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?

clip_image002

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.

clip_image014

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.

clip_image016

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).

clip_image024clip_image026

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).

clip_image028clip_image030

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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milodonharlani

Professores verum puto.

Robert W Turner

No no no! Ignore reality and look at this computer model please.

cirby

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.

Hoser

Glad you took the time to show the math. It wasn’t practical to do so when I posted
http://wattsupwiththat.com/2013/03/29/james-hansen-says-coal-is-greening-the-planet/#comment-1261256

george e. smith

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.

Pippen Kool

“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.

milodonharlani

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.

DocMartyn

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

Pippen Kool

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.

“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! ! ! ! !

Jquip

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.

Jimbo

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.

Jimbo

I forgot state the reason by I want more co2. It is HERE.

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.

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:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/14co2_distri_1960.jpg
and here the situation in 2000:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/14co2_distri_2000.jpg
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:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
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…

* Calling Ferdinand

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 …..

Leo Smith

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.

M Courtney

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.

Jquip

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.

geran

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….

Sisi

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?

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:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_cur.jpg
neither in the years since Mauna Loa:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1960_cur.jpg
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…

Thank you, Ferdinand

geran

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….

Ian W

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.

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”.

Sisi

@geran
Isn’t it ironic? 😀
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!
?

Jquip

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.

Jquip

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.

Doug Proctor

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.

geran

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

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 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

Sisi

@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!

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

Bart

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.

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?

bobl

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

Jquip

@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.

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…

Jquip

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.

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

ColdinOz

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.

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…

Doug Proctor

Hmmm. That would be a serious mistake of mine.

sailboarder

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.

joeldshore

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.

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.

AJ

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.

geran

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.

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…