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.
Atmospherically speaking, if we put in enough CO2 to raise the parts per million by five, each year recently, and the PPM goes up by two, each year since the 80’s or something, then what makes you think the CO2 we put in has anything at all to do with the increase? They do not appear to be related in any simple way, if at all. Particularly since, each year, Mother Nature with all her tricks, puts in and takes out, not in any balanced way, enough to raise the PPM, or lower the PPM, 150 PPM? This strains credulity.
Secondly, travelling about in forested areas, this 54-year-old notices that the vegetation is lush, really lush, far more than before. \
What does it all mean?
Louis Hooffstetter says:
July 1, 2013 at 11:13 pm
“Atmospheric testing of nuclear weapons during the 1950s and early 1960s doubled the concentration of 14C/C in the atmosphere.”
Sorry to be thick, but how did nuclear testing do this?<em?
Neutrons from the atmospheric nuclear explosions converted nitrogen nuclei to C14 nuclei.
TerryS says:
July 2, 2013 at 3:03 am
“If you add a pulse (P) of water to the bucket you can calculate how much is left after time (t) with the following formula:
P(t) = P * e^(-t/r)”
—
This is totally misleading
What you calculate there is how much of the water molecules from the pulse that are left. This is a totally different measure from what the Bern Formula calculates.
To explain I’ m going back to the example with pre-industrial levels of 278 ppm or 2173 Gt in the atmosphere and a natural flow of 771 Gt annually:
You correctly states that the residence time, given the above numbers, is 2173/771 = 2.82 years.
But that number has almost no interest. The interesting figure is the depletion time of excess CO2 level, and that depletion time has no connection to the residence time.
To see this you can imagine that you add 100 Gt in one pulse so the level increases from 2173 to 2273 Gt. It is nothing in your figures that tell how long time it will take to half the excess level, i.e. bring it down to 2223 Gt. To do that you must know how much the sinks increase from the natural level of 771 Gt in response to the excess level. As long as you do not have any figures for that you cannot calculate the depletion time of excess CO2.
That is what the Bern formula tells.
Ferdi: ” but that is rapidely countered by the change of CO2 in the atmosphere”
Without stating what you mean by “rapidly” that declaration is meaningless.
If found 8ppm/year/K on the inter-annual scale and 4ppm/year/K on inter-decadal scale. That could be the first approximation to the time scale of equilibration. How you arrived at the opposite figures I seem to have missed.
The time to equilibration could also be derived from the “800” year lag if that could be firmed up a bit IIRC it was given as 800+/-500 years. There is likely a need for at least two time constants over that kind of period and the gross assumption that a linear model can still be applied during a non linear transition between two climate states during which CO2 itself is likely to be acting as a significant positive feedback.
In the absence of anything more rigorous I retain my first approximation of 8ppm/a/K and 4ppm/a/K that suggests equilibration of the impulse response would be of the order of a century. To grab a figure I’d say time constant of 20-25 years with large error bars though again a single slab model is insufficient for the long term solution.
Now all that is more to do with thermal mixing and relationship of SST to OHC than it is to do with CO2. Thermal diffusion can be related to gas diffusion and someone at Lucia’s referred me to the Schmidt number, which for CO2 in salt water is about 660. ie CO2 equilibration will be about 600 times faster.
Now if the IPCC insist on ignoring the basic physical laws and seeing all this backwards, that may be explain how they manage to apply a 20 year Bern time constant to CO2 absorption.
The other gross error in using de-glaciation to bound the temp CO2 equilibrium response is that it totally ignores air pressure. Was atmospheric pressure the same during the last glacial max. ? Doubt it.
http://climategrog.wordpress.com/?attachment_id=259
Ferdinand,
The biosphere is not a net sink for C12. It is relatively neutral as over time it emits about as much as it consumes thru the process of decay. http://www.bomi.ou.edu/luo/pdf/Differentiation.pdf. In Duke Forest (FACE experiment) an increase in atmospheric CO2 taken up by the trees was re-introduced into the atmosphere about ten years later.
Greg Goodman says:
July 2, 2013 at 7:15 am
Then some of our trivial assumptions about the carbon cycle are wrong. “Way higher ” is how much higher? IIRC it’s not that much numerically. Maybe the lighter C12 also outgasses preferencially. It is afterall the water air interface in plants and plankton membranes that determines the preferential uptake. Why not preferentail release.
The d13C level of the deep oceans is 0 to 1 per mil, that of the surface is 1-5 per mil, due to biolife, of which part of organics drop down into the deep. The exchange of CO2 between ocean surface and atmosphere and back gives a drop of ~8 per mil in d13C. That can be seen in coralline sponges and atmospheric measurements (ice cores, firn, direct):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
The atmosphere was around -6.4 per mil pre-industrial, down to – 8 per mil currently.
The change over a glacial-interglacial transition is about 0.2 per mil. During the whole Holocene, the variability was +/- 0.2 ppmv. Since the start of the industrial revolution, the drop is 1.6 per mil in the atmosphere and 1 per mil in the ocean surface… Doesn’t seems to me that the oceans are the source of the decline of 13C in the atmosphere…
Greg Goodman says:
July 2, 2013 at 7:24 am
“The primary change is directly proportional to the change in temperature”
The rate of outgassing is proportional the deviation from the temperature at which the current concentration would be in equilbrium. d/dt(CO2) proportional to delta T NOT dT/dt.
So as long as the temperature remains elevated and (at the very least) the mixed layer of the world oceans has not re-equilibriated, the outgassing will continue.
Not true.
Henry’s Law says that the ratio of pCO2/[CO2] is constant, therefore if we add CO2 to the atmosphere (increase pCO2) [CO2] (the concentration in the ocean) will increase until equilibrium is re-established and both pCO2 and [CO2] are greater than their former values. This is a dynamic equilibrium, at all times there is a flux out and a flux into the atmosphere even though the net flux is zero. The effect of temperature is to change the Henry’s Law coefficient, which as Ferdinand has pointed out results in an increase in pCO2 of ~8ppm/ºC increase in SST. The pCO2 is increasing by between 2 and 3ppm/year, but global SST has only changed over the last 30 years by ~0.07ºC/year (HADISST) which would only account for ~0.5 ppm/yr. The annual fluctuation is around 0.1ªC which accounts for the temperature correlation on individual years, the current temperature modulates the Henry’s Law coefficient and so causes a fluctuation in pCO2 but the overall annual growth in SST is insufficient to account for the annual growth in pCO2.
This is consistent with measurements which show that [CO2] is increasing.
Ferdi: “… mainly influenced by wind speed. Assuming the latter relative constant, only the partial pressure difference is of interest.”
Assumptions, assumptions. Not so constant my friend.
http://climategrog.wordpress.com/?attachment_id=409
The nine cycle is in trade winds is particularly interesting for a number of other reasons.
Michael Moon says:
July 2, 2013 at 8:03 am
Atmospherically speaking, if we put in enough CO2 to raise the parts per million by five, each year recently, and the PPM goes up by two, each year since the 80′s or something, then what makes you think the CO2 we put in has anything at all to do with the increase? They do not appear to be related in any simple way, if at all. Particularly since, each year, Mother Nature with all her tricks, puts in and takes out, not in any balanced way, enough to raise the PPM, or lower the PPM, 150 PPM? This strains credulity.
And yet ‘Mother Nature’ fails to do so and the pCO2 goes up by approximately the same amount (~50% of human fossil fuel emissions) every year! So based on your logic we could say that the annual growth is not related to ‘Mother Nature’s tricks’.
Willis Eschenbach says:
July 2, 2013 at 12:26 am
“The “temperature dependent natural increase” in atmospheric CO2 is a doubling of CO2 for every 16 degrees C temperature rise…If the starting CO2 level is 350 ppmv and the temperature goes up half a degree, the CO2 level only goes up by about 7 ppmv …”
OMG 16 C. Let’s check.
The 20th century SST rise was 0.657 K. (HadSST2)
The CO2 kilogram per liter per Kelvin water solubility ratio is ~` -0.00008 kg per liter per Kelvin
The CO2 absolute mass in the atmosphere at the end of the 20th century was 368.75 ppmv which means 0.036875 x [44.0095/28.97] x 2.8838×10^15 kg
If we would assume the temperature increase and CO2 outgassing only in the upper 100m epipelagic zone of the ocean* then we can calculate the temperature dependent CO2 outgassing in absolute numbers as:
3.611×10^19 liters of water are in the upper 100 meters of ocean x 0.657 x 0.00008 = 1.898×10^15 kg CO2 outgassed.
I note this amount of then airborne CO2 for obvious reasons of well understood physical nature cannot sink back in the ocean/get diluted again until its surface temperature descends.
1.898×10^15 / 2.8838×10^15 = 0.658
-which is quite visibly higher number than 0.5 number which it would be for the atmospheric CO2 content doubling.
If you object that this is in mass not volume then:
1.898×10^15 / 5.148X10^18 [weight of the atmosphere] = 0.0368 mass% = 0.0242 volumetric% = 242 ppm – which is just number to be for idea compared to the 368.75 ppm at the end of the 20th century, nothing else, I don’t claim the 242 ppm from the 368.75 ppm was all outgassed from ocean, because there are carbon sinks – see 2. below.
Here you see:
1. Only the CO2 outgassing from the upper 100m sea surface layer due to the SST rise – by way less than 1K – can be in absolute numbers way higher than is the half of the then atmospheric CO2 content.
2. Part of the outgassed CO2 must have sunk at land, most probably by the higher temperature and by higher CO2 content induced biological sequestration enhancement – simply because the absolute number for theoretically predicted outgassing based on simple physics – although at right order of magnitude – is nevertheless significantly higher, than the actually observed rise of the CO2 content in the atmosphere.
Just btw: The 0.657 K SST rise in the 20th century IS very consistent with the Solanki reconstructed 20th century TSI rise in absolute numbers. See here.
——————————–
*((- mainly TSI change dependent, because water is extremely opaque to the mid-IR 288K spectra and therefore a GHE can’t have more than a negligible effect on the SST rise, moreover most probably more than canceled by the surface evaporation/latent heat transfer up the atmosphere and higher emissivity given by the higher temperature))
Ferdi, thanks for all the numbers and the graph: http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
I’d seen that before but not really studied it. It seems to show a response to cooling around 1600 and that the later increase was a process that started about 150-200 years before even the dawn of the “human emissions” of industrial era in 1850.
I presume you posted that because you consider it shows AGW dC13 impact but what I see is proof that warming affects the ration in the same way now as it did coming out of the Maunder Min.
Willis Eschenbach says:
July 2, 2013 at 12:26 am
sorry, correction of the sentence:
The CO2 absolute mass in the atmosphere at the end of the 20th century was 368.75 ppmv which means 0.00036875 x [44.0095/28.97] x 5.148×10^18 kg [mass of the atmosphere] = 2.8838×10^15 kg CO2 in the atmosphere.
Re: jkanders
What you calculate there is how much of the water molecules from the pulse that are left. This is a totally different measure from what the Bern Formula calculates.
This is exactly what the Bern Formula calculates. It calculates how much CO2 is left from a pulse of CO2 after a period of time.
According to the Bern Formula if I add 100Gt of CO2 then after 1 year there will be 89.33Gt left and after 2 years there will be 82Gt left.
The problem is that the Berne model does not mix the CO2. At the very start it evenly distributes the 100Gt pulse over the entire planet (or carbon sinks if you prefer) but it then has a molecule of CO2 that it placed above, say, Las Vegas staying above Las Vegas (until captured by a sink) and never getting to see the ocean (or any other place). This behaviour might not have been the way the model was designed to act, but it is the way it actually does act. The reason I know this is because that is what the formula physically represents.
100Gt will increase the ppm by about 13ppm so if you take a starting point of 278ppm, add 100Gt and then abide by the Berne models formula you get the following:
Year 0:
100% of planet has CO2 levels at 291ppm
Year 2:
8% of planet has CO2 levels at 281ppm
21% of planet has CO2 levels at 286ppm
71% of planet slightly below 291ppm
Year 4:
8% of planet at 279ppm
21% of planet at 283
25% of planet at 288
46% of planet slightly below 291ppm
Year 8:
8% of planet at 278ppm
21% of planet at 280ppm
25% of planet at 286ppm
46% between 289 and 291ppm
Year 32:
29% of planet at 278ppm
25% of planet at 280ppm
19% of planet at 285ppm
27% of planet at 290/291ppm
Clearly the above is ridiculous but that is the practical result of the Berne model.
For those interested here are some papers out this year on the greening of the biosphere over the past 30 years or so.
Ferdi: “The partial pressure of the atmosphere is currently around 400 microatm (~400 ppmv), while the partial pressure of the oceans at the highest temperature is about 750 microatm at equilibrium with the atmosphere. That gives a permanent flux ocean-atmosphere of X GtC/year.
Now the overall temperature of the oceans suddenly increases with 1°C. That makes that the partial pressure in seawater at equilibrium increases with ~16 microatm. That means that X increases:
Xi = X/(750-400)*(766-400) = 1.046 X”
Thanks again for the numbers. Now that show values where the temperature induced change of 16 is relatively unimportant in the ration. So this explains why out gassing in the tropics is relatively unimportant to global CO2.
It probably goes some way to explaining another thing that surprised me when I first noticed:
http://climategrog.wordpress.com/?attachment_id=231
It seems that GLOBAL , well mixed CO2 as reflected at MLO is determined largely by polar atmospheric pressure conditions, with a somewhat variable lag that probably depends upon atm. circulation patterns.
Your example of the hottest water is not the one that is most sensitive to change. Since the North pole is an ocean with large expanses of exposed water for a large part of the year, it seems to be more important than the continental south pole.
Perhaps you could give some numbers that help explain those observations.
Steve Short says:
July 2, 2013 at 2:57 am
Tallbloke says:
“The biological factors shouldn’t be omitted in this debate. There is a strong correlation between fish stocks and the ~60yr oceanic cycles. This is food chain derived. If there are less fish in the warm phases of the ocean cycles then it is because there is less food for the(m) to eat. At the base of the food chain are the plankton.”
Are you serious? There is no established relationship between world fish stocks and plankton abundance in a world where all sorts of things, not the least over fishing affecting fish stocks. I can’t for the life me figure out where you got that barmy idea from.
Here:
http://tallbloke.wordpress.com/2013/04/09/north-sea-fisheries-makes-a-recovery-cooler-seas-busier-plankton/
This is a very worthwhile article as it well illustrates that empirically determined metrics of atmospheric CO2 are far superior to the egregiously determined theoretical values which are shown to be just another part of the climate scam. This is the sort of science that unravels the global warming fraud, arguments on the exact particulars notwithstanding.
TerryS says:
July 2, 2013 at 3:03 am
Finally, if you add a mixing function to the Berne formula by calculating P(t) and then starting the calculation again with P = P(t) (this assumes it takes time t for CO2 to mix) then, with a mixing time somewhere between instant and 4 years you get a residency of between 5 and 14 years and a half life of between 7 and 20 years.
Thanks Terry, I think that vindicates my earlier comment that the residence and e-folding times are substantially similar.
The half life of 14C is 5730 years. So, it hasn’t gone much of anywhere in the last 50 years. What is being discussed is the mixing rate of 14C with all the 12C (and 13C) found in the Earth. It shouldn’t be too hard to understand that the mixing will reduce the amount of 14C in a high concentration medium at a rate consistent with the exchange of carbon in general. In fact, we should be able to compute the increases in 14C in other mediums based on their exchange rates..
Note that mixing is not the same as removing. It is just spreading around the 14C. If our system was in perfect equilibrium we would still see a reduction in 14C in high concentration mediums like our atmosphere, while the atmospheric C would remain constant. Of course, the same can be said for any other sources of C (like our emissions). So, the real answer lies in the various exchange rates between the different mediums. Clearly, burning fossil fuels is adding C from a source that was not participating in these exchanges previously (just like the 14C). And, it should take some time for the other mediums to increase their concentrations to account for this addition. However, the 14C was a one time injection over about 10-15 years. Hence, it provides us with a feeling for what would occur for every 10 years of C added through our emissions. Taking this into account, human C should decrease at the rate approximately 1/5 this value since it has now been at a high rate for 50 years. I think this agrees quite closely with Ferdinand’s value and is based simply on logic assuming all else remains equal.
Also keep in mind this assumes there are no other sources that are increasing the amount of C in the atmosphere. To get a complete picture we would have to understand all of these sources in complete detail. I don’t think that is the case.
Consider now that the atmosphere has had CO2 levels over 1000 ppm for most of the time that biological activities have been similar to today. For some reason the exchange rate between the various mediums maintained that concentration in the atmosphere. What is different these days? Well, that is the big question. One difference might be massive amount of colder sea water at the bottom of the oceans (from a higher albedo planet during ice ages and in ice itself).
Greg Goodman says:
July 2, 2013 at 7:46 am
1) that if we see , for example, 8ppmv/year/K in the recent good quality data, it should be assumed that either this continues unchanged for thousands of years and can be directly refuted by the last de-glaciation
Your calculation of the 8 ppmv/year/K is based on the increase of CO2 over the past 50 years of good data, but that is based on an arbitrary choosen baseline. The only real relationship is the direct relationship between temperature and the rate of change of CO2/year of about 4-5 ppmv/K. That is the variability of the CO2 increase around the trend. But that is largely compensated over the next years to average near zero.
You can’t derive the cause of the trend itself from that variability, but you do assume that the increase in rate of change is temperature related and thus directly the result of the temperature increase, ignoring the other variable that influences the increase: human emissions which are twice the observed increase.
The relationship of 8 ppmv/year/K only holds for the past 50 years, but already deviates a lot if you go back in time to the start of the previous century. Over the past centuries in the depth of the LIA, the backcalculation may already go below zero if the temperature passes the baseline…
if #1 does not work we can abandon d/dt(CO2) temperature relationship and assume almost instantaneous equilibration
There are several sources and sinks at work. The fast responses to temperature are the ocean surface layer and part of the biosphere. These have response rates of 1-3 years and are responsible for the nice match between temperature (changes) and rate of change of CO2. But that only removes and/or releases 10% of the change in the atmosphere. The medium speed responses are in the deep oceans and more permanent storage in the biosphere. The response times there are in the order of 40-50 years, as these exchanges are limited in flux, less in storage.
that the swing between two very different quasi-stable states of the climate : glacial and interglacial is, without further justification, applicable to steady change over a century or so without a change in climate state.
Even in more recent times, the ratio of 8 ppmv/K holds: the transition of the MWP to the LIA shows a dip of ~6 ppmv for a dip of ~0.8 K in temperature with a lag of ~50 years after the cooling started:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_1000yr.jpg
The resolution of the DSS ice core is ~20 years.
Thus I see no reason why the 4-5 ppmv/K for short variations (seasons to a few years) and the long range (multidecades to multimillennia) of 8 ppmv/K suddenly changes to over 100 ppmv/K over the medium range…
Greg Goodman says:
July 2, 2013 at 9:16 am
I presume you posted that because you consider it shows AGW dC13 impact but what I see is proof that warming affects the ration in the same way now as it did coming out of the Maunder Min.
As the d13C variability during the whole Holocene, including the Holocene “optimum”, the Roman WP, the MWP and all cooling periods inbetween is not more than +/- 0.2 per mil until about 1850 and the decrease since 1850 is about 1.6 per mil, I don’t see how it is possible that the current warm period could be the cause of the decrease…
I think you have misunderstood the Bern Formula TerryS. Where have you got the idea that the model assumes that the CO2 does not mix? The formula is simply superimpose different exponential sink rates, and an assumption of no mixing is not necessary for that.
Can you show me a quote from the IPCC reports which states this?
The other error I think you make is that you mix your formula for residence time based on the ratio between CO2 content in the atmosphere and the annual flow of CO2 in and out of the atmosphere. These measure totally different things.
Carbon sinks may increase or decrease with rising CO2 levels. However for now lets assume that carbon sinks remain constant so we can take a single effective “pulse” e-folding time – tau years. Man made emissions of fossil fuels are currently running at 5.5 Gtons per year, and the atmosphere currently contains 750g tons CO2.
Now consider a model where it is simply assumed that once a year a pulse of N0 = 5.5 Gtons of CO2 is added to the atmosphere. This then decays away with a lifetime Tau. Then the accumulation of fossil CO2 in the atmosphere for year n is given by.
CO2(n) = N0( 1 +sum(i=1,n-1) (exp(-n/Tau)))
= N0(1 + e^(-1/tau) + e^(-2/tau) + e^(-3/tau) + ……
Now take n -> ∞ and multiply both sides by exp(1/Tau)
CO2(∞)(exp(1/tau)-1) = N0exp(1/Tau)
CO2(∞) = N0/(1-1/exp(1/Tau))
Now try out some values for Tau :
So in the worst case with tau = 200 years and no cuts to carbon emissions – CO2 levels should stabilize at just below 1000 ppm.
Question to Nick Stokes or someone else: What exactly have I got wrong here ?
TerryS:
For what it’s worth, yours is the comment I found most appealing.
However, I don’t see why the Bern formula requires the segregation among sub-populations that you infer. To me, the formula is simply the impulse response of a linear system characterized (in the unlikely event that my math is correct) by the following ordinary differential equation:
dr^6/dt^6 + 1.08 dr^5/dt^5 + 0.27 dr^4/dt^4 + 0.016 dr^3/dt^3 + 0.00024 dr^2/dt^2
+ 0.00000053 dr/dt = dg^5/dt^5 + 0.95 dg^4/dt^4 + 0.19 dg^3/dt^3 + 0.0077 dg^2/dt^2
+ 0.000068 dg/dt + 0.000000074 g, where r is concentration and r is emissions–or, maybe, r and g are the differences between those two quantities and some magical quiescent values.
Looking at it in that light–and ignoring the differential equation’s implausibility–I don’t see the Bern formula as necessarily implying the segregation you describe.
On the other hand, despite the heroic efforts of the above disputants to explain why Prof. Pettersson has it wrong, I am unable, superposition being what it is, to see how the Bern formula can be consistent with the phenomenon he observed.