Empirical Validation of the Exponential Decay for Surplus CO2

Guest essay by Ari Halperin

My new scientific paper Empirical Validation of the Exponential Decay for Surplus CO2 further validates the conclusion that surplus CO2 in the air decays exponentially. The half-life is re-estimated down to 30-35 years. Further, if the CO2 sink rate has changed in the last 100 years, it has increased rather than decreased (i.e., the half-life has decreased). The paper uses pre-1958 concentrations, which were obtained by C.D. Keeling by re-analyzing certain 19th century instrumental measurements and merging them with the ice core measurements.

This pre-1958 data indicates that atmospheric CO2 concentrations steadily increased from 288 ppm in 1860 to 315 ppm in 1958. Thus, the IPCC opinion on atmospheric CO2 concentrations since 1860 is in a good agreement with the empirical data. I do not agree with criticism pointing to some pre-1958 measurements showing significantly higher concentrations. Such high readings were likely caused by local sources of CO2, such as industry, buildings, or even scientists’ own breath. The IPCC’s distortion of the carbon cycle was addressed in a recent article on WUWT.

A summary of the new paper and two relevant graphs appear below.

Surplus CO2 is naturally removed from the atmosphere by natural sinks at a rate proportional to the surplus CO2 concentration, on the multi-decadal scale. This result, analytically derived in (Halperin, Simple Equation of Multi-Decadal Atmospheric Carbon Concentration Change, 2015) is verified here by applying it to the pre-1958 data, which was not used in the original paper. The excellent match confirms the validity of the theoretical result. This paper also presents a more accurate estimate of the half-life of the surplus CO2 concentration: 30-35 years. The correspondent equilibrium concentration is estimated to be in the range of 267-285 ppm (larger equilibrium concentrations correspond to lower half-lives). Also, the paper finds that if the natural sink rate did change in the past 150 years, it increased at least during the period prior to 1958. The paper uses CO2 emissions data, corrected for some inaccuracies, introduced since 1992.

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Fig. 1. Comparison of the measured concentration of CO2 in the atmosphere (Keeling curve) to that computed using formula (2) with the same constant half-life from 1860-2013. From Halperin, Empirical Validation of the Exponential Decay for Surplus CO2

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Fig. 2. Comparison of the concentrations of CO2 in the atmosphere, based on historic measurements from 1872-1882 (Keeling & From, 1986) and computed using formula (2) with the same constant half-life, from 1860-1957. From Halperin, Empirical Validation of the Exponential Decay for Surplus CO2

Thus, the natural exponential decay of the surplus (over ~280 ppm) CO2 concentration with a half-life of about 30-35 years is established now for a multi-decadal timescale. The significance of this result is that the atmospheric CO2 concentration is unlikely to exceed 550 ppm in the 21st century, despite current exponential growth in the use of the fossil fuels. In the unlikely case that elevated atmospheric CO2 becomes undesirable, it will be possible to lower it significantly by decreasing emissions, although the exponential decay formula should be used in such a case with great caution, because this scenario has not been encountered before.

175 thoughts on “Empirical Validation of the Exponential Decay for Surplus CO2

  1. IMO, even under a business as usual scenario, CO2 is unlikely to settle higher than 600 ppm in the 22nd century. Much higher levels than this would benefit C3 photosynthesizing plants, but continued reliance on fossil fuels probably can’t get us to the ideal 800 to 1300 ppm range maintained in true greenhouses.

  2. For early C02 measurements, can you get them from ice cores?

    If so you can calibrate the recent against the historical and get an accurate measurement.

  3. Did they include all the EXTRA tree and plant growth caused by the EXTRA CO2, which, of course, causes there to be less EXTRA CO2 ??

    • I have done extensive calculations on excess CO2 half-life, and they do take plant growth into account. The plant growth amount involved is so small – relatively – that it makes no significant difference. I only use data from the satellite age (1979 onwards), and the half-life of excess CO2 comes out at around 13 years. I haven’t studied this paper in detail to see where the difference arises, and I don’t claim that my calculations are better, but I do think that this paper is much more likely to have put the figure too high than to have put it too low. I also think that for very large amounts of excess CO2 there would be at least two separate half-life values, namely a short-term value while the upper ocean predominates, and a longer-term value (many centuries) with the deeper ocean coming into play. I doubt that the CO2 values we are dealing with are large enough for the long term value to come into play.

      This paper covers a longer period than my calcs and gives a longer half-life. If the absorption process was slowing then their half-life should be a bit shorter (and only a little bit), so the discrepancy is not because of the period studied.

      • I looked at atm CO2 based on CDIC emissions data since 1850 to MLO concentration since 1958. I found three different rates of exponential growth in emissions. Scaling the latter period to MLO and backtracking lead to a ‘pre-industrial’ level of 295 ppmv. Somewhat higher than the current study. This similarly assumes constant rate of absorption, which is probably not accurate.

        https://climategrog.wordpress.com/co2-log-rise/

      • 1)
        Assuming a constant surplus CO2 half-life over the whole period of 1860 – 2013, the equilibrium concentration and the half life were best fitted

        If and exponential model is proposed, the fitting ( OLS? ) should be done on the exponential . It appears that all work here was done in ppm. This will not give the best estimation of the supposed model fit.

        My study showed three separate emissions growth rates. Attempting to model this as a single rate probably accounts for the visibly poor fit to the later data and somewhat different starting level.

  4. What is not discussed very often in public by alarmists, is why Ari Halperin’s number should matter at all.
    Two reasons:

    1) ‘Surplus’ CO2 being removed rapidly from the atmosphere, at an increasing rate, means that the hypothetical doubling of CO2 may never occur because we simply don’t have enough fossil fuels to burn or cannot burn them fast enough.

    2) If it ever looked like the dire predictions were actually coming true, then we could quickly remedy the situation in the space of a few decades by going full-on nuclear and the CO2 would quickly fall back down.

    Two very inconvenient truths for the catastrophists.

    • It has never been about climate It has always been about wealth redistribution and a one world government ( U.N.)

      • Marcus
        Absolutely.
        The most important lesson from the whole shameful imbroglio.

        Thanks, Marcus.

        Auto

  5. For me this piece supports a higher “starting point” of 288 vs 270ppm in calculating a human imprint on CO2 levels and supports a shorter residence period for the “evil substance”. If correct, this information means CO2 will not become a “threat” as it’s concentration will rapidly decline when oil becomes expensive enough to reduce consumption.
    It also casts serious doubt on the “scientific” pronouncements of the Leftist and Statists that Government must legislate “fossil fuel” use to prevent catastrophy. Bad science causes much harm. Witness the cholesterol panic, salt panic, the racist belief that genetic differences were/are dispositive in human learning and behavior and a lot of other silliness.

  6. Who gives thanks for the coccolithophores, sedimenting out the life-giving and beneficially warming carbon whaddyacallit?
    ===================

  7. I’d have thought that the natural decay rate of CO2 in the atmosphere was evident in the Mauna Loa graph. Just look at that annual sawtooth!

    • TonyN,

      Different processes at work: seasonal huge differences in temperature, which gives an enormous uptake and decay of fresh/old leaves, some 60 GtC/year. The decay rate of some extra CO2 shot in the atmosphere is mainly pressure driven, as well as for oceans (per Henry’s law) as for the biosphere: extra uptake in more permanent carbon forms (humus, peat,… coal). That removes some 4.5 GtC/year, an order of magnitude difference…

    • Simpler explanation than that Ferdinand.

      Most of the earth’s land is in the NH which also means that SH is mostly ocean. In May/June/July/Aug/Sept, the NH plants are in full growth and CO2 is is being absorbed by photosynthesis. Meanwhile, it is winter in the SH and those oceans absorb more CO2 because the water is cooler. Both hemispheres are absorbing CO2 at the same time for different reasons. In the NH winter months, the process is reversed. The result is the 3% ‘sawtooth’ within a year that Tony refers to. For CO2 to drop 3% in less than a year means that some of the CO2 sinks act very quickly to remove CO2.

      The corollary of this of course is that some of those natural processes also add 3% CO2 very quickly.

      Both of these hugely powerful effects that are capable of adding 3% to global atmospheric CO2 within six months and reducing global CO2 by 3% within six months are of course nothing to do with humans.

      It seems that atmospheric CO2 levels are capable of changing much more quickly – in both directions – than many people think.

      • Yup, a good explanation except for the fact that Bernard L neglected to mention that in April/May/June/July/Aug the NH dead biomass is in full decay mode and great quantities of CO2 is being emitted due to microbial decomposition.

      • Samuel,

        I was just describing the primary drivers. You are right in that biomass decay does obviously have an impact but it is secondary. Most of the NH summer it is less than the photosynthesis effect. The global atmospheric CO2 minimum is in September each year – which happens to be when NH photosynthesis slows or stops and the leaves fall – allowing the effects of biomass decay to show through and help drive atmospheric CO2 up again – at least until lower NH winter temperatures slow the decay down again. September is also when the temperature of the southern oceans picks up again, increasing their out-gassing of CO2 which then takes over as the main driver of atmospheric CO2 increases.

      • Bernard,

        I was aware of what you were doing …. but I’m quite persnickety when discussing science facts and the science of the natural world.

        The CAGW “warminists” have convinced a large majority of the populace that the bi-yearly 6 ppm avg. cycling of atmospheric CO2 as per the Keeling Curve Graph is a direct result of ….. NH summertime decrease due to photosynthesis ingassing by green biomass ….. and NH wintertime increase due to microbial decomposing outgassing by the dead biomass, …… which is not only a preposterous claim, but also a biological impossibility.

        And they have done likewise with the yearly average increase in CO2 ppm by blaming it on human emissions. Just another FUBAR claim.

        The NH springtime dead biomass outgassing of CO2 always begins 1 to 2 weeks earlier than the green biomass ingassing of CO2 ….. and the former does not require Sunlight and thus continues 24-7, night and day, as long as the temperature is above 50 F and there is sufficient moisture.

        And Bernard, when the NH foliage (leaves) begins to lose their “green” color ….. then you can be factually sure that the photosynthesis ingassing of CO2 has ALREADY terminated …… simply because an abscission layer has formed that prohibits any further activity by the leaves ….. other than to change “color” as the green chlorophyll decomposes and the foilage fall off.

        And the months of September and October are the normal “dry” months of the year with minimum rainfall and low humidity (H2O vapor) which drastically retards microbial decay of dead biomass ……… and by the time the moisture increases in November, the temperature has decreased below 40F which prevents any further microbial decay of dead biomass until next springtime.

        Bernard, your stored food (dead biomass) will not rot or decay iffen you keep it extremely dry or stored in your refrigerator-freezer ……. and Mother Nature’s dead biomass does not easily rot or decay during the NH fall and winter months.
        Cheers

      • Samuel, I don’t think you can teach us when fallen leaves and dead grass rot. The amount of production is calculable, and consumption of the produced material does not happen at the same time as the production. Using general and wordy arguments to prove the contrary – well it just doesn’t work.

      • Hugs,

        It doesn’t surprise me that you don’t believe the factual science that I include in my posted commentaries ……. but it utterly amazes me that you don’t believe your own nose when it informs you of rotting biomass in your vicinity. Or is your “olfactory” problem a religious “denial” one, …. a biological inherited one …… or simply the result of intentional miseducation during your adolescent years?

        Hugs, you need to trust your nose, to wit:

        Ooooh, that smell! Odors rise with the temperature

        Your nose doesn’t lie – odors intensify in the warm summer months, be they of rotting garbage on the sidewalk or fragrant flowers blooming in a garden.

        The combination of heat and humidity allows bacteria to grow faster and smells to travel farther, said Victoria Henshaw, who researches urban smells throughout the world.

        Read more @ http://usnews.nbcnews.com/_news/2013/07/17/19524140-ooooh-that-smell-odors-rise-with-the-temperature?lite

  8. @ John H. Harmon

    This is funny! You rant (rightly) about Leftist and Statist junk science, but swallow one of their most fatal canards (namely the bogus claim that there is no such thing as human races and consequently no legitimation for racial discrimination) hook, line and sinker. Selective skepticism?!

  9. If all the oil, gas, and coal reserves shown on IPCC AR5 Figure 6.1 were instantly transferred to atmospheric CO2 at IPCC’s current 57%/43% sink/source rate it would not be enough to meet the ppm concentration needed for IPCC AR5’s RCP 6.0 or 8.5. So IPCC AR5’s two worst case AOGCMs, melting ice sheets, meter sea level rise by 2500, etc. can never be realized.

  10. One of the things that climate science struggles to explain is how each year the increase in atmospheric CO2 is about half of the human emitted total.

    But that’s about what you’d expect if the atmospheric CO2 disappears exponentially from a given starting value. Human emitted CO2 has been growing following pretty much an exponential curve. Apply a growing exponential to a system described by a 1st order linear differential equation and the solution is a growing exponential curve growing at the same rate as the input signal.

    Set the input signal to zero and the response will then decay to zero at the rate set by the time constant of the system. The fact that the response to a growing exponential input is an exponential with the same exponent as the input signal is just what you’d expect.

    It most certainly does not mean that half of the input signal (CO2 level in this case) hangs around forever.

      • Also, it may be my bias, but I think I detect an increasing percentage of man’s yearly aliquot of CO2 being re-sequestered. And why shouldn’t previously unknown, or underestimated, sequestering feedbacks not be recruited as the CO2 level rises?
        ================

    • “They” swept 57% of it under the magic unicorn’s carpets/sinks to make the numbers work. Before 1750 Figure 6.1 shows a net sink of 0.4 Gt/y. After 2011 there is a net 4.0 change in sources and a new sink of 4.8 Gt/y. Also see Table 6.1.

  11. Hello Ari, there is a measurement and an already estimation that the half life of Co2 IN ATMOSPHERE IS AT ~ 5 YEARS.

    Are you claiming that your estimation is better than this, if so can you explain if it is based in measurement rather than some fictional thinking like that of IPCC?
    There is already many fictional and wishful assessments on that particular point, but there is only one based in real measurement and empirical evidence,,,,,, as far as I can tell, and there is no any real reason or justification in “scientifical” approach to discredited………and as it stand for that measurement the half life of CO2 in atmosphere is at ~5 years, why should I consider that you are even remotely better in that estimation?!

    All other estimation based in other than measurement and observation all fit one and the same category and you have to cue yours there and consider that it could be as wrong as any other of that fictional category.
    If you have no any good or acceptable reason why should the measurement be “Hand waved” than you are no any better than any one else before or after you claiming something different…it is still and simply another case of obfuscation of reality, regardless of the degree of it….

    cheers

    • Whiten, you are apparently confusing two quite different things. The residence half life of an individual molecule of CO2 may be on the order of 5 years or so. This is arguably shown by the bomb spike. But that is very different thing than the half life of all the CO2 in the atmosphere a function of aggregate sink rate fluxes.

      • Are you sure ristvan that what you say is correct….are you claiming that a piece of wood floating in the river will have a higher speed than that of the river itself or that when you piss in the river your piss will travel down the stream faster than the river itself, because from where I stand that is the main reason of “hand waving” the CO2 half life real measurement………..so if you think I still got this wrong please do explain so I see my error.
        I think I am not confused so far……..please let me see if that be the case…..appreciated……

        cheers

      • Each piece of wood floats in a different river, and the river is endlessly circling upon itself.
        ========

      • kim
        March 26, 2016 at 11:12 am

        Each piece of wood floats in a different river, and the river is endlessly circling upon itself.
        ========
        even in that particular view point any piece of wood floating in a different river still can not have a faster speed than the river it floats, so the average of the speed of all rivers is higher than the average of the speed of all pieces of wood floating …..that is why there is only one kind of figure of half life in principle….and no many and different ones considered at the same time….

      • ristvan
        March 26, 2016 at 10:38 am

        The residence half life of an individual molecule of CO2 may be on the order of 5 years or so.
        —————————
        Under the meaning of half life your above statement does not even make sense…..sorry but totally an intellectual rubbish…… that is not what half life time suppose to be meaning……under the half time residence every molecule has a different life span in atmosphere…..the half life simply gives the most probable range in % for the molecules……..for example 10% of all the molecules in atmosphere will not make it beyond one year, when 3-6% may be there at most for another 20- 25 years….that is according to the ~5 years half time of CO2… as mass, regardless of the measurement based in the actual counting of molecules…….
        Same principle for any other number you considered to be the half life of CO2 ///////only the number of years
        according to the % will be different…

        Do you think I got this wrong too?

        cheers

      • Arguably, only 50% of the Human CO2 Flux remains after any given year – this makes the half-life for emissions literally 1 year !

      • Whiten. Imagine a simple system of air containing CO2 over water in a box. There are 100 molecules in the air and 10000 in the water. Each year half of the molecules in the air move from air to water and 4/5ths as many molecules move from water to air. What is the half life of CO2 in the air?

        Each year half the molecules in the air move to the water. This is what ristvan means by half life of individual molecule. However each year the concentration of CO2 in the air only drops by 10%
        Year 1
        Original CO2 in air = 50
        Movement of molecules from water to air (molecules1) = 40
        Total molecules in air =90

        Year 2
        Total movement from air to water = 45
        of which original CO2 in air = 25
        and “new” molecules1 from water = 20
        Movement from water to air = 36
        Total molecules in air = 81

        The half life on the original molecules is 1 year, but the total concentration only drops by 10% each year. The C14 tests only show the half life of the original molecules, which is not what we are interested in from a climate perspective.

      • Ridiculous. Debating the effect of raising airborne CO2 from 9,999 parts in 10,000 by another one part in 10,000 — over a century — and presuming to know how much if any global warming results is the kind of specious argument that the climate alarmist crowd hangs its collective hat on.

        The ONLY verifiable, testable and empirical scientific evidence available shows that the rise in CO2 is entirely beneficial. More CO2 is completely harmless, and the rise in that harmless trace gas is greening the planet; keeping food costs down for the one-third of humanity that subsists on $2 a day or less.

        But the alarmist crowd doesn’t care about them. They’re expendable. All that matters to the climate alarmist clique is getting ‘carbon’ taxes passed, and turning over national sovreignty to the totally corrupt UN.

        Alarmists are not just anti-science; they are anti-humanity, too.

      • seaice1
        March 27, 2016 at 3:54 am

        Hello seaice1
        Thank you for your reply, appreciated really.

        Yes I can imagine the simple system you offer, but when it comes to the real NATURAL system in question, the Atmosphere and the CO2 relation, you see, the problem is that we roughly know about the total mass of CO2 in atmosphere, we roughly know the added total mass of CO2 and the ratio of human/natural for that mass, but what we do not know but try to calculate is the actual difference between the yearly emissions and the sinks.

        Any modeled method RELYING OR NOT on the residence time of CO2 gives a concentration increase as due to anthropogenic, man made and not a natural disbalance.
        From there then any one in that “club” tries to hypothesize, model further and further away and assume the CO2 residence time, with no regard that there already is an estimation of that through and based in measurement.
        It is not only backwards at that point, as some one else may say here :), but the amount of disbalance according to the MODELED estimations is too small to actually produce or account for the real trend of CO2 concentration and its acceleration as observed in reality.

        So, simply, as per your example offered, we do not know what the number or the mass of the molecules of CO2 moving from the surface (water in your example, the 4/5) to the atmosphere is, we simply model it and calculate it with no regard to what the residence time of CO2 is,,, and then after that the “club” tries to model/estimate and assume the residence time of CO2 by trying to fit it to the already produced numbers.

        All model estimations of CO2 emissions versus CO2 sinks give a disbalance at the present of about 30-35Gts where ~25Gts are human and the rest natural.
        Problem,that is too little for the acceleration of concentrations at 400ppm….but who cares it is an anthropogenic disbalance there….

        In the case of ~5years 1/2 life residence, there is no problem…….the conclusion is rather simple, no rocket science maths and models required……for the last 10 or 20 years in average the disbalance is equal to ~ 4 times the amount of X, where X is the average of human yearly emissions for the last 10 or 20 years,,,,,and there is no away to consider that disbalance as athropogenic.
        If considering that for the last 10 years the average of CO2 human emissions yearly were ~ 20Gts than the whole disbalance is ` 80-100Gts, whatever the yearly sink rate of CO2 the yearly emissions are ~80-100Gts higher than sinks in overall, where only 1/4 of it are human, hardly of any significant effect, especially when considering the very short life of CO2 in atmosphere.
        This has no problem with the reality of the CO2 concentration and its acceleration, actually explains it well enough….

        Sorry for going so wide and long.. :)

        cheers

    • Whiten,

      As ristvan already said: two completely different things: the residence time of 5 years is how long an individual molecule CO2 resides in the atmosphere before being swapped with a molecule CO2 from another reservoir. Swapping is pure exchange and doesn’t change the total amount of CO2 in the atmosphere.

      Take a river that passes a lake. All water in the lake has a residence time of ~5 years if the amount of water passing the lake is 20%/year of the lake’s volume:

      residence time = total volume or mass / throughput

      That is the case for CO2 too:

      residence time = 800 GtC / 150 GtC/year = ~5.3 years

      As long as supply and removal are equal, there is no change in height of the lake.

      The removal (decay rate) of any extra water, due to heavy rain on the lake has a completely different time span: That depends of the extra volume that is removed above the throughput, thus the difference between supply and removal, which depends of the extra height (= pressure) of the water in the lake. That is an exponential decay, as when the height lowers over time, the removal of the extra water decreases too. That formula (for a linear process) is:

      e-fold decay rate = disturbance / effect

      The half-life time then is the e-fold decay rate * 2 / e or for the current CO2 levels and sink rate:

      e-fold decay = 110 ppmv / 2.15 ppmv/year = ~51.2 years

      or a half life time of ~37.5 years, slightly above what Ari Halperin calculated, but anyway not far off and much longer than the residence time…

      • Ferdinand Engelbeen
        March 26, 2016 at 11:58 am

        Hello Ferdinand.

        always you strike me with your high end science calculations and intricate reasoning……..but when it comes to the ~5 years half time residence of CO2 is about a simple measurement that does not really care about your high science interpretation and calculation.
        It is rather simple……It was measured and calculated upon it that half of the mass of the CO2 from bomb tests (the trace CO2) was gone out of the atmosphere in a 5 years period,,,,,,,, that is what ~5 years half life means.
        Saying that this “trace” CO2 can sink faster than the sink speed of the system is ridiculous.

        Besides is the only one figure that seams to be the most correct in all climatology, not only because it is a measurement that no body so far has challenge it as wrong in the principle of the measuring method or the accuracy, but even when considering the reality and the absence of the acceleration of the warming for the last 20-25 years in accordance with the amount of human CO2 emissions, that figure is inside the range….it could not be above 10 years half life at most, if stretched at the maximum…..and this one the ~5 years seems to explain well why we should stop looking under the oceans and any other rock in this planet for the missing heat………aint missing…..it simply was not there in the first place…..and the ~5years half time of CO1 residence explains it very well……

        From where I stand the rest is only innuendos to keep confusing any one else….

        cheers

      • Whiten

        The e-fold decay rate of the 14CO2 bomb spike was about 14 years (if I remember well), but even that is not comparable with a 12CO2 (or total CO2) spike for a different reason:

        Over a year some 40 GtC circulates over the atmosphere and deep oceans. In 1960, at the height of the nuclear 14CO2 spike (app. a 14CO2 doubling), there was already a 12CO2 excess in the atmosphere which made that a small amount more CO2 did sink in the deep than was released: about 97.5% of all CO2 returned in total quantity.

        Not so for 14CO2: in 1960 about 100% of the spike did sink near the poles in ratio to 12CO2, but what returned in the same year was the 14C/12C ratio of ~1000 years ago, long before the nuclear tests. That makes that for 14CO2 only some 97.5% x 45% (5% extra loss due to radioactive decay) did return of the 100% spike at the sinks side. That gives that the decay rate of 14CO2 in the atmosphere was many times faster than for a 12CO2 spike… Here the scheme:

      • Whiten: always you strike me with your high end science calculations and intricate reasoning……..but when it comes to the ~5 years half time residence of CO2 is about a simple measurement that does not really care about your high science interpretation and calculation.

        That makes no sense.

        If Ari Halperin’s equations 1 and 2 are reasonably accurate, and his graphs and tabular results give them some credibility, then 37.5 years is the estimate of the time required for the concentration to reduce halfway back toward the equilibrium concentration after a bolus injection. It is a simple function of the rate parameter of the 3rd term in equation 2.

        Ferdinand Engelbeen’s analogy is apt, and worth your study.

      • matthewrmarler
        March 26, 2016 at 1:09 pm
        ……………..then 37.5 years is the estimate of the time required for the concentration to reduce halfway back toward the equilibrium concentration……………
        ————————–
        This is a joke, is not it…..what do you mean by equilibrium concentration?
        And what do you mean by reduction halfway back towards it……sorry have no idea what you saying and how it could relate to my comments and replies….pardon my simplicity…..

        and when it comes to half life time of CO2 residence in atmosphere , sorry by I will stick with the evidence for as long as no one can show error in the method of the measurement and also for as long as no one can clearly show why the mass of that CO2(the tracer) can have a different speed of sinking and much higher than the speed of overall sinking of CO2, when in principle it must have ~ the same as it can not force itself to sink faster……

        According to Ari the speed of overall sinking of CO2 is 6 to 7 times slower than that of the “tracer” CO2 from bomb tests……….any explanation how the “tracer” managed to sink faster than the speed of overall sinking, any one??????????
        The only argument I raised in direction of Ari Halperin…..

        You see only relying in complex and hard maths, or hypothesis and intellectual guesses when in the same time we reject and discard, without care,facts and evidence without any second thought simply because it does not please the majority, it gets us at a point that we will keep looking endlessly under any rock for imaginary missing things to balance our imaginary findings as per numbers involved………..

        You see the life residence of CO2 in atmosphere is a key to calculate and estimate the rest of the “shit”….is a need not to be hypothesized over or estimated outside the measuring method….it should be out of the hard measured thing and a reality checked, because nothing will really make sense any more……any one can claim otherwise any thing to his hearts content….and the outcome of the who is “right” or “wrong” or the “winner” will depend in the “authority” and who has the most complicated and complex maths that shock most than the rest……

        We have such a measurement and it is discarded and “hand waved” with prejudice, no care at all and with no any clear reasoning………

        cheers

      • Mike M. (period)
        March 26, 2016 at 1:04 pm

        whiten,
        If you doubt this, please explain what has caused the increase in atmospheric CO2. Emissions in the last five years are nowhere near large enough.
        ———————–

        Mike…..I am sorry that you have missed the point…..my point was exactly that the measurement that puts the residence time of CO2 at ~5years half time explains exactly what you are asking.

        It means that at the time of the measurement the overall yearly sink of CO2 must have been ~240 Gts and slightly increasing from then to present…and when it comes to the overall yearly CO2 emissions the amount above that of the sinks at present is 4xof the average of the yearly human CO2 emission for the last ~10years (or there is room to consider it even for the last 20 year)
        And that will mean that the actual yearly CO2 emissions are at ~240-250Gts + 80-90GTs= ~330-340Gts..
        That is a lot of CO2 emissions if the ~5 year half life of CO2 is correct…….and also it dwarfs our CO2 emissions a lot, especially the effect of our emissions is none existent at that amount if ~5year life time correct.

        Now pose the same question to Ari with his 30-35 years half life time of CO2……the sinks and yearly emissions of CO2 will be too low regardless of the time involved ( still not long enough) and the difference between will be far less than 80-90 Gts, not enough for the ppm increase, but rather good for claiming convincingly that AGW is imminent (at any given moment), regardless that it can not be found anywhere…..

        The numbers used above are simply wide approximation, just to make the point..:)

        hope this helps…:)

        cheers

      • Whiten, it is sort of weird to see you chewing out people who know what they are talking about and you don’t.

        “It is rather simple……It was measured and calculated upon it that half of the mass of the CO2 from bomb tests (the trace CO2) was gone out of the atmosphere in a 5 years period,,,,,,,, that is what ~5 years half life means.
        “Saying that this “trace” CO2 can sink faster than the sink speed of the system is ridiculous.”

        The ‘sink speed’ didn’t sink the system level at all.

        Even in the first post to educate you it was made clear that the radioactive CO2 can be cleared by replacement without the total system changing the CO2 concentration. In fact just when the example you gave was talking place, the 1960’s, the CO2 level was increasing! As the CO2 continued to increase, the radioactive CO2 was taken out of the atmosphere. That is a very clear example of how the residence time can be (and is) much shorter than the 1/2 life.

        Maybe you should lay off the vain imaginings and accept the elucidations politely proffered for the sole purpose of expanding your comprehension.

      • Error:

        The half-life time then is the e-fold decay rate * 2 / e/I>

        Never try to write something out of memory if your memory is over 70 years old…

        The half-life time is the e-fold decay rate * ln(2)

        Which makes that the half life time for the current sink rate is about 35.5 years

      • Crispin in Waterloo but really in Muizenburg
        March 26, 2016 at 3:45 pm

        Hello Crispin..

        :)

        Really like your reply to me, refreshing and really appreciated..

        Thank you…:)

        cheers

      • Whiten: You see only relying in complex and hard maths, or hypothesis and intellectual guesses when in the same time we reject and discard, without care,facts and evidence without any second thought simply because it does not please the majority, it gets us at a point that we will keep looking endlessly under any rock for imaginary missing things to balance our imaginary findings as per numbers involved………..

        That still makes no sense. Halperin’s equations 1 and 2 are straightforward, not “complex and hard maths”.

    • whiten,

      Ristvan and Ferdinand are correct. There are multiple lifetimes in the system. There is a lifetime associated with exchange between the surface reservoirs (atmosphere, surface ocean, biosphere); that is what the number you refer to. There is a different lifetime for the adjustment of the reservoirs to a change in one reservoir, that is something like 20 years. They are different because the amounts in the various reservoirs are not proportional to each other. There is yet another lifetime (hundreds of years) for equilibration of the surface reservoirs with the deep ocean. And an even longer lifetime for equlibration with minerals.

      If you doubt this, please explain what has caused the increase in atmospheric CO2. Emissions in the last five years are nowhere near large enough.

      Ari Halperin has made a related error that renders his results meaningless. He appears to use an equation that is far too simple compared to what is really going on (hard to be sure, since he provides no details). It might well give a good fit as long as growth in emissions is roughly exponential; but once that is not true, more deficiencies will become apparent. So it is useless for predicting the future.

      • Mike M. (period): He appears to use an equation that is far too simple compared to what is really going on (hard to be sure, since he provides no details).

        He has fitted a model that is like the models used in pharmacokinetics: it fits the observed (i.e. measured) gross result of a multitude of exchanges between parts of the system. It isn’t a mistake, it’s what is possible without much more detailed analyses of all the flows (e.g. the flow of C to the bottom of the ocean carried out by Kim’s coccolithophores; and the increased CO2 uptake in the undisturbed forests of the Earth.)

      • matthewrmarler,

        You wrote: “It isn’t a mistake, it’s what is possible without much more detailed analyses of all the flows …”

        It is indeed a mistake, since it is meaningless without the more detailed analysis. There is plenty of data available to make that more detailed analysis and it has in fact been done. See the comment by Willis Eschenbach below.

      • Mike M. (period),

        The IPCC uses the Bern model, which as Willis showed, may be as valid as a single overall decay model that Ari used.

        The first decay rate is very fast in the Bern model, but that is limited to about 10% of the change in the atmosphere due to the Revelle/buffer factor in the ocean surface.
        The second decay rate is what goes into the deep oceans, which doesn’t show any sign of saturation. Which is near impossible in the near future, as the cold oceans at the sink places are by far undersaturated.
        If everything gets into equilibrium after a few hundred years, the remaining extra CO2 in the deep oceans and the atmosphere is about 1% (3 ppmv in the atmosphere) from all human emissions since 1850.
        The third decay rate, the biosphere, has no known limits, but is a lot slower.

        The main point is that the Bern model was originally based on 3000 and 5000 GtC emissions, but they assume that the saturation of the deep oceans is similar even at much lower emissions and also exists for vegetation.

        Thus in my opinion the Bern model gives a quite pessimistic view on decay rates which are – until now – not confirmed as the decay rate is surprisingly linear in the past 55 years:

        Excess CO2 / net sink rate:
        In 2012:
        110 ppmv / 2.15 ppmv/year = 51.2 years or a half life time of 37.5 years.
        The figures for 1988 (from Peter Dietze):
        60 ppmv, 1.13 ppmv/year, 53 years, half life time 39 years
        In 1959:
        25 ppmv, 0.5 ppmv/year, 50 years, half life time 37 years

      • Mike M. (period)
        March 26, 2016 at 1:04 pm

        please find my reply to your comment above…really sorry about that.. :)

      • Mike,

        Whiten is technically correct in that the half life of that particular CO2 that was injected into the atmosphere is quite short. Ristvan and Ferdinand are arguing something different. They are saying that even though that particular atmospheric CO2 has gone, it does not matter because it has been replaced by some other CO2 from somewhere else. You make a key point in that increased human emissions do not explain all the increase in atmospheric CO2 which seems to have increased in a remarkably linear fashion in recent decades. Ristvan and Ferdinand don’t know where that ‘extra’ CO2 comes from so they are being pedantic when they say Whiten is ‘wrong’. Everyone in this thread should own up to not knowing why the apparently short half-life of new CO2 in the atmosphere is overwhelmed by some other source of ‘new’ CO2. Because it is not understood, it could reverse one day unexpectedly. Your point is crucial – it seems not to be man-made.

      • Bernard Lodge,

        You wrote: “Ristvan and Ferdinand don’t know where that ‘extra’ CO2 comes from”

        We most certainly do know where it comes from. It comes mainly from burning fossil fuels with an important source from changes in land use.

        You wrote: “Everyone in this thread should own up to not knowing why the apparently short half-life of new CO2 in the atmosphere is overwhelmed”

        You might not know that, but I DO know the reason for that. It is mainly because the amount if dissolved inorganic carbon (DIC) in the ocean is not proportional to the amount of CO2 in the atmosphere. A 10% change in CO2 results in a change of something like 1% in DIC. So there are different time constants for the exchange of carbon atoms and the change of CO2 concentration.

      • Bernard Lodge,

        Ristvan and Ferdinand don’t know where that ‘extra’ CO2 comes from

        It is pretty clear to me where the extra CO2 comes from:

        With human emissions twice the increase in the atmosphere and all supporting evidence:
        http://www.ferdinand-engelbeen.be/klimaat/co2_origin.html
        there is little doubt that humans are to blame for the increase, but that says next to nothing about the consequences…

        Again, there is a huge difference (some order of magnitude) between residence time and excess decay time.

        The first is the average time that an individual CO2 molecule (whatever the source) resides in the atmosphere before being swapped with a CO2 molecule from another reservoir.
        The second is how long it takes to reduce any extra injection of CO2 in the atmosphere above equilibrium (whatever the source) to 1/e of the original excess.

        One can compare the difference as what happens with the turnover of goods in a factory which gives the residence time of the capital supplied by the shareholders at one side and the return on investment on the other side: the gain or loss of the same capital after a year. Both are somehow linked, but the turnover doesn’t tell you anything about the gain or loss of the factory…

      • Ferdinand Engelbeen
        March 26, 2016 at 4:10 pm

        Bernard Lodge,

        Ristvan and Ferdinand don’t know where that ‘extra’ CO2 comes from

        It is pretty clear to me where the extra CO2 comes from:
        ————————————————————————

        It seems to be pretty clear, the extra CO2 comes from your own graph….. :)
        Is that graph really yours? It will be strange if it is not……you still consider emissions and sinks in ppm and in the graph is even per year…what could there be wrong! :)

        Sorry do not mean to insult, really, but after all is your own graph that one, or is it not?

        But it seems that you at least understand that Bernard Lodge is right when it says that you were having the wrong argument with me, regardless of the point I been even wronger or right or whatever…..

        cheers

      • Whiten,

        Human emissions are based on fossil fuel sales (taxes!) and burning efficiency. Because of the human nature to avoid taxes, probably somewhat underestimated. Increase in the atmosphere is from lots of monitoring stations around the world.

        Just a matter of looking up the data, the latest official emission data are at:
        http://www.eia.gov/cfapps/ipdbproject/IEDIndex3.cfm?tid=90&pid=44&aid=8
        The CO2 data at:
        http://www.esrl.noaa.gov/gmd/dv/iadv/

        Thus in the past 55 years, human emissions were twice the net increase in the atmosphere. One needs a lot of reasoning to explain that human emissions are not to blame for the increase…

        What you (and Bernard) mix up is the residence time of ~5 years with the time that is needed to remove any extra amount of CO2 (whatever the source) injected into the atmosphere (~52 years).
        The first is pure exchange and doesn’t remove one gram of CO2 (whatever the origin) extra out of the atmosphere, as long as inputs and outputs are equal. It does remove the original human CO2 out of the atmosphere, specifically into the deep oceans, and replace them with CO2 out of the deep of ~1000 years ago at a rate of ~20%/year.
        The second is how much the difference is between total inputs and total outputs: currently ~4.5 GtC (2.15 ppmv) more natural sink than natural source, that is about half the human emissions. That is caused by the extra pressure (110 ppmv) of CO2 in the atmosphere above the dynamic equilibrium of the oceans (and plant alveoli’s) with the atmosphere for the current ocean temperature per Henry’s law.

        The seasonal swings are huge: they make that about 150 GtC (~70 ppmv) is exchanged in and out between the atmosphere and the oceans and biosphere within a year. Every year again. The residual at the end of the year is only +2 +/- 1 ppmv. The year to year variability (+/- 1 ppmv) in the natural cycle is mainly temperature variability driven, the +2 ppmv is mainly human caused.

        There is little variability in the natural cycle, compared to the enormous changes between winter and summer, which is dominated by the growth and wane of NH extra-tropical forests. The point is that forests don’t suddenly grow 10% more leaves in spring from one year to the next, neither do the oceans for a similar seasonal temperature change.

        Thus the ~5 years residence time says next to nothing about the removal of the human emissions (as mass, not the original molecules) out of the atmosphere…

      • Ferdinand Engelbeen
        March 27, 2016 at 1:52 am

        Engelbeen, with all due respect to you, you still do not get the point…..the actual amount of human CO2 emissions does not mean much unless the residence time of CO2 emission in atmosphere considered.
        According to the measurements the added CO2 mass due to the human emissions stand at about 1/4 -1/5 of all added CO2 mass in atmosphere for approximately the last 120 years.
        What that means is that the actual effect of ARF depends in the residence time of CO2 in atmosphere.
        There is no many different residence times for CO2, is only one, the question is,which one it is.
        There is many estimations of it, all hypothesized and model calculated apart from one that is due and based in actual measurement.
        All others apart from this one make ARF and human emissions as dominating the increase/acceleration of ppm(s) and the overall increase off CO2 mass in atmosphere, for the last 30-40 years.

        So apart from that residence time estimated by relying in actual measurements any other estimation by any other means so far falls on the same category, that of anthropogenic change of CO2 concentration.

        I am not challenging the actual , as you say measured human yearly emissions, actually I am saying that by knowing that we can estimate accurately enough the overall yearly emissions by calculating what is the overall difference between yearly sinks and emissions.
        But that calculation depends on the residence time of CO2 in atmosphere.
        Simple as that.
        Different residence times give different numbers.

        So far all estimations, apart from the ~5 years 1/2 life residence time, give an “indisputable” anthropogenic change for the last 30-40 years at least with a projection of it increasing “hugely” in the future, as the “lion” share will be with anthropogenic emissions.

        All modeled estimations show that the disbalance driving the ppm increase, the CO2 concentration, is not natural and is caused by man…….the only difference there is the degree of it. And the numbers there do not fit the reality of the ppm trend and its acceleration, as per the reality check….none of these estimation does..
        While the only one based in actual measurement shows completely the opposite.

        Sorry but as I said already, earlier, I will keep and stick with the estimation from measurement instead from picking and choosing from a wide range of model estimations.
        The numbers from it fit the reality rather better and with no problem
        What more one can ask for..

        cheers

      • whiten:

        According to the measurements the added CO2 mass due to the human emissions stand at about 1/4 -1/5 of all added CO2 mass in atmosphere for approximately the last 120 years.

        Whiten, here you make an essential error: while human emissions are ~9 GtC/year and natural emissions are ~150 GtC/year, natural sinks each year in the past 55 years were larger than the natural emissions. Thus despite the huge difference in emissions, the direct net addition from nature was zero, nada, nothing, in direct mass.

        We don’t have accurate figures for the period before 1959, except from ice cores which are averaged over 10 to 600 years, depending of the accumulation rate. But these show a quite linear ratio between temperature and CO2 levels, with some lag. Than gives about 16 ppmv/°C, some 10-15 ppmv since the LIA. That is all. The rest of the 110 ppmv increase is not caused by temperature.

        actually I am saying that by knowing that we can estimate accurately enough the overall yearly emissions by calculating what is the overall difference between yearly sinks and emissions.

        It is just the opposite:
        We know the amounts in the atmosphere with high accuracy. We know the main in/out fluxes with rough accuracy, based on δ13C, O2 and temperature/solubility changes. That gives us the average residence time of a molecule CO2 (whatever the source) in the atmosphere. That gives different residence times ranging between 5-14 years, depending of the approach.
        But again, the residence time doesn’t say anything about the fate of any extra CO2 injected in the atmosphere…

        We know the amounts and thus the increase in the atmosphere with high accuracy and we know human emissions with reasonable accuracy, thus we know the net sink rate with reasonable accuracy. That gives us the real decay rate of any extra CO2 (whatever the source: humans, volcanoes, land clearing,…) above equilibrium: just above 50 years or a half life time of 30-35 years…

        the numbers there do not fit the reality of the ppm trend and its acceleration, as per the reality check….

        You need a different reality check. For the previous plot, I have calculated the effect of temperature (short and medium term) and human emissions with the observed average sink rate, it is a nice fit with reality:

      • Mike M. (period): It is indeed a mistake, since it is meaningless without the more detailed analysis. There is plenty of data available to make that more detailed analysis and it has in fact been done.

        As far as I can tell from reading the supplied references, there is not plenty of data available to make the more detailed analysis: there is barely sufficient data for gross estimates of the unknown rates. With data available, the decay rate of atmospheric CO2 can not be more precisely estimated than Halperin has done. That makes his model meaningful. Even if the Bern model is true, the increase in accuracy only becomes apparent after a few multiples of 35 years elapse after the end of human fossil fuel use, because the principle additions are slow processes.

        Again, pharmacokinetics has examples. The “terminal half life” of a drug can be much longer than its “initial half life” because the molecules come off their preferred binding sites much more slowly than they can be transferred from plasma or fat. You may have read of the same phenomenon with regard to drug treatment of HIV, where the body can clear 99.9% of the HIV, leaving a tiny inaccessible reservoir of HIV..

    • ‘Ridiculous. Debating the effect of raising airborne CO2 from 9,999 parts in 10,000 by another one part in 10,000 — over a century’

      The one in 10,000 happens to be extremely important so don’t spread this drivel.

  12. the atmospheric CO2 concentration is unlikely to exceed 550 ppm in the 21st century, despite current exponential growth in the use of the fossil fuels.In the unlikely case that elevated atmospheric CO2 becomes undesirable, it will be possible to lower it significantly by decreasing emissions, although the exponential decay formula should be used in such a case with great caution, because this scenario has not been encountered before.

    1. I don’t think the current growth rate of fossil fuels is best described as exponential. Even if it were, future growth rate will be difficult to maintain a positive sign.
    2. unlikely case that elevated atmospheric CO2 becomes undesirable, It most definitely is undesirable to some people.
    3. it will be possible to lower [CO2 concentrations] significantly by decreasing emissions. Yes. What should be emphasized is that the rate of reduction in CO2 would likely be much faster than many predict. But it also means significant reductions in CO2 can come only from significant reductions in the use of fossil fuels.

      • Going downhill, which is what is happening to the excess CO2. It doesn’t precipitate, or condense like water, but it sediments to the depths from the deaths of the living beasties above.
        ==============

  13. The calculated CO2 looks more believable than the measurements. Neither global average temperature trend nor anthropogenic CO2 emissions were linear so how would atmospheric CO2 be linear?

  14. The joys of trying to model a complex system when several of the significant inputs (CO2 seqestration rate in this case) are not really known. The IPCC models are blowing smoke.

    • I agree. There may be countless models, all significantly different, which match the evidence.

      What the evidence can do is suggest which models are wrong, not which ones are right.

      • rabbit: What the evidence can do is suggest which models are wrong, not which ones are right.

        The model presented here today requires validation/testing against out-of-sample data, i.e. future data. The evidence can show which models are accurate enough for prediction, design and control. For example, pharmacokinetic models can be accurate enough to prescribe dosing regimens, and Newton’s laws are accurate enough to guide interplanetary missions.

        Halperin’s model produces mse estimates of about 5%, which is better than the models used in calibrated medical measuring instruments, and better than most pharmacokinetic models for most people.

    • Mmm. yes:

      Although one need to be careful about cause and effect. In this case every single line of evidence shows that humans are the main cause of the CO2 increase in the atmosphere, while temperature as cause is far from ideal before 1959 (and has no support whatever in any observation):

  15. Earth’s carbon cycle contains 45,000 Gt (E15 gr) of stores and reservoirs with a couple hundred Gt/y ebbing and flowing between those reservoirs. (IPCC AR5 Fig 6.1) Mankind’s net contribution to this bubbling, churning caldron of carbon/carbon dioxide is 4 Gt/y. Seems relatively trivial to me.

    Mankind’s alleged atmospheric CO2 contribution between 1750 and 2011 added 2 W/m2 of radiative forcing to the earth’s atmosphere. (IPCC AR5 Fig SPM.5) Incoming solar RF is 340 W/m2, albedo RF is 100 W/m2 +/- 30, latent heat RF from the water cycle’s evaporation is 88 W/m2 +/- 8. Mankind’s 2 W/m2 is obviously trivial. The popular GHE theory is a perpetual loop flowing from cold to hot violating two fundamental thermodynamic laws. Physics must be optional for “climate” science. What really counts is the net RF balance at ToA which 7 out of 8 balance models (Trenberth et. al. 2011) show as cooling, not warming.

    Every year the pause/hiatus/lull/stasis continues (IPCC AR5 Box TS.3) IPCC’s atmospheric and ocean general circulation models diverge further from reality.

    As Carl Sagan observed, we have been bamboozled, hustled, conned by those wishing to steal our money and rob us of our liberties. Hardly a new agenda.

    • Nicholas:

      Earth’s carbon cycle contains 45,000 Gt (E15 gr) of stores and reservoirs with a couple hundred Gt/y ebbing and flowing between those reservoirs.

      Nicholas,

      How much carbon is stored in different reservoirs is not of the slightest interest for what happens with CO2 levels in the atmosphere, only the exchanges between the reservoirs matter.

      How much carbon is exchanged between the atmosphere and other reservoirs is not of the slightest interest for the CO2 levels in the atmosphere, as long as what comes in equals what goes out.

      Human emissions are one-way additions, natural sinks are larger than natural emissions, so taking away about halve human emissions (as mass, not original molecules) per year. Thus the “trivial” human emissions are the main cause of the increase, supported by all available evidence…

      About the consequences, one can have a discussion, but the cause of the increase is clear…

      • From what I can tell the anthropogenic “proof” argument goes something like this:

        “The atmospheric CO2 concentration increased between 1750 and 2011 (Based on WAGs & SWAGs, ice cores, hockey sticks and tea leaves). We don’t know of natural variations that explain it, therefore it must be due to mankind. However, mankind’s contribution was greater than the CO2 increase so let’s create some magical sinks for exactly 57% of it to make the numbers work.”

        The uncertainty of the stores is +/- 850 GT. Some of the sinks that IPCC swept mankind’s contributions under have uncertainties of +/- 50%. With that amount of uncertainty in the reservoirs and fluxes there is absolutely no way of knowing for certain whether natural variations were the cause or not. Whatever the case mankind’s 4 Gt/y is trivial.

        And there are the insignificant RF and useless AOGCM’s.

      • Nicholas,

        In real science (not Mann’s ‘realscience‘), the default position is the Null Hypothesis. And since there has been no unusual change in global T, and nothing else out of the ordinary, the Null Hypothesis has not been falsified.

        The alarmist crowd acts as if the Null was falsified. But going as far back as you like, current temperatures are well within historical parameters.

        Therefore, the Alternative Hypothesis fails: the alarmists’ conjecture that unusual and unprecedented changes are happening.

        But they’re not. The past century has been the most benign in the entire temperature record. There is no comparable century long time frame in which global T has fluctuated so little: ±0.7ºC. Just prior to the current Holocene, global T fluctuated by tens of whole degrees — within only a decade or two.

        Conclusion: They are lying for money. Or worse, the eco-lemmings here who try to argue the alarmist case are doing it for nothing. That makes them not only wrong, but stupid.

      • Nicholas,

        It is hard to discuss things out if you make a ridicule of what is known and what not.

        What is in the reservoirs is roughly known, but is of no interest, except for what is in the atmosphere: that is known to +/- 0.4 GtC (+/- 0.2 ppmv) for 95% of the atmosphere. That is also the accuracy of the yearly increase in the atmosphere.

        What is emitted by humans is known to -0.5/+1.0 GtC/year.

        Thus the difference between these two is known to about +/- 0.9/1.4 GtC (0.5 ppmv).

        That is the net sink rate, wherever the sinks are, how they changed over the years or reversed from sink to source or back. It doesn’t matter at all if the natural sources and sinks were 10 GtC/year or 100 GtC/year or 1000 GtC/year. Or that vegetation was a net source and later a net sink. Only the net difference over a year counts for the amount of CO2 in the atmosphere which was always more sink than source in the past 55+ years.

        Thus if you don’t have a better argument than the accuracy of the amounts in and fluxes between the different reservoirs, you have no argument at all…

      • You are 100% correct, Nicholas. It is absolutely ridiculous. But, you will never sway Ferdinand. Or, at least, if you ever do, you will be much more successful than I, and I have been trying for years. In his view, nature is in perfect balance, until we upset it, and there is no evidence anywhere that will dissuade him from that point of view.

      • Ferdinand Engelbeen @ March 26, 2016 at 2:47 pm

        “Only the net difference over a year counts for the amount of CO2 in the atmosphere which was always more sink than source in the past 55+ years.”

        And, the pseudo-mass balance argument rears its ridiculous head once again.

      • Bart, i have to disagree with you here… He doesn’t believe in his point of view. There is no way in hades that he would waste a single euro betting that your carbon growthrate/ temperature graph could happen by chance. He KNOWS that all the myriad of matching features in the graph (aside from the variability) are not just going to happen by chance. He’s not an idiot! In lieu of this and also in lieu of it being presidential primary season, i’ve decided to give him an appropriate nickname:

        “Lying Ferd”…

      • Bart,

        As usual, there is zero evidence that temperature is the main cause of the increase in the atmosphere and all evidence points to humans as cause.

        The only way that the natural cycle can be the main cause is if it increased a fourfold in the period 1959-current, as that is what human emissions did and so did the increase in the atmosphere and the net sink rate. The sinks don’t discriminate between human and natural emissions.

        As there is evidence that the natural cycle did not increase at all in a growing amount of CO2 in the atmosphere (= increased residence time), your alternative explanation is fully rejected.

        Fonzie,

        As you clearly don’t understand the difference in opinion between Bart and me, calling someone a “liar” is just mud throwing without arguments…

      • dbstealey. The null hypothesis has been rejected – and that was before the recent record temperatures.
        http://www.physics.mcgill.ca/~gang/eprints/eprintLovejoy/neweprint/Anthro.climate.dynamics.13.3.14.pdf

        To quote
        “We statistically formulate the hypothesis of warming through natural variability by using centennial scale probabilities of natural fluctuations… Even in the most unfavourable cases, we may reject the natural variability hypothesis at confidence levels > 99%.”

      • seaice1 quotes:

        To quote
        “We statistically formulate the hypothesis of warming through natural variability by using centennial scale probabilities of natural fluctuations… Even in the most unfavourable cases…

        “We” do, eh? That is nothing but grant-trolling double talk; bullcrap, doubled and squared. The climate Null Hypothesis has never been falsified.

        To falsify the Null Hypothesis, past parameters must be exceeded, and the evidence must show that human emissions are the cause. That has never been demonstrated. Climate Scientology™ is grant money-fueled propaganda that cannot withstand even the mildest scrutiny. Those money-grubbing fakirs never have the balls to debate their claims with honest skeptics.

        The only people who buy into their pseudo-scientific ‘statistics’ are the crowd of religious eco-True Believers, who don’t know the Scientific Method from astrology.

      • seaice1,

        The article you quoted starts already with a wrong statement: that they find a temperature sensitivity of ~3°C for 2xCO2. That is what the GCM’s in average do find too, but already rejected by the real increase in the atmosphere which is between 1-1.5°C for 2xCO2, getting lower the longer the “pause” gets…

        Thus that is no proof that humans are responsible for the current recent increase in temperature, the more that several periods in the past 10,000 years were warmer with lower CO2…

      • afonzarelli: “Lying Ferd”…

        That is uncalled-for. Fredinand Englebeen’s comments on this thread have been admirably clear, cogent, accurate, and on point.

        Paraphrasing “bones”, the people criticizing Halperin and Engelbeen here today seem totally ignorant of modeling rates with compartment models and the corresponding differential equations.

      • dbstealey. The null hypothesis has been rejected in that published, peer reviewed paper. You do not like the way it was done, nonetheless it is incorrect to say that it has not been done. All you can say is that you reject the conclusion. I don’t really understand the basis on which you reject the conclusion. It seems to be based on wishful thinking rather than challenging the actual work in the paper. You believe that drawing a couple of lines on a graph is more meaningful than the detailed analysis provided in the paper. Good luck to you. However, if you are going to stick to your method, if the temperatures go above the top line I presume you will acknowledge that the null hypothesis has been rejected, even using your arbitrary method?

        Perhaps you could explain the criteria you are using. You plot the temperatures from 1855 to present day. You calculate the trend, then slide this up and down until all the points are within the lines – or as many as you can get without it looking a bit false. If it looks really false, then the null hypothesis is rejected.

        If this is the method, there is an obvious flaw. It includes all data in the trend analysis. There is no way to separate out natural from proposed AGW. It would be better to use a period from 1855 to say 1945 for the trend, then slide this up and down to see if the current points fit nicely within them. With you penchant for plotting all the data in the middle of the page and not using the axes properly it is difficult to see. I have a plot here
        http://www.woodfortrees.org/plot/hadcrut4gl/from:1855/to:2016/compress:3/plot/hadcrut4gl/from:1855/to:1945/trend/offset:0.25/plot/hadcrut4gl/from:1855/to:1945/trend/offset
        I think you can see that if you extrapolate the lines, the recent data is clearly outside the “natural” limits demonstrated by the early data.

        And no, I don’t think this proves anything. I will stick with the published analysis of experts, who know how to do this sort of thing properly.

        Ferdinand Englebeen
        ” that they find a temperature sensitivity of ~3°C for 2xCO2. That is what the GCM’s in average do find too, but already rejected by the real increase in the atmosphere which is between 1-1.5°C for 2xCO2, getting lower the longer the “pause” gets…”
        The pause is no more.

      • seaice1 sauys:

        The null hypothesis has been rejected in that published, peer reviewed paper.

        Right there you’re off your rocker.

        I’ve successfully and repeatedly challenged the false notion that anything unusual or unprecedented is happening iwth global T. But since you’re off your rocker, why waste my time with you?

        For others with common sense, this shows there’s nothing unusual or unprecedented happening:

      • seaice1,

        The current peak is completely caused by the near-ending El Niño, not part of the “pause” or human influence (until now). Wait a year or two and we will see what the residual temperature increase will be, if any…

        Further in the same plot of WfT:
        1885-1950: +15 ppmv CO2, +0.45°C
        1950-2016: +90 ppmv CO2, +0.70°C

        As the influence of more CO2 decreases logarithmically, it looks like that the “maximum allowable” 2°C temperature will not even be reached with the “business as usual” scenario of 2xCO2 before 2100…

      • Ferdinand Engelbeen. -Oh, I was under the impression that El Nino was a natural event and they had been going on for a long time. I also saw several posts here explaining that this was not a “Godzilla” El Nino. At the time I thought this was rather shooting WUWT in the foot, as it prevents claiming record temperatures were caused by an exceptional El Nino. Now you reap what you sow. Record temperatures cannot be cause by unexceptional El Nino.
        dbstealey. I think you are hoist in your own petard. You plot goes to 2010. The current anomaly is close to 1. This is very clearly outside the “natural” limits you set yourself in your graph. You have just demonstrated that the natural variability has clearly been exceeded.

        No point claiming El Nino. El Nino is natural, and thus included within the natural variation over the last 150 years.

        “Right there you’re off your rocker.” Remember what Judith Curry said -insults are often a sign of intellectual dishonesty.

      • seaice1 sez:

        You have just demonstrated that the natural variability has clearly been exceeded.

        Idiocy, doubled & squared. And what you presume to be ‘insults’ are simply facts.

        And Ferdinand has forgotten more than you will ever learn about this subject.

      • “off you rocker” means mad, out of control, crazy, nuts. This is not fact, but insult. I will leave others to draw conclusions about the worth of listening to someone who does not understand what a fact is.

        Out of interest, why don’t you extend that graph to present day and see if anything unusual is happening? You don’t have to make it a work of art, just look up current anomaly and plot it approximately.

      • seaice1,

        I notice all your arguments amout to mere assertions. Opinions. But the real world contradicts what you are trying to sell people here.

        So who should we believe? Planet Earth? Or ‘seaice1’?

        Because one of you is wrong. And it is not Planet Earth, which is doing nothing either unprecedented or unusual. In fact, the past century’s global temperatures have been more benign, and flatter, than anything in the entire past temperature record. Your climate alarmism is based on politics, and on the fact that you are incapable of admitting that Planet Earth is right, thus making you wrong.

        Future generations will wonder in bemused amazement that the early 21st century’s developed world went into hysterical panic over a globally averaged temperature increase of a few tenths of a degree, and, on the basis of gross exaggerations of highly uncertain computer projections combined into implausible chains of inference, proceeded to contemplate a roll-back of the industrial age.
        ~~Richard Lindzen

        Lindzen is absolutely correct. He made that statement many years ago, and it is as correct now as when he wrote it. It’s no wonder you’re afraid to use your name, Harold, because otherwise those future generations would know what a fool you are. You cannot admit that your alarming predictions have all failed. Honest skeptics would have admitted they were wrong; they would reject their falsified conjecture, and try to figure out where they went wrong. Instead, you double down and continue your alarmist lies.

        “If an honest man is wrong, after demonstrating that he is wrong, he either stops being wrong or he stops being honest.”

        You have never stopped being wrong.

  16. Nice piece of work Ari. I argued not long ago in a comment on CO2 and the greening of the planet, that the sequestration rate in the biosphere is increasing exponentially with a simple thought experiment:

    We have a growth of a fringe of new green plants around arid regions. This fringe causes some increase in soil moisture along the fringe zone and seeds from it are sown in a new, inner, concentric fringe zone, etc (perhaps until the Sahara greens over again). Meanwhile the plants of the first “fringe” are also growing larger and sequestering more CO2, along with the new fringes going moving inward into the arid zone. Note that this accelerated removal of CO2 is also going on in the Oceans. This means that with a relatively steady increase in fossil fuel emissions, an accelerating sequestration rate will mean the atmospheric content will level off perhaps more quickly. Your work and possibly a higher exponential rate of reduction of CO2 from the atmosphere than you calculate will certainly give CAGW a decent burial.

  17. This negates hundreds of models predicated on steady decay. It also is an interesting addition to the idea that CO2 radiation absorption is saturated.

  18. There is no “surplus” CO2 in the atmosphere. The 14C bomb tests pre-1963 added a known amount of CO2 to the atmosphere, mostly over the far north from many russian atomic bomb tests.
    That 14CO2 mixed with the existing bulk of total atmosphere CO2. It took about a year for the northern 14CO2 to mix throughout the southern hemisphere atmosphere. The 14CO2 is then measured with time.
    The observed (measured) 14CO2 declined after 1963 (1964 in the SH).
    The measured 14CO2 ten years later had dropped to 1/2 the peak in 1963/4 toward the long term base line.
    Therefore tracer 14C was removed from the atmosphere at an exponential rate with a t1/2 of 10 years.
    The physics of the 14CO2 is exactly the same as “natural” CO2, therefore natural CO2 declines at exactly the same rate as the tracer.

    There are claims that the 14CO2 added to the atmosphere does not represent the total CO2. Those arguments are simply false. The observed drop of atmosphere CO2 into long-term sinks is proof that the CO2 biogeochemical cycle is very fast, about 5 to 7 percent of all atmosphere CO2 is lost to very long term sinks of multi-century to millenial time scales. The deep sources, geological and oceanic, are very much larger than claimed by IPCC and the Bern model. The OCO-2 data support the huge natural turnover of CO2 on a global basis.
    The claim that any CO2 remains “permanently” in Earth’s atmosphere shows a gross mis-representation of the observed facts.

    Another look at this issue

    https://wattsupwiththat.com/2013/07/01/the-bombtest-curve-and-its-implications-for-atmospheric-carbon-dioxide-residency-time/#comment-1352246

    gives a more info on this subject.

    • BW,

      Sorry, but there is a problem with the 14CO2 spike decay: what returns from any 12CO2 spike via the deep oceans still is 99% 12CO2 after ~1,000 years residence in the deep. What returns as 14CO2 is the ratio of ~1,000 years ago, long before the nuclear tests. That makes that 14CO2 spike decay is many times faster than of a 12CO2 spike, see my response here.

      • I really wonder how difficult this can be even when you have explained it clearly many times with different ways. Please keep going on!

    • Hi, Constructing the global decay rate of the radiocarbon above gives the result of 16 years. This is a result of real observations. The residence times shorter than this like 7.6 years or 5 years are simply wrong in the recycling system of the atmosphere, the ocean and the biosphere. This 16 years is applicable for anthropogenic CO2 in the atmosphere but not the total CO2. Engelbeen has explained the reasons for this many times. The residence time is somewhere 50…55 years for thte total CO2 giving the half life time 0.69*55 = 38 years.

    • bw,
      You are exactly correct. Can no one here write down a simple rate equation and solve it? If goes like this: Let N(t) be the number of CO2 molecules in the atmosphere as a function of time, t. On an annual average, N(t) increases with contributions from both human and natural sources and decreases via losses to sinks. The rate of decrease is exactly the same as the rate of decrease shown by the washout of 14C from the atmosphere after the cessation of atmospheric bomb tests. (Aside from small isotopic selection effects on the biological uptakes of carbon.) But mostly the 14C concentration just gets diluted to insignificance when mixed in the oceans. Almost none of it comes back on a short term basis because there is no significant reservoir of 14C in the oceans.

      The conclusion that you can reach by this sort of analysis is that there are huge exchanges of CO2 between atmosphere and ocean and land surfaces on an annual basis. It is primarily the human contributions that disturb what would otherwise be a stable N(t) at constant temperatures.

      • bones March 26, 2016 at 9:19 pm

        bw,
        You are exactly correct. Can no one here write down a simple rate equation and solve it? If goes like this: Let N(t) be the number of CO2 molecules in the atmosphere as a function of time, t. On an annual average, N(t) increases with contributions from both human and natural sources and decreases via losses to sinks. The rate of decrease is exactly the same as the rate of decrease shown by the washout of 14C from the atmosphere after the cessation of atmospheric bomb tests.

        Bones, you were doing well up to the last sentence. Let me see if I can explain why.

        Consider a steady-state atmospheric condition with no net change in the CO2 contents. In this steady state, volcanoes and land emissions and whatever put CO2 molecules into the atmosphere, and the sinks take them out at the same rate, so the atmospheric concentration stays the same. The individual molecules stay in the atmosphere a while, and then they are removed from the atmosphere by natural processes.

        Now, if N(t) is the number of molecules of CO2 in the atmosphere per your notation above, note that during the process I just described there is no change in N(t). Remember it is steady-state … but despite that, we still have an average atmospheric residence time of ~ 12 years.

        This shows clearly that the rate of change in N(t) is NOT related to the ~12-year half-life of the airborne residence time of 14C in the atmosphere, because they measure different things.

        The rate of change in N(t) is the rate at which a PULSE of CO2 injected into the atmosphere decays back to the pre-injection state. This is different from and has nothing to do with how long an average CO2 molecule stays in the atmosphere (usually called “airborne residence time”, which you term the “washout rate”).

        w.

  19. Eric, thank you for this interesting post. While what you have done is certainly valid work, I fear that it has not proven what you think it has proven.

    You say that the decay of a pulse of atmospheric CO2 can be accurately modeled using a single exponential decay time constant tau in the range of 35-40 years or so. I agree, as does Mark Jacobson here.

    The IPCC says that the decay of CO2 is long-tailed, and as such it is better modeled by using three different time constants tau1, tau2, and tau3 of 2.6, 18, and 171 years, acting respectively on fractions f1, f2, and f3 of 32%, 28%, and 25% of the CO2 respectively, with an additional fraction f0 of 15% of the CO2 which never decays.

    Now to me, that seem highly unlikely. IF every time a pulse of CO2 were added to the atmosphere fifteen percent of it never decayed … it wouldn’t take long (geologically) for volcanic eruptions to fill the atmosphere with CO2.

    However, that’s not the current problem. The current problem is that we simply don’t have enough data to reliably distinguish between the two different explanations. The two calculated results are very similar over the early part of the record, and they won’t start to diverge significantly until something like 2025 or so.

    Let me recommend that you use the values above for tau 1 to 3, and fractions f0 to f3, to replicate the IPCC method and compare it to your own calculations. You may be surprised by what you find. Here’s what I found:

    You can see the problem … I used ice core data for 1850-1959, and I used fossil emissions, concrete production emissions, and land-use change data for total anthropogenic emissions.

    Best regards, I look forwards to seeing your figures.

    w.

    • Willis,

      Excellent comment. Thanks for looking up the actual numbers and computing how different models compare.

      You wrote: “with an additional fraction f0 of 15% of the CO2 which never decays … that seem highly unlikely .. it wouldn’t take long (geologically) for volcanic eruptions to fill the atmosphere with CO2.”

      That would be so if the 15% *never* decayed, but that is not what the conventional model actually assumes. That final 15% gradually decays as a result of reactions with minerals on the ocean floor. But the process takes many thousands of years (perhaps even hundreds of thousands) so although important on geological time scales, it does not matter for models run over a time scale of centuries.

      • Thanks, Mike. Since the longest tau in the Bern model is 171 years, that means that the “gradual decay” you talk about must be on the order of “many thousands of years” and “perhaps even hundreds of thousands” of years as you say. But if that is the case, then volcanic eruptions would definitely build up CO2 in the atmosphere. Per the IPCC, volcanoes add about .1 gigatonnes per century to the atmosphere. 15% of this would be about .015 Gtonnes per year.

        Now, when we have exponential decay with constant addition, an equilibrium is reached when

        (1 – alpha) * additional atmospheric C (gigatonnes) = the annual addition of C (gigatonnes)

        where alpha = exp(-1/tau).

        Assuming tau is on the order of say 50,000 years as you suggest, this means we’d have an additional 750 gigatonnes of carbon in the air at equilibrium. Since 2.18 tonnes of airborne C is the equivalent of one ppmv, that would mean that 750 / 2.18 = 344 ppmv of our atmospheric CO2 is due to volcanic eruptions … I’m sure you can see the problem.

        Regards,

        w.

      • Willis,

        You wrote: “Assuming tau is on the order of say 50,000 years as you suggest, this means we’d have an additional 750 gigatonnes of carbon in the air at equilibrium. Since 2.18 tonnes of airborne C is the equivalent of one ppmv, that would mean that 750 / 2.18 = 344 ppmv of our atmospheric CO2 is due to volcanic eruptions … I’m sure you can see the problem.”

        Very nice calculation. So how much of the atmospheric CO2 is due to eruptions? I think the answer is “all of it”. If there were no volcanoes, all of the CO2 would get incorporated into rocks; the volcanoes return that CO2 to the atmosphere. So a few tens of thousands of years seems plausible for the lifetime.

    • Willis Eschenbach: The IPCC says that the decay of CO2 is long-tailed, and as such it is better modeled by using three different time constants tau1, tau2, and tau3 of 2.6, 18, and 171 years, acting respectively on fractions f1, f2, and f3 of 32%, 28%, and 25% of the CO2 respectively, with an additional fraction f0 of 15% of the CO2 which never decays.

      Can a model that complex be reliably calculated from present data?

      The current problem is that we simply don’t have enough data to reliably distinguish between the two different explanations.

      That would seem to answer my question. Of two models that fit the data equally well, the one with the more parameters will have the less reliable parameter estimates, and less reliable forecast success against out of sample data.

      • MRM: Of two models that fit the data equally well, the one with the more parameters will have the less reliable parameter estimates, and less reliable forecast success against out of sample data.

        It happens all the time in pharmacodynamics. You can find examples here:Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications, Fourth EditionJul 4, 2007
        by Johan Gabrielsson and Daniel Weiner

        Sorry I can’t give page or chapter numbers. I don’t have the book. I took a course under Gabrielsson, and I reviewed that edition of the book at a Joint Statistical Meetings when it was new.

      • matthewrmarler,

        You wrote “Can a model that complex be reliably calculated from present data?”

        Yes. See below.

        Quoting Willis: “The current problem is that we simply don’t have enough data to reliably distinguish between the two different explanations.”

        Willis got this wrong, but I overlooked it. Again, see below.

        “Of two models that fit the data equally well, the one with the more parameters will have the less reliable parameter estimates, and less reliable forecast success against out of sample data.”

        That is, in general, a very wise position.

        If the only data available were CO2 concentrations, your comments would be spot on. But there is considerable other data. There is C-14 data following atom bomb tests. There is good data on the position of CO2 equilibrium between the atmosphere and the ocean and data that tells us about physical mixing within the ocean. There is stable isotope (C12 & C13) data and data on O2 that constrains what is taken up by the biosphere vs. what is taken up by the oceans. Ari Halperin’s model can not fit all that data. The Bern model can and is likely the simplest model that can fit all the data.

      • oops. belongs here.

        Mike M. (period) : The Bern model can and is likely the simplest model that can fit all the data.

        Thank you for that post. I looked up “Bern Model” on wikipedia and there is no entry. What is a good reference?

      • Except data isn’t showing a steady rate, not even percentage, of sequestration, hence steady decay is likely too simple.
        ==========

      • Mike M. (period),

        Ari Halperin’s model can not fit all that data. The Bern model can and is likely the simplest model that can fit all the data.

        Ari Halperin’s model does fit the CO2 data in the atmosphere, that is all what is in discussion. Mathematically it doesn’t matter if you use one overall decay rate or several separate ones, except if saturation is involved. Until now, that is only the case for the ocean surface layer, which rapidly (less than a year half life) saturates at 10% of the atmospheric change.

        That means that the overall decay rate is slightly faster than the second decay rate in the Bern model (deep ocean sink), due to the saturated first decay + the slower third decay rate in vegetation.

        Where the Bern model goes wrong is that it first separates the same CO2 pulse/increase in the atmospehre in different compartments each with their own decay rate, while the real decays are working parallel on the common total increase in the atmosphere. See the comment of TerryS here.

        The Bern model also assumes a fast saturation of the deep oceans – for which is no sign – and some saturation of the biosphere – which is impossible…

      • matthewrmarler,

        Bern model already mentioned in:
        http://www.john-daly.com/carbon.htm

        Full discussion with Fortunate Joos (from Bern University, one of the creators of the model) and Peter Dietze of a model comparable to what Ari has done.

        A short description:
        http://www.climate.unibe.ch/~joos/model_description/model_description.html
        Official formula that gives the Bern model plot:
        http://unfccc.int/resource/brazil/carbon.html
        See also the reference to TerryS in my previous comment.

      • Ferdinand,

        When I wrote “The Bern model can and is likely the simplest model that can fit all the data” I did not intend to endorse the Bern model. I am not all that familiar with it. The first part of my statement was based on the assumption that in developing it they used all pertinent data, not just atmospheric concentrations (which are insufficient to decipher what is going on). As to the simplest model, I doubt that one can fit all the data with fewer than three time constants.

      • Mike M. (period) March 26, 2016 at 2:06 pm

        Quoting Willis:

        “The current problem is that we simply don’t have enough data to reliably distinguish between the two different explanations.”

        Willis got this wrong, but I overlooked it. Again, see below.

        I looked below and didn’t find a dang thing about what you might have “overlooked”. A link or a quotation to wherever it is that you have shown I’m wrong is desperately needed, because at this point you’re just making groundless unsubstantiated accusation of error.

        Not impressed. (period)

        w.

      • Ferdinand Engelbeen: Bern model already mentioned in:
        http://www.john-daly.com/carbon.htm

        Thank you for that and the other links. I do not see where the Bern model is explicitly fit to the other flows mentioned by Mike M. There is reference to other flows, but the only comparison of model to data is to the atmospheric CO2 concentration.

      • Mike M: The first part of my statement was based on the assumption that in developing it they used all pertinent data, not just atmospheric concentrations (which are insufficient to decipher what is going on).

        It looks like they used their intuition to get approximate transfer coefficients (equivalently, half-lives) rather than any actual data about the transfer rates or other measured concentrations. That is not unreasonable, but the results are unreliable for forecasting.

      • Willis,

        “Quoting Willis: “The current problem is that we simply don’t have enough data to reliably distinguish between the two different explanations.”
        Willis got this wrong, but I overlooked it.”

        The thing that I overlooked was the fact that you got this wrong. The reason that you got this wrong is (quoting myself): “But there is considerable other data. There is C-14 data following atom bomb tests. There is good data on the position of CO2 equilibrium between the atmosphere and the ocean and data that tells us about physical mixing within the ocean. There is stable isotope (C12 & C13) data and data on O2 that constrains what is taken up by the biosphere vs. what is taken up by the oceans.”

        And I noted that CO2 concentration data alone is insufficient to distinguish between the models.

      • Mike M. (period) March 26, 2016 at 5:50 pm says:

        Willis,

        “Quoting Willis: “The current problem is that we simply don’t have enough data to reliably distinguish between the two different explanations.”
        Willis got this wrong, but I overlooked it.”

        The thing that I overlooked was the fact that you got this wrong. The reason that you got this wrong is (quoting myself): “But there is considerable other data. There is C-14 data following atom bomb tests. There is good data on the position of CO2 equilibrium between the atmosphere and the ocean and data that tells us about physical mixing within the ocean. There is stable isotope (C12 & C13) data and data on O2 that constrains what is taken up by the biosphere vs. what is taken up by the oceans.”

        And I noted that CO2 concentration data alone is insufficient to distinguish between the models.

        Mmmm … I fear that we are talking at cross-purposes. There are two very different things here which it appears you are conflating.

        One is the average atmospheric residence time of a CO2 molecule. This measures how long your average CO2 molecule remains airborne. This is shown in the bomb test data, which gives a half-life of 12.8 years for the airborne residence time.

        The other is the decay time of a pulse of CO2 injected into the atmosphere. This is the number being investigated by the IPCC, as well as by my own analyses. This has a half-life of about 23 years (33 years e-folding time).

        Here’s the problem with your claim. The bomb test data means NOTHING about the pulse decay time. They are entirely unrelated, because they are measuring different things.

        As a result, the bomb test 14C data is useless for determining whether single or multiple pulse decay times fit the CO2 pulse decay observations better. They have nothing to do with each other.

        Regards,

        w.

      • Willis,

        You wrote: “There are two very different things here which it appears you are conflating. One is the average atmospheric residence time of a CO2 molecule. … The other is the decay time of a pulse of CO2 injected into the atmosphere. … The bomb test data means NOTHING about the pulse decay time. They are entirely unrelated, because they are measuring different things.”

        They are certainly two different things. But they are not unrelated; both are affected by the processes that exchange carbon between the atmosphere, the ocean, and the biosphere. If you have a model for those exchanges, then you could calculate what the model says each of those two lifetimes should be. If both lifetimes agree with the respective data sets, then the model might be correct. If either lifetime differs significantly from observation, then the model must be wrong.

        I have so far only had a chance to look briefly at Ari Halperin’s paper. It looks like his model, as expressed in his equation (16), will predict exactly the same values for atmospheric residence time and pulse decay time. If so, then it must be wrong since it disagrees with observation.

        If I get around to looking at this more carefully and posting something more detailed, I will start a new thread.

      • Ferdinand Engelbeen, thank you for the updated link to Dietze and Jost. It looks to me like there is insufficient data to justify the extra complication, and estimate the extra parameters. compared to Halperin’s model; rates of CO2 transfer into the conceptually separate sinks are just not very well known.

      • matthewrmarler,

        For a first order process, the “e-folding” time is the time required for the concentration to drop to 1/e of its initial value (e being the base of natural logarithms, my apologies if that seems condescending). It is equal to the inverse of the first order rate constant and also equal to (half life)/ln(2).

      • Thanks, Mike M, for the reply to Matthew. I’d also note that exponential decay can be expressed mathematically as

        e(-t/tau)

        where “t” is time and “tau” is the time constant, also known as the “e-folding time”. As you can see, when time t is equal to tau, it reduces to e-1 = 1 / e

        w.

      • A two-fold change is a change by a factor of two, a three-fold change is a change by a factor of three…… an e-fold change is a change by a factor of e.

        HTH

  20. If somebody claims that the decay rate of 14C is applicable to the the total CO2 decay rate or the decay rates of anthropogenic and the total CO2 are the same, then he/she does not understand the effects of the recycling system of the atmosphere, the ocean and the biosphere.

  21. Mike M. (period) : The Bern model can and is likely the simplest model that can fit all the data.

    Thank you for that post. I looked up “Bern Model” on wikipedia and there is no entry. What is a good reference?

      • Thanks db,

        The whole country still is in shock… No relatives or friends directly involved, be it with some good luck: a niece and nephew of our son in law were one metro train before and after the one which was bombed… Such a blind hate from a few cowards…

      • Washington Post editors blame Brussels attack on Trump’s foreign policy. I kid you not.

        H/t Clarice.
        ========

      • Thanks Kim for the update…

        There is always someone who want to take political advantage of any disaster…

        Until now not too bad here, despite that there were several mistakes made by the security services. But that is easy to tell after what happened. If you have to weed within thousands of information items it is a hell of a job to know what may be important and what not…

        Only the former mayor of Molenbeek is under fire from everybody by letting the situation there rotten for too many years… Not a unique situation in some suburbs of any large city.

      • Is it true that EU edicts forestall Germany from dispersing its recent immigrants, with the argument that it is a human right to remain segregated?
        ===========

  22. Open Question:
    Since plants have a preference for 12C over 13C, the selectivity is undoubtedly even greater for 14C. It would seem to me that 12C should have a shorter residence time than 14C. If estimates on the rate of decline for 14C based on sequestration are correct, what correction would need to be applied for the rate of decline for the 13C/12C mix that constitutes the CO2 in the atmosphere?

    • Clyde Spencer,

      The isotopic ratio only slightly changes for the 13C/12C ratio:

      From water to atmosphere -10 per mil δ13C
      From atmosphere to water -2 per mil δ13C
      Average -8 per mil for an atmosphere – ocean carbon cycle in steady state

      That means that the real change is less than 1% in ratio between 13CO2 and 12CO2 from water to atmosphere and reverse.
      That plays a huge role in the 13C/12C ratio decline caused by low-13C (about -24 per mil) fossil fuel burning, where only 1/3rd of the decline is measured if all fossil CO2 was retained in the atmosphere and not “thinned’ by the ~40 GtC/year deep ocean circulation with a much higher 13C/12C ratio…

      I suppose that the change in 14C/12C ratio is higher than for the 13C/12C ratio, but have no figures for that.

      • Ferdinand,

        Could you please explain your reference to only 1/3rd of the decline? My analysis indicates that the long term average δ13C value for the incremental atmospheric CO2 is close to -13 per mil (so about half of the unthinned value). Do you get a different value?

        Thanks.

  23. OK, long + interesting thread:

    Guest essay by Ari Halperin

    My new scientific paper Empirical Validation of the Exponential Decay for Surplus CO2 further validates the conclusion that surplus CO2 in the air decays exponentially.
    _________

    But zero response to Ari Halperin

    – surplus CO2 decays exponentially.
    __________

    Send More Experts!

    • Johann Wundersamer: But zero response to Ari Halperin

      – surplus CO2 decays exponentially.

      I agree.

      Willis Eschenbach, notice, did not criticize Halperin, but asked him for a comparison to a different model where the decay was due to 3 processes with different rates. If we had atmospheric data out to the restoration of the previous equilibrium (actually a near steady-state), then if the Bern model were correct the log of the concentration would be approximately piecewise linear, with the three slopes related to the 3 rate constants.

      It seems to me that the critics of Ari Halperin have not bothered to read the papers that the essay here is based on.

      Halperin makes the case that the concentration curve can be represented as a simple kinetic model with two inputs (calculated from other data) and a single elimination rate constant. And that produces the exponential decay that you highlighted.

  24. Problem with that elongated discussions is –

    – loose of control.
    ________

    at the supermarket waiting in line 2 minutes before the cashier everybody gets hyperventilating.

    out on the parking place, stowing the purchased into the car, the men 20 minutes expert discuss the last baseball scores;
    the woman talk ‘engagemant ships’ – everybody is IN CONTROL of HIS time.

    everyone relaxed, no adherence to ‘the world outside’.

    I’m in control – ‘real world’ can wait unending.

  25. The ocean biosphere is assessed as 90% of the total biosphere by the Census of Marine Life. I have yet to see any representation of the carbon cycle that includes this. Of the remaining 10%, about 7.5% is in soils which makes the above ground contribution about 2.5%.
    We really don’t understand the carbon cycle, but the closer I look, the more insignificant our contribution becomes.

      • Did you look yourself?
        Fig 6.1 gives 3Gt for marine biota as in other similar diags. This is just what I was commenting on.
        It is wildly wrong.
        If land vegetation is ~500Gt and soils ~2000 Gt as in IPCC diag. then ocean biota is about 25,000Gt not 3Gt as in IPCC.

        This is highly significant once you are looking at fluxes. It is a volatile component and may (who knows?) be increasing at the rate of terrestrial vegetation – ie 12-20% pa or more.

        Also: It can impact UV penetration causing near surface heating. It will be emitting cloud seeding molecules. Changes in equatorial Pacific surface biota map well with El Nino heat. Cloud seeding as it dies of for La Nina???

        IPCC is floundering in the dark on this issue – as most elsewhere.

        d

      • Nicholas

        I’m reluctant to express my thinking on this any further because it’s held together by excessive amounts of handwavium, but the 13PgC in figure 6.1 for marine biota to deep sea might be much higher – possibly 200X our emissions – potentially a big sink.

        btw, I agree in general with your analysis above.

  26. FERD’s whole thesis boils down to “WE’RE ALL GONNA DIE!!!’

    To which I say Baloney. We all do die, but not from CAGW. There has been no net problem only beneficial effects, from very slowly rising CO2 levels and if due to anthropogenic reasons, not yet proven. Then they will begin to plunge within 50 years. Transport is being electrified and more efficient, as well. Electric generation becomes less CO2 emission dependent, and more efficient, too. (Pick your solution dreaming about Wind, or Solar; burning clathrates CH4, or my choice, Fusion.)

    Indeed the entire result of this blather is that by 2050 we will have some people calling for a program of emitting CO2 to save the Plants and the Planet. They will say that Humanity will need to protect the dumb plants from eating all the CO2 in the atmosphere.

    • Yup, the sun and the biome conspire, yes, they do, to almost irreversibly sequester carbon. We must forgive them, they can’t help themselves, it’s in their nature.
      ==============

    • Stas Peterson,

      I have made it clear many times that I am sure that humans are the cause of the increase of CO2 in the atmosphere, based on all available evidence.
      I have made it also clear many times that in my opinion the effect of that increase is small and more beneficial than harmful…

      So where is your opinion based on?

  27. Stas peterson:FERD’s whole thesis boils down to “WE’RE ALL GONNA DIE!!!’

    Your comment is absurd. Ferdinand Englebeen said very clearly that the increase in CO2 since 0industrialization began is due to human fossil fuel use. He did not say that the increase in CO2 concentration was harmful.

  28. Ari, you quote that:

    “The paper uses pre-1958 concentrations, which were obtained by C.D. Keeling by re-analyzing certain 19th century instrumental measurements and merging them with the ice core measurements.”

    Others have reviewed these pre-1958 concentrations (some 180 odd technical papers on atmospheric CO2 measurements from 1812 to 1961) and have come to very different conclusions to Keeling. The following paper indicates that atmospheric CO2 concentration has fluctuated coonsiderably over the period, exhibiting three high level maxima around 1825, 1857 and 1942, the latter showing more than 400 ppm.

    http://www.geocraft.com/WVFossils/Reference_Docs/180_yrs_Atmos_CO2_Analysis_by_chemical_methods_Beck_2007.pdf

    Would you consider using the data from this paper to evaluate how well your method works in situations where CO2 concentrations have both risen and fallen?

  29. There is another carbon-14 observation that enlightens this debate. Each year, cosmic rays create roughly 8 kg of carbon-14 in the upper atmosphere, and has done so for millions of years. One in eight thousand carbon-14 atoms decays into nitrogen every year. For equilibrium, there must be 64,000 kg of carbon-14 on Earth (so it will decay at the same rate it is being created). But there is only 800 kg of carbon-14 in the atmosphere (I’m rounding to one significant figure). Where is the rest of it? And how does a net transfer of 8 kg of carbon-14 take place into this reservoir each year? You will find more details at the posts starting with the one below.

    http://homeclimateanalysis.blogspot.com/2015/09/carbon-14-origins-and-reservoir.html

    So far as I can tell, the remaining 63,200 kg must be in the deep ocean, where the concentration of carbon-14 is 80% of that in the atmosphere. We have something like 40 Pg (petagrams) of carbon moving into the deep ocean each year, and 40 Pg coming back, so a net flow of 8 kg takes place into the deep ocean. We can write down analytical equations for the resulting two-reservoir system, and solve them directly or numerically.

    http://homeclimateanalysis.blogspot.com/2015/10/carbon-14-analytic-solution-to.html

    We also note that absorption by the ocean, and emission, are governed by Henry’s Law. Absorption by the oceans increases in proportion to concentration in the atmosphere. According to this model, the residence time of CO2 in the atmosphere is around 17 years. According to the bomb test data, its about 15 years. If we consider how long it will take humans to double the atmospheric concentration of CO2, the answer is: roughly 6000 years, because we have to double the concentration in the oceans too.

    http://homeclimateanalysis.blogspot.com/2015/12/carbon-cycle-with-ten-petagrams-per-year.html

    Or so it seems to me, anyways.

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