Studies of Carbon 14 in the atmosphere emitted by nuclear tests indicate that the Bern model used by the IPCC is inconsistent with virtually all reported experimental results.
Guest essay by Gösta Pettersson
The Keeling curve establishes that the atmospheric carbon dioxide level has shown a steady long-term increase since 1958. Proponents of the antropogenic global warming (AGW) hypothesis have attributed the increasing carbon dioxide level to human activities such as combustion of fossil fuels and land-use changes. Opponents of the AGW hypothesis have argued that this would require that the turnover time for atmospheric carbon dioxide is about 100 years, which is inconsistent with a multitude of experimental studies indicating that the turnover time is of the order of 10 years.
Since its constitution in 1988, the United Nation’s Intergovernmental Panel on Climate Change (IPCC) has disregarded the empirically determined turnover times, claiming that they lack bearing on the rate at which anthropogenic carbon dioxide emissions are removed from the atmosphere. Instead, the fourth IPCC assessment report argues that the removal of carbon dioxide emissions is adequately described by the ‘Bern model‘, a carbon cycle model designed by prominent climatologists at the Bern University. The Bern model is based on the presumption that the increasing levels of atmospheric carbon dioxide derive exclusively from anthropogenic emissions. Tuned to fit the Keeling curve, the model prescribes that the relaxation of an emission pulse of carbon dioxide is multiphasic with slow components reflecting slow transfer of carbon dioxide from the oceanic surface to the deep-sea regions. The problem is that empirical observations tell us an entirely different story.
The nuclear weapon tests in the early 1960s have initiated a scientifically ideal tracer experiment describing the kinetics of removal of an excess of airborne carbon dioxide. When the atmospheric bomb tests ceased in 1963, they had raised the air level of C14-carbon dioxide to almost twice its original background value. The relaxation of this pulse of excess C14-carbon dioxide has now been monitored for fifty years. Representative results providing direct experimental records of more than 95% of the relaxation process are shown in Fig.1.
Figure 1. Relaxation of the excess of airborne C14-carbon dioxide produced by atmospheric tests of nuclear weapons before the tests ceased in 1963
The IPCC has disregarded the bombtest data in Fig. 1 (which refer to the C14/C12 ratio), arguing that “an atmospheric perturbation in the isotopic ratio disappears much faster than the perturbation in the number of C14 atoms”. That argument cannot be followed and certainly is incorrect. Fig. 2 shows the data in Fig. 1 after rescaling and correction for the minor dilution effects caused by the increased atmospheric concentration of C12-carbon dioxide during the examined period of time.
Figure 2. The bombtest curve. Experimentally observed relaxation of C14-carbon dioxide (black) compared with model descriptions of the process.
The resulting series of experimental points (black data i Fig. 2) describes the disappearance of “the perturbation in the number of C14 atoms”, is almost indistinguishable from the data in Fig. 1, and will be referred to as the ‘bombtest curve’.
To draw attention to the bombtest curve and its important implications, I have made public a trilogy of strict reaction kinetic analyses addressing the controversial views expressed on the interpretation of the Keeling curve by proponents and opponents of the AGW hypothesis.
(Note: links to all three papers are below also)
Paper 1 in the trilogy clarifies that
a. The bombtest curve provides an empirical record of more than 95% of the relaxation of airborne C14-carbon dioxide. Since kinetic carbon isotope effects are small, the bombtest curve can be taken to be representative for the relaxation of emission pulses of carbon dioxide in general.
b. The relaxation process conforms to a monoexponential relationship (red curve in Fig. 2) and hence can be described in terms of a single relaxation time (turnover time). There is no kinetically valid reason to disregard reported experimental estimates (5–14 years) of this relaxation time.
c. The exponential character of the relaxation implies that the rate of removal of C14 has been proportional to the amount of C14. This means that the observed 95% of the relaxation process have been governed by the atmospheric concentration of C14-carbon dioxide according to the law of mass action, without any detectable contributions from slow oceanic events.
d. The Bern model prescriptions (blue curve in Fig. 2) are inconsistent with the observations that have been made, and gravely underestimate both the rate and the extent of removal of anthropogenic carbon dioxide emissions. On basis of the Bern model predictions, the IPCC states that it takes a few hundreds of years before the first 80% of anthropogenic carbon dioxide emissions are removed from the air. The bombtest curve shows that it takes less than 25 years.
Paper 2 in the trilogy uses the kinetic relationships derived from the bombtest curve to calculate how much the atmospheric carbon dioxide level has been affected by emissions of anthropogenic carbon dioxide since 1850. The results show that only half of the Keeling curve’s longterm trend towards increased carbon dioxide levels originates from anthropogenic emissions.
The Bern model and other carbon cycle models tuned to fit the Keeling curve are routinely used by climate modellers to obtain input estimates of future carbon dioxide levels for postulated emissions scenarios. Paper 2 shows that estimates thus obtained exaggerate man-made contributions to future carbon dioxide levels (and consequent global temperatures) by factors of 3–14 for representative emission scenarios and time periods extending to year 2100 or longer. For empirically supported parameter values, the climate model projections actually provide evidence that global warming due to emissions of fossil carbon dioxide will remain within acceptable limits.
Paper 3 in the trilogy draws attention to the fact that hot water holds less dissolved carbon dioxide than cold water. This means that global warming during the 2000th century by necessity has led to a thermal out-gassing of carbon dioxide from the hydrosphere. Using a kinetic air-ocean model, the strength of this thermal effect can be estimated by analysis of the temperature dependence of the multiannual fluctuations of the Keeling curve and be described in terms of the activation energy for the out-gassing process.
For the empirically estimated parameter values obtained according to Paper 1 and Paper 3, the model shows that thermal out-gassing and anthropogenic emissions have provided approximately equal contributions to the increasing carbon dioxide levels over the examined period 1850–2010. During the last two decades, contributions from thermal out-gassing have been almost 40% larger than those from anthropogenic emissions. This is illustrated by the model data in Fig. 3, which also indicate that the Keeling curve can be quantitatively accounted for in terms of the combined effects of thermal out-gassing and anthropogenic emissions.
Figure 3. Variation of the atmospheric carbon dioxide level, as indicated by empirical data (green) and by the model described in Paper 3 (red). Blue and black curves show the contributions provided by thermal out-gassing and emissions, respectively.
The results in Fig. 3 call for a drastic revision of the carbon cycle budget presented by the IPCC. In particular, the extensively discussed ‘missing sink’ (called ‘residual terrestrial sink´ in the fourth IPCC report) can be identified as the hydrosphere; the amount of emissions taken up by the oceans has been gravely underestimated by the IPCC due to neglect of thermal out-gassing. Furthermore, the strength of the thermal out-gassing effect places climate modellers in the delicate situation that they have to know what the future temperatures will be before they can predict them by consideration of the greenhouse effect caused by future carbon dioxide levels.
By supporting the Bern model and similar carbon cycle models, the IPCC and climate modellers have taken the stand that the Keeling curve can be presumed to reflect only anthropogenic carbon dioxide emissions. The results in Paper 1–3 show that this presumption is inconsistent with virtually all reported experimental results that have a direct bearing on the relaxation kinetics of atmospheric carbon dioxide. As long as climate modellers continue to disregard the available empirical information on thermal out-gassing and on the relaxation kinetics of airborne carbon dioxide, their model predictions will remain too biased to provide any inferences of significant scientific or political interest.
References:
Climate Change 2007: IPCC Working Group I: The Physical Science Basis section 10.4 – Changes Associated with Biogeochemical Feedbacks and Ocean Acidification
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch10s10-4.html
Climate Change 2007: IPCC Working Group I: The Physical Science Basis section 2.10.2 Direct Global Warming Potentials
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-10-2.html
GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 15, NO. 4, PAGES 891–907, DECEMBER 2001 Joos et al. Global warming feedbacks on terrestrial carbon uptake under the Intergovernmental Panel on Climate Change (IPCC) emission scenarios
ftp://ftp.elet.polimi.it/users/Giorgio.Guariso/papers/joos01gbc[1]-1.pdf
Click below for a free download of the three papers referenced in the essay as PDF files.
Paper 1 Relaxation kinetics of atmospheric carbon dioxide
Paper 2 Anthropogenic contributions to the atmospheric content of carbon dioxide during the industrial era
Paper 3 Temperature effects on the atmospheric carbon dioxide level
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Gösta Pettersson is a retired professor in biochemistry at the University of Lund (Sweden) and a previous editor of the European Journal of Biochemistry as an expert on reaction kinetics and mathematical modelling. My scientific reasearch has focused on the fixation of carbon dioxide by plants, which has made me familiar with the carbon cycle research carried out by climatologists and others.
“The 90 GtC is for the total oceans, of which about 50 GtC goes in and out the mixed layer ”
So you’re saying every year 40 Gtn gets through the mixed layer, in and out inside a year?
Is that the figure for deep water turn over?
Greg says:
July 7, 2013 at 11:04 am
As long as we’re agreed that it is the rate of change that’s fine.
You wished to invoke the 150 Gtn figure. Now that is not an annual rate of change , the annual figure is about 4 Gtn/a
Agreed with the 4 GtC/a, as that is the real rate of change.
The 150 GtC is not part of it (except for the 4 GtC deficit), it is only the overall turnover rate of all inflows and outflows. But it is responsible for the thinning of bomb spike 14C, as good as it is responsible for the thinning of the 13C depleted effect of fossil fuel burning. Therefore it doesn’t matter if that was exchanged in halve a year, as for thinning only the total amount replaced x concentration of the isotope matters.
That has nothing to do with mass removal (which is less than 3% of the turnover) but with turnover flows and concentrations.
Greg says:
July 7, 2013 at 12:02 pm
Is that the figure for deep water turn over?
According to my own estimate, based on the thinning of the 13C decrease in the atmosphere from fossil fuel burning:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
But I have no objection if you want to use other deep ocean exchange rates and see what happens…
So you’re saying every year 40 Gtn gets through the mixed layer, in and out inside a year?
The upwelling around the Pacific equator (near Chile) in general is directly to the surface, which the fishermen there do like very much. The downwelling in the NW Atlantic is directly into the deep…
Greg says:
July 7, 2013 at 9:45 am
So you are assuming that the ‘equilibrium’ has not moved during the last 150 years of absorbing emissions. Maybe that is based on some other undeclared assumption. It is always useful to list what assumptions one is making.
Sorry, again an omission…
The extra assumption is that the equilibrium setpoint is what it was in the far distant and more nearby pre-industrial era: around 290 ppmv at the current temperature. With a change of 8 ppmv/K for any change in temperature.
An assumption which is backed by CO2/T ratio’s over 800 kyears ice cores and several other proxies.
Ferdi: ” Therefore it doesn’t matter if that was exchanged in halve a year”
It matters if you are trying to calculate the time constant which is precisely what you were doing.
Quick review of the carbon cycle magnitude per NASA in Gt.:
Ocean to atmosphere 90
Microbial respiration land 60
Plant respiration land 60
Human 9
———
Total surface to atmosphere 219
Photosynthesis land 123
Atmosphere to Ocean 92
——-
Total surface to atmosphere 215
http://geosciencebigpicture.com/?attachment_id=719
So if this is anywhere near right carbon should be accumulating in the atmosphere at about 4Gt/yr these days, less in the past, and likely more in the future.
While we sweat out the details of which sinks are pressure, temperature, pH, or chemically limited, it is worth bearing in mind the magnitude of the sinks. Temperature and partial pressure apply everywhere (albeit differently). Chemical and pH limitations apply mostly to the ocean which constitutes less than half of the total cycle.
Please notice that while lip service is given to photosynthesis and respiration in the photic zone of the ocean, no attempt is made to ascribe C flux values for these except the 2 Gt budgeted for carbonate rain. It is worth noting that carbonate precipitation actually increases pCO2 in the water as a result of the pH change.
The entire carbon cycle on land is biological. Uptake will select against the heavy isotopes and output will be weighted light. (Chemical weathering is not mentioned above and both silicate and carbonate weathering will be isotiopically blind on the atmosphere side, but the carbonate itself will be weighted light.)
The ocean is the repository for biologically rejected isotopes. They travel by the rivers and the winds from land and also accumulate from biological rejection by plankton. Ocean sinks and sources are nearly half non biological (inorganic) and blind to isotopes.
Ferdinand says that 40Gt goes into (and presumably comes out of) the deep ocean so that leaves 50Gt of ocean flux that is probably biological.
Therefore, 80% of the carbon cycle shares an isotopic signature similar to human production.
Willis Eschenbach: “Another person who conflates residence time and pulse half-life”
Nick Stokes: “Another post refusing to understand the difference between residence time and replacement time”
Ferdinand Engelbeen:”The basic point of this paper is completely wrong. The residence time has nothing to do with the decay time of some injected extra amount of CO2.”
The basic point of Paper 1 has nothing to do with the difference between residence time and the relaxation time (which I understand quite well and do my best to explain in the paper). The basic point regards the bombtest curve, which shows that the relaxation of the excess 14CO2 created by the bomb tests conforms to a monoexponential decay function and hence can be characterized by a single RELAXATION TIME (not residence time) estimated to 14 years. That information (describing the ‘impulse response function’ for CO2) is all one requires to estimate how much emissions contribute to increasing the atmospheric CO2 level. It forms the basis for my conclusion in Paper 2 that only half of the increase indicated by the Keeling curve is of human origin.
I do point out, however, that the bombtest curve tends towards a final value that certainly is lower than 5% and consistent with the expected value 1.5%. This means that the removal of excess CO2 from the air is practically irreversible (Keq <0.05), for which reason the residence time would be expected to be practically equal to the relaxation time. Reported experimental values of the residence time may be expected to provide satisfactory estimates of the relaxation time and have been thus apprehended by experimentalists such as Bolin, Revelle, Suess, etc.
So, the available empirical information on the relaxation of airborn CO2 is fully consistent with what one would expect to find when there is a practically irreversible uptake of atmospheric CO2 by one vastly predominant sink (the hydrosphere): An essentially monoexponential decay with a relaxation time of the same order of magnitude as the reported residence times (5–15 years).
The IPCC disregards this empirical information, claiming that the relaxation kinetics are adequately described by the impulse response function prescribed by the Bern model. Parameter values in that model have been so chosen that they result in an impulse response function consistent with the presumption that emissions account for 100% of the CO2 increase indicated by the Keeling curve. The model designers have started with a prejudiced view on the CO2 increase caused by emissions, and as IPCC authors disqualify all experimental data (relaxation times as well as residence times) that are inconsistent with the model. That is not an acceptable approach in empirical science. Paper 1 shows that the Bern model prescriptions are gravely inconsistent with, and therefore falsified by, the empirical observations made.
Willis Eschenbach: “Another person who conflates residence time and pulse half-life”
Nick Stokes: “Another post refusing to understand the difference between residence time and replacement time”
Ferdinand Engelbeen:”The basic point of this paper is completely wrong. The residence time has nothing to do with the decay time of some injected extra amount of CO2.”
The basic point of Paper 1 has nothing to do with the difference between residence time and the relaxation time (which I understand quite well and do my best to explain in the paper). It deals with the bombtest curve, which shows that the relaxation of the excess 14CO2 created by the bomb tests conforms to a monoexponential decay function and hence can be characterized by a single RELAXATION TIME estimated to 14 years. That information (describing the ‘impulse response function’ for CO2) is all one requires to estimate how much emissions contribute to increasing the atmospheric CO2 level. It forms the basis for my conclusion in Paper 2 that only half of the increase indicated by the Keeling curve is of human origin.
I do point out, however, that the bombtest curve tends towards a final value that certainly is lower than 5% and consistent with the expected value 1.5%. This means that the removal of excess CO2 from the air is practically irreversible (Keq <0.05), for which reason the residence time would be expected to be practically equal to the relaxation time. Reported experimental values of the residence time may be expected to provide satisfactory estimates of the relaxation time and have been thus apprehended by experimentalists such as Bolin, Revelle, Suess, etc.
So, the available empirical information on the relaxation of airborn CO2 is fully consistent with what one would expect to find when there is a practically irreversible uptake of atmospheric CO2 by one vastly predominant sink (the hydrosphere): An essentially monoexponential decay with a relaxation time of the same order of magnitude as the reported residence times (5–15 years).
The IPCC disregards this empirical information, claiming that the relaxation kinetics are adequately described by the impulse response function prescribed by the Bern model. Parameter values in that model have been so chosen that they result in an impulse response function consistent with the presumption that emissions account for 100% of the CO2 increase indicated by the Keeling curve. The model designers have started with a prejudiced view on the CO2 increase caused by emissions, and as IPCC authors disqualify all experimental data (relaxation times as well as residence times) that are inconsistent with the model. That is not an acceptable approach in empirical science. Paper 1 shows that the Bern model prescriptions are gravely inconsistent with, and therefore falsified by, the empirical observations made.
Gosta, I presume the double post was an accident but this seems also identical to what you posted July 7, 2013 at 4:04 am
Perhaps it would be worth commenting on the C14 dilution question, rather then just repeating your reply to Willis’ trivial remark three days ago.
Ferdi, I’ve been thinking about this. The rate of change for the annual variation is (crudely) estimated by 300 Gtn/annum which leads to 2.67 years. This will apply to all species and is probably an inaccurate assessment of the short time constant 1.18 years as I already said.
But the dilution argument seems non negligible.and would lead to a dilution of the excess.
The volume of that exchange seems to be 90 Gtn (thanks, genoderm, for the source) which leads to a tau of about 9 years.
So it would appear that some correction to the C14 curve is required before the fitting or the results are combined mathematically. It looks like this is going to give a result close to 22 years.
I hope Gosta will be able to comment on this rather then replying to Willis et al again.
The volume of that exchange seems to be 90 Gtn (thanks, genoderm, for the source) which leads to a tau of about 9 years.
This is another relaxation process due to an annual dilution of 800/90=11%
x=-k.dx/dt where dx/dt is 11% per year. The solution of that is an exponential decay with tau=1/0.11 years
Implications for paper2:
Since Gosta’s El Nino figure is a 6 month reaction this should be compared to the time constant derived from the 6 month flux. From above that’s 2.67 years and, I think, more correctly from the double exponential fit giving 1.17 or Bern 1.18 years.
Paper 2:
when a typical 6 monthly change gives an approximate time constant of 800/300 it does not seem appropriate to use 14 years for this calculation for an El Nino variation of 6 months.
1–Exp[-0.5/2.67] ≈ 0.53 ; 5 / 0.17 ≈ 29..4 ppm/ ̊C.
1–Exp[-0.5/1.18] ≈ 0.35 ; 5 / 0.35 ≈ 14.3 ppm/ ̊C.
These results being close to the classical result. Lance Wallace confirmed such a time constant could be determined from the C14 curve.
Perhaps Gosta will be able to comment on that line of reasoning.
It would appear that the C14 curve corroborates rather then refutes at least the first two periods of the Bern model. The third one and the large residual that it implies needs checking.
It would be interesting to see some account taken of the dilution argument Ferdi raised, in the form of a correction to the C14 curve similar to the correction Gosta did for C13.
This will lengthen the 14 year (or rather produce a splitting of the two time constants by a non negligible Kep). This also implies a more significant residual.
Without pre-empting the results , I suspect this will show a smaller residual than the Bern 22%.
It would be good if Gosta did this since it was his paper , however he does not seem too interested in any discussion of his work, so someone else may need to do this.
Greg says:
July 7, 2013 at 1:29 pm
Ferdi: ” Therefore it doesn’t matter if that was exchanged in halve a year”
It matters if you are trying to calculate the time constant which is precisely what you were doing.
You did put me on the wrong leg with this… I was thinking that it was a matter of misunderstanding/language, but it is not. Something did go wrong in the way you calculate the residence time.
Take the 4 GtC/year removal of CO2 in two options:
– halve a year the outflux is 0.67 GtC/month in a square drop, next halve a year there is no outflux.
– the outflux is 0.33 GtC/month throughout the year.
If you are right, the 4 GtC/0.5 year gives halve the decay time of the 4 GtC/year, while in fact the same quantity/year is removed.
If you want the real decay time in years, you must use the average removal over a full year, which in both cases is equal…
This argument would be so much easier if certain people understood calculus. The evidence is very clear. CO2 in the atmosphere evolves according to the equation
dCO2/dt = k*(T – Teq)
All the carefully worded constructs of Ferdinand et al. are essentially rationalizations of how they want things to be. That is why mathematics is the language of science. Math is incorruptible. It obeys absolute rules which cannot be twisted based on personal preference.
The one simple equation above negates every flailing assertion by those who believe humans are controlling atmospheric CO2. It contains everything one needs to know to reconstruct the history of atmospheric CO2 since precise measurements began. And, it is entirely independent of human inputs.
That’s it. Continuing to argue about it merely highlights the detractors’ unfamiliarity with higher mathematics. As time relentlessly marches on, and the inexorable forces of nature continue to increase the divergence between the human-induced hypothesis and the real world, the contention will eventually be laid to rest.
gymnosperm says:
July 7, 2013 at 5:22 pm
Ferdinand says that 40Gt goes into (and presumably comes out of) the deep ocean so that leaves 50Gt of ocean flux that is probably biological.
The 50 GtC in/out the ocean’s surface, the “mixed layer” is mainly temperature related: it is there that the largest summer-winter temperatures difference occurs on a very large surface. The biological pump of course is at work, but works opposite to the temperature “pump”.
Therefore, 80% of the carbon cycle shares an isotopic signature similar to human production
The natural carbon cycle isotopic signature in the atmosphere is opposite to the human production: There is slightly more uptake by the biosphere (land and ocean vegetation, animals, mirobes,…) than release of CO2. That means that, due to the isotopic discrimination, relative more 13CO2 is left in the atmosphere. Human emit CO2 that is relative 13CO2 depleted…
Greg Goodman says:
July 8, 2013 at 5:28 am
It would appear that the C14 curve corroborates rather then refutes at least the first two periods of the Bern model. The third one and the large residual that it implies needs checking.
It would be interesting to see some account taken of the dilution argument Ferdi raised, in the form of a correction to the C14 curve similar to the correction Gosta did for C13.
This will lengthen the 14 year (or rather produce a splitting of the two time constants by a non negligible Kep). This also implies a more significant residual.
As has been discussed the C14 decay curve isn’t representative of CO2 because it’s the result of a different set of sources and sinks.
C14 is created in the atmosphere from Nitrogen, unlike CO2 the C14 is diluted by CO2 from fossil fuel combustion which contains no C14, also the oceans from which CO2 returns is depleted in C14 due to exchange with deep water (C14 age range 400-1200 years).
Gösta Pettersson says:
July 7, 2013 at 6:51 pm
deals with the bombtest curve, which shows that the relaxation of the excess 14CO2 created by the bomb tests conforms to a monoexponential decay function and hence can be characterized by a single RELAXATION TIME estimated to 14 years.
That information (describing the ‘impulse response function’ for CO2) is all one requires to estimate how much emissions contribute to increasing the atmospheric CO2 level.
That is essentially wrong: the 14CO2 bomb spike relaxation time has very little connection with the relaxation time for an injection of extra CO2 in the atmosphere. The 14CO2 bomb relaxation is mainly caused by the year-by-year exchange of part of the atmospheric CO2 with CO2 out of the deep oceans, which contains “normal” levels of CO2 compared to the CO2 bomb spike. The deep ocean exchanges are about 5% of the atmospheric CO2 content. Other reservoirs also contribute, but these give part of the higer 14CO2 levels back in other seasons/years.
The real decay rate of any excess CO2 injection (whatever the cause) is over 50 years, as that doesn’t depend on exchange rates, but depends on the difference between all inputs together and all outputs together. That is currently 4-5 GtC/year, while the offset to the temperature controlled equilibrium currently is about 210 GtC (100 ppmv). That has nothing to do with the residence time of 14CO2 or any other CO2 molecule in the atmosphere.
Bart says:
July 8, 2013 at 9:53 am
CO2 in the atmosphere evolves according to the equation
dCO2/dt = k*(T – Teq)
Completely right for the short term (1-3) years variability, wrong for the longer-term (3-50 years) variability, as that is based on an arbitrary choosen baseline: that is curve fitting.
Moreover, the result of the above formula on short term is an increase of CO2 in the atmosphere, which itself influences dCO2/dt, effectively reducing it to near zero within a few years, if no other variables like human emissions are involved (which makes it happen even faster).
That is when the CO2 level increased to maximum about 16 ppmv for (T-Teq) = 1 K.
And it violates about all known observations, including the above discussed bomb spike curve. That should show an increase in reduction speed, as any increase in natural tunover must follow the increase in human emissions, which more than doubled since 1960. Thus one should observe a halving of the residence time over the past 50 years…
Ferdinand Engelbeen says:
July 8, 2013 at 11:12 am
“Completely right for the short term (1-3) years variability, wrong for the longer-term (3-50 years) variability, as that is based on an arbitrary choosen baseline: that is curve fitting.”
Everything is curve fitting. But, we have a physical basis, and it is what we see in the data. You cannot arbitrarily agree with the relationship in the short term, and not in the long. If you had a better grip on differential equations, and the existence and uniqueness theorems for their solution, you would realize that you are babbling incoherently.
“Moreover, the result of the above formula on short term is an increase of CO2 in the atmosphere, which itself influences dCO2/dt, effectively reducing it to near zero within a few years, if no other variables like human emissions are involved (which makes it happen even faster).”
If that were the case, it would be evident in the data. It isn’t, and it isn’t.
“Thus one should observe a halving of the residence time over the past 50 years…”
Words, words, words. You can convince yourself of anything with words. That is why mathematics is the language of science.
Mathematics has never been the language of science. There is a group of people for whom it replaces science; these are often the same people who equate mathematics with nature. For the rest of us, it is just a tool. It has no independent validity and it is not incorruptible; on the contrary, it is often used to cover up bad ideas.
Ferdinand Engelbeen says:
July 8, 2013 at 10:57 am
To be clear, the sentence:
The 14CO2 bomb relaxation is mainly caused by the year-by-year exchange of part of the atmospheric CO2 with CO2 out of the deep oceans, which contains “normal” levels of CO2 compared to the CO2 bomb spike.
Should be read as:
The 14CO2 bomb relaxation is mainly caused by the year-by-year exchange of part of the atmospheric CO2 with CO2 out of the deep oceans, which contains “normal” levels of 14CO2 compared to the 14CO2 bomb spike.
Which makes that every year 5% (40 GtC deep ocean circulation/800 GtC in the atmosphere) of the 14C bomb spike is replaced by CO2 which has only 45% – or less (45% is for 400 years old deep water) – of the initial bomb spike 14C concentration.
That gives a decay rate of 50 % (first years extra) / 2.75 (first years loss) = 18.2 years.
Thus most of the 14 years decay rate is largely due to the exchanges with the deep oceans, and only for a small part with the mass distribution of some extra CO2 in the atmosphere into other reservoirs.
Bart says:
July 8, 2013 at 11:38 am
“Moreover, the result of the above formula on short term is an increase of CO2 in the atmosphere, which itself influences dCO2/dt, effectively reducing it to near zero within a few years, if no other variables like human emissions are involved (which makes it happen even faster).”
If that were the case, it would be evident in the data. It isn’t, and it isn’t.
If you don’t accept any data which doesn’t fit your hypothesis, then we are end of discussion. All you have is a nice fit, caused by a completely arbitrary baseline. If the hypothesis is right, then it should fit all observations. If one and only one observation is violated, then the hypothesis is rejected.
So my question is to explain two things:
– What is the effect of more CO2 on dCO2/dt.
– Does the circulation of CO2 increase in ratio with the human emissions and how affects that the residence time.
If that is the same climate system you are talking about the decay constant can be approximated by the first figure. In the second case the rate of change is being limited by something else. This is why if REPEATEDLY said that this is a crude and inaccurate way of estimating it and you need to solve the ODE , as Gosta does, to get a valid result.
Now since you are obviously quite unwilling to learn anything here and I’ve explained it a least ten times, I have better things to do than to try in vain to explain to one Engelbeen how this should be done.
I thank you for your input, you have good knowledge of the various concentration issues and have informed me about a number of things.
Since Gosta also seems uninterested in defending or correcting his work this thread has become a waste of time.