Dusting for Fingerprints in the Holocene

Oh, this is great information. Thank you David. It is one of the key points that is always brought up when CO2 is discussed.

Hold it now … I just realized that the scales are different.Flinders reef was 0 around 1700 and is now <-1 in 2000. Yucatan makes an arch between -2.5 and -4.5 with extreme variability between 1500 and 2000. The Flanders Reef series isn't long enough to say anything meaningful when it is compared to the Yucatan record. Variability of 2 full units in the ratio is very common. If the ratio goes negative due to fossil fuel input then why has the Flinders reef dropped from 0 to -1 while in the Yucatan it was in the -5 range for 1400 years ……. must have been a lot of Aztecks (sp?) burning a lot of coal. Mind you the Yucatan area is full of gypsum …wonder what the C ratio is in gypsum, ie does C12 – C13 speciate when gypsum crystallizes in the evaporite forming process or alternatively what was the C13 – C12 ratio when the gypsum formed in ocean water?
Is the ratio a regional thing versus a global proxy?

Ditto the thanks David…… I had no idea there were so many examples of the ratio change…. minus human influence. More stuff well within natural variability. I’ve always argued that the isotope doesn’t matter. I think we assume we know more than what we really know.
The Yucatan graph is a bit off if anyone is trying to argue the isotope ratio, at least for that place, is indicative of warming or cooling. And, it is problematic. Not only is the vertical divergence off, so is the frequency.
Just from experience, looking at the graph, I’d say a methodology of some sort, or sampling size changed for gathering information prior to about 1200-1400 as opposed to after. It doesn’t invalidate much of anything…. other than going back beyond 1200.
For those that can’t see, what I’m on about, the intersession between the RWP and MWP is missing, but if you look, @ about 1200-1400….. the graph changes its characteristics.
I hate graphs that look like that…..

I think the isotope ratio is interesting and worth thinking about. It does possibly reflect human origin, and should be taken seriously as an argument. However . . .
We do not know enough about total CO2 sources and sinks to determine whether the increase in overall CO2 *would not have happened* but for human fossil fuel use. Further we do know that CO2 has risen at a remarkably steady pace in recent decades, despite ups and downs in fossil fuel use. Both of these facts should give us pause.
Finally, many argue that the amount of human emissions is greater than the total increase and, therefore, humans are responsible for the increase (meaning, the biosphere is able to handle part of the human emissions, but not all). However, even if the isotope ratio changes (more CO2-12), consider this analogy:
I run a small business on a cash basis. At the beginning of the year I have $1000, 3 of which are marked with a red dot. Throughout the course of the year I exchange thousands of dollars with many vendors and customers, including occasional transactions with one tiny customer who marks red dots on all his bills. At the end of the year, after thousands of transactions of cash flowing in and out, I count my cash, and it turns out I have $1001, 4 of which are marked with a red dot. According to AGW advocates, the tiny customer who pays only with bills marked with a red dot (i) *must* be the sole source of my $1 profit, and (ii) but for that tiny customer, I would not have made my $1 in profit. It should be easy to see that this is not a valid conclusion. The conclusion is even more shaky if David Middleton’s post is correct, because then we would have to say that there might even be another customer (we’re not quite sure) who sometimes also pays with bills marked with a red dot.

It seems obvious that the Seuss effect is not just an anthropogenic fingerprint; instead it is the fingerprint of Life. Most plants and virtually all animals consist almost entirely of C12 and are depleted of C13 and C14. Hence when the global biomass increases, the proportion of total atmospheric carbon that is C12 increases, and the proportion that is C14 declines accordingly. The Seuss effect provides conclusive proof that a warm Earth enables life to thrive.

Since Coal is from dead plants so that is not the origin, I was wonder where the C-13 actually came from and ran into this little gem…

Many thanks to Geophysical Institute, University of Alaska Fairbanks for permission to use the following extract…
… The very rare carbon 14 is another matter, though, because it is radioactive. By losing an electron, every atom of C-14 eventually will decay into an atom of N-14; that is, it will turn into ordinary nitrogen….
1998 by Macquarie University
http://dwb4.unl.edu/Chem/CHEM869Z/CHEM869ZLinks/www.all.mq.edu.au/online/edu/egypt/carbdate.htm

That mess brings to mind this article:

…..“Publishers now employ more people to censor books for content that might offend any organized lobbying group, than they do to check the correctness of facts.” Unchecked errors spread: in 1999 the Boston Globe reported, “Some educators have traced the transmission of errors from one textbook to another and compare the process to the spread of a virus through a population.”
An exasperated William Bennetta explained why so many teachers accept inferior textbooks from these publishers, “[T]he major schoolbook companies… have long recognized that the teacher corps in America includes some desperate dumbbells, and the companies have learned to produce books that the dumbbells will like.” Alistair B. Fraser…, concluded bleakly, “Apparently, most teachers believe everything they teach.” … Cornell professor Donald Hayes, …. reported on results of sampling 788 textbooks used between 1860 and 1992: “Honors high school texts are no more difficult than an eighth grade reader was before World War II.” (And in an essay written over half a century ago Randall Jarrell complained that 1930’s textbooks were much easier than the ones from the 19th century!) So by now our teachers, and their teachers, and their teachers, have been dragged through the same swamp of bad textbooks. They know not what they do, and they know not that they know not….

No wonder CAGW has spread so easily.

I am gravely concerned that the concentration of CO2 is below 500ppm. To me, this means we are in a highly vulnerable state. This concentration (or lack of) has been fine during this fairly benign period of Geological History we’ve been in now since the commencement of the Quaternary. We have not had any really major disturbances other than the general dominance of high latitude Continental Glaciation for much of the Q. But no really big extraterrestrial strikes, no widespread volcanic catastrophes, etc. Not if but when the next one of these happens, if we are still below 500ppm I worry that photosynthesis will behave as if the level were far lower (e.g. due to the impacts of the disturbance). From there, a mass die off of photosynthesis based life could occur.

The increase in light isotope C must be caused by fossil fuel burning because we can’t think of any other reason.
Except that warming seas become more stratified and starve the calcareous phytoplankton which usually preferentially fix light C and export it to the deep ocean. So, fewer phytos, less light C pull down, more 12C in the atmosphere.
Oh, yes, we’ve disrupted vegetation cover causing a lot of dust. Dissolved silica runs into the oceans where it feeds diatoms which are the little beasties that get first helpings of nutrients until the silica runs out. Diatoms are not as discriminatory against 13C as the calcareous phytos, so they export proportionately less 12C, signal in atmosphere goes up.
Oh, and of course there’s the fact that oil and surfactant polluted seas warm faster, stratify more, starving the phytos. And waves break less, less CO2 is driven into the ocean which means that phytos are CO2 starved. Some change their metabolism to C4 ( a better way of fixing carbon in times of C famine), C4 phytos outcompete C3 types and, as any fule know, C4 metabolism is less discriminatory against 13C which means proportionately more heavy C is exported to the deep ocean.
And oil polluted seas engage less with the wind,: this reduces currents, pulling up less nutrient-rich water from below. So this starves the phytos which export less light C.
But it must be us burning fossil fuel, because we can’t think of anything else it can be.
Unless the introduction of European earth worms has altered the silica run-off from those areas where they have been introduced to improve agriculture.
Or something else is happening we haven’t noticed yet.
But it must be us.
The graph used on Sceptical Science should be compared with others: far be it from me to suggest that Mr Cook would use sharp practice in his articles, but other depictions show that the ‘anthropogenic’ 12C signal begins in about 1700AD. Which is odd as even the intelligent men in Ironbridge hadn’t yet started destroying Gaia at that date. But it must be us. We can’t think of anything else. [puts fngers in ears] I’m not listening.
JF
PETM: sea erosion breaches a major oil reservoir. Kriegesmarine Effect happens. Big temperature rise. Would such a small event have such a large effect? Well, we are dumping enough light oil down our rivers every fortnight to cover the entire ocean surface and that’s giving us about .2 deg C/decade. During WWII the spilled oil was enough to drive the temperature up by .3 deg C in a few months. I think. All wwe need to do is clean up our act and watch what happens. I bet on cooling.

Can anyone please explain to me why the measured increase in atmospheric CO2 is almost linear; yet the worlds population increase & usage of CO2 generating fuels would more likely be exponential during the 20th C?
Something is not right!

The SUESS effect was first noticed to correct carbon dating before the 1950s when bomb testing first started. C14 is naturally produced by cosmic rays in the upper atmosphere and about 10kg are produced each year this way. After the industrial revolution the concentration of C14 began to get diluted slightly as fossil fuels were burned. This is because fossil fuels essentially contain no C14. The effect was first noticed by Suess who introduced a correction for carbon dating. A recent study from 2002 has measured that the effect up until 1950 was to decrease C14 concentrations by 2.4+- 0.35%. By 1950 CO2 levels had risen above pre-industrial values by about 12%. This also provides evidence that just 20% of the increase in CO2 levels by 1950 was due to fossil fuels.
Both these results imply that a maximum of just one quarter of the increase in CO2 concentrations since 1750 are of fossil fuel origin. This means that at least 75% of the observed increase in CO2 is of natural origin. Perhaps a further 15% of this could also be due to human causes – land change, deforestation but it is hard to avoid the conclusion that the majority of it is natural. How can this be ? Have we disrupted the overall carbon cycle such that each year there is a surplus in the recycling of natural CO2 ? Or is this 60% effect due to natural warming which would have occurred anyway ? It seems to me that there could be an error in the estimates that the IPCC use for the lifetime(s) of CO2 in the atmosphere?
The lifetime of a given sample of CO2 molecules is the time needed for 1/e of the CO2 molecules to leave the atmosphere. An unintended experiment was carried out in the 1960s due to nuclear testing which released large amounts of radioactive C14 into the atmosphere. C14 measurements show how this pulse of CO2 decayed with time and derive a lifetime value. The evidence from the delta C13 measurements, and the Seuss effect would support a lifetime of about 7 years. The direct C14 measurements give a value around 10 -14 years. In both cases the fraction of CO2 molecules in the atmosphere for current emission levels reaches a limit of < 10% of today’s atmosphere. It is only by assuming much higher lifetimes of over 100 years that the IPCC predictions are possible.
So the whole AGW model depends on a long lifetime for CO2. The IPCC carbon model (WG1) is described on page 213 of WG1 and states :

The CO2 response function used in this report is based on the revised version of the Bern Carbon cycle model used in Chapter 10 of this report (Bern2.5CC; Joos et al. 2001 [1] ) using a background CO2 concentration value of 378 ppm. The decay of a pulse of CO2 with time t is given by:

a0 + sum(i=1,3)(ai.exp(-t/Taui)) , Where a0 = 0.217, a1 = 0.259, a2 = 0.338, a3 = 0.186, Tau1 = 172.9 years, Tau2 = 18.51 years, and Tau3 = 1.186 years.
If you look carefully at this formula you will see that it is made up of 3 independent CO2 lifetimes each with different amplitudes, plus a constant term implying that 22% of anthropogenic CO2 will remain in the atmosphere for ever!
One objection I have to the form of this model is the concept of using 3 different lifetimes purely from a logical viewpoint, as it kind of assumes that there are 3 different types of CO2 molecule in different queues waiting to leave the atmosphere. I suspect that the model in this form also violates the second law of thermodynamics, since whether there are 3 holes in a bucket of water or just 1 large hole is irrelevant to the rate at which the water leaks out of the bucket !

Dixon wrote
‘spilled oil. I need to think that through.’
Search for the Ceres picture of the world, zoom in on the Mississippi overflow into the Gulf.
Find the earlier pictures of the Gulf oil spill and see the way the air above the slick is eating stratocumulus clouds at the edges.
Thinking is good! Wigley should have done it, then he would not have needed to ask ‘why the blip’.
JF

clivebest says:
March 29, 2012 at 2:00 am
A recent study from 2002 has measured that the effect up until 1950 was to decrease C14 concentrations by 2.4+- 0.35%. By 1950 CO2 levels had risen above pre-industrial values by about 12%. This also provides evidence that just 20% of the increase in CO2 levels by 1950 was due to fossil fuels.
The common problem with this is that one need to make a distinction between the origin of the CO2 molecules which are in the atmosphere and the origin of the increase in total amount of CO2 in the atmosphere. Look at the example that Bart showed: we add a some blue colored water to a bucket where clear water is added to the top and leakes away at the bottom and is recirculated via a huge tank with near unlimited capacity. The water in the bucket wil be colored somewhat by the blue addition (which shows the origin), how much, that entirely depends of the ratio between colored and clear water addition. But the addition of blue water also increases the height of the waterlevel in the bucket. That is INdependent of the original flow in- and out. The original height of course depends of the initial flow, but the increase in height only depends of the additional flow.
So what is important in this case? What rests in the atmosphere of original human emissions (the blue coloured ones…) is not important at all, only the total increase (the increase in height) is important. The bomb 14C decline ratio only shows how fast the atmosphere is exchanging CO2 with other reservoirs (about 20% per year or a residence time of ~5 years), but that doesn’t say anything about how fast an excess amount of CO2 in total is removed (that is 4 GtC/year of the total 800 GtC in the atmosphere, or a 1/e decay time of ~55 years). Two completely different time constants without any relationship. Here a graph which shows (based on realistic figures) the difference between what happens with the total amount of CO2 in the atmosphere if humans should add 200 GtC from fossil fuel at once to the pre-industrial atmosphere and what happens to the human “fingerprint”:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/fract_level_pulse.jpg where FA is the fraction of “human” CO2 in air, FL the fraction in the ocean surface (not important here), tCA total carbon in air and nCA natural carbon in air.
The human fingerprint is gone after some 50 years, but the effect of the one-time addition on the total amount still is measurable after 160 years…
While I don’t agree with the Bern model, what they do is comparing the decay time between the atmosphere and different compartiments: the fastest is for the ocean’s surface, but that has a limited capacity (~10% of the increase), the medium term for the deep oceans and vegetation and the lowest for long-term processes like rock weathering, carbonate sedimentation,… My objection is that there is currently no limit in sight for the deep ocean and vegetation uptake, thus the slowest and residual terms are highly questionable.

Carbon dating is over-rated and based on simplistic assumptions. First that all atmosheric C-14 is from N-14 decay and that this decay rate is constant based on non-constant solar/cosmic rays. The non-constant production rate becomes a greater problem over time, causing an increased proxy error. Carbon dating is based on the assumption that C-13/14 ratios are set by metabolism with atmospheric Carbon and then begin a fixed decay rate upon the death of the organism. Biologists in the sixties divided life into “Bacteria” and “Eukaruota”, only to further divide the single celled life forms into “Bacteria” and “Archaea” a decade later. This was based on RNA and metabolism differences of lifeforms in the worlds most extreme environments. Living in the intestional tracts of termites and cattle, thriving at high-temperature, high-pressure thermal vents, these “new” life-forms are abundant in the Antarctic and feed on “elemental” CO2 and CH4 flowing from under-sea vents. These “natural” Carbon sources have reduced C-14 and therefore, the marine animals that are fed further up the food chain have reduced C-14 ratios as well. Fresh killed seals and penquins have a “Carbon dated age” of over 3,000 years old. The “elemental” production of Carbon is NOT constant, and is UNKNOWN, introducing further errors.
See “Amazing ! New ! Wrongco’s Proxy Crock !” for more of the ridiculous proxy madness.

Julian Flood says:
March 28, 2012 at 10:30 pm
It is simple to show that the ocean temperature increase is not the cause of the CO2 increase or d13C decline: the temperature influence on CO2 pressure in seawater is too small (16 microatm/degr.C) and seawater CO2 has a too high d13C level (0-1 per mil for deep ocean waters, 1-4 per mil for ocean surface waters, the atmosphere is at -8 per mil). Thus any substantial release of CO2 from the oceans would increase the d13C level of the atmosphere while we observe a fast decline.
It is impossible to make a differentiation between the use of fossil fuels and of burning/decayling vegetation. But there is an alternative: we know with reasonable accuracy how much oxygen our fossil fuel burning uses. We know with some accuracy since 1990 how much oxygen is removed from the atmosphere. The difference is what the total biosphere is using or producing. It shows that the total biosphere (land and sea plants, animals and insects) is producing more oxygen that it uses. Thus the total biosphere is a net source of oxygen, thus a net sink for CO2 and preferably 12CO2. Thus leaving relatively more 13CO2 in the atmosphere and not the cause of the decline in d13C.
As oceans and biosphere are the only main huge sources and sinks, there is little doubt left that humans are entirely responsible for the d13C decline (and the CO2 increase). Other sources are too high in d13C (volcanoes, carbonate rock weathering) and too small in emissions. The difference in methabolism between C4 and C3 plants plays no role here, as both have d13C levels below atmospheric, thus both increase the d13C level when there is more growth than decay. And the earth is greening…

MrD says:
March 28, 2012 at 11:50 pm
Something is not right!
Exactly how linear and how exponential are we talking about? See the graph below. Would you happen to have a graph that shows the use of fuels is more exponential?
http://www.woodfortrees.org/plot/esrl-co2/from:1958/plot/esrl-co2/from:1958/trend

FerdiEgb says: “A simple calculation learns you dat without that customer, you would have had a net loss of 1 dollar per year.”
No. It is true that at some level we could argue that I wouldn’t have gained the extra dollar if I didn’t have that customer. But you are ignoring all the other customers who paid in much greater sums. It doesn’t make any sense to say that the guy who paid me an extra $100 wasn’t responsible for the increase, while the guy who paid me an extra $1 is responsible for the whole increase. Especially if there would have been an offsetting purchase from another customer if my $1 customer didn’t his $1 worth of my goods.
*Even if* humans were the only possible source of CO2-12, which is very doubtful, to conclude that humans are causing the general increase in CO2 requires two massive unproven assumptions: (i) we know what all the other sources and sinks are and what their amounts are, and (ii) we know how all the sources and sinks interact with each other with enough precision to be able to calculate how they interact with humans’ minor contribution.

clivebest says:
March 29, 2012 at 1:57 am
“If you look carefully at this formula you will see that it is made up of 3 independent CO2 lifetimes each with different amplitudes, plus a constant term implying that 22% of anthropogenic CO2 will remain in the atmosphere for ever!”
The idea here is to model a “fat tail” response with a sum of exponentials. Presumably, the constant term models an exponential which has a time constant much longer than any interval of interest.
I’m not saying it is an accurate equation, just helping understand the theoretical basis.
FerdiEgb says:
March 29, 2012 at 7:27 am
“Ice cores give direct measurements of the C13/C12 ratio of CO2 in trapped air. These were measured by cold crushing the ice, cryogenic freezing, distillation of CO2 and measuring with a mass spectrometer.”
And, there is no reference, no “control” experiment possible to verify that the measurements of ancient CO2 are valid. We do not really know how the trapped gases diffuse through the ice over eons of time. We have only a model.
FerdiEgb says:
March 29, 2012 at 8:10 am
“…we add a some blue colored water to a bucket where clear water is added to the top and leaks away at the bottom and is recirculated via a huge tank with near unlimited capacity.”
It isn’t all recirculated. A goodly part is sequestered more or less permanently. The relevant question is, how fast is the rate of semi-permanent sequestration? I have seen no evidence which convinces me that anyone has a good handle on that rate.

climatereflections says:
March 29, 2012 at 10:58 am
(i) we know what all the other sources and sinks are and what their amounts are, and (ii) we know how all the sources and sinks interact with each other with enough precision to be able to calculate how they interact with humans’ minor contribution.
We only know to a certain extent what the individual sinks and sources are and their variability. And we have little idea what the interactions are. But that is not important at all: we know quite exactly the result at the end of the year. Not only in gain or loss, but also the variability in gain or loss over the past 50+ years. Even if all or some of the input flows doubled or halved, that is near fully compensated by a similar increase or decrease of the output flows. See:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em.jpg
The average increase in the atmosphere is around 50% of the emissions, the variability of the increase is also about 50% around the trend. That is mainly a result in sink capacity changes due to temperature variability. But in all years nature as a whole was a net absorber of CO2, not a source. In this case, human emissions are the single non-natural source of CO2 (and hardly a sink). Thus one must compare the non-natural source to the combination of natural sources and sinks, no matter what the individual natural sources and sinks did or how they changed.
Even if you don’t do any bookkeeping at all during the day, and only know that you have added some 2 dollars of your own money at the beginning of the day to your cash register, you know that your bussiness is not going well if you find only 1 dollar extra in cash at the end of the day… And if that remains so for 50+ consecutive days, better look for another job…

Bart says:
March 29, 2012 at 11:37 am
And, there is no reference, no “control” experiment possible to verify that the measurements of ancient CO2 are valid. We do not really know how the trapped gases diffuse through the ice over eons of time. We have only a model.
The gas diffusion through ice was (theoretically) calculated, based on the “warm” (-20 degr.C) Siple Dome ice core which shows some remelt layers. That gives a theoretical broadening of the resolution for middle depths from 20 to 22 years and for the near bottom part from 20 to 40 years. But even so, that doesn’t change the average levels over that broader period of time, only that faster variations than the resolution wouldn’t be observed.
Even if that gives some fractionation of the isotope ratios, that would be seen in high fluctuations from sample to sample (if the sampling was over a too short time span). But the resolution gets better with increased accumulation rates, including a 20 years overlap with direct measurements at the South Pole for the period 1960-1980.
For the colder (-40 degr.C) ice cores in central Antarctica, there is no sign at all for any migration over 800,000 years. If that was the case, the rather constant ratio between CO2 levels and temperature (proxy) would fade over time with each 100,000 years period back in time.

Reply: FerdiEgb

As long as the year by year emissions increase, I don’t think that there will be a limit to atmospheric CO2 levels…

It is clear that emissions cannot increase forever. We have about 50-100 years of economic Oil and Coal left . Optimistically there are probably also another 50 years of natural gas. Therefore emissions are bound to stabilise and atmospheric CO2 will level off by the end of this century and then slowly decline. This will happen independently of green eco-politics and anti-growth hype. We have a choice whether to use the next 50 – 100 years to develop radical new energy sources or follow the eco-route back to low density living. Should we give up growth and return to a quasi-neolithic “green” society based on sustainable energy ( wind, wood burning, and the sun) which could at most support 1/10th of the current world population, or should we invest in nuclear fusion ? All renewable energy is way too low density( 2-3 watts/m2 ) to support urban life – so It is either nuclear or neolithic. Take your choice.

FerdiEgb says:
March 29, 2012 at 12:19 pm
“The gas diffusion through ice was (theoretically) calculated, based on…”
Repeating what I stated, albeit with flourishes and handstands, does not change what I said.
“But that is not important at all: we know quite exactly the result at the end of the year.”
Still flogging that dead horse, I see. I honestly had a little glimmer of hope we had gotten through to you last time.

FerdiEgb says:
March 29, 2012 at 2:57 pm
“The estimate of migration speed in the Siple Dome is based on direct measurements, not on a model.”
Not a chance. Nobody was around in the deep past to sample the air, record it, and have it available to compare to the derived measurement today.
Nothing is completely reliable until it has been tested in the lab, and the theory compared to observation in a closed loop fashion. That is why all new commercial products are tested thoroughly before they go to market, and sample tested thereafter to ensure maintenance of performance. You never know for sure what will come out when the theory is tested against reality. A precise match between prediction and observation on the first test run is, by far, the exception rather than the rule.

FWIW to anyone reading this thread: The fundamental reason I doubt that the recently recorded rise in CO2 is most significantly of human origin is the simple fact that accidents do not happen in Nature. If the feedback loop governing CO2 concentration is so weak as effectively to allow 100% accumulation of the anthropogenically released CO2 in the oceans and atmosphere, then it is too weak to have established an equilibrium and maintained it tightly for thousands of years before the Industrial Age.
Ferdinand has constructed a narrative which, superficially, appears plausible. But, it is based on unfounded confidence in measurements which have large error bars, models for the carbon cycle which have not been completely validated and are very likely substantially incomplete, and neglect of the fundamental dynamism of the system.
A similar narrative was constructed for Anthropogenic Global Warming and, so long as the Global Average Temperature Metric (GATM) appeared to be rising in the latter third of the 20th century, researchers had high confidence that the hypothesis was correct. But, then they hit a brick wall when the GATM stalled after 1998. The evidence that a global cooling cycle has now commenced, which will endure for the next 20-30 years, is compelling. And, it is now apparent that inconvenient facts which were neglected or ignored in constructing the AGW narrative should never have been ignored, e.g., in particular, the rising GATM of the early third of the 20th century which, with hindsight, we can now see is nearly identical to the rise in the latter third.
You cannot just neglect fundamental discrepancies with the knowledge base, and a plausible narrative, especially one which takes short cuts in neglecting inconvenient data or knowledge, is NOT proof. Until the discrepancies are resolved, the hypothesis remains just that.

Bart says:
March 29, 2012 at 4:25 pm
If the feedback loop governing CO2 concentration is so weak as effectively to allow 100% accumulation of the anthropogenically released CO2 in the oceans and atmosphere, then it is too weak to have established an equilibrium and maintained it tightly for thousands of years before the Industrial Age.
The deep oceans and vegetation have sufficient capacity to allow sequestering of 100% of the emissions. As already explained to climatereflections, the limiting factor is the diffusion speed, which is directly proportional to the pressure difference between pCO2(atm) and pCO2(aq), all other confounding variables (water temperature, wind speed, sink and upwelling flows) being equal. The time factor is important here: historical CO2 had multi decades to millennia to maintain equilibria around the temperature dictated setpoint. The current injection of human emissions is higher than what the decay rate (~55 years e-fold factor) can cope with on short time intervals.

FactChecker says:
March 29, 2012 at 1:22 pm
Does anyone know what happened to Murry Salby? Did he disappear down a black hole? I haven’t heard mention of that guy for a long time now… anyone knows what happened to him?

FactChecker,
Murry Salby published his new textbook ‘Physics of the Atmosphere and Climate’ in Jan 2012 by Cambridge University Press. I have it and use it for reference often.
I do not know the status of his paper on the carbon cycle and the atmosphere.
John

Some of the discussion here questions whether the observed rise in atmospheric CO2 is anthropogenic. It undoubtedly is, and there are many lines of evidence that establish that this is the case, see Ferdinand Engelbeens’ excellent webpage on the subject http://www.ferdinand-engelbeen.be/klimaat/co2_measurements.html .
I have looked into this subject in some detail in the process of writing a rebuttal of Prof. Robert Essenhigh’s paper on the residence time of CO2, which was published by the journal, see http://pubs.acs.org/doi/abs/10.1021/ef200914u
On the Atmospheric Residence Time of Anthropogenically Sourced Carbon Dioxide
Gavin C. Cawley*
Abstract: A recent paper by Essenhigh (Essenhigh, R. H. Energy Fuels 2009, 23, 2773−2784) (hereafter ES09) concludes that the relatively short residence time of CO2 in the atmosphere (5–15 years) establishes that the long-term (≈100 year) rise in atmospheric concentration is not due to anthropogenic emissions but is instead caused by an environmental response to rising atmospheric temperature, which is attributed in ES09 to “other natural factors”. Clearly, if true, the economic and political significance of that conclusion would be self-evident and indeed most welcome. Unfortunately, however, the conclusion is false; it is straightforward to show, with considerable certainty, that the natural environment has acted as a net carbon sink throughout the industrial era, taking in significantly more carbon than it has emitted, and therefore, the observed rise in atmospheric CO2 cannot be a natural phenomenon. The carbon cycle includes exchange fluxes that constantly redistribute vast quantities of CO2 each year between the atmospheric, oceanic, and terrestrial reservoirs. As a result, the residence time, which depends upon the total volume of these fluxes, is short. However, the rate at which atmospheric concentrations rise or fall depends upon the net difference between fluxes into and out of the atmosphere, rather than their total volume, and therefore, the long-term rise is essentially independent of the residence time. The aim of this paper is to provide an accessible explanation of why the short residence time of CO2 in the atmosphere is completely consistent with the generally accepted anthropogenic origin of the observed post-industrial rise in atmospheric concentration. Furthermore, we demonstrate that the one-box model of the carbon cycle used in ES09 directly gives rise to (i) a short residence time of ≈4 years, (ii) a long adjustment time of ≈74 years, (iii) a constant airborne fraction, of ≈58%, in response to exponential growth in anthropogenic emissions, and (iv) a very low value for the expected proportion of anthropogenic CO2 in the atmosphere. This is achieved without environmental uptake ever falling below environmental emissions and, hence, is consistent with the generally accepted anthropogenic origin of the post-industrial increase in atmospheric carbon dioxide.
This paper summarises the evidence that establishes that the origin of the rise is indeed anthropogenic (Ferdinand’s web page is referenced in my article, it is strongly recommended).
The challenge to any theory of even a partially natural origin of the observed increase is to explain how the annual rise can be less than anthropogenic emissions, without contravening the principle of conservation of mass.

FerdiEgb says:
March 29, 2012 at 7:27 am
“Ice cores give direct measurements of the C13/C12 ratio of CO2 in trapped air. These were measured by cold crushing the ice, cryogenic freezing, distillation of CO2 and measuring with a mass spectrometer.
The d13C level in the atmosphere over the Holocene can be followed in the Taylor Dome ice core:
http://medias.obs-mip.fr/paleo/taylor/indermuehle99nat.pdf
The average variability is +/- 0.15 per mil over the Holocene, up to 1,000 years ago.”
Ferdinand, this seems to be supported only by the Antarctica ide cores and not by Greenland? Whilst from Antarctica we have only a couple of points for 100 years in Greenland ice core we have 100+, so I wonder if we do not lose a lot of natural variability using the Antarctica data for C13 as well as CO2 concentration due to the long time of about 80 years until the air is !trapped! in the antarctic ice?

Lars P. says:
March 30, 2012 at 1:38 pm
Ferdinand, this seems to be supported only by the Antarctica ide cores and not by Greenland? Whilst from Antarctica we have only a couple of points for 100 years in Greenland ice core we have 100+, so I wonder if we do not lose a lot of natural variability using the Antarctica data for C13 as well as CO2 concentration due to the long time of about 80 years until the air is !trapped! in the antarctic ice?
The Greenland ice cores have a quite good resolution (even yearly for the ice layers). Unfortunately the CO2 and d13C levels are unreliable. There is some seasalt/carbonate dust deposit (as good as is the case for Antarctica, mainly for coastal cores), which doesn’t interfere with the CO2 levels, except when highly acidic volcanic dust from Iceland is also settled down in the ice, which frequently is the case. That increases the measured free CO2 levels in situ and probably increases the d13C levels too (I haven’t seen any figures of d13C measurements from the Greenland cores), as sea carbonate is 0-5 per mil d13C while air d13C was around -6.4 per mil…
The resolution of the ice cores heavily depends of the accumulation rate, which is very high near the coast (Law Dome, Siple Dome) with a range of 8-40 years, but as drawback that the measured time period is rather short (150-1000 years for Law Dome), as you have less ice layers when bedrock is (nearly) reached. Taylor Dome goes back several 10 kyr, but its resolution is worse (don’t know it exactly). Vostok and Dome C go back 420 kyr and 800 kyr with a resolution of some 600 years.

Lars P. says:
March 30, 2012 at 1:48 pm
climatereflections says:
March 29, 2012 at 4:04 pm
“Is this additional uptake over the last several decades reflected primarily in vegetation? Other sinks? Is it temporary?”
It is expected in the models that roughly half, more or less, of whatever goes into the atmosphere will end up in the oceans without considering any other sinks. So, again, there is consistency with the hypothesis that the rising atmospheric concentration is due to anthropogenic inputs. However, this expectation is more or less ex post facto, and we do not fundamentally know what share should end up in the oceans from basic principles.
The natural flows both in and out are huge, on the order of at least 30 times greater than the anthropogenic input flux. It does not take a lot of long term variation in the natural flows to completely swamp out the anthropogenic signal.

Bart says:
March 30, 2012 at 5:42 pm
The natural flows both in and out are huge, on the order of at least 30 times greater than the anthropogenic input flux. It does not take a lot of long term variation in the natural flows to completely swamp out the anthropogenic signal.
As Gavin already said:
However, the rate at which atmospheric concentrations rise or fall depends upon the net difference between fluxes into and out of the atmosphere, rather than their total volume, and therefore, the long-term rise is essentially independent of the residence time.
It doesn’t matter at all that the natural flows in and out are 3 times or 30 times or 300 times the human emissions, it only matters what the difference is between the natural inflows and outflows at the end of the year. Nature as a whole is a net sink for CO2, proven at least for the past 50+ years. Even if one of the natural inflows doubled in some years and halved in other years, that doesn’t matter, as the net balance over the past 50+ years shows that in every year nature as a whole was more sink than source. The observed natural variation around the trend is about +/- 2 GtC for an increase currently around 4 GtC/yr with human emissions around 8 GtC/yr. Thus there is no sign of a swamp out, neither of huge natural variations.

The attribution of increases in atmospheric CO2 since ~1850 to man’s burning of fossil fuel is said by the IPCC centric scientists ( in FAR, SAR, AR3 and AR4) to be unequivocally established by a construction (from earlier proxies and recently measurements) of two concurrent opposing trends in the composition of the atmosphere. Those two concurrent opposing constructed trends in atmospheric composition (which the IPCC scientists say is the fingerprint of mankind’s effect on atmospheric composition) are the decline in the relative concentration of atmospheric carbon 13 (parts per thousand referred against a standard value of C13 concentration) and the increase of volume mixing ratio (ppmv) of atmospheric CO2.
If either of these opposing trends is shown not to be primarily driven by man’s activities then the IPCC’s anthropogenic case is significantly weakened to the state of being refuted.
There are large uncertainties in the produced amounts from natural sources of CO2 which have the same carbon 13 concentration as CO2 from man’s burning of fossil fuels. Until these uncertainties are reduced by further research then the IPCC’s anthropogenic case for changes in the composition of the atmosphere then the IPCC’s case is based on ignorance of those natural sources.
Significant funds need to be timely diverted to the natural sources of atmospheric carbon away from the IPCC centric scientist’s/institution’s bias and myopic focus on fossil fuel burning.
This would allow a more respectable independence in the science, some overdue advance toward balance and certainly some restoration of the declining trust in climate science which has been caused directly and entirely by the IPCC.
John

FerdiEgb says:
March 31, 2012 at 12:42 am
“For the oceans as main source, the increase in oceanic carbon mass and decreasing d13C in air and oceans are sufficient proof that the oceans are not the source.”
No, it isn’t. This is a dynamic system, and you are using static models.
“At what point ends a hypothesis as hypothesis and do you accept that it is accepted knowledge?”
When it stops assuming the answer before it is proven, and starts relying on confirmational data.
“It doesn’t matter at all that the natural flows in and out are 3 times or 30 times or 300 times the human emissions, it only matters what the difference is between the natural inflows and outflows at the end of the year.”
Wrong. Wrong, wrong, wrong, wrong, wrong. We’ve been over this too many times for me to have any hope that you will get it, but it is stunningly bad logic.
gavincawley says:
March 31, 2012 at 4:09 am
“We know that the rise is of anthropogenic origin because the observation is consistent with that hypothesis, but inconsistent with the hypothesis of a natural origin.”
With your concept of what “natural sources” can do tied in a straightjacket of a priori baseless assumptions.
“…then the observation that the annual rise being less than annual anthropogenic emissions means that total natural emissions must be less than total natural uptake.”
NO!!!! It does not mean that at all. You are assuming the sinks do not expand due to an increase in atmospheric partial pressure. They do. You are wrong.
You guys… you do not even realize you are heading down the same path that led church leaders of old to proclaim that the Sun revolved around the Earth, or the ancient shamans to believe that the Volcano God had to be appeased. In each case, those guys thought they were basing their beliefs on the best available evidence, too. Your arguments are mind-numbingly flaccid, and you do not even realize it. This is not to say that you may not be right, but if so, only in the sense that a stopped clock may be right twice a day. Your arguments are not conclusive in any way, shape, or form.
I’m done with this thread. We’ve said all there is to say. Further lack of response on my part should not be taken as evidence of acquiescence. We will know the truth as the data record of reliable measurements increases. In the meantime, it is rather a moot point, since temperatures are not increasing in line with the AGW hypothesis anyway.

Bottom line: This is a dynamic system, and you guys are doing static analysis. And, you are assuming greater precision in the quantification of natural fluxes than actually exist, and when anthropogenic influx is less than 3% of natural fluxes, you do not need a lot of error to destroy the conclusion.

Bart writes “With your concept of what “natural sources” can do tied in a straightjacket of a priori baseless assumptions.”
No, the mass balance argument makes no assumptions about the nature of the sources or sinks. It is away of inferring something we can’t directly measure (the difference between total natural emissions and total natural uptake) from two quantities that we can directly measure, namely anthropogenic emissions and the annual rise in atmospheric CO2. I would be happy to go through the argument with you step by step if you like and you can point out the step where the error in the argument appears.
“NO!!!! It does not mean that at all. You are assuming the sinks do not expand due to an increase in atmospheric partial pressure. They do. You are wrong.
No, this is not correct, the mass balance argument makes no such assumption. Furthermore in my paper I use a one-box model of the carbon cycle very similar to that used by Essenhigh, where the flux out of the atmosphere is proportional to the atmospheric CO2 concentration (starting on page 5508). Thus my analysis explicitly includes the expansion of the sinks.

Bart wrote “Bottom line: This is a dynamic system, and you guys are doing static analysis.”
This incorrect, in my paper I discuss a simple one-box model of the carbon cycle, which is a dynamical system described by a differential equation. It is not a static analysis.
“And, you are assuming greater precision in the quantification of natural fluxes than actually exist”
The mass balance argument does not require any knowledge of the magnitudes of the natural fluxes, hence the uncertainty of our best estimates of them is irrelevant. The mass balance argument relies only on knowledge of anthropogenic emissions and of atmospheric concentrations, both of which are known with more than adequate certainty for the purposes of the mass balance analysis.
“and when anthropogenic influx is less than 3% of natural fluxes, you do not need a lot of error to destroy the conclusion.”
This is incorrect, as has been pointed out earlier in the thread, the rate of increase in atmospheric CO2 depends on the difference between total uptake and total emissions, not the magnitude of the fluxes themselves, and anthropogenic emissions are large compared to the difference between total natural emissions and total natural uptake.
However, the mass balance argument does not depend on our knowledge of the magnitude of the natural fluxes, so this objection is irrelevant.

John Whitman says:
March 31, 2012 at 9:54 am
What is the uncertainty in the amount of the natural 150 CtC/yr CO2 production that has the same net carbon 13 conc as CO2 from burning fossil fuels?
There are only rough estimates of the CO2 production from natural sources with a low 13C/12C ratio. That are mainly vegetation decay/burning and natural “fossil” carbon from methane and oil leaks and coal or peat burning.
That may be important if there were huge natural disasters in the recent past, but that is not the case, taking into account that the measured increase in CO2 and decrease in d13C is the equivalent of burning down 1/3rd of all land vegetation (!).
Even if there was some extra natural supply from low 13C sources, the total d13C decrease caused by all human use of fossil fuels is high enough to have caused a threefold drop in d13C as what is observed, Thus any extra source must have a higher d13C level than the atmosphere, not a lower one. And not a source, but a replacement, as an extra source in mass would give an increase in the atmosphere higher than the human emissions, not lower. As both the ocean surface and the biosphere have a limited storage capacity and most of what is absorbed in one season returns in the next, mainly the deep oceans are responsible for most of the high d13C exchange.
One can calculate how much carbon with the deep oceans need to be exchanged to get the right d13C drop in the atmosphere:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
The deviation until 1960 might be caused by the biosphere (as a net source), which is not taken into account in this calculation.

John Whitman If you use the Law dome CO2 data to extend the mass balance analysis back prior to to the start of the Mauna Loa record, it still shows that the annual rise in atmospheric CO2 was less than total anthropogenic emissions (land use change + fossil fuel) going back at least as far as 1840 (see figures 4 and 5 of my paper). This indicates that the natural environment has been a net carbon sink going back at least as far as that, and hence has been opposing the observed rise rather than causing it. This contradicts the hypothesis that the rise is partly due to a rebound from the LIA.
The airborne fraction (the ratio of the rise in CO2 and cumulative anthropogenic emissions) has stayed pretty much constant at about 0.45 going right back to the 1840s. It would be quite a coincidence if a rebound from the LIA caused an increase in atmospheric CO2 that was in so close a relationship to anthropogenic emissions!
I would be interested to see Prof. Salby’s paper, so if anyone can tell me the identity of the journal or news about likely publication date I would be grateful. I did send him a pre-print of my paper, but I recieved no response.

John Whitman says:
March 31, 2012 at 11:34 am
Hey, I noticed you shortened your handle here at WUWT!
Not my intention, I still am the same Ferdinand Engelbeen, but the new WordPress rules which needed a login. Seems that I ever used that shortened login. Did cause me to resent the first comment here which were both promptly sent to the dust bin by WordPress and prompted a reaction of one of the Mods, because I was too impatient to wait for the dust bin to be searched by the poor Mods (sorry)…
The part of the atmospheric CO2 increase which could be considered as resulting from the temperature rebound from the LIA over the same period roughly 55 ppmv.
That is a little too high: even if we assume a full degree C increase of the ocean surface since the LIA, that wouldn’t be more than 16 ppmv. That is the increase in “fugacity”, or steady state equilibrium level with the above atmosphere for seawater for 1°C temperature increase. As increased land temperatures give more CO2 sequestering by plants, the overall increase in atmospheric CO2 at steady state probably is in the order of 8 ppmv, as was the case for the previous 800 kyr. Thus at maximum 8 ppmv of the 100+ ppmv rise in the past 160 years is from the rebound from the LIA.
What is the base of the temperature caused 55 ppmv increase by Prof. Salby?

FerdiEgb says:
March 31, 2012 at 11:31 am
There are only rough estimates of the CO2 production from natural sources with a low 13C/12C ratio. That are mainly vegetation decay/burning and natural “fossil” carbon from methane and oil leaks and coal or peat burning.

FerdiEgb,
And in addition the significant uncertainty extends to the concept of significantly varying amounts of relatively low carbon 13 concentrations being emitted from the upper ocean marine organic matter. For the IPCC’s AGW fingerprint from lowering carbon 13 relative concentration in the atmosphere to hold any validity it must be assumed by the IPCC that the oceans must emit CO2 with standard reference atmosphere carbon 13 relative concentrations; oceans assumed emitting CO2 without the leanness in carbon 13 of that is contained in man’s burning of fossil fuels; it is odd the IPCC does that given that the oceans are the dominant actor in the earth’s carbon cycle by far. Yet, there is quite insufficient science showing that IPCC assumption is credible. It is like the IPCC has a conclusion that man was responsible and is arguing backwards to justify it and in the process proceeds by just hand waving forth an assumption about the dominant part of the carbon cycle, the oceans, without doing the science.
Carbon cycle science is primitive and needs independent skeptical attention. Funding orgs need support it independent of the IPCC’s advocacy of only research whose outcome supports their predetermined conclusions.
John

John Whitman says:
March 31, 2012 at 1:52 pm
And in addition the significant uncertainty extends to the concept of significantly varying amounts of relatively low carbon 13 concentrations being emitted from the upper ocean marine organic matter.
Some error here: plant life in the upper oceans use preferentially 12C for their organics, which leaves more 13C in the surrounding waters. That makes that surface waters are higher in 13C than the deep ocean waters. Thus any release from the deep oceans (at around zero per mil d13C) or the ocean’s surface (at 1-5 per mil) will increase the d13C level of the atmosphere (currently at -8 per mil).
Don’t underestimate what is already known from the carbon cycle. Not everything is known in detail but the main flows are quite well known.

FerdiEgb says:
March 31, 2012 at 2:34 pm
“… the main flows are quite well known.”
More argument by assertion. Countless failed hypotheses have been buried with similar epitaphs on their headstones.

Bart says:
April 1, 2012 at 9:17 am
More argument by assertion. Countless failed hypotheses have been buried with similar epitaphs on their headstones.
See:
http://www.sciencemag.org/content/287/5462/2467.abstract

FerdiEgb says:
March 31, 2012 at 12:21 pm
What is the base of the temperature caused 55 ppmv increase by Prof. Salby?

FerdiEgb,
I liked your full name better as a handle. : ) It was more dignified.
For us to dialog on my interpretations of Prof Salby’s treatment of the delta natural CO2 emission resulting from delta surface temperature (the temperature-CO2 climate feedback) then I suggest you first read chapter 8-Radiative Transfer, section 8.7-The Greenhouse Effect, subsection 8.7.1-Feedback in the Climate System in Prof Salby’s book ‘The Physics of the Atmosphere and Climate’ (published Jan 2012 by Cambridge University Press). The references in that subsection will take you to many other chapters within his book so you would be looking over 70 pages of his almost 700 page book.
It looks to me like there are significant oceanic sources emitting natural CO2 which is carbon 13 lean; natural ocean sources of emission with the similar carbon 13 leanness as the leanness in CO2 from man’s burning of fossil fuels; the magnitudes of emission rate of those natural oceanic sources of carbon 13 lean CO2 appear to be on the order of magnitude of the emission rate of the anthropogenic CO2 sources from burning fossil fuel over comparable time periods like the twentieth century. A finding like that would significantly weaken the basis of the IPCC’s anthropogenic CO2 fingerprinting which they say shows predominately anthropogenic causes for increased modern era CO2.
As we hopefully, in the future, have a common base (Prof Salby’s treatment in his book) then I look forward to your continued discussion on this matter.
John

FerdiEgb says:
March 31, 2012 at 11:31 am
Even if there was some extra natural supply from low 13C sources, the total d13C decrease caused by all human use of fossil fuels is high enough to have caused a threefold drop in d13C as what is observed, Thus any extra source must have a higher d13C level than the atmosphere, not a lower one. And not a source, but a replacement, as an extra source in mass would give an increase in the atmosphere higher than the human emissions, not lower. As both the ocean surface and the biosphere have a limited storage capacity and most of what is absorbed in one season returns in the next, mainly the deep oceans are responsible for most of the high d13C exchange.

FerdiEgb,
Again, my interpretation of Salby’s treatment in his new book, is that the natural variation (excluding variation from fossil fuel burning) in carbon 13 relative concentration in the atmosphere for the satellite era (past thirty years) does seem to be inconsistent with your statement. I think it shows there are natural sources of carbon 13 lean CO2 that have emission rates comparable in magnitude to the sources from mankind burning fossil fuels over the same period. That would effective counter the assumption of yours that we would need massive vegetation destroying natural disasters of global dimension over the satellite era to have a major natural source of carbon 13 lean CO2 comparable to the anthropogenic source of CO2 from the burning of fossil fuels.
John

Bart, If you feel that the mass balance argument is based on assumptions that are incorrect, or information that we don’t actually know, it would be very easy for you to point out the step where the problem ocurrs and I will be proven wrong. It is hard to understand your reluctance just to go through about six steps saying whether you agree with them or not. It would be ar less typing than was involved in your previous post. Do you agree with step #1? If you do, we will have narrowed down the steps where the error may lie. If you don’t then it is your chance to prove me wrong.

John Whitman says:
April 1, 2012 at 12:09 pm
Most of all natural CO2 is around zero per mil d13C: that is all inorganic carbon (carbonate -rock- layers from plankton shells), sclero sponges, corals,… That is also the case for the inorganic carbonates dissolved in the (deep) oceans and ocean sediments, therefore also for volcanic CO2 from subduction volcanoes.
Low 13C CO2 comes mainly from organics and some from fractionation processes in the deep mantle (but even mantle plume volcanic releases still are around/above atmospheric d13C). Thus any substantial reduction of atmospheric d13C, which is already low, comes from organics. Either from living organisms or from fossil organics. See:
http://homepage.mac.com/uriarte/carbon13.html
Thus while the bulk exchanges between the oceans and the atmosphere provide the atmosphere with a positive d13C CO2, some seeping of methane, oil or other organics from the (deep) oceans may influence the atmospheric d13C to the negative side.
The problem is that all these exchanges had only a small variability (+/- 0.15) around -6.4 per mil over the 450 years before the start of the industrial revolution. The same for the ocean surface waters: +4.95 +/- 0.15 at Jamaica (broadly the same over the whole North Atlantic Gyre). See:
C:\Users\Familie\Documents\Thuis\telenet\klimaat\klim_img\sponges.gif
Since about 1850, there is a constant accellerating drop in d13C as well as in the atmosphere as in the ocean’s surface and at the same time an increase of CO2 in the atmosphere and in the ocean’s surface. That is incompatible with an extra release from the oceans: both the d13C drop as the DIC (dissolved inorganic carbon) increase in the oceans is opposite that expectation. The only alternative possibility is an enormous release (and oxydation) of organics from the (deep) oceans, be it methane clathrates or oil leaks. But think about the quantities involved: the BP oil spill of the Gulf is not even measurable in the CO2 increase. Moreover, that would be additional to the human emissions, but the human emissions are already twice what is observed as increase in the atmosphere. As the conservation of mass dictates: the difference with what is observed must be absorbed somewhere. The only alternative that is fast enough is the biosphere. That should sequester all the extra carbon from the oceans plus halve that of the human emissions. But that gives another contradiction: if that was true, the low 13C carbon from the oceans + halve the human emissions would be completely replaced by high 13C carbon from what remains from photosynthesis, the net result is that only the human emissions are responsible for the increase in the atmosphere and the d13C decline and that nature only shuffled some organic carbon from the ocean reservoir to the biosphere reservoir.
In reality, not such an increase of extra organics releases from the oceans is observed. And both oceans and the biosphere are net sinks for CO2.

FerdiEgb says:
April 1, 2012 at 9:39 am
“See: http://www.sciencemag.org/content/287/5462/2467.abstract“
Reminds me of this.

Bart says:
April 1, 2012 at 3:26 pm
No, it was before that. I showed that the only variable you could know was a difference, which did not tell you what the natural flows were.
Again, it is totally unimportant what the absolute height of any of the in and outflows are, it is only important what the difference between all the inflows and all the outflows is. It doesn’t make any damn change to the amounts in the atmosphere, as long as the total flows into and the total flows out are equal. No matter if these are 10 or 100 or 1000 GtC/year. Only the difference between ins and outs is important and that is what we know: the difference between what humans emit and what we measure as increase.
Again, it seems very difficult for a lot of people to understand that the natural flows between the atmosphere and the other reservoirs are of not the slightest interest to know natural flows between the atmosphere and the other reservoirs .
That is not what I said. I said:
Again, it seems very difficult for a lot of people to understand that the natural flows between the atmosphere and the other reservoirs are of not the slightest interest to know how much nature supplies to or removes from the atmosphere.
What nature supplies or removes to/from the atmosphere is not inflows or outflows, but the difference between inflows and outflows. If inflows and outflows are equal, there is zero supply and no change in the total amount present in the atmosphere. Again flows are not important, the difference at the end of the year is important.

FerdiEgb says:
April 2, 2012 at 4:34 am
“Again flows are not important, the difference at the end of the year is important.”
It is useless. See above.

Bart, I agree that the carbon cycle is a dynamical system, as I said in my paper I use a one-box model of the carbon cycle (essentially the same as Prof. Essenhigh’s) to capture the first order dynamics of the system, defined by a differential equation, which provides a crude model of the expansion of the sinks. It gives the same story as the mass balance argument.
I’m glad we agree that the environment is a net carbon sink. You have yet to explain how the natural environment can be causing atmospheric CO2 to rise whilst being a net sink. It is a bit like saying I can cause my bank balance to increase by withdrawing more money than I deposit (see the last part of my post for a more detailed explanation).
It is important to note that the mass balance analysis is not a model of the carbon cycle, and it applies equally well whether the carbon cycle is static or dynamic. It doesn’t predict anything, it just uses a principle of physics (conservation of mass) that allows you to infer the difference between natural uptake and natural emissions. This is true whether natural emissions are constant or whether they are variable.
As for the carbon cycle being dynamic, rather than M in your equation, it should be dM as it is the change in the mass of the atmospheric reservoir, rather than the mass itself. The equation is then more properly represented as
dM = A + N – U
This is a difference equation, and hence does define a simple dynamical system if you want to view it that way. If A, N and U were constant, then dM would also be constant, but of course nobody is claiming that any of these quantities are constant. N-U changes from year to year, as clearly demonstrated by the figures you were invited to investigate in my previous post.
Now if you wanted to make even the simplest model of the carbon cycle, it would have to include the expansion of the sinks (as you point out) due to the rise in atmospheric CO2, so lets do that. Essenhigh forms his one-box model by making U proportional to M (if you look at the data this clearly isn’t a reasonable assumption, which is why I use a linear relationship with an intercept). We then have
dM = A + N – kM
where k is a constant. Now if you want a continuous time model, you can use a differenttal equation instead, which gives you (c.f. equation 4 in my paper).
dM/dt = A + N – kM
If you solve the equation you will still find that if the rate of growth of atmospheric CO2 is less than the rate of anthropogenic emissions then the rate of natural emissions must be less than the rate of natural uptake. That is because conservation of mass applies to both static and dynamical systems, and the mass balance argument is merely an application of conservation of mass, nothing more.
Now if you want to separate natural uptake into uptake of “anthropogenic” CO2 and “natural” CO2, then that is fine. Indeed that is exactly what I do in my paper (c.f. equations7 and 8). If you do that, you still end up with a situation where if the rate at which CO2 is increasing in the atmosphere is less than the rate of anthropogenic emissions then the rate of natural uptake must be greater than the rate of natural emissions.
you write “So, we only know N-UA-UN. Suppose UA = A. Then M = N – UN, N is greater than UN, and the rise is entirely natural.” This is an absurd argument, which we can see if we recast it in a more familiar setting (as indeed I did in my paper in an analogy adapted from one of Ferdinands):
Consider a husband and wife that share a jar in which they keep their savings. He deposits 8 euro per month, all in Belgian minted coins, and never makes any withdrawals. She on the other hand deposits 1000 euro a month, all in French minted coins (so we can tell the difference) but withdraws 1004 euros a month from the jar. Clearly the total amount in the jar will rise by 4 euro a week, and most people would agree that the rise in their savings is purely due to the husband (as his deposits exceeded his withdrawals) and not his wife (as her withdrawals exceed her deposits).
Your argument is akin to saying that if the wifes withdrawals contained 8 Belgian coins then that particular month the increase in their savings was purely due to her having taken four more coins out of the jar than she had put in, which is clearly absurd.

Phil. says:
April 2, 2012 at 10:52 am
gavincawley says:
April 2, 2012 at 11:05 am
FerdiEgb says:
April 2, 2012 at 11:36 am
I honestly can’t see how to answer you fellows without becoming churlish and abusive, so I will be brief: This is pitiful stuff.
Go back and read what I wrote at 10:03 am, this time for comprehension. Because, you guys are embarrassing yourselves.

gavincawley says:
April 2, 2012 at 2:33 pm
Gavin – why don’t you try reading and understanding what I wrote at 10:03 am? You’re just digging your hole deeper.
Your analogy fails because you have artificially contrived a situation in which all of the inputs and outputs are known. It is equivalent, in my example, to saying you know both N and U individually. You DO NOT.
There are children pilfering coins from the jar. The taxman steals in occasionally to grab his share. And, a rich uncle occasionally makes a contribution. You have no idea how much each of these is contributing or taking away, so you have excluded them from your calculation. And, your result is useless for drawing up a budget, or determining which coins came from where or from whom.

Bart says:
April 2, 2012 at 1:49 pm
Bart, I have reread that comment:
UA = natural uptake of anthropogenic emissions
UN = natural uptake of natural emissions
So, we only know N-UA-UN. Suppose UA = A. Then M = N – UN, N is greater than UN, and the rise is entirely natural. Equality would never be precisely the case, but it depends on the sequestration time.
What you suppose there is that the anthro CO2 is sequestered near instantly, while the natural CO2 largely remains in the atmosphere. That is impossible. Both anthro and natural CO2 are 99% 12CO2. Natural sinks don’t make any differentiation between anthro or natural 12CO2. And the differences in the 13CO2 are too small to make a substantial difference in mass transfer. Thus there is no practical difference in sequestration time between anthro and natural CO2.
The current amount sequestered by oceans and biosphere together is about 4 GtC/year. With a current CO2 level about 210 GtC above steady state (for the current temperature), that gives an e-fold time of about 52.5 years, far from instantly. No matter the origin of the CO2 molecules flying around in the atmosphere.
Thus we have a yearly, growing, addition of 8 GtC of human CO2 and a natural sink capacity of only 4 GtC/year (growing in near constant ratio with the emissions) at the current extra CO2 pressure in the atmosphere. There is no way that you can explain that any natural source is responsible for the increase in the atmosphere, while the human emissions are not…

To reinforce Ferdinand’s comment above, I also agree that the uptake doesn’t significantly differentiate between anthropogenic CO2 and natural CO2 (indeed it can’t 12C is 12C is 12C, it isn’t labelled by source). So the one box dynamical model of the cabon cycle used in my paper divides the uptake according to the mixing ratio.

FerdiEgb says:
April 2, 2012 at 3:19 pm
“With a current CO2 level about 210 GtC above steady state (for the current temperature)…”
How do you calculate the steady state for the current temperature? If it is based on ice core data, I would consider such an estimate tentative and unproven, at the very least.

FerdiEgb says:
April 2, 2012 at 3:19 pm
One final point on your last post:
“The current amount sequestered by oceans and biosphere together is about 4 GtC/year.”
How do we know what the current amount is? Don’t list for me all the known sinks and their estimated capacities. Justify that the list is exhaustive (something more compelling than “we don’t know of any others”), and that the estimates are supremely accurate (remember, it takes less than 3% variation of what we currently “know” to completely swamp the anthropogenic input).

gavincawley says:
April 2, 2012 at 4:10 pm
“So please, give a direct answer to the question as posed.”
No. It is a red herring. Read my post at 10:03 am. When you understand it… I was going to say, get back to me, but when you do, you will have no further questions.

Bart wrote: “This is circular logic.This is N – U, not U. You have built in the a priori assumption that N = 0.
No Bart, the 4GtC/year is the amount sequestered by the natural environment, not the amount taken in, they are not the same thing. If you were familiar with carbon cycle you would know that the total uptake U is much larger than that, so it is obviously not an estimate of U itsel.
Consider the oceans, according to fig 7.3 in the IPCC AR4 WG1 report, the oceans emit about 90.6 GTC/year into the atmosphere, but also takes about 92.2 GTC/year out of the atmosphere. So most of the flux between the oceans and atmosphere is an exchange flux that exchanges molecules of CO2 from the atmosphere, however an exchange does not alter the mass of the atmopsheric reservoir. However ocanic uptake is 1.6GTC/year higher than oceanic emissions, so 1.6CTG/year of carbon goes into the ocean and doesn’t come back out again. So the amount sequestered is the difference between the amount taken in and the amount taken out.
Sequestration and uptake are not the same thing; sequestration is N-U, uptake is U. We don’t need to know the precise value of U to know the value of N-U, as you have already conceded the mass balance argument tells us that.

Bart wrote: ”
dM/dt = c*(A + N) – kM
where c is a factor of perhaps roughly 1/2, which models the relatively rapid dissolution of a portion of the atmospheric CO2 into the oceans.
No bart, i you did that your model would violate the principle of conservation of mass. The original equation
dM/dt = A + N – U
was a restatement of conservation of mass, so if you arbitrarily halve A and N then obviously that principle no longer holds.

Bart says:
April 2, 2012 at 4:21 pm
Size matters. A small input to a negative feedback system with adequate bandwidth to respond can be easily attenuated to negligibility, whereas a large input creates… a larger excursion. Since we do not have any direct measurement of everything that is coming in from nature (e.g., an extended expulsion from upwelling of deep ocean currents), we cannot rule out the possibility.
We don’t know the variability of most natural inflows and outflows with sufficient accuracy, but we do know the variability of the net natural balance. That is +/- 1.5% of the estimated total inflows and outflows. Or a variability of about halve the human emissions total inflow. Thus any response to a change in the natural balance must be equal to or faster than a response to the human emissions…
A response from the natural sinks to any increase in the atmosphere must be the same whatever caused the increase. The current response is about 4 GtC/year, while the emissions are at about 8 GtC/year…

Bart says:
April 2, 2012 at 4:31 pm
Before we get too far afield, let us pause to make the current point. You are now arguing, Ferdinand, that you have a problem with the sequestration rate being what you think is required. That’s fine, and a valid argument to have. But, in doing so, we must acknowledge that the mass balance argument is insufficient to convict anthropogenic emissions of the crime of increasing atmospheric concentrations, and you must rely upon other data to prosecute the case.
If I can only get that concession from you, I will be happy for now.
The mass balance itself is sufficient to prove that the human emissions are the sole cause of the increase in the atmosphere, as long as the increase is less than the emissions. It is as simple as that. If the increase in the atmosphere was more than the emissions, then we would have a part from the emissions and a part from nature adding to the increase. In both cases, the sequestering is less than the emissions or less than the sum of the emissions + extra natural supply. If there was no increase or even a decrease in the atmosphere, then the sequestration rate was larger than the emissions and any additional supply by nature.

gavincawley says:
April 3, 2012 at 2:41 am
“The original equation
dM/dt = A + N – U
was a restatement of conservation of mass, so if you arbitrarily halve A and N then obviously that principle no longer holds.”
Why can you not see this? What is this mental block? If you want to treat this problem rigorously, you have to include state variables for all three reservoirs, oceans, land, and atmosphere. If you choose to focus just on the atmosphere alone, then you have to make approximations, and conservation of mass DOES NOT HOLD FOR THE ATMOSPHERE ALONE.
Sheesh.

Bart wrote “If you want to treat this problem rigorously, you have to include state variables for all three reservoirs, oceans, land, and atmosphere.
Yes, and indeed that is what e.g. GEOCarb does (and more). If you adopt such a model you will still find that if the rise in atmospheric CO2 is less than anthropogenic emissions, then the total natural uptake is greater than the total natural emissions. The scientists who study the carbon cycle have been working on this for decades. I am using a greatly simplified model here because it is sufficient to make the basic point.
“If you choose to focus just on the atmosphere alone, then you have to make approximations, and conservation of mass DOES NOT HOLD FOR THE ATMOSPHERE ALONE.”
The simple model I gave earlier obeys conservation of mass for the whole carbon cycle, not just the atmosphere. I could have included a variable to record the mass of the non-atmospheric reservoirs, but they are irrelevant to the central point.
Do you agree that total natural uptake (ocean+land) has exceeded total natural emissions (ocean+land) for each of the last fifty years, yes or no?

tallbloke, If you think Ferdinand and I are wrong, the I would invite you to try proving it. The argument involves half a dozen steps, are you willing to go through them with me, so you can point out where the error lies? I am making it as easy as I can for you to prove me wrong, so if you are condfident I am wrong, why not give it a go?
Step #1 Do you agree that the carbon cycle obeys conservation of mass, such that the annual increase in atmospheric CO2 is the difference between total emissions from all sources minus total uptake by all sinks? Yes or no, if “no” then please justify your objection.

The kicker is, there is a valid debate to be had here. But, these guys aren’t even stepping up to the plate. They’re hanging out at the dugout, holding their bats upside down, and insisting that the pitcher already walked them (hope you know enough about American baseball to appreciate the metaphor).

Tallbloke, yes change would be a more general term and I am happy to go with that as well.
Step #2 The carbon cycle is a closed system, i.e. carbon isn’t spontaneously created or destroyed (except for the insignificant amounts of 14C of course) but is exchanged between reservoirs (atmospheric, oceanic and terrestrial) and there are natural sources of CO2 into the atmopsher, anthropogenic sources and natural sinks that take CO2 out of the atmosphere and no other sources or sinks into or out of the atmosphere.
Do you agree with that. yes or no, if no, please explain.

clivebest: Indeed, see my paper in Energy and Fuels http://pubs.acs.org/doi/abs/10.1021/ef200914u . However you don’t actually need differential equations to prove that the rise is anthropogenic. Ferdinand Engelbeen also has a very good website on this issue, see http://www.ferdinand-engelbeen.be/klimaat/co2_measurements.html .

@tallbloke – is that a response to step #2? Note that increase in woody biomass would be a component of the natural sink.
Do you agree with step #2, yes or no?

@tallbloke increased biomass would be both a natural sink (gross primary production) and a natural source (respration), this is no big deal, the ocean is both a source and a sink as well. Soil respiration (i.e. rotting) is also a natural source.
None of that affects whether the carbon cycle is a closed system or not. Perhpas I could rephrase it, do you agree that no carbon dioxide enters or leaves the atmosphere other than due to anthropogenic emissions, or uptake by natural sources (which take carbon out of another natural reservoir and put it into the atmosphere) or natural sinks (which take carbon out of the atmosphere and put it into a natural reservoir)?
I am not specifying what these natural reservoirs actually are, apart from that they are part of the planet (i.e. e.g. we don’t have aliens stealing CO2 for some nefarious purpose). Neither am I specifying what these natural sources actually are, or how they operate, just that they exist.
Do you agree with this, yes or no?

Bart wrote: “Write down the equations. Carefully label what is known and what is unknown. In the end, you will come up with the difference between natural inflow and outflow as being the only fundamental quantity known, but with nothing more than handwaving to assert how much of each there is individually.”
You agreed that the mass balance argument means that we can infer the difference between total natural emissions and total natural uptake as it is equal to the difference between the annual change in atmospheric CO2 and anthropogenic emissions. Have you changed your mind now?

Note that the model I gave is arbitrary. AGW advocates like it because it gives them a factor of 1/2 that, when N and k are set to zero, gives an atmospheric rise of approximately half the accumulated emissions, and they think this is some way-out, weird coincidence that proves their bias.
But, we can as easily introduce another coupling constant “c” such that
Mdot = N + A + a*(O – 0.5*M/c)
Odot = a*(0.5*M/c – O) – 2*k*O
It is left as an exercise to the reader that this can produce an approximate first order differential equation for the atmospheric concentration of
dM/dt = c*(A + N) – kM
Thus, “c” can be anything, and assuming it is near 1/2 is just cherry picking to confirm one’s bias.

tallbloke says:
April 3, 2012 at 1:22 pm
Well, drop back later. I’m bailing out. I’m really sick of this. Whatever the triplets write after this, the reader should be aware that it has been demonstrated that they did not know what they were talking about before this post, and it is unlikely they will have gained greater wisdom or knowledge after.

Tallbloke, I said “such as”, indicating that this was an example of the kind of “denier argument” that Singer saus should be dropped so that the skeptics can retain credibility. This in no way implies that you had used that argument, I’m sorry that you have taken umbridge over this, but the error is in your parsing of the sentence, not in my writing.

Bart says:
April 3, 2012 at 12:30 pm
I wish to point out a small matter here in my derivation.
Under the assumption that “a” is much greater than “k”, then this transfer function is approximately
H(s) := a/( (s+2*a) * (s+k) )
The term a/(s + 2*a) is a wide bandwidth process with dc gain of 1/2. Thus, we can further approximate
H(s) := 0.5 / (s + k)
I should not have dropped the “s” in the numerator of the first Laplace transform version of the transfer function. The zero at “a” is actually “activated” before the pole at “2*a” in the frequency response plot. If doing it over again, I would write:
Under the assumption that “a” is much greater than “k”, then this transfer function is approximately
H(s) := (s+a) / ( (s+2*a) * (s+k) )
The term (s+a) / (s + 2*a) is the transfer function of a wide bandwidth lead/lag network with dc gain of 1/2. Thus, we can further approximate
H(s) := 0.5 / (s + k)
Nothing important changes – I just like to have things in perfect order.

Bart, let’s start with the basic equation
dM/dt = c*(A + N) – kM
With as constraint that 0 < dM/dt < A
For brevity and clarity, let us assume that the throughput from oceans and vegetation is roughly constant and that kM is entirely into the oceans. N is solely an increase in output from volcanoes, so that there is no return flow, at least not on non-geological times…
As well as for human emissions as for volcanic releases, there is no transfer function for their release into the atmosphere, that is simply additional. Thus c = 1, which BTW always is the case for A.
As M is constantly measured, we know the change over a year, for the past 50+ years. That can be expressed as dM/dt = b*A, where 0 < b < 1.
Be aware that dM/dt is about total quantity, regardless of the ratio between N and A in M.
By substitution in the basic equation, that gives;
b*A = A + N – kM
or
N = kM – (1-b)*A
as b < 1, that means that kM > N, what is observed. Thus in fact, N is only throughput, but we can make that clear in the next item.
In another year, a huge solar flare hits the earth and awakens all volcanoes, so that they double their emissions. The above equation now is:
2*N = kM – (1-b)*A
To reach that, either k or M should be (near) doubling. That is only possible by an increase of k or an increase of M. Either way, kM remains higher than 2*N as the observed term (1-b)*A hardly changed but anyway still is positive.
Thus despite a doubling of the extra natural input, there is no change in the observed atmospheric increase. That is only possible if the sinks increased at (near) the same rate as the sources increased. Thus simply doubling the throughput without adding anything net to the mass in the atmosphere. An increase in k is very unlikely (one expects even a decrease, as more constraints in oceanic uptake come in), an increase (near doubling!) in M beyond 0 < dM < A is not observed either.
The only alternative explanation which fits all equations and observations is that N is small, compared to A. Over the past 50 years, that is what is observed: natural variability around the trend is about +/- 2 GtC while the emissions currently are at 8 GtC/year.

tallbloke says:
April 4, 2012 at 3:46 am
Bart said:
“Again, your static thinking is evident. When trees capture CO2, they grow. When they grow, they soak up more CO2, and they reproduce to produce more CO2 gobbling trees.
All of the CO2 sinks do this -their capacities grow with increasing CO2. The only question is, how fast do they grow?”
The Idso’s have a very good database for the reaction of a lot of different species on increased CO2. In average, plants grow with 50% when CO2 is doubled, in the best circumstances. In the real world, the circumstances are mostly less than best, thus the 50% is a maximum. More plants is more problematic (and much slower), as seedlings in dense forests have little chance of growing, except if an old tree falls down, thus mainly replacement. The main way to obtain more plants is when the area expands, as (land) glaciers melt and/or tundra becomes forest and/or deserts become tundra. That played a role mainly during the glacial – interglacial transitions, where the increase in temperature of the oceans dominated the CO2 levels, plant area only played a secondary role but relative more important once the interglacial was reached (+/- 10 ppmv over the Holocene).
Oxygen for ozone formation (and back…) is an equilibrium process, mainly in the stratosphere. In the troposphere typical at 80 ppbv, or 0,08 ppmv, hardly of influence on the oxygen levels (10% of the measurement error of the oxygen measurements). Near everything else on earth that could be oxydised is already oxydised: metals, silicon and other minerals…
Based on the oxygen and d13C measurements, some 20% of human emissions (in quantity) is captured by the vegetation cycle and 30% by the oceans. No static thinking at all, as the total quantity captured follows broadly the emissions with a surprising stable ratio over the past 50 years.

Guys… your argument hinges on c being approximately 1/2. Your brothers in arms have gone to A LOT of trouble to construct their “theories” about how CO2 passes between atmosphere and ocean to make it so. If you do not even know enough to know this, then you do not know enough to be pontificating about the matter at all.
I didn’t make this up.I didn’t choose c := 1/2 out of a hat. I would LOVE for you to insist that c is something other than approximately 1/2. It totally kills your argument at its very foundation.

Perhaps there is some confusion because I did not define the following terms clearly (amended here):
A = anthropogenic input flux
N = natural input flux
These are the time derivatives of concentration, not the concentration itself. M is the time integral of terms in A, N, and M itself.
The “k” term is a constant. It does not change. It quantifies the expansion of the sinks as M increases, i.e., it is a sensitivity term. In the real world, it may vary somewhat, but you should assume it is constant.
Ferdinand, your fundamental argument is that M := 1/2 * integral(A). Keep that in mind when looking at the conclusions you are driven to with your math. E.g.,
N = kM – (1-b)*A
means
M = (N + (1-b)*A)/k
A is on the order of something like a couple of ppmv/year equivalent/ If “k” is “large”, then it cannot possibly account for the measured concentration. That is the point I have been driving at all along.
IF “k” is “small”, then the equation works out to approximately
M = c*integral(A + N)
with c = 1/2 and N = 0, this gives the solution you want. But, it is not the only solution which is allowed by the observations.That is the point I have been driving at all along.

Bart writes “From that point of view, a crystal radio receiver could never work, because every rectified half wave would have the same area.”
You have missed Ferdinand’s point. As you have used an analogy, so will I. If I have jar containing 30 sweets, and every day I take 20 sweets out and eat them, but also buy a packet of 20 sweets and put them in the jar, then there has been a turnover of 20 sweets, but it hasn’t affected the number of sweets in the jar at the end of the day.
Likewise the oceans emit about 90GtC/year of carbon into the atmosphere each year (IIRC) but take in about 92GtC/year. So the oceans cause a turnover of about 90GtC/year, which has no effect on the amount of CO2 in the atmosphere, and a net flux of about 2GtC/year, which means the oceans also take about 2GtC/year out of the atmospheric reservoir.
You can disagree with the figures if you like, however Ferdinand’s point about an exchange flux not affecting atmospheric CO2 levels stands.
Also you may think think your model obeys mass balance, you have not gone through the mass balance argument step by step. For a very good reason, which is that you know that if you did go through it step by step you would not be able to identify a flaw, hence your unwillingness to give direct answers to direct questions.

clivebest wrote “The Net e-folding time for CO2 is ~52.5 years. This means that if humans stabilize emissions at roughly current values of 8Gt per year, and continue to emit 8 Gt/year forever then….the final CO2 content of the atmosphere will be 500 ppm. Is this so terrible ?”
This is not correct. It is the difference in partial pressure between the atmosphere and surface ocean that drives the oceanic sink. If the atmospheric concentration stabilises, then as the surface ocean takes up more CO2, the partial pressure difference falls as they come back into equilibrium and the sink would shrink. While we keep anthropogenic emission at current rates the atmospheric concentration will continue to rise. If the sinks can’t deal with our emissions now, why should they be able to cope with the same levels in the future when they are heading towards saturation (thankfully they are not there yet)?

clivebest says:
April 4, 2012 at 9:53 am
“For B the net increase in CO2 is due to A – PLUS an increase in N . The sink increases ONLY in response to the natural increase in N, because (he argues) they are coupled together.”
No, I am not arguing that at all. The sinks do not discriminate. But, if the sinks are strongly activated, they will bleed out the anthropogenic component before it can build up. Therefore, in that case, the natural input has to be the driver. Since the natural component cannot be quantified by current knowledge, there is no limit on how large it can be, so there is no way to eliminate the possibility.
gavincawley says:
April 4, 2012 at 10:59 am
“You have missed Ferdinand’s point.”
If I have a bucket into which I am alternately pouring in a liter of water, then emptying it out, then my average volume of water is 1/2 liter. If I now alternatingly put in 2 liters and empty it out, my average volume is 1 liter. The exchange volume matters.
“Likewise the oceans emit about 90GtC/year of carbon into the atmosphere each year (IIRC) but take in about 92GtC/year.”
You do not KNOW this. These are estimates which are calculated under the constraint that your model for the entire system is correct. You have to impose such constraints to get an answer, because you have too many unknowns for the equations. But, it is circular logic. It proves nothing.
“…if you did go through it step by step you would not be able to identify a flaw…”
I have already identified the flaw. I have repeated it over and over and over. It just sails right over your head. The flaw is this: you are assuming that the atmosphere acts as a pure accumulator (no ultimate sinks) and that the natural balance is perfectly steady. There is no evidence available which confirms either of these assumptions.
Look, this is very simple. The response to both N and A is precisely the same. If the constant “k” is large (sinks are very active), then the atmospheric concentration will closely track (c/k)*(N+A). In this case, A is not large enough to account for the measured concentration, so N has to be the driver. In the case where “k” is small, the concentration will track c*integral(N+A). If “c” is close to 1/2, then the accumulation has to be driven by A. If “c” is substantially less than 1/2, then N is playing a significant role, too.

Bart wrote: “If I have a bucket into which I am alternately pouring in a liter of water, then emptying it out, then my average volume of water is 1/2 liter. If I now alternatingly put in 2 liters and empty it out, my average volume is 1 liter. The exchange volume matters.”
That is an inappropriate example. The average volume of water in the bucket is only 1/2 becase you are putting one liter in as a discrete action and then taking one liter out as a discrete action. However the carbon cycle is continuous, not discrete. If you put one liter in and took one liter out, but by alternating putting one tea spoonfull in and one spoonful out then the average amount of water in the bucket would be half a teaspoon full, but the volume of the exchange would be the same. At the end of the exercise the level of water in the bucket would be exactly the same as it was at the start. This is because an exchange doesn’t affect the volume of the reservoir. To do that you need a difference between the amount in and amount out, and it is this difference that matters, not the volume.
“I have already identified the flaw. I have repeated it over and over and over.”
No you have not identified a flaw as you refused to go through the step by step analysis and instead went off at a tangent based on an issue that is not actually part of the mass balance argument. If you really want to prove me wrong, then the easiest way is to go through the six steps one by one, saying where you agree and where you dont. By continually avoiding this you are just demonstrating that you know as well as everybody else that you will not be able to identify the flaw.

gavincawley says:
April 4, 2012 at 12:32 pm
“The average volume of water in the bucket is only 1/2 becase you are putting one liter in as a discrete action and then taking one liter out as a discrete action. However the carbon cycle is continuous, not discrete.”
We were speaking specifically of vegetation, and eras of growth and decay.
But, you do bring up a point about why I made the crystal radio receiver analogy. The continuous action of varying rates of growth and decay across the entire spectrum of vegetation would tend to low pass filter the cycling, and the average difference becomes a steady difference. Just like in a crystal radio, where the signal is rectified, then smoothed through a low pass filter. The average of the rectified signal is then what comes out of your speaker.
A final way to look at it: take the reductio. Are you telling me there would be no difference in CO2 concentration if the Earth were a dead planet, with no vegetation at all, compared to what it is now?
“If you put one liter in and took one liter out, but by alternating putting one tea spoonfull in and one spoonful out then the average amount of water in the bucket would be half a teaspoon full, but the volume of the exchange would be the same.”
Take a breath. Try again. Think it through.
“If you really want to prove me wrong…”
I have already proven you wrong. I have laid it out for you on a silver platter with bone china and crystal goblets. If you do not understand now, I do not see much hope that you ever will.

Bart wrote “I have already proven you wrong. I have laid it out for you on a silver platter with bone china and crystal goblets.”
no, you have attacked the straw man of an argument I did not make, not the mass balance argument. You can tell this by the fact that we only got as far as step #1 in the argument I am actually making.
“If you do not understand now, I do not see much hope that you ever will.”
Well perhaps going through my argument step by step and point out my error when I make it. That will make it much easier for me to understand where I am going wrong. Unfortunately you seem to be extremly unwilling to do the one simple thing that would resolve the issue very quickly,

Clivebest wrote “However, in the longer term an equilibrium must be attained so long as fluxes remain sufficiently stable over many decay lifetimes”
However I have pointed out that the fluxes will not remain stable as the net oceanic sink will dissapear as the partial pressure of the surface waters equilibriates with the atmosphere. At that point the adjustment time will grow as the uptake into the thermocline is no longer the bottleneck.
I have the feeling that this is an argument that cannot be resolved by resorting to more complex models”
Yes, exactly, such as CEOCARB or the type of model that Archer describes in his primer (and research articles). As I said, such simple models as those discussed on this thread are only really useful for qualitative analysis of the most basic behaviour of the carbon cycle and we need to bear their limitations in mind.
The mass balance argument however is not a model, and it is useful for quantative analysis of the observations.

Further to what Ferdinand has just said, the one box model of the carbon cyle used in my paper produces a constant airborne fraction of IIRC about 0.58 as a consequence of exponential growth in anthropogenic emissions (which is a reasonable approximation to what we have actually seen); it isn’t an assumption that is built into the model. The reason that it is 0.58 rather than 0.45 is that the model is based on a differential equation that is only a first order local approximation of reality at best, but produces results in good qualatative agreement with reality.

gavincawley says:
April 4, 2012 at 12:45 pm
David Archer has written a primer on the carbon cycle that explains in great detail how the carbon cycle will respond, it is a lot more complex than the very simple models being discussed on this thread
This is the only point where I differ with you in your essay. Archer sees different constraints, some true, some questionable. The constraint in uptake for the ocean surface is certainly true for the Revelle factor, as can be seen in the increase of DIC (dissolved inorganic carbon) which is only 10% of the increase of CO2 in the atmosphere. Thus even if the equilibrium between the atmosphere and the ocean’s mixed layer is very fast (order of ~1.5 years), that reservoir can only take in 10% of the increase. The deep ocean exchange is quite different: the main intake is in the polar waters, mainly in the NE Atlantic where the CO2 partial pressure difference pCO2(atm) – pCO2(aq) is about 250 microatm (400-150 microatm), as the waters there are extremely cold. This pressure difference pushes a lot more CO2 directly in the deep oceans, which are at some 5 degr.C. The deep ocean waters contain some 37,000 GtC as DIC, but are far from saturated. Thus any extra CO2 coming in via the THC will simply mix up with the rest of the carbon mass, depending how readily that mixes and comes up some 800-1000 years later into the warm equatorial Pacific. There a lot of CO2 is released, due to the high temperature.
Archer now uses the same 10% rule for the deep oceans as for the ocean surface, but that isn’t true, as the deep oceans still are far from saturated and any considerations of the Revelle factor only holds for the air-ocean surface interchange (which at polar waters only increases), not for deep ocean waters. Thus if we assume that the ~370 GtC that humans have emitted ultimately all end in the deep oceans, that would increase the deep oceans carbon content with ~1%. At the ultimate steady state with the atmosphere, that would also give a 1% rise in the atmosphere above the pre-industrial CO2 level, or 3 ppmv.
The reasoning also holds a fortiory for the biosphere: there is no limit in the storage capacity of the biosphere, as the millions of years old gigantic coal beds show. This too is a relative fast and increasing (semi) permanent storage. Thus there is no reason to think that some 30% of the increase in the atmosphere remains there near forever…

Ferdinand, I would agree that things get more difficult as you get into the more advanced issue and things become more uncertain and I am comfortable with there being disagreement. My primary interest is to try and put an end to the argument that the rise in atmospheric CO2 is natural; this sort of argument is enormously damaging to the “skeptic camp” and does neither side of the discussion any good. It would be nice if the advanced issues could be discussed once the very basics are more widely accepted.

gavincawley says:
April 4, 2012 at 2:01 pm
“The reason you will not engage in that exercise is that you know tha on that basis you will fail to identify an error and will be proven wrong.”
No. It is because I know the error in your reasoning, and going through it with you will do me no good. You are trivially wrong.
It will not do you any good, either, because you appear not to know when you are making implicit assumptions and, when I point them out to you, you deny them.
This system is trivially Controllable through N. It is elementary that you can therefore always find a natural forcing which will produce the output you want. The size of N (or, rather, the deviation from historical norms) needed is what counts. If it is “small” compared to A, then it is not significantly driving the rise. If it is large, however, then it is. How large or small it will be depends completely on the parameters, which I have reduced to “c” and “k” in the model I have profferred. If the sinks are active, then the rise is not most significantly anthropogenically driven. If the diffusion of CO2 into the oceans is not approximately 1/2 of the net atmospheric transfer, then the rise is not most significantly anthropogenically driven. If the sinks are weakly active and the diffusion is about equal, then the rise is anthropogenic.
Those are the twin pillars upon which anthropogenic attribution is founded: weak sinks, and even atmospheric/ocean distribution. That edifice was not constructed by me on that foundation, but by the authors of papers stretching back decades who recognized the requirements for anthropogenic attribution. There is a mound of modeling assumptions which have gone into that construct, from buffering action of the oceans to discounting of unknown processes. It is a shaky foundation. Whether it stands far into the future, we will just have to wait to see.
“My primary interest is to try and put an end to the argument that the rise in atmospheric CO2 is natural; this sort of argument is enormously damaging to the “skeptic camp” and does neither side of the discussion any good.”
I have not been arguing that it is natural. I have been saying that there is not enough information to clinch the argument. Given popular perceptions, maybe it harms the skeptic camp. Than again, maybe it doesn’t. Since it isn’t a front burner issue right now, given the very obvious shortcomings in the rest of the AGW conjecture after a decade of stagnation in the temperature metric, I doubt it is hurting anything right now.
I am much more put off by those who deny the basic greenhouse physics through misguided appeals to the 2nd law or whatever. But, again, the basic stagnation and incipient downturn in temperatures will carry the day, and I am not overly concerned about it.

smokey – in barts analogy the average volume in the bucket is half a litre, in mine it is half a teaspoon full, i you used 1ml pipette it would be half a millilitre, but the exchange is a litre in each case. Consider what happens when the exchange is performed one molecule at a time. The fact that the two almost identical analogies produce different results illustrates the flaw in the analogy.
The point is that the increase or decrease in the contents of the bucket depends on the difference between total flow into the bucket minus total flow out of the bucket. If you make the flow in the same as the flow out, you can have an exchange as large as you like, but it doesn’t change the level in the bucket.