac{dm_1}{dt}+\frac{1}{\tau}m_1=\frac{dM}{dt}+\frac{\lambda}{\tau}M.
    This defines a system whose impulse response h(t) is given by:
    h(t)=\delta(t)-\frac{(1-\lambda)}{\tau}e^{-t/\tau},
    where \delta(t) is the unit impulse, i.e., a function that equals zero for t\ne0 and whose integral over any interval that includes t=0 is unity.
    Now, we can obtain the response of m_1(t) to M(t) by convolving M(t) with that impulse response:
    m_1(t)=\int\limits_{-\infty}^{t}M(\zeta)h(t-\zeta)d\zeta
    That tells us that the current response depends on the entire stimulus history since the beginning of time. But we’re interested only in the response component m'_1(t) caused by the human-emissions-rate unit step that occurs at time t=0.
    So in place of the value M(t) corresponding to all the carbon currently participating in the carbon cycle we’ll take as our stimulus a function M'(t) = \mathrm{max}(0, t), i.e., a unit ramp. Plugging that as well as the above-determined function for the impulse response into the above convolution equation yields the following equation for the difference m'_1(t) between what m_1(t) is and what it would have been in the absence of the emissions step:
    m'_1(t)=\int\limits_{0}^{t} \left[ \delta(\zeta-t)- (\lambda-1)e^{(\zeta-t)/\tau}\right]\zeta d\zeta=\lambda t+(1-\lambda)(\tau)(1-e^{-t/\tau}).
    Contrary to what my last comment said, that is, m'_1(t)‘s response to an additional-emissions rate dM'/dt exhibits a slope that initially equals unity but decays to the constant-M gain \lambda.

    By the way, the reason I detected the error is that I returned to my above comment last night as I was thinking that if I find some numbers to use I may attempt a numerical solution. In that connection I’ll mention that numerically convolving the above impulse response with M'(t) requires a special accommodation for its Dirac delta function. Although the accommodation is trivial, that impulse response additionally suffers from a lack of intuitive appeal. More straightforward would be to convolve e_a\equiv dM'/dt with the impulse response’s integral, i.e., with:
    h_{-1}(t) = \lambda+(1-\lambda)e^{-t/\tau}
    (By calling that quantity e_a I’m implying–incorrectly–that all anthropogenic emissions come from outside the existing carbon cycle. But I don’t think that matters much at this model’s level.)
    As another aside I’ll mention that if I use this version of Pettersson’s model I may modify it to reflect the “missing sinks” by making only a portion of the added M go directly into the first reservoir (and thus implicitly directing the remainder directly into the second).

  254. Note to mods: I don’t know whether this is just my machine, but to me it appears that WordPress, my Chrome installation, or something else exhibits a bit of whimsy in its selection the font size for LaTeX portions. In some places it’s fine, whereas in others it’s very large and sometimes squashed.

    Probably nothing you can do about it, but I thought I’d let you know.

  255. dbstealey says:
    November 27, 2013 at 10:44 am

    What happened to Argon?
    The partial pressure of argon is ≈.01 bar, no?

    Yes, I rounded off N2 a little too high…

    http://mistupid.com/chemistry/aircomp.htm

    Lewis P Buckingham says:
    November 27, 2013 at 11:36 am

    from my little physics, each gas behaves as if it alone occupies the space.

    Indeed, it doesn’t matter if the 0.0004 bar CO2 is in high vacuum or together with 0.9996 bar of other molecules. In both cases the same amount of CO2 dissolves in water (if the water doesn’t get boiling under such high vacuum!).

  256. Ferdinand Engelbeen says:
    November 26, 2013 at 8:53 am

    “…to dwarf the human emissions, the increased turnover (total sinks still ~4.5 GtC/yr larger than total sources) must mimic human emissions at exact the same timing and increase rate…”

    Not so. With feedback as an additional variable, there is a wide range of possible natural forcing.

    “…for each different period in time, you need a different offset and factor to match the T-dCO2/dt trend…”

    Nonlinear systems are like that. You can linearlize them about a current operating point but, if they stray too far from that point, you have to re-linearize. This is standard and unremarkable.

    “Further, Bart’s graph of the current increase in uptake is a little misleading. If you plot the variables with the same units then you get this:”

    Ferdinand’s plot merely shows the robustness of linear regressions, something which is well known. Mine was the best fit up to the middle of the data.

    But, he still has atmospheric CO2 rate of change leveling off in the last decade, while human emissions continue marching upward.

    “And if you look at the trends of Bart’s plot then you see that the trends don’t match, thus the integral of T gives a too high CO2 level.”

    This is a meaningless exercise. The data are bulk global averages, and do not perfectly represent the actual dynamics. Moreover, they are polluted by noise and “adjustments”. Far from being a knock against the integral temperature model, this shows that the relationship is so powerful that it still shines through even with non-ideal measurements.

    Willis Eschenbach says:
    November 26, 2013 at 12:38 pm

    “And that means that with a constant temperature, as time goes on and on the amount of CO2 in the atmosphere will increase without limit … which seems very doubtful.”

    See my comment to Ferdinand about nonlinear systems above. At the current time, and for at least the last 55 years, this relationship has held with high fidelity. It does not mean that the relationship always holds for all time in the same form. For example, a change in the concentration of CO2 in upwelling waters can result in a shift in the k and Teq.

    The long term dynamics are an interesting puzzle, but they do not prevent us from being able to make conclusions about how the system is behaving within a local neighborhood of the current system state. Again, this is standard operating procedure for nonlinear systems modeling.

  257. Bart says:
    November 30, 2013 at 7:32 am

    Not so. With feedback as an additional variable, there is a wide range of possible natural forcing.

    Except that the increase rate in the atmosphere, the sink rate, the 13C/12C and 14C/12C decay rates all show similar curves, thus whatever the “natural” forcing, it must be increasing in ratio with human emissions.

    Nonlinear systems are like that.

    The temperature – CO2 system was (surprisingly) highly linear over 800,000 years: 8 ppmv/K. Now in the past 50 years it would be highly non-linear?

    Ferdinand’s plot merely shows the robustness of linear regressions, something which is well known. Mine was the best fit up to the middle of the data.

    No, you plotted the data with different units for similar variables. That gives a false impression of the real deviation of the trends. The period 1975-1995 shows a similar “pause” in dCO2/dt increase, but that increased thereafter:

  258. Chronology of Events – With respect, I first published this Hypothesis in January 2008.

    At that time, I notified many senior climate scientists, including Richard Lindzen, Roy Spencer, Fred Singer, Tim Ball and more.

    Ideas that radically change consensus take about a decade to gain widespread acceptance.

    Five years and counting…

    Regards, Allan MacRae of the Clan MacRae :-}

    http://wattsupwiththat.com/2013/09/27/reactions-to-ipcc-ar5-summary-for-policy-makers/#comment-1431798

    http://climateaudit.org/2013/09/24/two-minutes-to-midnight/#comment-441473

    Ladies and Gentlemen;

    With 95% certainty, the following Conclusions will be the 97% consensus view of competent climate scientists a decade from now.*

    Regards to all, Allan :-)

    Abstract/Conclusions:

    The evidence from the modern data record AND the ice core record indicates that atmospheric CO2 does not primarily drive Earth’s temperature, and temperature primarily drives atmospheric CO2. This does not preclude the Mass Balance Argument being correct, but its relevance to the “environmental catastrophe debate” (catastrophic global warming, etc.) is moot, because increased atmospheric CO2 has NO significant impact on temperature, and is beneficial to both plant and animal life. Claims that increased atmospheric CO2, from whatever source, causes dangerous runaway global warming, wilder weather, increased ocean acidification, and other such alarmist claims are NOT supported by the evidence.

    The climate models cited by the IPCC fail because, at a minimum, these models employ a highly exaggerated estimate of climate sensitivity to increased atmospheric CO2. In fact, since Earth’s temperature drives atmospheric CO2 rather than the reverse, which is assumed by the IPCC-cited climate models, these models cannot function correctly. The IPCC-cited climate models also grossly under-estimate the magnitude of natural climate variation.

    _______________________________________

    Hypothesis:

    My January 2008 paper was published at

    http://icecap.us/index.php/go/joes-blog/carbon_dioxide_in_not_the_primary_cause_of_global_warming_the_future_can_no/

    My hypothesis was stated as follows:
    “The IPCC’s position that increased CO2 is the primary cause of global warming is not supported by the temperature data. In fact, strong evidence exists that disproves the IPCC’s scientific position. This UPDATED paper and Excel spreadsheet show that variations in atmospheric CO2 concentration lag (occur after) variations in Earth’s Surface Temperature by ~9 months. The IPCC states that increasing atmospheric CO2 is the primary cause of global warming – in effect, the IPCC states that the future is causing the past. The IPCC’s core scientific conclusion is illogical and false.
    There is strong correlation among three parameters: Surface Temperature (“ST”), Lower Troposphere Temperature (“LT”) and the rate of change with time of atmospheric CO2 (“dCO2/dt”). For the time period of this analysis, variations in ST lead (occur before) variations in both LT and dCO2/dt, by ~1 month. The integral of dCO2/dt is the atmospheric concentration of CO2 (“CO2″).”

    The paper was published in January 2008 at

    http://icecap.us/images/uploads/CO2vsTMacRae.pdf

    My initial data and analyses were included at the time of publication in January 2008 in Excel at

    http://icecap.us/images/uploads/CO2vsTMacRaeFig5b.xls

    The original critique of my paper occurred in February 2008 at

    http://climateaudit.org/2008/02/12/data-smoothing-and-spurious-correlation/

    The critique was generally erroneous, but was a necessary and worthwhile process. My thanks to all involved.

    My hypothesis was initially rejected, but two factors apparently changed that conclusion.

    Statistician William Briggs conducted an independent analysis of my hypo that was generally supportive of my conclusion.

    http://wmbriggs.com/blog/?p=122

    Then it became known that Pieter Tans, unknown to me until months later, had delivered a paper on November 28, 2007 that came to the same conclusion regarding dCO2/dt correlating with temperature. Tans’ slides, which were apparently posted months later, are at

    http://esrl.noaa.gov/gmd/co2conference/pdfs/tans.pdf

    Tans’ conclusion on slide 23/23, with which I have no major objection, was:
    “2/3 of the interannual variance of the CO2 growth rate is explained by the delayed response of the terrestrial biosphere to interannual variations of temperature and precipitation.”

    Tans also concluded on slide 10/23:
    “The observed increase in atmospheric carbon dioxide since pre-industrial times is entirely due to human activities.”
    This is the “Mass Balance Argument” that has been ably debated, particularly by Ferdinand Engelbeen and Richard Courtney, and may be correct or incorrect.

    Suddenly there was a collapse of opposition to my observation that dCO2/dt correlated with T – someone in authority had said so too.

    But then if CO2 lagged temperature, how could CO2 drive temperature? Faced with this dilemma, some quickly dismissed this “CO2 lags temperature” observation, calling it a “feedback effect”. This is a Cargo Cult argument, based on the false religious assumption “We KNOW that CO2 drives temperature; therefore it MUST BE a feedback effect.” Then the subject went into limbo until Murry Salby raised it again circa 2011.

    Atmospheric CO2 also lags Earth’s temperature by ~800 years in the ice core record, on a much longer time scale.

    Atmospheric CO2 lags Earth’s temperature at all measured time scales.

    For the record:

    I suggest that climate science is poorly defined, and the science has regressed due to the “Great Leap Backward” of CO2 hysteria in recent decades – the attribution of too many alleged and false crises to increased atmospheric CO2.

    I have limited confidence in the absolute accuracy of the surface temperature record, which appears to have a significant warming bias. I suggest the satellite temperature record, in existence since 1979, is much more accurate that the surface temperature record.

    I suggest that atmospheric CO2 measurements are reasonably accurate since 1958, and relatively but not absolutely accurate before then.

    My primary concern at this point is the probability of imminent global cooling, which may or may not be severe. In the longer term over thousands of years, catastrophic natural global cooling is inevitable. I suggest that the primary focus of climate science should not be alleged humanmade global warming and its mitigation; rather it should primarily focus on natural global cooling and its mitigation.

    * We wrote more than a decade ago:

    http://www.apegga.org/Members/Publications/peggs/WEB11_02/kyoto_pt.htm

    “Climate science does not support the theory of catastrophic human-made global warming – the alleged warming crisis does not exist.”

    “The ultimate agenda of pro-Kyoto advocates is to eliminate fossil fuels, but this would result in a catastrophic shortfall in global energy supply – the wasteful, inefficient energy solutions proposed by Kyoto advocates simply cannot replace fossil fuels.”

    - Dr. Sallie Baliunas, Dr. Tim Patterson, Allan M.R. MacRae, P.Eng. (PEGG, November 2002)

    Respectfully submitted, Allan MacRae

    September 30, 2013

  259. Allan,

    Everybody, “warmers” as well as skeptics agree that the short term (1-3 years) variability in CO2 is caused by the short term variability of temperature.

    But that says next to nothing about the cause of the CO2 trend over the past 150 years, which is much higher than what the temperature trend predicted over the past 800 kyr. The CO2 trend now leads the temperature trend…

  260. Ferdinand Engelbeen says: November 30, 2013 at 2:47 pm

    Ferdinand:
    Everybody, “warmers” as well as skeptics agree that the short term (1-3 years) variability in CO2 is caused by the short term variability of temperature.

    Allan:
    Misleading or false.
    Everyone certainly did NOT agree when I published in January 2008. There was strong objection to my hypo in ClimateAudit, including a paper by Willis entitled “Data Smoothing and Spurious Correlation”, which was much appreciated, but wrong.

    http://climateaudit.org/2008/02/12/data-smoothing-and-spurious-correlation/

    My new observation was that atmospheric dCO2/dt varied with temperature T, and thus CO2 lagged T by ~9 months. Pieter Tans made the same point a month or so earlier but I did not find out until later, when his PowerPoint slides were posted and brought to my attention. Also, Tans like other warmists said this was a “feedback effect” – which was also wrong.

    Ferdinand:
    But that says next to nothing about the cause of the CO2 trend over the past 150 years, which is much higher than what the temperature trend predicted over the past 800 kyr.

    Allan:
    Possibly correct, possibly false, but irrelevant to my comments since CO2 does not primarily drive temperature. See Richard Courtney’s able commentary on your Mass Balance Argument, not repeated here. For the CAGW policy debate, the source of increasing CO2 is irrelevant, since increased atmospheric CO2 is, on balance, strongly beneficial to humankind and the environment.

    Ferdinand:
    The CO2 trend now leads the temperature trend…

    Allan:
    False or misleading – Please examine the global cooling trend from 1940-75 when CO2 increased, and also the current ~17 year global temperature “Hiatus Hernia”. Atmospheric CO2 does not significantly drive Temperature.

    Please read this again, as posted above:
    The evidence from the modern data record and the ice core record indicates that atmospheric CO2 does not primarily drive earth’s temperature, and temperature primarily drives atmospheric CO2. This does not preclude the Mass Balance Argument being correct, but its relevance to the “environmental catastrophe debate” (catastrophic global warming, etc.) is moot, because increased atmospheric CO2 has no significant impact on temperature.

    Regards, Allan

  261. Ferdinand Engelbeen says:
    November 30, 2013 at 8:49 am

    “…thus whatever the “natural” forcing, it must be increasing in ratio with human emissions.”

    A) not necessarily so

    B) If it were, so what?

    “Now in the past 50 years it would be highly non-linear?”

    “Highly” is a subjective term. I would not call a relationship which has held to be linear fairly steady for 55 years now “highly nonlinear”.

    When we go to the proxy measurements, things become speculative. We do not have any closed loop test possible to prove the relationships. If you have ever worked on a complex practical system, I you have before related that you worked in process controls, you know that you know nothing for certain until you have been able to replicate the behavior over repeated trials. Surely, Ferdinand, you have been in situations where you expected one explanation for an anomaly, and in the end found it was something totally different than what you expected?

    Fortunately, it is not necessary to rely upon the proxies. The information of the past 55 years from direct measurements is enough to determine what is presently happening, and that is that CO2 in the atmosphere is tracking the integral of temperature.

    “No, you plotted the data with different units for similar variables.”

    The scaling and offsetting is implicit in the plot. The only thing different I have plotted is an additional vertical axis to give the other units. If you cover up that axis, then it is the same as a fit to the first half of the data in the same units. Try it yourself. Do a fit to the first half, and plot your results.

    “The period 1975-1995 shows a similar “pause” in dCO2/dt increase, but that increased thereafter:”

    Indeed, and there was a similar divergence. But, in both cases, dCO2/dt was tracking the temperature. If temperatures resume their climb, then both dCO2/dt and the emissions will continue to rise, though with an additional offset so that you will continually have to be adjusting the amount of emissions which stay in the atmosphere downward to maintain some semblance of a fit.

    However, if temperatures go into a sustained decline, such as appears likely at this time, you will see such divergence that your link to the emissions will become untenable. I am counting on this to be the final nail in the coffin of attribution of the CO2 rise to human activity.

  262. Allan MacRae says:
    November 30, 2013 at 1:07 pm

    Thank you, Allan. I noticed the relationship independently in a “Eureka!” moment when it suddenly became clear what had been happening. I did indeed find out afterward that you had already discovered the relationship, and written about it in the WUWT pages. I would bet that someone else may well have noticed before even you.

    For my part, I am uninterested in primogeniture. My hope is that someone with the stature and encyclopedic knowledge of the climate system of Salby, or others, will make the necessary investigations to put it all on a sound footing, and banish the foolish assumption of piddly human inputs driving this enormous system, like fleas on the back of an elephant believing they control his movements.

  263. Thanks Bart for your comments of December 1, 2013 at 9:14 am

    Allan says:

    On the ECS Mainstream Debate

    The ECS mainstream debate is the dominant climate science debate between global warming alarmists (aka “warmists”) and climate skeptics (aka “deniers” :-)).

    Warmists say ECS is high, about 3C or greater and DANGEROUS and skeptics say ECS is 1C or less and NOT dangerous.

    Since CO2 clearly LAGS temperature at all measured time scales, this ECS mainstream debate requires that, in total, “the future is causing the past”, which I suggest is demonstrably false.

    In summary, in climate science we do not even agree on what drives what, and it is probable that the majority, who reside on BOTH sides of the ECS mainstream debate, are BOTH WRONG.”

    A belated Happy US Thanksgiving to all my American friends!

    Happy Hanukkah to all my Jewish friends!

    And an early Merry Christmas to all! And to all a good night!

    Regards, Allan

    Epilogue

    And all our yesterdays have lighted fools
    The way to dusty death. Out, out, brief candle!
    Life’s but a walking shadow, a poor player
    That struts and frets his hour upon the stage
    And then is heard no more. It is a tale
    Told by an idiot, full of sound and fury,
    Signifying nothing.

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